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0597

1v2

[co

nd-m

atm

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sci]

24

Nov

201

5

Electronic structure magnetism and antisite disorder in CoFeCrGe and CoMnCrAl

quaternary Heusler alloys

Enamullah1dagger Y Venkateswara1dagger Sachin Gupta12dagger Manoj Raama

Varma3 Prashant Singh4 K G Suresh1 and Aftab Alam1lowast

1Department of Physics Indian Institute of Technology Bombay Mumbai 400 076 India2Advanced Institute for Materials Research Tohoku University Sendai-980-8577 Japan

3National Institute for Interdisciplinary Sciences and Technology (CSIR) Thiruvananthapuram India and4Ames Laboratory US Department of Energy Iowa State University Ames Iowa 50011-3020 USA

(Dated October 26 2021)

We present a combined theoretical and experimental study of two quaternary Heusler alloysCoFeCrGe (CFCG) and CoMnCrAl (CMCA) promising candidates for spintronics applicationsMagnetization measurement shows the saturation magnetization and transition temperature to be3 microB 866 K and 09 microB 358 K for CFCG and CMCA respectively The magnetization values agreefairly well with our theoretical results and also obey the Slater-Pauling rule a prerequisite for halfmetallicity A striking difference between the two systems is their structure CFCG crystallizes infully ordered Y-type structure while CMCA has L21 disordered structure The antisite disorder addsa somewhat unique property to the second compound which arises due to the probabilistic mutualexchange of Al positions with CrMn and such an effect is possibly expected due to comparableelectronegativities of Al and CrMn Ab-initio simulation predicted a unique transition from halfmetallic ferromagnet to metallic antiferromagnet beyond a critical excess concentration of Al in thealloy

PACS numbers 7550Cc 6143-j 8575-d 3115A-

I INTRODUCTION

Spintronics technology based on the spin degree offreedom of electrons has potential advantages over con-ventional electronics such as high speed data process-ing low power consumption large circuit integrationdensity etc and is rapidly growing1 There are manymaterials such as simple transition metal oxides (CrO2Fe3O4) perovskite manganites transition metal chalco-genides diluted magnetic semiconductors and manyHeusler alloys(HA) which are promising for spintronicsapplications12 The striking feature of these materials istheir half metallic (HM) property From the band con-cept half metallicity arises due to the existence of finitedensity of states for one spin subband (majority chan-nel) and a finite band gap for the other (minority chan-nel) at the Fermi level (EF) The imbalance in the twodensities of states results in 100 spin polarization ofconduction (majority) electrons at EF A ferromagneticmaterial having HM property is called HM-ferromagnetHaving such type of band structure in the material makesit promising for spin injection and spin manipulation inspintronic devices Among the systems mentioned HAemerge out to be the most favored as HM- ferromag-nets because of their high Curie temperature (TC) andstructural compatibility3ndash6 compared to those of conven-tional semiconductors Conventional or full HA crystal-lize in the ordered L21 structure with composition X2YZin which X and Y are the transition metals whereas Z isa nonmagnetic element A new structure arises when oneof X is replaced by a different transition metal ie thestoichiometry becomes 1111 and such alloys are knownas quaternary Heusler alloys7ndash17 (QHA) with the formula

XXprimeYZ The resulting compound crystallizes in LiMg-PdSn prototype structure (or Y-structure) If Y and Zatoms randomly occupy either of the sites the resultingstructure is XXprimeY2XX

primeZ2 Such a structure is refereedto as L21 disordered structure

Along with the theoretical prediction of halfmetallic-ity in HA18 a lot of experimental work on Co-basedquaternary HA has been reported1019ndash21 In this regardstructural analysis electronic and magnetic propertiesalong with the prediction of high spin polarization inQHA have also been studied experimentally20 Element-specific magnetic moments and spin resolved densityof states in QHA are measured using x-ray absorptionspectroscopy19 Spin polarization measurements in CoFe-CrAl using point contact Andreev reflection (PCAR)technique reveals 63 of spin polarized electrons atEF

21 It has frequently been observed that among all theHeusler alloys Co-based HA are the perfect materials forspintronic applications because of the high value of TC

and spin polarization

In this paper we report a detailed theoretical and ex-perimental study of two alloys CoFeCrGe (CFCG) andCoMnCrAl (CMCA) CFCG is found to have the LiMg-PdSn prototype (Y-structure) with space group F43mwhereas CMCA has L21 disordered structure Magneti-zation measurement shows the saturation magnetizationof 3microB and 09microB for CFCG and CMCA respectivelywhich obeys Slater-Pauling rule2223 First principle cal-culation also yields the same results In addition wehave also studied the possible effect of antisite disorder(L21 disorder) between (Mn1minusxAl1+x) and (Cr1minusxAl1+x)pairs in CMCA alloy Interestingly a unique transitionfrom half metallic to metallic state occurs if we go beyond

2

370 Al-excess in both Mn-Al and Cr-Al pairs

II EXPERIMENTAL TECHNIQUES AND

COMPUTATIONAL DETAILS

A Experimental Techniques

Both the polycrystalline alloys ie CFCG and CMCAwere synthesized by arc melting the stoichiometricamounts of constituent elements with purity of at least9999 in water cooled copper hearth under high pu-rity argon atmosphere To compensate the weight lossin CMCA due to Mn evaporation 2 extra Mn wastaken The formed ingots were melted several times forbetter mixing As-cast samples were sealed in evacuatedquartz tubes and annealed for 7 days at 8000C followedby icewater mixture quenching To check phase purityof samples X-ray diffraction (XRD) patterns were takenat room temperature using XrsquoPert Pro diffractometerwith Cu K-α radiationXRD analysis is done with the help of FullProf suite

that uses the least square refinement between experimen-tal and calculated intensities It contains a number ofprograms such as DICVOl06 for indexing XRD patternGFourier for calculating and visualizing electron den-sity within the unit cell etc for different purposes inXRD and neutron diffraction (ND) data analysis Pro-file Matching well known as Lebail fitting is done by re-fining lattice constant peak profile shape parameters ofpseudo-Voigt function as described in FullProf manual24

GFourier program is used for the calculation and visual-ization of electron density within the unit cell The visu-alization is very useful in identifying the atomic positionsof constituent elements within the unit cell for known orunknown crystals ie denser the electron density con-tours indicate the position of heavier element among theconstituent elements in the unit cell The function to beminimized in the Rietveld Method is

χ2 =

nsum

i=1

wiyi minus yci2 (1)

with wi = 1σ2i where σ2

i is the variance of theldquoobservationrdquo yi Here yi and yci are the observed andthe calculated scattering intensities for a diffraction an-gle 2θi

24 The smaller the value of χ2 the better is therefinementThe patterns for CMCA were the same before and af-

ter annealing but for CFCG alloy a small amount ofsecondary phase was seen after annealing Thereforeas-prepared CFCG and annealed CMCA were used formagnetization M(HT) measurements M(HT) was mea-sured using a Physical Property Measurement System(PPMS) (Quantum Design) High temperature magne-tization measurements were performed with an oven at-tached to the PPMS

As discussed in the introduction full Heusler alloy(FHA) structure comprises of four inter-penetrating facecentered cubic (fcc) sublattices and can be thought of asthe superposition of rock salt(NaCl) and zinc blend(ZnS)type structures25 In NaCl structure each Na(Cl) atomis surrounded by six Cl(Na) atoms whereas in ZnS struc-ture each Zn is surrounded by four S atoms and vice-versa The atomic sites of NaCl structure is called oc-tahedral sites whereas the sites in ZnS are known astetrahedral sites The ionic nature of bonds in NaClarises due to the large difference in the electronegativ-ity values between the constituent elements The cova-lent bonding nature arises when the difference in elec-tronegativity values of the constituent elements is verysmall eg in ZnS structure In HA if one considersmost electronegative element (usually from p-block) at(000)fcc site (121212)fcc site will be occupied bythe least electronegative element (usually low valancetransition metals)25 The remaining two fcc sublatticesie (141414)fcc and (343434)fcc sites will beoccupied by the intermediate electronegative elementsamong the constituent elements The same nomencla-ture for atomic sites is used here also even thoughthey are not surrounded by number of atoms that gavethe name For example octahedral sites (000)fcc and(121212)fcc are surrounded by eight atoms insteadof the six atoms suggested by its name For a FHA of thetype X2YZ X atoms are of the intermediate electroneg-ativity values and occupy 8c(141414) (two fcc sub-lattices with atoms at (141414) and (343434))Y occupies 4a(000) (one fcc sublattice at (000)) and Zatom occupies 4b (12 12 12) (one fcc sublattice at(121212)) Wyckoff positions of the space group Fm-3m25 The unit cell can be shifted translationally or ro-tationally by any amount in the crystal and its structureremains the same If the unit cell of the above atomic po-sitions is shifted by (121212) new atomic positionswill be X at 8c Y at 4b and Z at 4a Wyckoff sites Therecan be other similar combinations For the case of QHAif Z atom is considered at 4a (000) position the remain-ing three atoms X Xprime and Y will be placed in three differ-ent fcc sublattices 4b(121212) 4c(141414) and4d(343434) in three non-degenerate ways such thatthere are only three independent atomic arrangements inthe Y structure As discussed any translation of the unitcell does not change the crystal structure and shifting ofthese configurations by (141414) (121212) or(343434) of unit cell will simply change the originof the atoms but not the configuration Three config-urations are shown for CFCG in Fig1 For exampleif the atomic positions of Cr and Co are interchangedin Fig1(a) the resulting structure is same as the initialone because if that primitive cell is inverted along thebody diagonal the atomic arrangements will be same asthe initial one These are energetically non-degenerateconfigurations Similarly the other two configurationsin Fig1 can be understood In this way there are onlythree non-degenerate (distinct) atomic arrangements for

3

CoFeCrGeCoMnCrAl

E-E

0 (eV

ato

m)

Type1 Type2 Type3

00

01

02

03

(a) (b) (c)

FIG 1 Site preference energy plot for the different configura-tions of CFCG(triangle up) and CMCA(triangle down) E0reference energy corresponds to Type1 structure Primitiveunit cells (a) (b) and (c) are three non-degenerate configura-tions of CFCG corresponding to Type1 Type2 and Type3

XXprimeYZ type quaternary Heusler alloy The structurefactor for quaternary Heusler alloy XXprimeYZ having Z at4a(000) Y at 4b(121212) X at 4c(141414) andXprime at 4d(343434) is given below

Fhkl = 4(fz+fyeπi(h+k+l)+fxe

π

2i(h+k+l)+fxprimee

minusπ

2i(h+k+l))

(2)with unmixed (hkl) values Here fx fxprime fy and fz are the

atomic scattering factors for the atoms X Xprime

Y and Zrespectively Therefore

F111 = 4 [(fz minus fy)minus i(fx minus fxprime)] (3)

F200 = 4 [(fz + fy)minus (fx + fxprime)] (4)

F220 = 4 [(fz + fy) + (fx + fxprime)] (5)

are used to classify the ordering of the crystal structure

B Computational Details

First principle calculations were done using a spinpolarized density functional theory (DFT) implementedwithin Vienna ab-initio simulation package(VASP)26

with a projected augmented-wave basis27 We usedPerdew-Bueke-Ernzerhof (PBE) for the electronicexchange-correlation functional 243 k-mesh were usedfor Brillouin zone integration A plane wave cut-off of 288eV with the energy convergence criteria of 01 meVcellIn order to study the effect of antisite disorder in CMCAwe use a 3times3times3 super cell involving 108 atomscell with27 atoms of each kind Guided by the experimental find-ings two types of antisite disorder were investigated iebetween Mn and Al (CoMn1minusxCrAl1+x) and Cr and Al

FIG 2 Electronic density of individual atoms in the unit cellof CFCG at (a) z=00c (b) z=025c (c) z=05c and (d)z=075c plane

(CoMnCr1minusxAl1+x) Stability of such antisite disorderwas checked by calculating the formation energy (∆E)as defined below for a general ABCD alloy

∆E = E[A1minusxB1+xCD]minus[

2(1minus x) E(A2CD)

+ 2(1 + x) E(B2CD)]

(6)

FIG 3 Rietveld refinement of XRD data of CMCA(top) andCFCG(bottom)

4

TABLE I χ2 values of the Rietveld method for three distinctatomic arrangements (from Fig 1) for CFCG and CMCA

Alloy Configuration Type1 Type2 Type3CFCG χ

2 = 204 χ2 = 222 χ

2 = 229

CMCA χ2 = 172 χ

2 = 172 χ2 = 199

III RESULTS AND DISCUSSION

A Experimental

Rietveld refinement of powder X-ray diffraction(XRD)data using FullProf suite reveals that both CFCG andCMCA crystallize in the cubic structure with lattice con-stants 577plusmn001A and 576plusmn001A respectivelyχ2 values of Rietveld refinement for three distinct

atomic arrangements (as depicted in Fig 1) are pre-sented in Table I for both the alloys

For CFCG the constituent elements are nearest neigh-bors in the periodic table due to which their atomic scat-tering factors are nearly identical Hence the intensitiesof superlattice peaks (111) and (200) are very small incomparison to that of (220) peak This can be under-stood from Eq(1) Therefore one can do the refinementwith all the three configurations shown in Fig1 and canbe fitted to XRD data The best fit between observedand calculated intensities is observed for the first con-figuration In this configuration constituent elementsGe and Cr are at 4a(000) and 4b(121212) octa-hedral sites whereas Co and Fe are at 4c(141414)and 4d(343434) tetrahedral sites respectively25 ForCFCG Cr is the least electronegative (166 Pauli units)28

and therefore it forms ionic type sublattice with Ge(which has more electronegativity of 201 Pauli unit) andbecomes stable by donating its electrons to other ele-ments in the alloy Ge tries to accept electrons fromother elements As a result the electronic density at Crsite decreases whereas it increases at Ge site The X andXprime atoms(here Fe and Co) have intermediate electroneg-ativities and occupy tetrahedral sites25 The electronicdensities of various atoms in the unit cell can be visu-alized from the contour plot shown in Fig2 generatedfrom XRD refinement It is clear from Fig2(a) and (c)that most of the charge is distributed around Ge atomicsite while Cr site has the least density Fe and Co aresurrounded by intermediate charge in comparison to Crand Ge sites in Fig2(b) and (d) This configuration isenergetically most favorable as found from our calcula-tion Therefore crystal structure shown in Fig1(a) isthe most stableFor CMCA the superlattice peak (200) is more intense

in comparison to (111) peak and is clearly visible in theXRD pattern (Fig 3) This suggests that there is consid-erable amount of disorder between octahedral sites Thisis like B2 disorder in X2YZ HA but in QHA it should notbe treated as B2 disorder because X and Xprime are differentatoms It is rather an L21 type disorder where (000)

0 200 400 600 800 1000010203040506070

Magnetization (

em

ug

)

Temperature (K)

TC=866 K

500 Oe

CFCG

0 200 400 600 800 10000

4

8

12

16

20

TC=358 K

Magnetization (

em

ug

)

Temperature (K)

CMCA 500 Oe

-60 -40 -20 0 20 40 60

-3

-2

-1

0

1

2

3

CFCG

Mo

me

nt (

Bfu

)

Field (kOe)

300 K 5 K

-45 -30 -15 0 15 30 45

-08

-04

00

04

08

Field (kOe)

Mo

me

nt (

Bfu

)

5 K 300 K

CMCA

FIG 4 (Top) Temperature dependence of magnetization Mat 500 Oe TC is calculated from the minima of the first orderderivative of M vs T curve (Bottom) Magnetic moment vslsquoHrsquo at 300K and 5K for CFCG(left) and CMCA(right)

and (121212) fcc sublattices are randomly occupiedby the Z and Y atoms From Eq(1) it is clear that|F111|

2 reduces as compared to |F200|2 because fz = fy

due to equal probability of finding the Z and Y atoms atthose sites Hence the intensity which is proportional to|F111|

2 rarr 0 when |fx minus fxprime | rarr 0 Here |fx minus fxprime | asymp 0as X and Xprime are nearest neighbors Similar to CFCG(Fig1) CMCA also has three different configurationswith the exception that there is a probability of exchangeof atoms between the octahedral sites ie (000) and(121212)fcc sublattices Even though XRD can befitted with all the three configurations the configura-tion in which octahedral site (121212)fcc containsthe least electronegative element is energetically favor-able Here Mn and Cr have least electronegativity andhence the two configurations (Fig1(a) and (b)) contain-ing Cr or Mn at (121212)fcc sublattice are favorableElectronegativity of Al is also of the same order as thatof Mn or Cr and consequently Al also tries to occupyat (121212)fcc As such Al occupies different octa-hedral sites (000)fcc and (121212)fcc As a conse-quence the atoms which were initially at (121212)fccsites occupy both octahedral sites randomly like Al Dueto this behavior (111) peak vanishes in XRD Al atomsoccupying (121212)fcc try to lose electrons Fig3(b)shows the XRD refinement by considering equal proba-bility of finding Mn or Al atoms in octahedral site Theconventional unit cell is shifted by (141414) whiledoing the refinement and so the space group changes toFm3m ( 225) In this space group the occupancies areCo at 4a Cr at 4b and MnAl at 8c Wyckoff sites AsMn and Cr are neighboring elements swapping of these

5

elements will not be distinguishable from XRD Due tothis reason χ2 value is same for the first and second con-figurations as seen in Table I Therefore the conclusionis that CFCG is fully ordered while CMCA has L21 dis-ordered structureIt is observed in HA that if more than one atom

has nearly same electronegative values some degree ofdisorder can be expected For example CoMnCrAlCoFeCrAl8 and Co2Cr1minusxFexAl

29 HA have disorder be-tween Cr and Al sites Disorder in these systems arisesbecause of the same electronegativity values of Cr and Alatoms Consequently Al atom acts as an electron donorand occupies one of the octahedral sites (121212)fccwith almost same probability of occupancy as that of Cratoms Similarly Mn2CoAl

30 and Co2MnAl31 have a dis-order between Mn and Al sites This type of disorder isseen in HA containing Zn as well Zn also tries to occupyboth octahedral sites (121212)fcc and (000)fcc sub-lattice because Al and Zn atoms have the nature that insome cases they lose electrons and in some other casesthey accept electrons because of their low electronega-tivity and proximity to the p-block of the periodic tableHowever one can also synthesize perfectly ordered sys-tems in HA containing Al atoms such as CoFeTiAl29 (Ystructure) Co2TiAl

32(L21 structure) The scenario is abit different in this case Since Ti atom has the leastelectronegativity among the constituent atoms behavesas a charge donor and tries to occupy the (121212)fccand does not allow Al to occupy the same site Hencethere will be no disorder in these systems Thereforeon the basis of data available on a number of alloys wecould propose an empirical relation between relative elec-tronegativity values and the occurrence of disorderTop plots of Fig 4 show the temperature (T) de-

pendence of magnetization in constant field of 500 Oefor CFCG (left) and CMCA (right) showing the ferro-paramagnetic transition The Curie temperature hasbeen determined by taking the minima of the first or-der derivative of Magnetization vs Temperature (M-T)curve The estimated TC values are about 358K and866K for CMCA and CFCG respectively High TC ofthese alloys enable them to be potential candidates forroom temperature applicationsFigure 4 (bottom) shows the field dependence of mag-

netization for the two alloys The absence of hysteresisreveals the soft magnetic nature of the alloys Both thealloys show saturation at 5K and 300K The saturationmoment at 5 K is estimated to be 3 microB and 09 microB forCFCG and CMCA respectively The total moment inHeusler compounds can be estimated from the Slater-Pauling rule by counting the number of valence electronsin the primitive cell33 In QHA the total moment (m)per unit cell can be expressed as10

m = (Nv minus 24)microB (7)

where Nv (sd electrons for transition metals and spelectrons for main group element) is the number of va-lence electrons per unit cell As CFCG and CMCA have

-50

-25

00

25

50

-50

-25

00

25

50

-2 -1 0 1 2-9

-6

-3

0

3

6

9

E - E

F (eV)

W L Γ X W L Γ XWave Vector (k)

W W

Majority ( ) Minority ( )

E - EF (eV)

DoS

(sta

tes

eV)

TDOS

CMCA

Minority ( )

Majority ( )

(a)

-50

-25

00

25

50

-50

-25

00

25

50

-2 -1 0 1 2-9

-6

-3

0

3

6

9

E - E

F (eV)

W L Γ X W L Γ XWave Vector (k)

W W

Majority ( ) Minority ( )

E - EF (eV)

DoS

(sta

tes

eV)

TDOS

CFCG

Minority ( )

Majority ( )

(b)

FIG 5 Spin resolved band structure(left) and density ofstates (right) for CMCA(a) and CFCG(b) at experimentallattice constant(aexp) Both systems clearly show half metal-lic behavior with a band gap sim0328 eV for CMCA andsim0481eV for CFCG

27 and 25 valence electrons respectively according toSlater-Pauling rule (using Eq7) the moment in thesecompounds should be 3 and 1 microB But experimentallyobserved magnetic moment for CMCA (09microB) slightlydeviates from the Slater-Pauling rule because of the pres-ence of disorder On the other hand in CFCG the agree-ment is very good In addition to the experiment thetheoretically calculated moments also agree fairly wellwith the Slater-Pauling prediction (described in the nextsection)

B Theoretical

To check the stability we have first calculated thesite preference energies for various atomic configurationsConsidering the symmetry of the XXprimeYZ structure we fixthe Z-atom at 4d position and permute rest three atomson 4a 4b and 4c Wyckoff sites Out of six possible con-figurations only three are energetically non-degeneratenamely Type1 Type2 and Type3 as shown in the Fig1for both CFCG and CMCA Type1 (where X atom sitsat 4a Xprime at 4b and Y at 4c) is found to be energeti-cally the most stable configuration as also configured byexperiment

Figure 5 shows the spin polarized band structureand density of states (DoS) for CMCA(top) andCFCG(bottom) respectively Half metallicity is obviousin both the systems with a finite state (at EF) in major-ity channel but gapped in minority Calculated magneticmoment for CMCA is 098 microB (microexpt = 09 microB) whilefor CFCG is 299 microB (microexpt = 30 microB) which follows the

6

-16 -12 -8 -4 0 4 8 12 16x()

-200

-160

-120

-80

-40∆E

(m

eVa

tom

)

Co Mn1-xCr Al1+x

Co Mn Cr1-xAl1+x

0

2

4

6

8

-16 -12 -8 -4 0 4 8 12 16x()

0

2

4

6

8

Co Mn1-xCr Al1+x

Co Mn Cr1-xAl1+x

To

tal

ma

gn

eti

c m

om

en

t (m

t) (

micro B)

Fe

rmi

en

erg

y (

EF)

(eV

)

05

10

15

20

00

05

10

15

20

0000

05

10

15

-16 -12 -8 -4 0 4 8 12 16x()

00

05

10

15

n (EF)n (EF)(∆Eg)

CoMnCr1-xAl1+x

CoMn1-xCrAl1+x

025

050

075 (∆E

g) (e

V)

000

050

000

025

075

(n (

EF)

)

(st

ates

-eV

-1a

tom

)n

(E

F)

(a) (b) (c)

FIG 6 (a) Formation energy (∆E) vs antisite disorder (x) for CoMnCr1minusxAl1+x (triangle UP) and CoMn1minusxCrAl1+x (triangleDN) (b) Concentration (x) dependence of DoS at EF for majority spin (triangle UP) minority spin (triangle DN) and bandgap (∆Eg)darr (circle) for CoMnCr1minusxAl1+x (top) and CoMn1minusxCrAl1+x (bottom) (c) x-dependence of total magnetic moment(mt) and change in Fermi energy (EF) for the same two alloying

Slater-Pauling ruleIntrinsic defects such as antisite disorder is fairly com-

mon in QHA Our XRD data clearly indicate the signa-ture of L21 disorder in CMCA where Al site is expectedto mix with Mn (and possibly with Cr) Electronic struc-ture of any material is extremely sensitive to such defectsand has not received much attention in the literatureWe have performed first principle calculation to checkthe stability electronic structure and magnetism for twosets of antisite disorders namely CoMn1minusxCrAl1+x andCoMnCr1minusxAl1+x These are done by using a 3times3times3supercell of the primitive 4-atom cellFigure 6(a) shows the formation energy (∆E) of

CoMn1minusxCrAl1+x (triangle down) and CoMnCr1minusxAl1+x

(triangle up) for both excess (positive x-vale) and deficit(negative x-value) of Al in the compound Negative val-ues of ∆E indicates that Al indeed prefers to mix withMn and Cr Mn is relatively much more preferable to mixdue to a larger negative ∆E as also revealed by our XRDdata Detailed analysis of such antisite disorder can beaccurately probed with neutron diffraction experimentFigure 6(b) shows the value of DoS at EF for ma-

jority nuarr (triangle up) and minority ndarr(triangle down)spin channels The associated band gap (∆Eg)darr in theminority spin is also represented (solid circle) Top(bottom) panel are the results for CoMnCr1minusxAl1+x

(CoMn1minusxCrAl1+x) Interestingly deficit of Al (nega-tive x) up to x ≃ 1481 maintains the half metallicityhowever excess of Al (positive x) causes a transition fromhalf metallic to metallic beyond x ≃ 370 in both thecases At 741 excess Al the minority spin tend tohave a small DoS at EF ndarr(EF) ≃ 003 stateseV-atom(CoMnCr1minusxAl1+x) and nuarr(EF) ≃ 002 stateseV-atom(CoMn1minusxCrAl1+x) Such transition is something uniqueand has never been observed beforeIt turns out that this metallic transition is intimately

connected with a magnetic transition where the sys-tem goes from a ferromagnetic state to an antiferromag-

netic state This is shown in Fig6(c) where the totalmagnetic moment changes discontinuously at the sameconcentration (x sim741) at which the system loses itshalfmetallicity EF almost remains unchanged with vary-ing x (square symbol) Although we have theoreticallystudied the effect of antisite disorder up to x sim1481such a large disorder may not be expected to survive inthe actual sample

IV CONCLUSIONS

In conclusion CFCG and CMCA are found to be twointeresting materials the former crystallizes in Y typestructure while the latter shows an L21 disordered struc-ture which is due to the random occupancy of octahe-dral site atoms Al with CrMn Both the alloys showhalf metallic ferromagnetic behavior with a specific sitepreference for the constituent atoms CFCG is more use-ful because of its high Curie temperature (866 K) whileCMCA shows an intrinsic antisite disorder which allowsa larger tunability of its properties Magnetization mea-surement yields magnetic moments which obey the SlaterPauling rule and which also agree with our theoreticalprediction in both the cases Ab-initio electronic struc-ture simulation confirms the stability and half metallicityin both the compounds L21 disorder in CMCA is furtherinvestigated by simulating antisite disorder which alsoindicates the possibility of halfmetallic ferromagnetic be-havior in presence of small disorder However it changesto a metallic antiferromagnetic state beyond a certainexcess Al in the alloy

7

V ACKNOWLEDGEMENTS

Enamullah acknowledges IIT Bombay for providing fi-nancial assistance to carry out postdoctoral research PSwould like to thank US Department of Energy (DOE)Office of Science Materials Science and Engineering Di-vision for support

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3 R Farshchi and M Ramsteiner J Appl Phys 113191101 (2013)

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5 M Hashimoto A Trampert J Herfort and K H PloogJ Vac Sci Technol B 25 1453 (2007)

6 M Hashimoto J Herfort A Trampert H -P Schonherrand K H Ploog J Phys D Appl Phys 40 1631 (2007)

7 L Bainsla K G Suresh A K Nigam M Manivel RajaB S D Ch S Varaprasad Y K Takahashi and K HonoJ Appl Phys 116 203902 (2014)

8 L Bainsla A I Mallick M Manivel Raja A K NigamB S D Ch S Varaprasad Y K Takahashi A Alam KG Suresh and K Hono Phys Rev B 91 104408 (2015)

9 K Ozdogan E Sasioglu and I Galanakis J Appl Phys113 193903 (2013) X Dai G Liu G H Fecher C FelserY Li and H Liu J Appl Phys 105 07E901 (2009)

10 V Alijani J Winterlik G H Fecher S S Naghavi andC Felser Phys Rev B 83 184428 (2011)

11 X Dai G Liu G H Fecher C Felser Y Li and H LiuAppl Phys Lett 105 07E901 (2009)

12 M Singh H S Saini and M K Kashyap J Mater Sci48 1837 (2013)

13 V Alijani J Winterlik G H Fecher S S Naghavi SChadov T Gruhn and C Felser J Phys Condens Mat-ter 24 046001 (2012)

14 I Galanakis K Ozdogan E Sasioglu and B Aktas PhysRev B 75 172405 (2007)

15 H Z Luo H W Zhang Z Y Zhu L Ma S F Xu GH Wu X X Zhu C B Jiang and H B Xu J ApplPhys 103 083908 (2008)

16 I Galanakis and E Sasioglu Appl Phys Lett 99 052509(2011)

17 M Meinert Jan-Michael Schmalhorst C Klewe G ReissE Arenholz T Bohnert and K Nielsch Phys Rev B 84132405 (2011)

18 G Y Gao L Hu K L Yao B Luo and N Liu J AlloyCompd 551 539 (2013)(and references therein)

19 P Klaer B Balke V Alijani J Winterlik G H FecherC Felser and H J Elmers Phys Rev B 84 144413(2011)

20 V Alijani S Ouardi G H Fecher J Winterlik S SNaghavi X Kozina G Stryganyuk C Felser E IkenagaY Yamashita S Ueda and K Kobayashi Phys Rev B84 224416 (2011)

21 L Bainsla A I Mallick A A Coelho A K Nigam BS D Ch S Varaprasad Y K Takahashi A Alam KG Suresh and K Hono J Magn Magn Mater 394 82(2015)

22 J C Slater Phys Rev 49 931 (1936)23 L Pauling Phys Rev 54 899 (1938)24 wwwilleusitesfullprofphptutorialshtml25 T Graf C Felser and S S P Parkin Progress in Solid

State Chemistry 39 1 (2011)26 G Kresse and J Furthmuller Phys Rev B 54 11169

(1996) Comput Mater Sci 6 15 (1996)27 G Kresse and D Joubert Phys Rev B 59 1758 (1999)28 httpsenwikipediaorgwikiElectronegativity29 T Graf and C Felser Spintronics- From Materials to De-

vices pp 33-34 (Springer New York London 2013)30 Y J Zhang G J Li E K Liu and J L Chen J Appl

Phys 113 123901 (2013)31 A Vinesh V D Sudheesh N Lakshmi and K Venu-

gopalan AIP Conf Proc 1591 1521 (2014)32 W Zhang Z Qian Y Sui Y Liu X Huang W Su M

Zhang Z Liu G Liu and G Wu Physica B 367 205(2005)

33 I Galanakis P H Dederichs and N Papanikolaou PhysRev B 66 174429 (2002)

3

CoFeCrGeCoMnCrAl

E-E

0 (eV

ato

m)

Type1 Type2 Type3

00

01

02

03

(a) (b) (c)

FIG 1 Site preference energy plot for the different configura-tions of CFCG(triangle up) and CMCA(triangle down) E0reference energy corresponds to Type1 structure Primitiveunit cells (a) (b) and (c) are three non-degenerate configura-tions of CFCG corresponding to Type1 Type2 and Type3

XXprimeYZ type quaternary Heusler alloy The structurefactor for quaternary Heusler alloy XXprimeYZ having Z at4a(000) Y at 4b(121212) X at 4c(141414) andXprime at 4d(343434) is given below

Fhkl = 4(fz+fyeπi(h+k+l)+fxe

π

2i(h+k+l)+fxprimee

minusπ

2i(h+k+l))

(2)with unmixed (hkl) values Here fx fxprime fy and fz are the

atomic scattering factors for the atoms X Xprime

Y and Zrespectively Therefore

F111 = 4 [(fz minus fy)minus i(fx minus fxprime)] (3)

F200 = 4 [(fz + fy)minus (fx + fxprime)] (4)

F220 = 4 [(fz + fy) + (fx + fxprime)] (5)

are used to classify the ordering of the crystal structure

B Computational Details

First principle calculations were done using a spinpolarized density functional theory (DFT) implementedwithin Vienna ab-initio simulation package(VASP)26

with a projected augmented-wave basis27 We usedPerdew-Bueke-Ernzerhof (PBE) for the electronicexchange-correlation functional 243 k-mesh were usedfor Brillouin zone integration A plane wave cut-off of 288eV with the energy convergence criteria of 01 meVcellIn order to study the effect of antisite disorder in CMCAwe use a 3times3times3 super cell involving 108 atomscell with27 atoms of each kind Guided by the experimental find-ings two types of antisite disorder were investigated iebetween Mn and Al (CoMn1minusxCrAl1+x) and Cr and Al

FIG 2 Electronic density of individual atoms in the unit cellof CFCG at (a) z=00c (b) z=025c (c) z=05c and (d)z=075c plane

(CoMnCr1minusxAl1+x) Stability of such antisite disorderwas checked by calculating the formation energy (∆E)as defined below for a general ABCD alloy

∆E = E[A1minusxB1+xCD]minus[

2(1minus x) E(A2CD)

+ 2(1 + x) E(B2CD)]

(6)

FIG 3 Rietveld refinement of XRD data of CMCA(top) andCFCG(bottom)

4

TABLE I χ2 values of the Rietveld method for three distinctatomic arrangements (from Fig 1) for CFCG and CMCA

Alloy Configuration Type1 Type2 Type3CFCG χ

2 = 204 χ2 = 222 χ

2 = 229

CMCA χ2 = 172 χ

2 = 172 χ2 = 199

III RESULTS AND DISCUSSION

A Experimental

Rietveld refinement of powder X-ray diffraction(XRD)data using FullProf suite reveals that both CFCG andCMCA crystallize in the cubic structure with lattice con-stants 577plusmn001A and 576plusmn001A respectivelyχ2 values of Rietveld refinement for three distinct

atomic arrangements (as depicted in Fig 1) are pre-sented in Table I for both the alloys

For CFCG the constituent elements are nearest neigh-bors in the periodic table due to which their atomic scat-tering factors are nearly identical Hence the intensitiesof superlattice peaks (111) and (200) are very small incomparison to that of (220) peak This can be under-stood from Eq(1) Therefore one can do the refinementwith all the three configurations shown in Fig1 and canbe fitted to XRD data The best fit between observedand calculated intensities is observed for the first con-figuration In this configuration constituent elementsGe and Cr are at 4a(000) and 4b(121212) octa-hedral sites whereas Co and Fe are at 4c(141414)and 4d(343434) tetrahedral sites respectively25 ForCFCG Cr is the least electronegative (166 Pauli units)28

and therefore it forms ionic type sublattice with Ge(which has more electronegativity of 201 Pauli unit) andbecomes stable by donating its electrons to other ele-ments in the alloy Ge tries to accept electrons fromother elements As a result the electronic density at Crsite decreases whereas it increases at Ge site The X andXprime atoms(here Fe and Co) have intermediate electroneg-ativities and occupy tetrahedral sites25 The electronicdensities of various atoms in the unit cell can be visu-alized from the contour plot shown in Fig2 generatedfrom XRD refinement It is clear from Fig2(a) and (c)that most of the charge is distributed around Ge atomicsite while Cr site has the least density Fe and Co aresurrounded by intermediate charge in comparison to Crand Ge sites in Fig2(b) and (d) This configuration isenergetically most favorable as found from our calcula-tion Therefore crystal structure shown in Fig1(a) isthe most stableFor CMCA the superlattice peak (200) is more intense

in comparison to (111) peak and is clearly visible in theXRD pattern (Fig 3) This suggests that there is consid-erable amount of disorder between octahedral sites Thisis like B2 disorder in X2YZ HA but in QHA it should notbe treated as B2 disorder because X and Xprime are differentatoms It is rather an L21 type disorder where (000)

0 200 400 600 800 1000010203040506070

Magnetization (

em

ug

)

Temperature (K)

TC=866 K

500 Oe

CFCG

0 200 400 600 800 10000

4

8

12

16

20

TC=358 K

Magnetization (

em

ug

)

Temperature (K)

CMCA 500 Oe

-60 -40 -20 0 20 40 60

-3

-2

-1

0

1

2

3

CFCG

Mo

me

nt (

Bfu

)

Field (kOe)

300 K 5 K

-45 -30 -15 0 15 30 45

-08

-04

00

04

08

Field (kOe)

Mo

me

nt (

Bfu

)

5 K 300 K

CMCA

FIG 4 (Top) Temperature dependence of magnetization Mat 500 Oe TC is calculated from the minima of the first orderderivative of M vs T curve (Bottom) Magnetic moment vslsquoHrsquo at 300K and 5K for CFCG(left) and CMCA(right)

and (121212) fcc sublattices are randomly occupiedby the Z and Y atoms From Eq(1) it is clear that|F111|

2 reduces as compared to |F200|2 because fz = fy

due to equal probability of finding the Z and Y atoms atthose sites Hence the intensity which is proportional to|F111|

2 rarr 0 when |fx minus fxprime | rarr 0 Here |fx minus fxprime | asymp 0as X and Xprime are nearest neighbors Similar to CFCG(Fig1) CMCA also has three different configurationswith the exception that there is a probability of exchangeof atoms between the octahedral sites ie (000) and(121212)fcc sublattices Even though XRD can befitted with all the three configurations the configura-tion in which octahedral site (121212)fcc containsthe least electronegative element is energetically favor-able Here Mn and Cr have least electronegativity andhence the two configurations (Fig1(a) and (b)) contain-ing Cr or Mn at (121212)fcc sublattice are favorableElectronegativity of Al is also of the same order as thatof Mn or Cr and consequently Al also tries to occupyat (121212)fcc As such Al occupies different octa-hedral sites (000)fcc and (121212)fcc As a conse-quence the atoms which were initially at (121212)fccsites occupy both octahedral sites randomly like Al Dueto this behavior (111) peak vanishes in XRD Al atomsoccupying (121212)fcc try to lose electrons Fig3(b)shows the XRD refinement by considering equal proba-bility of finding Mn or Al atoms in octahedral site Theconventional unit cell is shifted by (141414) whiledoing the refinement and so the space group changes toFm3m ( 225) In this space group the occupancies areCo at 4a Cr at 4b and MnAl at 8c Wyckoff sites AsMn and Cr are neighboring elements swapping of these

5

elements will not be distinguishable from XRD Due tothis reason χ2 value is same for the first and second con-figurations as seen in Table I Therefore the conclusionis that CFCG is fully ordered while CMCA has L21 dis-ordered structureIt is observed in HA that if more than one atom

has nearly same electronegative values some degree ofdisorder can be expected For example CoMnCrAlCoFeCrAl8 and Co2Cr1minusxFexAl

29 HA have disorder be-tween Cr and Al sites Disorder in these systems arisesbecause of the same electronegativity values of Cr and Alatoms Consequently Al atom acts as an electron donorand occupies one of the octahedral sites (121212)fccwith almost same probability of occupancy as that of Cratoms Similarly Mn2CoAl

30 and Co2MnAl31 have a dis-order between Mn and Al sites This type of disorder isseen in HA containing Zn as well Zn also tries to occupyboth octahedral sites (121212)fcc and (000)fcc sub-lattice because Al and Zn atoms have the nature that insome cases they lose electrons and in some other casesthey accept electrons because of their low electronega-tivity and proximity to the p-block of the periodic tableHowever one can also synthesize perfectly ordered sys-tems in HA containing Al atoms such as CoFeTiAl29 (Ystructure) Co2TiAl

32(L21 structure) The scenario is abit different in this case Since Ti atom has the leastelectronegativity among the constituent atoms behavesas a charge donor and tries to occupy the (121212)fccand does not allow Al to occupy the same site Hencethere will be no disorder in these systems Thereforeon the basis of data available on a number of alloys wecould propose an empirical relation between relative elec-tronegativity values and the occurrence of disorderTop plots of Fig 4 show the temperature (T) de-

pendence of magnetization in constant field of 500 Oefor CFCG (left) and CMCA (right) showing the ferro-paramagnetic transition The Curie temperature hasbeen determined by taking the minima of the first or-der derivative of Magnetization vs Temperature (M-T)curve The estimated TC values are about 358K and866K for CMCA and CFCG respectively High TC ofthese alloys enable them to be potential candidates forroom temperature applicationsFigure 4 (bottom) shows the field dependence of mag-

netization for the two alloys The absence of hysteresisreveals the soft magnetic nature of the alloys Both thealloys show saturation at 5K and 300K The saturationmoment at 5 K is estimated to be 3 microB and 09 microB forCFCG and CMCA respectively The total moment inHeusler compounds can be estimated from the Slater-Pauling rule by counting the number of valence electronsin the primitive cell33 In QHA the total moment (m)per unit cell can be expressed as10

m = (Nv minus 24)microB (7)

where Nv (sd electrons for transition metals and spelectrons for main group element) is the number of va-lence electrons per unit cell As CFCG and CMCA have

-50

-25

00

25

50

-50

-25

00

25

50

-2 -1 0 1 2-9

-6

-3

0

3

6

9

E - E

F (eV)

W L Γ X W L Γ XWave Vector (k)

W W

Majority ( ) Minority ( )

E - EF (eV)

DoS

(sta

tes

eV)

TDOS

CMCA

Minority ( )

Majority ( )

(a)

-50

-25

00

25

50

-50

-25

00

25

50

-2 -1 0 1 2-9

-6

-3

0

3

6

9

E - E

F (eV)

W L Γ X W L Γ XWave Vector (k)

W W

Majority ( ) Minority ( )

E - EF (eV)

DoS

(sta

tes

eV)

TDOS

CFCG

Minority ( )

Majority ( )

(b)

FIG 5 Spin resolved band structure(left) and density ofstates (right) for CMCA(a) and CFCG(b) at experimentallattice constant(aexp) Both systems clearly show half metal-lic behavior with a band gap sim0328 eV for CMCA andsim0481eV for CFCG

27 and 25 valence electrons respectively according toSlater-Pauling rule (using Eq7) the moment in thesecompounds should be 3 and 1 microB But experimentallyobserved magnetic moment for CMCA (09microB) slightlydeviates from the Slater-Pauling rule because of the pres-ence of disorder On the other hand in CFCG the agree-ment is very good In addition to the experiment thetheoretically calculated moments also agree fairly wellwith the Slater-Pauling prediction (described in the nextsection)

B Theoretical

To check the stability we have first calculated thesite preference energies for various atomic configurationsConsidering the symmetry of the XXprimeYZ structure we fixthe Z-atom at 4d position and permute rest three atomson 4a 4b and 4c Wyckoff sites Out of six possible con-figurations only three are energetically non-degeneratenamely Type1 Type2 and Type3 as shown in the Fig1for both CFCG and CMCA Type1 (where X atom sitsat 4a Xprime at 4b and Y at 4c) is found to be energeti-cally the most stable configuration as also configured byexperiment

Figure 5 shows the spin polarized band structureand density of states (DoS) for CMCA(top) andCFCG(bottom) respectively Half metallicity is obviousin both the systems with a finite state (at EF) in major-ity channel but gapped in minority Calculated magneticmoment for CMCA is 098 microB (microexpt = 09 microB) whilefor CFCG is 299 microB (microexpt = 30 microB) which follows the

6

-16 -12 -8 -4 0 4 8 12 16x()

-200

-160

-120

-80

-40∆E

(m

eVa

tom

)

Co Mn1-xCr Al1+x

Co Mn Cr1-xAl1+x

0

2

4

6

8

-16 -12 -8 -4 0 4 8 12 16x()

0

2

4

6

8

Co Mn1-xCr Al1+x

Co Mn Cr1-xAl1+x

To

tal

ma

gn

eti

c m

om

en

t (m

t) (

micro B)

Fe

rmi

en

erg

y (

EF)

(eV

)

05

10

15

20

00

05

10

15

20

0000

05

10

15

-16 -12 -8 -4 0 4 8 12 16x()

00

05

10

15

n (EF)n (EF)(∆Eg)

CoMnCr1-xAl1+x

CoMn1-xCrAl1+x

025

050

075 (∆E

g) (e

V)

000

050

000

025

075

(n (

EF)

)

(st

ates

-eV

-1a

tom

)n

(E

F)

(a) (b) (c)

FIG 6 (a) Formation energy (∆E) vs antisite disorder (x) for CoMnCr1minusxAl1+x (triangle UP) and CoMn1minusxCrAl1+x (triangleDN) (b) Concentration (x) dependence of DoS at EF for majority spin (triangle UP) minority spin (triangle DN) and bandgap (∆Eg)darr (circle) for CoMnCr1minusxAl1+x (top) and CoMn1minusxCrAl1+x (bottom) (c) x-dependence of total magnetic moment(mt) and change in Fermi energy (EF) for the same two alloying

Slater-Pauling ruleIntrinsic defects such as antisite disorder is fairly com-

mon in QHA Our XRD data clearly indicate the signa-ture of L21 disorder in CMCA where Al site is expectedto mix with Mn (and possibly with Cr) Electronic struc-ture of any material is extremely sensitive to such defectsand has not received much attention in the literatureWe have performed first principle calculation to checkthe stability electronic structure and magnetism for twosets of antisite disorders namely CoMn1minusxCrAl1+x andCoMnCr1minusxAl1+x These are done by using a 3times3times3supercell of the primitive 4-atom cellFigure 6(a) shows the formation energy (∆E) of

CoMn1minusxCrAl1+x (triangle down) and CoMnCr1minusxAl1+x

(triangle up) for both excess (positive x-vale) and deficit(negative x-value) of Al in the compound Negative val-ues of ∆E indicates that Al indeed prefers to mix withMn and Cr Mn is relatively much more preferable to mixdue to a larger negative ∆E as also revealed by our XRDdata Detailed analysis of such antisite disorder can beaccurately probed with neutron diffraction experimentFigure 6(b) shows the value of DoS at EF for ma-

jority nuarr (triangle up) and minority ndarr(triangle down)spin channels The associated band gap (∆Eg)darr in theminority spin is also represented (solid circle) Top(bottom) panel are the results for CoMnCr1minusxAl1+x

(CoMn1minusxCrAl1+x) Interestingly deficit of Al (nega-tive x) up to x ≃ 1481 maintains the half metallicityhowever excess of Al (positive x) causes a transition fromhalf metallic to metallic beyond x ≃ 370 in both thecases At 741 excess Al the minority spin tend tohave a small DoS at EF ndarr(EF) ≃ 003 stateseV-atom(CoMnCr1minusxAl1+x) and nuarr(EF) ≃ 002 stateseV-atom(CoMn1minusxCrAl1+x) Such transition is something uniqueand has never been observed beforeIt turns out that this metallic transition is intimately

connected with a magnetic transition where the sys-tem goes from a ferromagnetic state to an antiferromag-

netic state This is shown in Fig6(c) where the totalmagnetic moment changes discontinuously at the sameconcentration (x sim741) at which the system loses itshalfmetallicity EF almost remains unchanged with vary-ing x (square symbol) Although we have theoreticallystudied the effect of antisite disorder up to x sim1481such a large disorder may not be expected to survive inthe actual sample

IV CONCLUSIONS

In conclusion CFCG and CMCA are found to be twointeresting materials the former crystallizes in Y typestructure while the latter shows an L21 disordered struc-ture which is due to the random occupancy of octahe-dral site atoms Al with CrMn Both the alloys showhalf metallic ferromagnetic behavior with a specific sitepreference for the constituent atoms CFCG is more use-ful because of its high Curie temperature (866 K) whileCMCA shows an intrinsic antisite disorder which allowsa larger tunability of its properties Magnetization mea-surement yields magnetic moments which obey the SlaterPauling rule and which also agree with our theoreticalprediction in both the cases Ab-initio electronic struc-ture simulation confirms the stability and half metallicityin both the compounds L21 disorder in CMCA is furtherinvestigated by simulating antisite disorder which alsoindicates the possibility of halfmetallic ferromagnetic be-havior in presence of small disorder However it changesto a metallic antiferromagnetic state beyond a certainexcess Al in the alloy

7

V ACKNOWLEDGEMENTS

Enamullah acknowledges IIT Bombay for providing fi-nancial assistance to carry out postdoctoral research PSwould like to thank US Department of Energy (DOE)Office of Science Materials Science and Engineering Di-vision for support

lowast aftabphyiitbacin enamullahphyiitbacindagger Authors have equal contribution1 C Felser G H Fecher and B Balke Angew Chem IntEd 46 668 (2007)

2 I Galanakis and P H Dederichs (Eds) Half -MetallicAlloys Springer Berlin Heidelberg (2005)

3 R Farshchi and M Ramsteiner J Appl Phys 113191101 (2013)

4 M Hashimoto J Herfort H -P Schonherr and K HPloog Appl Phys Lett 87 102506 (2005)

5 M Hashimoto A Trampert J Herfort and K H PloogJ Vac Sci Technol B 25 1453 (2007)

6 M Hashimoto J Herfort A Trampert H -P Schonherrand K H Ploog J Phys D Appl Phys 40 1631 (2007)

7 L Bainsla K G Suresh A K Nigam M Manivel RajaB S D Ch S Varaprasad Y K Takahashi and K HonoJ Appl Phys 116 203902 (2014)

8 L Bainsla A I Mallick M Manivel Raja A K NigamB S D Ch S Varaprasad Y K Takahashi A Alam KG Suresh and K Hono Phys Rev B 91 104408 (2015)

9 K Ozdogan E Sasioglu and I Galanakis J Appl Phys113 193903 (2013) X Dai G Liu G H Fecher C FelserY Li and H Liu J Appl Phys 105 07E901 (2009)

10 V Alijani J Winterlik G H Fecher S S Naghavi andC Felser Phys Rev B 83 184428 (2011)

11 X Dai G Liu G H Fecher C Felser Y Li and H LiuAppl Phys Lett 105 07E901 (2009)

12 M Singh H S Saini and M K Kashyap J Mater Sci48 1837 (2013)

13 V Alijani J Winterlik G H Fecher S S Naghavi SChadov T Gruhn and C Felser J Phys Condens Mat-ter 24 046001 (2012)

14 I Galanakis K Ozdogan E Sasioglu and B Aktas PhysRev B 75 172405 (2007)

15 H Z Luo H W Zhang Z Y Zhu L Ma S F Xu GH Wu X X Zhu C B Jiang and H B Xu J ApplPhys 103 083908 (2008)

16 I Galanakis and E Sasioglu Appl Phys Lett 99 052509(2011)

17 M Meinert Jan-Michael Schmalhorst C Klewe G ReissE Arenholz T Bohnert and K Nielsch Phys Rev B 84132405 (2011)

18 G Y Gao L Hu K L Yao B Luo and N Liu J AlloyCompd 551 539 (2013)(and references therein)

19 P Klaer B Balke V Alijani J Winterlik G H FecherC Felser and H J Elmers Phys Rev B 84 144413(2011)

20 V Alijani S Ouardi G H Fecher J Winterlik S SNaghavi X Kozina G Stryganyuk C Felser E IkenagaY Yamashita S Ueda and K Kobayashi Phys Rev B84 224416 (2011)

21 L Bainsla A I Mallick A A Coelho A K Nigam BS D Ch S Varaprasad Y K Takahashi A Alam KG Suresh and K Hono J Magn Magn Mater 394 82(2015)

22 J C Slater Phys Rev 49 931 (1936)23 L Pauling Phys Rev 54 899 (1938)24 wwwilleusitesfullprofphptutorialshtml25 T Graf C Felser and S S P Parkin Progress in Solid

State Chemistry 39 1 (2011)26 G Kresse and J Furthmuller Phys Rev B 54 11169

(1996) Comput Mater Sci 6 15 (1996)27 G Kresse and D Joubert Phys Rev B 59 1758 (1999)28 httpsenwikipediaorgwikiElectronegativity29 T Graf and C Felser Spintronics- From Materials to De-

vices pp 33-34 (Springer New York London 2013)30 Y J Zhang G J Li E K Liu and J L Chen J Appl

Phys 113 123901 (2013)31 A Vinesh V D Sudheesh N Lakshmi and K Venu-

gopalan AIP Conf Proc 1591 1521 (2014)32 W Zhang Z Qian Y Sui Y Liu X Huang W Su M

Zhang Z Liu G Liu and G Wu Physica B 367 205(2005)

33 I Galanakis P H Dederichs and N Papanikolaou PhysRev B 66 174429 (2002)

4

TABLE I χ2 values of the Rietveld method for three distinctatomic arrangements (from Fig 1) for CFCG and CMCA

Alloy Configuration Type1 Type2 Type3CFCG χ

2 = 204 χ2 = 222 χ

2 = 229

CMCA χ2 = 172 χ

2 = 172 χ2 = 199

III RESULTS AND DISCUSSION

A Experimental

Rietveld refinement of powder X-ray diffraction(XRD)data using FullProf suite reveals that both CFCG andCMCA crystallize in the cubic structure with lattice con-stants 577plusmn001A and 576plusmn001A respectivelyχ2 values of Rietveld refinement for three distinct

atomic arrangements (as depicted in Fig 1) are pre-sented in Table I for both the alloys

For CFCG the constituent elements are nearest neigh-bors in the periodic table due to which their atomic scat-tering factors are nearly identical Hence the intensitiesof superlattice peaks (111) and (200) are very small incomparison to that of (220) peak This can be under-stood from Eq(1) Therefore one can do the refinementwith all the three configurations shown in Fig1 and canbe fitted to XRD data The best fit between observedand calculated intensities is observed for the first con-figuration In this configuration constituent elementsGe and Cr are at 4a(000) and 4b(121212) octa-hedral sites whereas Co and Fe are at 4c(141414)and 4d(343434) tetrahedral sites respectively25 ForCFCG Cr is the least electronegative (166 Pauli units)28

and therefore it forms ionic type sublattice with Ge(which has more electronegativity of 201 Pauli unit) andbecomes stable by donating its electrons to other ele-ments in the alloy Ge tries to accept electrons fromother elements As a result the electronic density at Crsite decreases whereas it increases at Ge site The X andXprime atoms(here Fe and Co) have intermediate electroneg-ativities and occupy tetrahedral sites25 The electronicdensities of various atoms in the unit cell can be visu-alized from the contour plot shown in Fig2 generatedfrom XRD refinement It is clear from Fig2(a) and (c)that most of the charge is distributed around Ge atomicsite while Cr site has the least density Fe and Co aresurrounded by intermediate charge in comparison to Crand Ge sites in Fig2(b) and (d) This configuration isenergetically most favorable as found from our calcula-tion Therefore crystal structure shown in Fig1(a) isthe most stableFor CMCA the superlattice peak (200) is more intense

in comparison to (111) peak and is clearly visible in theXRD pattern (Fig 3) This suggests that there is consid-erable amount of disorder between octahedral sites Thisis like B2 disorder in X2YZ HA but in QHA it should notbe treated as B2 disorder because X and Xprime are differentatoms It is rather an L21 type disorder where (000)

0 200 400 600 800 1000010203040506070

Magnetization (

em

ug

)

Temperature (K)

TC=866 K

500 Oe

CFCG

0 200 400 600 800 10000

4

8

12

16

20

TC=358 K

Magnetization (

em

ug

)

Temperature (K)

CMCA 500 Oe

-60 -40 -20 0 20 40 60

-3

-2

-1

0

1

2

3

CFCG

Mo

me

nt (

Bfu

)

Field (kOe)

300 K 5 K

-45 -30 -15 0 15 30 45

-08

-04

00

04

08

Field (kOe)

Mo

me

nt (

Bfu

)

5 K 300 K

CMCA

FIG 4 (Top) Temperature dependence of magnetization Mat 500 Oe TC is calculated from the minima of the first orderderivative of M vs T curve (Bottom) Magnetic moment vslsquoHrsquo at 300K and 5K for CFCG(left) and CMCA(right)

and (121212) fcc sublattices are randomly occupiedby the Z and Y atoms From Eq(1) it is clear that|F111|

2 reduces as compared to |F200|2 because fz = fy

due to equal probability of finding the Z and Y atoms atthose sites Hence the intensity which is proportional to|F111|

2 rarr 0 when |fx minus fxprime | rarr 0 Here |fx minus fxprime | asymp 0as X and Xprime are nearest neighbors Similar to CFCG(Fig1) CMCA also has three different configurationswith the exception that there is a probability of exchangeof atoms between the octahedral sites ie (000) and(121212)fcc sublattices Even though XRD can befitted with all the three configurations the configura-tion in which octahedral site (121212)fcc containsthe least electronegative element is energetically favor-able Here Mn and Cr have least electronegativity andhence the two configurations (Fig1(a) and (b)) contain-ing Cr or Mn at (121212)fcc sublattice are favorableElectronegativity of Al is also of the same order as thatof Mn or Cr and consequently Al also tries to occupyat (121212)fcc As such Al occupies different octa-hedral sites (000)fcc and (121212)fcc As a conse-quence the atoms which were initially at (121212)fccsites occupy both octahedral sites randomly like Al Dueto this behavior (111) peak vanishes in XRD Al atomsoccupying (121212)fcc try to lose electrons Fig3(b)shows the XRD refinement by considering equal proba-bility of finding Mn or Al atoms in octahedral site Theconventional unit cell is shifted by (141414) whiledoing the refinement and so the space group changes toFm3m ( 225) In this space group the occupancies areCo at 4a Cr at 4b and MnAl at 8c Wyckoff sites AsMn and Cr are neighboring elements swapping of these

5

elements will not be distinguishable from XRD Due tothis reason χ2 value is same for the first and second con-figurations as seen in Table I Therefore the conclusionis that CFCG is fully ordered while CMCA has L21 dis-ordered structureIt is observed in HA that if more than one atom

has nearly same electronegative values some degree ofdisorder can be expected For example CoMnCrAlCoFeCrAl8 and Co2Cr1minusxFexAl

29 HA have disorder be-tween Cr and Al sites Disorder in these systems arisesbecause of the same electronegativity values of Cr and Alatoms Consequently Al atom acts as an electron donorand occupies one of the octahedral sites (121212)fccwith almost same probability of occupancy as that of Cratoms Similarly Mn2CoAl

30 and Co2MnAl31 have a dis-order between Mn and Al sites This type of disorder isseen in HA containing Zn as well Zn also tries to occupyboth octahedral sites (121212)fcc and (000)fcc sub-lattice because Al and Zn atoms have the nature that insome cases they lose electrons and in some other casesthey accept electrons because of their low electronega-tivity and proximity to the p-block of the periodic tableHowever one can also synthesize perfectly ordered sys-tems in HA containing Al atoms such as CoFeTiAl29 (Ystructure) Co2TiAl

32(L21 structure) The scenario is abit different in this case Since Ti atom has the leastelectronegativity among the constituent atoms behavesas a charge donor and tries to occupy the (121212)fccand does not allow Al to occupy the same site Hencethere will be no disorder in these systems Thereforeon the basis of data available on a number of alloys wecould propose an empirical relation between relative elec-tronegativity values and the occurrence of disorderTop plots of Fig 4 show the temperature (T) de-

pendence of magnetization in constant field of 500 Oefor CFCG (left) and CMCA (right) showing the ferro-paramagnetic transition The Curie temperature hasbeen determined by taking the minima of the first or-der derivative of Magnetization vs Temperature (M-T)curve The estimated TC values are about 358K and866K for CMCA and CFCG respectively High TC ofthese alloys enable them to be potential candidates forroom temperature applicationsFigure 4 (bottom) shows the field dependence of mag-

netization for the two alloys The absence of hysteresisreveals the soft magnetic nature of the alloys Both thealloys show saturation at 5K and 300K The saturationmoment at 5 K is estimated to be 3 microB and 09 microB forCFCG and CMCA respectively The total moment inHeusler compounds can be estimated from the Slater-Pauling rule by counting the number of valence electronsin the primitive cell33 In QHA the total moment (m)per unit cell can be expressed as10

m = (Nv minus 24)microB (7)

where Nv (sd electrons for transition metals and spelectrons for main group element) is the number of va-lence electrons per unit cell As CFCG and CMCA have

-50

-25

00

25

50

-50

-25

00

25

50

-2 -1 0 1 2-9

-6

-3

0

3

6

9

E - E

F (eV)

W L Γ X W L Γ XWave Vector (k)

W W

Majority ( ) Minority ( )

E - EF (eV)

DoS

(sta

tes

eV)

TDOS

CMCA

Minority ( )

Majority ( )

(a)

-50

-25

00

25

50

-50

-25

00

25

50

-2 -1 0 1 2-9

-6

-3

0

3

6

9

E - E

F (eV)

W L Γ X W L Γ XWave Vector (k)

W W

Majority ( ) Minority ( )

E - EF (eV)

DoS

(sta

tes

eV)

TDOS

CFCG

Minority ( )

Majority ( )

(b)

FIG 5 Spin resolved band structure(left) and density ofstates (right) for CMCA(a) and CFCG(b) at experimentallattice constant(aexp) Both systems clearly show half metal-lic behavior with a band gap sim0328 eV for CMCA andsim0481eV for CFCG

27 and 25 valence electrons respectively according toSlater-Pauling rule (using Eq7) the moment in thesecompounds should be 3 and 1 microB But experimentallyobserved magnetic moment for CMCA (09microB) slightlydeviates from the Slater-Pauling rule because of the pres-ence of disorder On the other hand in CFCG the agree-ment is very good In addition to the experiment thetheoretically calculated moments also agree fairly wellwith the Slater-Pauling prediction (described in the nextsection)

B Theoretical

To check the stability we have first calculated thesite preference energies for various atomic configurationsConsidering the symmetry of the XXprimeYZ structure we fixthe Z-atom at 4d position and permute rest three atomson 4a 4b and 4c Wyckoff sites Out of six possible con-figurations only three are energetically non-degeneratenamely Type1 Type2 and Type3 as shown in the Fig1for both CFCG and CMCA Type1 (where X atom sitsat 4a Xprime at 4b and Y at 4c) is found to be energeti-cally the most stable configuration as also configured byexperiment

Figure 5 shows the spin polarized band structureand density of states (DoS) for CMCA(top) andCFCG(bottom) respectively Half metallicity is obviousin both the systems with a finite state (at EF) in major-ity channel but gapped in minority Calculated magneticmoment for CMCA is 098 microB (microexpt = 09 microB) whilefor CFCG is 299 microB (microexpt = 30 microB) which follows the

6

-16 -12 -8 -4 0 4 8 12 16x()

-200

-160

-120

-80

-40∆E

(m

eVa

tom

)

Co Mn1-xCr Al1+x

Co Mn Cr1-xAl1+x

0

2

4

6

8

-16 -12 -8 -4 0 4 8 12 16x()

0

2

4

6

8

Co Mn1-xCr Al1+x

Co Mn Cr1-xAl1+x

To

tal

ma

gn

eti

c m

om

en

t (m

t) (

micro B)

Fe

rmi

en

erg

y (

EF)

(eV

)

05

10

15

20

00

05

10

15

20

0000

05

10

15

-16 -12 -8 -4 0 4 8 12 16x()

00

05

10

15

n (EF)n (EF)(∆Eg)

CoMnCr1-xAl1+x

CoMn1-xCrAl1+x

025

050

075 (∆E

g) (e

V)

000

050

000

025

075

(n (

EF)

)

(st

ates

-eV

-1a

tom

)n

(E

F)

(a) (b) (c)

FIG 6 (a) Formation energy (∆E) vs antisite disorder (x) for CoMnCr1minusxAl1+x (triangle UP) and CoMn1minusxCrAl1+x (triangleDN) (b) Concentration (x) dependence of DoS at EF for majority spin (triangle UP) minority spin (triangle DN) and bandgap (∆Eg)darr (circle) for CoMnCr1minusxAl1+x (top) and CoMn1minusxCrAl1+x (bottom) (c) x-dependence of total magnetic moment(mt) and change in Fermi energy (EF) for the same two alloying

Slater-Pauling ruleIntrinsic defects such as antisite disorder is fairly com-

mon in QHA Our XRD data clearly indicate the signa-ture of L21 disorder in CMCA where Al site is expectedto mix with Mn (and possibly with Cr) Electronic struc-ture of any material is extremely sensitive to such defectsand has not received much attention in the literatureWe have performed first principle calculation to checkthe stability electronic structure and magnetism for twosets of antisite disorders namely CoMn1minusxCrAl1+x andCoMnCr1minusxAl1+x These are done by using a 3times3times3supercell of the primitive 4-atom cellFigure 6(a) shows the formation energy (∆E) of

CoMn1minusxCrAl1+x (triangle down) and CoMnCr1minusxAl1+x

(triangle up) for both excess (positive x-vale) and deficit(negative x-value) of Al in the compound Negative val-ues of ∆E indicates that Al indeed prefers to mix withMn and Cr Mn is relatively much more preferable to mixdue to a larger negative ∆E as also revealed by our XRDdata Detailed analysis of such antisite disorder can beaccurately probed with neutron diffraction experimentFigure 6(b) shows the value of DoS at EF for ma-

jority nuarr (triangle up) and minority ndarr(triangle down)spin channels The associated band gap (∆Eg)darr in theminority spin is also represented (solid circle) Top(bottom) panel are the results for CoMnCr1minusxAl1+x

(CoMn1minusxCrAl1+x) Interestingly deficit of Al (nega-tive x) up to x ≃ 1481 maintains the half metallicityhowever excess of Al (positive x) causes a transition fromhalf metallic to metallic beyond x ≃ 370 in both thecases At 741 excess Al the minority spin tend tohave a small DoS at EF ndarr(EF) ≃ 003 stateseV-atom(CoMnCr1minusxAl1+x) and nuarr(EF) ≃ 002 stateseV-atom(CoMn1minusxCrAl1+x) Such transition is something uniqueand has never been observed beforeIt turns out that this metallic transition is intimately

connected with a magnetic transition where the sys-tem goes from a ferromagnetic state to an antiferromag-

netic state This is shown in Fig6(c) where the totalmagnetic moment changes discontinuously at the sameconcentration (x sim741) at which the system loses itshalfmetallicity EF almost remains unchanged with vary-ing x (square symbol) Although we have theoreticallystudied the effect of antisite disorder up to x sim1481such a large disorder may not be expected to survive inthe actual sample

IV CONCLUSIONS

In conclusion CFCG and CMCA are found to be twointeresting materials the former crystallizes in Y typestructure while the latter shows an L21 disordered struc-ture which is due to the random occupancy of octahe-dral site atoms Al with CrMn Both the alloys showhalf metallic ferromagnetic behavior with a specific sitepreference for the constituent atoms CFCG is more use-ful because of its high Curie temperature (866 K) whileCMCA shows an intrinsic antisite disorder which allowsa larger tunability of its properties Magnetization mea-surement yields magnetic moments which obey the SlaterPauling rule and which also agree with our theoreticalprediction in both the cases Ab-initio electronic struc-ture simulation confirms the stability and half metallicityin both the compounds L21 disorder in CMCA is furtherinvestigated by simulating antisite disorder which alsoindicates the possibility of halfmetallic ferromagnetic be-havior in presence of small disorder However it changesto a metallic antiferromagnetic state beyond a certainexcess Al in the alloy

7

V ACKNOWLEDGEMENTS

Enamullah acknowledges IIT Bombay for providing fi-nancial assistance to carry out postdoctoral research PSwould like to thank US Department of Energy (DOE)Office of Science Materials Science and Engineering Di-vision for support

lowast aftabphyiitbacin enamullahphyiitbacindagger Authors have equal contribution1 C Felser G H Fecher and B Balke Angew Chem IntEd 46 668 (2007)

2 I Galanakis and P H Dederichs (Eds) Half -MetallicAlloys Springer Berlin Heidelberg (2005)

3 R Farshchi and M Ramsteiner J Appl Phys 113191101 (2013)

4 M Hashimoto J Herfort H -P Schonherr and K HPloog Appl Phys Lett 87 102506 (2005)

5 M Hashimoto A Trampert J Herfort and K H PloogJ Vac Sci Technol B 25 1453 (2007)

6 M Hashimoto J Herfort A Trampert H -P Schonherrand K H Ploog J Phys D Appl Phys 40 1631 (2007)

7 L Bainsla K G Suresh A K Nigam M Manivel RajaB S D Ch S Varaprasad Y K Takahashi and K HonoJ Appl Phys 116 203902 (2014)

8 L Bainsla A I Mallick M Manivel Raja A K NigamB S D Ch S Varaprasad Y K Takahashi A Alam KG Suresh and K Hono Phys Rev B 91 104408 (2015)

9 K Ozdogan E Sasioglu and I Galanakis J Appl Phys113 193903 (2013) X Dai G Liu G H Fecher C FelserY Li and H Liu J Appl Phys 105 07E901 (2009)

10 V Alijani J Winterlik G H Fecher S S Naghavi andC Felser Phys Rev B 83 184428 (2011)

11 X Dai G Liu G H Fecher C Felser Y Li and H LiuAppl Phys Lett 105 07E901 (2009)

12 M Singh H S Saini and M K Kashyap J Mater Sci48 1837 (2013)

13 V Alijani J Winterlik G H Fecher S S Naghavi SChadov T Gruhn and C Felser J Phys Condens Mat-ter 24 046001 (2012)

14 I Galanakis K Ozdogan E Sasioglu and B Aktas PhysRev B 75 172405 (2007)

15 H Z Luo H W Zhang Z Y Zhu L Ma S F Xu GH Wu X X Zhu C B Jiang and H B Xu J ApplPhys 103 083908 (2008)

16 I Galanakis and E Sasioglu Appl Phys Lett 99 052509(2011)

17 M Meinert Jan-Michael Schmalhorst C Klewe G ReissE Arenholz T Bohnert and K Nielsch Phys Rev B 84132405 (2011)

18 G Y Gao L Hu K L Yao B Luo and N Liu J AlloyCompd 551 539 (2013)(and references therein)

19 P Klaer B Balke V Alijani J Winterlik G H FecherC Felser and H J Elmers Phys Rev B 84 144413(2011)

20 V Alijani S Ouardi G H Fecher J Winterlik S SNaghavi X Kozina G Stryganyuk C Felser E IkenagaY Yamashita S Ueda and K Kobayashi Phys Rev B84 224416 (2011)

21 L Bainsla A I Mallick A A Coelho A K Nigam BS D Ch S Varaprasad Y K Takahashi A Alam KG Suresh and K Hono J Magn Magn Mater 394 82(2015)

22 J C Slater Phys Rev 49 931 (1936)23 L Pauling Phys Rev 54 899 (1938)24 wwwilleusitesfullprofphptutorialshtml25 T Graf C Felser and S S P Parkin Progress in Solid

State Chemistry 39 1 (2011)26 G Kresse and J Furthmuller Phys Rev B 54 11169

(1996) Comput Mater Sci 6 15 (1996)27 G Kresse and D Joubert Phys Rev B 59 1758 (1999)28 httpsenwikipediaorgwikiElectronegativity29 T Graf and C Felser Spintronics- From Materials to De-

vices pp 33-34 (Springer New York London 2013)30 Y J Zhang G J Li E K Liu and J L Chen J Appl

Phys 113 123901 (2013)31 A Vinesh V D Sudheesh N Lakshmi and K Venu-

gopalan AIP Conf Proc 1591 1521 (2014)32 W Zhang Z Qian Y Sui Y Liu X Huang W Su M

Zhang Z Liu G Liu and G Wu Physica B 367 205(2005)

33 I Galanakis P H Dederichs and N Papanikolaou PhysRev B 66 174429 (2002)

5

elements will not be distinguishable from XRD Due tothis reason χ2 value is same for the first and second con-figurations as seen in Table I Therefore the conclusionis that CFCG is fully ordered while CMCA has L21 dis-ordered structureIt is observed in HA that if more than one atom

has nearly same electronegative values some degree ofdisorder can be expected For example CoMnCrAlCoFeCrAl8 and Co2Cr1minusxFexAl

29 HA have disorder be-tween Cr and Al sites Disorder in these systems arisesbecause of the same electronegativity values of Cr and Alatoms Consequently Al atom acts as an electron donorand occupies one of the octahedral sites (121212)fccwith almost same probability of occupancy as that of Cratoms Similarly Mn2CoAl

30 and Co2MnAl31 have a dis-order between Mn and Al sites This type of disorder isseen in HA containing Zn as well Zn also tries to occupyboth octahedral sites (121212)fcc and (000)fcc sub-lattice because Al and Zn atoms have the nature that insome cases they lose electrons and in some other casesthey accept electrons because of their low electronega-tivity and proximity to the p-block of the periodic tableHowever one can also synthesize perfectly ordered sys-tems in HA containing Al atoms such as CoFeTiAl29 (Ystructure) Co2TiAl

32(L21 structure) The scenario is abit different in this case Since Ti atom has the leastelectronegativity among the constituent atoms behavesas a charge donor and tries to occupy the (121212)fccand does not allow Al to occupy the same site Hencethere will be no disorder in these systems Thereforeon the basis of data available on a number of alloys wecould propose an empirical relation between relative elec-tronegativity values and the occurrence of disorderTop plots of Fig 4 show the temperature (T) de-

pendence of magnetization in constant field of 500 Oefor CFCG (left) and CMCA (right) showing the ferro-paramagnetic transition The Curie temperature hasbeen determined by taking the minima of the first or-der derivative of Magnetization vs Temperature (M-T)curve The estimated TC values are about 358K and866K for CMCA and CFCG respectively High TC ofthese alloys enable them to be potential candidates forroom temperature applicationsFigure 4 (bottom) shows the field dependence of mag-

netization for the two alloys The absence of hysteresisreveals the soft magnetic nature of the alloys Both thealloys show saturation at 5K and 300K The saturationmoment at 5 K is estimated to be 3 microB and 09 microB forCFCG and CMCA respectively The total moment inHeusler compounds can be estimated from the Slater-Pauling rule by counting the number of valence electronsin the primitive cell33 In QHA the total moment (m)per unit cell can be expressed as10

m = (Nv minus 24)microB (7)

where Nv (sd electrons for transition metals and spelectrons for main group element) is the number of va-lence electrons per unit cell As CFCG and CMCA have

-50

-25

00

25

50

-50

-25

00

25

50

-2 -1 0 1 2-9

-6

-3

0

3

6

9

E - E

F (eV)

W L Γ X W L Γ XWave Vector (k)

W W

Majority ( ) Minority ( )

E - EF (eV)

DoS

(sta

tes

eV)

TDOS

CMCA

Minority ( )

Majority ( )

(a)

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-25

00

25

50

-50

-25

00

25

50

-2 -1 0 1 2-9

-6

-3

0

3

6

9

E - E

F (eV)

W L Γ X W L Γ XWave Vector (k)

W W

Majority ( ) Minority ( )

E - EF (eV)

DoS

(sta

tes

eV)

TDOS

CFCG

Minority ( )

Majority ( )

(b)

FIG 5 Spin resolved band structure(left) and density ofstates (right) for CMCA(a) and CFCG(b) at experimentallattice constant(aexp) Both systems clearly show half metal-lic behavior with a band gap sim0328 eV for CMCA andsim0481eV for CFCG

27 and 25 valence electrons respectively according toSlater-Pauling rule (using Eq7) the moment in thesecompounds should be 3 and 1 microB But experimentallyobserved magnetic moment for CMCA (09microB) slightlydeviates from the Slater-Pauling rule because of the pres-ence of disorder On the other hand in CFCG the agree-ment is very good In addition to the experiment thetheoretically calculated moments also agree fairly wellwith the Slater-Pauling prediction (described in the nextsection)

B Theoretical

To check the stability we have first calculated thesite preference energies for various atomic configurationsConsidering the symmetry of the XXprimeYZ structure we fixthe Z-atom at 4d position and permute rest three atomson 4a 4b and 4c Wyckoff sites Out of six possible con-figurations only three are energetically non-degeneratenamely Type1 Type2 and Type3 as shown in the Fig1for both CFCG and CMCA Type1 (where X atom sitsat 4a Xprime at 4b and Y at 4c) is found to be energeti-cally the most stable configuration as also configured byexperiment

Figure 5 shows the spin polarized band structureand density of states (DoS) for CMCA(top) andCFCG(bottom) respectively Half metallicity is obviousin both the systems with a finite state (at EF) in major-ity channel but gapped in minority Calculated magneticmoment for CMCA is 098 microB (microexpt = 09 microB) whilefor CFCG is 299 microB (microexpt = 30 microB) which follows the

6

-16 -12 -8 -4 0 4 8 12 16x()

-200

-160

-120

-80

-40∆E

(m

eVa

tom

)

Co Mn1-xCr Al1+x

Co Mn Cr1-xAl1+x

0

2

4

6

8

-16 -12 -8 -4 0 4 8 12 16x()

0

2

4

6

8

Co Mn1-xCr Al1+x

Co Mn Cr1-xAl1+x

To

tal

ma

gn

eti

c m

om

en

t (m

t) (

micro B)

Fe

rmi

en

erg

y (

EF)

(eV

)

05

10

15

20

00

05

10

15

20

0000

05

10

15

-16 -12 -8 -4 0 4 8 12 16x()

00

05

10

15

n (EF)n (EF)(∆Eg)

CoMnCr1-xAl1+x

CoMn1-xCrAl1+x

025

050

075 (∆E

g) (e

V)

000

050

000

025

075

(n (

EF)

)

(st

ates

-eV

-1a

tom

)n

(E

F)

(a) (b) (c)

FIG 6 (a) Formation energy (∆E) vs antisite disorder (x) for CoMnCr1minusxAl1+x (triangle UP) and CoMn1minusxCrAl1+x (triangleDN) (b) Concentration (x) dependence of DoS at EF for majority spin (triangle UP) minority spin (triangle DN) and bandgap (∆Eg)darr (circle) for CoMnCr1minusxAl1+x (top) and CoMn1minusxCrAl1+x (bottom) (c) x-dependence of total magnetic moment(mt) and change in Fermi energy (EF) for the same two alloying

Slater-Pauling ruleIntrinsic defects such as antisite disorder is fairly com-

mon in QHA Our XRD data clearly indicate the signa-ture of L21 disorder in CMCA where Al site is expectedto mix with Mn (and possibly with Cr) Electronic struc-ture of any material is extremely sensitive to such defectsand has not received much attention in the literatureWe have performed first principle calculation to checkthe stability electronic structure and magnetism for twosets of antisite disorders namely CoMn1minusxCrAl1+x andCoMnCr1minusxAl1+x These are done by using a 3times3times3supercell of the primitive 4-atom cellFigure 6(a) shows the formation energy (∆E) of

CoMn1minusxCrAl1+x (triangle down) and CoMnCr1minusxAl1+x

(triangle up) for both excess (positive x-vale) and deficit(negative x-value) of Al in the compound Negative val-ues of ∆E indicates that Al indeed prefers to mix withMn and Cr Mn is relatively much more preferable to mixdue to a larger negative ∆E as also revealed by our XRDdata Detailed analysis of such antisite disorder can beaccurately probed with neutron diffraction experimentFigure 6(b) shows the value of DoS at EF for ma-

jority nuarr (triangle up) and minority ndarr(triangle down)spin channels The associated band gap (∆Eg)darr in theminority spin is also represented (solid circle) Top(bottom) panel are the results for CoMnCr1minusxAl1+x

(CoMn1minusxCrAl1+x) Interestingly deficit of Al (nega-tive x) up to x ≃ 1481 maintains the half metallicityhowever excess of Al (positive x) causes a transition fromhalf metallic to metallic beyond x ≃ 370 in both thecases At 741 excess Al the minority spin tend tohave a small DoS at EF ndarr(EF) ≃ 003 stateseV-atom(CoMnCr1minusxAl1+x) and nuarr(EF) ≃ 002 stateseV-atom(CoMn1minusxCrAl1+x) Such transition is something uniqueand has never been observed beforeIt turns out that this metallic transition is intimately

connected with a magnetic transition where the sys-tem goes from a ferromagnetic state to an antiferromag-

netic state This is shown in Fig6(c) where the totalmagnetic moment changes discontinuously at the sameconcentration (x sim741) at which the system loses itshalfmetallicity EF almost remains unchanged with vary-ing x (square symbol) Although we have theoreticallystudied the effect of antisite disorder up to x sim1481such a large disorder may not be expected to survive inthe actual sample

IV CONCLUSIONS

In conclusion CFCG and CMCA are found to be twointeresting materials the former crystallizes in Y typestructure while the latter shows an L21 disordered struc-ture which is due to the random occupancy of octahe-dral site atoms Al with CrMn Both the alloys showhalf metallic ferromagnetic behavior with a specific sitepreference for the constituent atoms CFCG is more use-ful because of its high Curie temperature (866 K) whileCMCA shows an intrinsic antisite disorder which allowsa larger tunability of its properties Magnetization mea-surement yields magnetic moments which obey the SlaterPauling rule and which also agree with our theoreticalprediction in both the cases Ab-initio electronic struc-ture simulation confirms the stability and half metallicityin both the compounds L21 disorder in CMCA is furtherinvestigated by simulating antisite disorder which alsoindicates the possibility of halfmetallic ferromagnetic be-havior in presence of small disorder However it changesto a metallic antiferromagnetic state beyond a certainexcess Al in the alloy

7

V ACKNOWLEDGEMENTS

Enamullah acknowledges IIT Bombay for providing fi-nancial assistance to carry out postdoctoral research PSwould like to thank US Department of Energy (DOE)Office of Science Materials Science and Engineering Di-vision for support

lowast aftabphyiitbacin enamullahphyiitbacindagger Authors have equal contribution1 C Felser G H Fecher and B Balke Angew Chem IntEd 46 668 (2007)

2 I Galanakis and P H Dederichs (Eds) Half -MetallicAlloys Springer Berlin Heidelberg (2005)

3 R Farshchi and M Ramsteiner J Appl Phys 113191101 (2013)

4 M Hashimoto J Herfort H -P Schonherr and K HPloog Appl Phys Lett 87 102506 (2005)

5 M Hashimoto A Trampert J Herfort and K H PloogJ Vac Sci Technol B 25 1453 (2007)

6 M Hashimoto J Herfort A Trampert H -P Schonherrand K H Ploog J Phys D Appl Phys 40 1631 (2007)

7 L Bainsla K G Suresh A K Nigam M Manivel RajaB S D Ch S Varaprasad Y K Takahashi and K HonoJ Appl Phys 116 203902 (2014)

8 L Bainsla A I Mallick M Manivel Raja A K NigamB S D Ch S Varaprasad Y K Takahashi A Alam KG Suresh and K Hono Phys Rev B 91 104408 (2015)

9 K Ozdogan E Sasioglu and I Galanakis J Appl Phys113 193903 (2013) X Dai G Liu G H Fecher C FelserY Li and H Liu J Appl Phys 105 07E901 (2009)

10 V Alijani J Winterlik G H Fecher S S Naghavi andC Felser Phys Rev B 83 184428 (2011)

11 X Dai G Liu G H Fecher C Felser Y Li and H LiuAppl Phys Lett 105 07E901 (2009)

12 M Singh H S Saini and M K Kashyap J Mater Sci48 1837 (2013)

13 V Alijani J Winterlik G H Fecher S S Naghavi SChadov T Gruhn and C Felser J Phys Condens Mat-ter 24 046001 (2012)

14 I Galanakis K Ozdogan E Sasioglu and B Aktas PhysRev B 75 172405 (2007)

15 H Z Luo H W Zhang Z Y Zhu L Ma S F Xu GH Wu X X Zhu C B Jiang and H B Xu J ApplPhys 103 083908 (2008)

16 I Galanakis and E Sasioglu Appl Phys Lett 99 052509(2011)

17 M Meinert Jan-Michael Schmalhorst C Klewe G ReissE Arenholz T Bohnert and K Nielsch Phys Rev B 84132405 (2011)

18 G Y Gao L Hu K L Yao B Luo and N Liu J AlloyCompd 551 539 (2013)(and references therein)

19 P Klaer B Balke V Alijani J Winterlik G H FecherC Felser and H J Elmers Phys Rev B 84 144413(2011)

20 V Alijani S Ouardi G H Fecher J Winterlik S SNaghavi X Kozina G Stryganyuk C Felser E IkenagaY Yamashita S Ueda and K Kobayashi Phys Rev B84 224416 (2011)

21 L Bainsla A I Mallick A A Coelho A K Nigam BS D Ch S Varaprasad Y K Takahashi A Alam KG Suresh and K Hono J Magn Magn Mater 394 82(2015)

22 J C Slater Phys Rev 49 931 (1936)23 L Pauling Phys Rev 54 899 (1938)24 wwwilleusitesfullprofphptutorialshtml25 T Graf C Felser and S S P Parkin Progress in Solid

State Chemistry 39 1 (2011)26 G Kresse and J Furthmuller Phys Rev B 54 11169

(1996) Comput Mater Sci 6 15 (1996)27 G Kresse and D Joubert Phys Rev B 59 1758 (1999)28 httpsenwikipediaorgwikiElectronegativity29 T Graf and C Felser Spintronics- From Materials to De-

vices pp 33-34 (Springer New York London 2013)30 Y J Zhang G J Li E K Liu and J L Chen J Appl

Phys 113 123901 (2013)31 A Vinesh V D Sudheesh N Lakshmi and K Venu-

gopalan AIP Conf Proc 1591 1521 (2014)32 W Zhang Z Qian Y Sui Y Liu X Huang W Su M

Zhang Z Liu G Liu and G Wu Physica B 367 205(2005)

33 I Galanakis P H Dederichs and N Papanikolaou PhysRev B 66 174429 (2002)

6

-16 -12 -8 -4 0 4 8 12 16x()

-200

-160

-120

-80

-40∆E

(m

eVa

tom

)

Co Mn1-xCr Al1+x

Co Mn Cr1-xAl1+x

0

2

4

6

8

-16 -12 -8 -4 0 4 8 12 16x()

0

2

4

6

8

Co Mn1-xCr Al1+x

Co Mn Cr1-xAl1+x

To

tal

ma

gn

eti

c m

om

en

t (m

t) (

micro B)

Fe

rmi

en

erg

y (

EF)

(eV

)

05

10

15

20

00

05

10

15

20

0000

05

10

15

-16 -12 -8 -4 0 4 8 12 16x()

00

05

10

15

n (EF)n (EF)(∆Eg)

CoMnCr1-xAl1+x

CoMn1-xCrAl1+x

025

050

075 (∆E

g) (e

V)

000

050

000

025

075

(n (

EF)

)

(st

ates

-eV

-1a

tom

)n

(E

F)

(a) (b) (c)

FIG 6 (a) Formation energy (∆E) vs antisite disorder (x) for CoMnCr1minusxAl1+x (triangle UP) and CoMn1minusxCrAl1+x (triangleDN) (b) Concentration (x) dependence of DoS at EF for majority spin (triangle UP) minority spin (triangle DN) and bandgap (∆Eg)darr (circle) for CoMnCr1minusxAl1+x (top) and CoMn1minusxCrAl1+x (bottom) (c) x-dependence of total magnetic moment(mt) and change in Fermi energy (EF) for the same two alloying

Slater-Pauling ruleIntrinsic defects such as antisite disorder is fairly com-

mon in QHA Our XRD data clearly indicate the signa-ture of L21 disorder in CMCA where Al site is expectedto mix with Mn (and possibly with Cr) Electronic struc-ture of any material is extremely sensitive to such defectsand has not received much attention in the literatureWe have performed first principle calculation to checkthe stability electronic structure and magnetism for twosets of antisite disorders namely CoMn1minusxCrAl1+x andCoMnCr1minusxAl1+x These are done by using a 3times3times3supercell of the primitive 4-atom cellFigure 6(a) shows the formation energy (∆E) of

CoMn1minusxCrAl1+x (triangle down) and CoMnCr1minusxAl1+x

(triangle up) for both excess (positive x-vale) and deficit(negative x-value) of Al in the compound Negative val-ues of ∆E indicates that Al indeed prefers to mix withMn and Cr Mn is relatively much more preferable to mixdue to a larger negative ∆E as also revealed by our XRDdata Detailed analysis of such antisite disorder can beaccurately probed with neutron diffraction experimentFigure 6(b) shows the value of DoS at EF for ma-

jority nuarr (triangle up) and minority ndarr(triangle down)spin channels The associated band gap (∆Eg)darr in theminority spin is also represented (solid circle) Top(bottom) panel are the results for CoMnCr1minusxAl1+x

(CoMn1minusxCrAl1+x) Interestingly deficit of Al (nega-tive x) up to x ≃ 1481 maintains the half metallicityhowever excess of Al (positive x) causes a transition fromhalf metallic to metallic beyond x ≃ 370 in both thecases At 741 excess Al the minority spin tend tohave a small DoS at EF ndarr(EF) ≃ 003 stateseV-atom(CoMnCr1minusxAl1+x) and nuarr(EF) ≃ 002 stateseV-atom(CoMn1minusxCrAl1+x) Such transition is something uniqueand has never been observed beforeIt turns out that this metallic transition is intimately

connected with a magnetic transition where the sys-tem goes from a ferromagnetic state to an antiferromag-

netic state This is shown in Fig6(c) where the totalmagnetic moment changes discontinuously at the sameconcentration (x sim741) at which the system loses itshalfmetallicity EF almost remains unchanged with vary-ing x (square symbol) Although we have theoreticallystudied the effect of antisite disorder up to x sim1481such a large disorder may not be expected to survive inthe actual sample

IV CONCLUSIONS

In conclusion CFCG and CMCA are found to be twointeresting materials the former crystallizes in Y typestructure while the latter shows an L21 disordered struc-ture which is due to the random occupancy of octahe-dral site atoms Al with CrMn Both the alloys showhalf metallic ferromagnetic behavior with a specific sitepreference for the constituent atoms CFCG is more use-ful because of its high Curie temperature (866 K) whileCMCA shows an intrinsic antisite disorder which allowsa larger tunability of its properties Magnetization mea-surement yields magnetic moments which obey the SlaterPauling rule and which also agree with our theoreticalprediction in both the cases Ab-initio electronic struc-ture simulation confirms the stability and half metallicityin both the compounds L21 disorder in CMCA is furtherinvestigated by simulating antisite disorder which alsoindicates the possibility of halfmetallic ferromagnetic be-havior in presence of small disorder However it changesto a metallic antiferromagnetic state beyond a certainexcess Al in the alloy

7

V ACKNOWLEDGEMENTS

Enamullah acknowledges IIT Bombay for providing fi-nancial assistance to carry out postdoctoral research PSwould like to thank US Department of Energy (DOE)Office of Science Materials Science and Engineering Di-vision for support

lowast aftabphyiitbacin enamullahphyiitbacindagger Authors have equal contribution1 C Felser G H Fecher and B Balke Angew Chem IntEd 46 668 (2007)

2 I Galanakis and P H Dederichs (Eds) Half -MetallicAlloys Springer Berlin Heidelberg (2005)

3 R Farshchi and M Ramsteiner J Appl Phys 113191101 (2013)

4 M Hashimoto J Herfort H -P Schonherr and K HPloog Appl Phys Lett 87 102506 (2005)

5 M Hashimoto A Trampert J Herfort and K H PloogJ Vac Sci Technol B 25 1453 (2007)

6 M Hashimoto J Herfort A Trampert H -P Schonherrand K H Ploog J Phys D Appl Phys 40 1631 (2007)

7 L Bainsla K G Suresh A K Nigam M Manivel RajaB S D Ch S Varaprasad Y K Takahashi and K HonoJ Appl Phys 116 203902 (2014)

8 L Bainsla A I Mallick M Manivel Raja A K NigamB S D Ch S Varaprasad Y K Takahashi A Alam KG Suresh and K Hono Phys Rev B 91 104408 (2015)

9 K Ozdogan E Sasioglu and I Galanakis J Appl Phys113 193903 (2013) X Dai G Liu G H Fecher C FelserY Li and H Liu J Appl Phys 105 07E901 (2009)

10 V Alijani J Winterlik G H Fecher S S Naghavi andC Felser Phys Rev B 83 184428 (2011)

11 X Dai G Liu G H Fecher C Felser Y Li and H LiuAppl Phys Lett 105 07E901 (2009)

12 M Singh H S Saini and M K Kashyap J Mater Sci48 1837 (2013)

13 V Alijani J Winterlik G H Fecher S S Naghavi SChadov T Gruhn and C Felser J Phys Condens Mat-ter 24 046001 (2012)

14 I Galanakis K Ozdogan E Sasioglu and B Aktas PhysRev B 75 172405 (2007)

15 H Z Luo H W Zhang Z Y Zhu L Ma S F Xu GH Wu X X Zhu C B Jiang and H B Xu J ApplPhys 103 083908 (2008)

16 I Galanakis and E Sasioglu Appl Phys Lett 99 052509(2011)

17 M Meinert Jan-Michael Schmalhorst C Klewe G ReissE Arenholz T Bohnert and K Nielsch Phys Rev B 84132405 (2011)

18 G Y Gao L Hu K L Yao B Luo and N Liu J AlloyCompd 551 539 (2013)(and references therein)

19 P Klaer B Balke V Alijani J Winterlik G H FecherC Felser and H J Elmers Phys Rev B 84 144413(2011)

20 V Alijani S Ouardi G H Fecher J Winterlik S SNaghavi X Kozina G Stryganyuk C Felser E IkenagaY Yamashita S Ueda and K Kobayashi Phys Rev B84 224416 (2011)

21 L Bainsla A I Mallick A A Coelho A K Nigam BS D Ch S Varaprasad Y K Takahashi A Alam KG Suresh and K Hono J Magn Magn Mater 394 82(2015)

22 J C Slater Phys Rev 49 931 (1936)23 L Pauling Phys Rev 54 899 (1938)24 wwwilleusitesfullprofphptutorialshtml25 T Graf C Felser and S S P Parkin Progress in Solid

State Chemistry 39 1 (2011)26 G Kresse and J Furthmuller Phys Rev B 54 11169

(1996) Comput Mater Sci 6 15 (1996)27 G Kresse and D Joubert Phys Rev B 59 1758 (1999)28 httpsenwikipediaorgwikiElectronegativity29 T Graf and C Felser Spintronics- From Materials to De-

vices pp 33-34 (Springer New York London 2013)30 Y J Zhang G J Li E K Liu and J L Chen J Appl

Phys 113 123901 (2013)31 A Vinesh V D Sudheesh N Lakshmi and K Venu-

gopalan AIP Conf Proc 1591 1521 (2014)32 W Zhang Z Qian Y Sui Y Liu X Huang W Su M

Zhang Z Liu G Liu and G Wu Physica B 367 205(2005)

33 I Galanakis P H Dederichs and N Papanikolaou PhysRev B 66 174429 (2002)

7

V ACKNOWLEDGEMENTS

Enamullah acknowledges IIT Bombay for providing fi-nancial assistance to carry out postdoctoral research PSwould like to thank US Department of Energy (DOE)Office of Science Materials Science and Engineering Di-vision for support

lowast aftabphyiitbacin enamullahphyiitbacindagger Authors have equal contribution1 C Felser G H Fecher and B Balke Angew Chem IntEd 46 668 (2007)

2 I Galanakis and P H Dederichs (Eds) Half -MetallicAlloys Springer Berlin Heidelberg (2005)

3 R Farshchi and M Ramsteiner J Appl Phys 113191101 (2013)

4 M Hashimoto J Herfort H -P Schonherr and K HPloog Appl Phys Lett 87 102506 (2005)

5 M Hashimoto A Trampert J Herfort and K H PloogJ Vac Sci Technol B 25 1453 (2007)

6 M Hashimoto J Herfort A Trampert H -P Schonherrand K H Ploog J Phys D Appl Phys 40 1631 (2007)

7 L Bainsla K G Suresh A K Nigam M Manivel RajaB S D Ch S Varaprasad Y K Takahashi and K HonoJ Appl Phys 116 203902 (2014)

8 L Bainsla A I Mallick M Manivel Raja A K NigamB S D Ch S Varaprasad Y K Takahashi A Alam KG Suresh and K Hono Phys Rev B 91 104408 (2015)

9 K Ozdogan E Sasioglu and I Galanakis J Appl Phys113 193903 (2013) X Dai G Liu G H Fecher C FelserY Li and H Liu J Appl Phys 105 07E901 (2009)

10 V Alijani J Winterlik G H Fecher S S Naghavi andC Felser Phys Rev B 83 184428 (2011)

11 X Dai G Liu G H Fecher C Felser Y Li and H LiuAppl Phys Lett 105 07E901 (2009)

12 M Singh H S Saini and M K Kashyap J Mater Sci48 1837 (2013)

13 V Alijani J Winterlik G H Fecher S S Naghavi SChadov T Gruhn and C Felser J Phys Condens Mat-ter 24 046001 (2012)

14 I Galanakis K Ozdogan E Sasioglu and B Aktas PhysRev B 75 172405 (2007)

15 H Z Luo H W Zhang Z Y Zhu L Ma S F Xu GH Wu X X Zhu C B Jiang and H B Xu J ApplPhys 103 083908 (2008)

16 I Galanakis and E Sasioglu Appl Phys Lett 99 052509(2011)

17 M Meinert Jan-Michael Schmalhorst C Klewe G ReissE Arenholz T Bohnert and K Nielsch Phys Rev B 84132405 (2011)

18 G Y Gao L Hu K L Yao B Luo and N Liu J AlloyCompd 551 539 (2013)(and references therein)

19 P Klaer B Balke V Alijani J Winterlik G H FecherC Felser and H J Elmers Phys Rev B 84 144413(2011)

20 V Alijani S Ouardi G H Fecher J Winterlik S SNaghavi X Kozina G Stryganyuk C Felser E IkenagaY Yamashita S Ueda and K Kobayashi Phys Rev B84 224416 (2011)

21 L Bainsla A I Mallick A A Coelho A K Nigam BS D Ch S Varaprasad Y K Takahashi A Alam KG Suresh and K Hono J Magn Magn Mater 394 82(2015)

22 J C Slater Phys Rev 49 931 (1936)23 L Pauling Phys Rev 54 899 (1938)24 wwwilleusitesfullprofphptutorialshtml25 T Graf C Felser and S S P Parkin Progress in Solid

State Chemistry 39 1 (2011)26 G Kresse and J Furthmuller Phys Rev B 54 11169

(1996) Comput Mater Sci 6 15 (1996)27 G Kresse and D Joubert Phys Rev B 59 1758 (1999)28 httpsenwikipediaorgwikiElectronegativity29 T Graf and C Felser Spintronics- From Materials to De-

vices pp 33-34 (Springer New York London 2013)30 Y J Zhang G J Li E K Liu and J L Chen J Appl

Phys 113 123901 (2013)31 A Vinesh V D Sudheesh N Lakshmi and K Venu-

gopalan AIP Conf Proc 1591 1521 (2014)32 W Zhang Z Qian Y Sui Y Liu X Huang W Su M

Zhang Z Liu G Liu and G Wu Physica B 367 205(2005)

33 I Galanakis P H Dederichs and N Papanikolaou PhysRev B 66 174429 (2002)