Journal of Magnetism and Magnetic Materials 325 (2013) 144–146

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Journal of Magnetism and Magnetic Materials

0304-88

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Letter to the Editor

Enhanced magnetization and conductive phase in NiFe2O4

Ching Cheng

Department of Physics, National Cheng Kung University, Tainan 70101, Taiwan

a r t i c l e i n f o

Article history:

Received 8 May 2012

Received in revised form

29 June 2012Available online 22 July 2012

Keywords:

Ni ferrite

Magnetic property

Structure

Density functional calculation

53/$ - see front matter & 2012 Elsevier B.V. A

x.doi.org/10.1016/j.jmmm.2012.07.020

ail address: ccheng@mail.ncku.edu.tw

a b s t r a c t

Recent advances on nanometer films observed magnetization enhanced NiFe2O4 (NFO) in insulating

phase as well as in conductive state with highly spin-polarized current which together can be

integrated for potential applications in spintronics. In this brief report, we demonstrate, using

density-functional-based calculations, how various cation distributions and magnetic orders can lead

to a quadruple enhanced magnetization in NFO and the possible tuning of their electronic properties.

The ground-state phase was identified as a structure having a tetragonal symmetry space group of

P4322 which is consistent with the most recent experimental conclusion. The energetically most likely

phase exhibiting enhanced magnetization is an insulating inverse spinel phase while the experimen-

tally observed conductive phase likely originates from a phase with cation inversion.

& 2012 Elsevier B.V. All rights reserved.

Bulk nickel ferrite, NiFe2O4 (NFO), is a semiconductor with aroom-temperature resistivity of 1 kO cm and shows soft ferrimag-netic order below 850 K with a relatively low magnetization of2 mB per formula unit ð2 mB=fuÞ, i.e. about 300 emu cm�3 [1]. It isbelieved to have a completely inverse spinel structure in its bulkform. Recent advances on NFO nanometer films observedenhanced magnetic moments and succeeded in possible tuningof their electronic properties from insulating to conductive statepossessing highly spin-polarized current [2–6]. These magnetiza-tion enhanced materials can hence be integrated for spintronicsdevices [6]. The enhanced magnetization and conductive propertyare commonly attributed to cation inversion in the experimentaldiscussions [2,4,6]. The enhanced magnetization was observedexperimentally to depend on the growth temperature, sizes,substrates, etc. [2,4,6]. The interface/surface states might contri-bute directly to the effect too. However, a double or quadrupleenhancement of the magnetization in a 12-nm film which consistsof 110 atomic layers (along the growth direction (001)) is beyondthe effect of interface/surface as the enhanced magnetization ofthe film as a whole requires an even further enhancement in theinterface/surface layers, considering the middle of the film retain-ing the bulk property. That is why the cation inversion is usuallyconjectured in the experimental papers and cation inversion isknown to occur in spinel ferrite thin films [7,8] as well as innanoparticles [9–11]. The present paper, by performing density-functional-based calculations, studies the possible origins of theseinteresting experimental observations from the bulk considera-tion. We demonstrate, through exploring various magnetic ordersand cation distributions in this material, that the energetically

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most probable phase exhibiting enhanced magnetization is aninsulating inverse spinel phase while the metallic property onlyexists in the normal spinel phases, i.e. due to the cation inversion.

The structure of spinel ferrites (AB2O4) is constructed by fillingone-eighth of the tetrahedral sites and half of the octahedral sites(denoted as A and B site, respectively, hereafter) in the fccsublattice of oxygen. In the inverse spinel structure of the bulkNFO, the Ni cations occupy the B site while the Fe cationsdistribute equally between the A and B sites. A normal spinel,which is considered as a structure with cation inversion in NFO,corresponds to the structure with Ni and Fe cations occupying Aand B site respectively. In addition to the distinction between theinverse and normal spinel structures, there are several possibledistributions for cations at B sites (divided into two groups anddenoted as the B1 and B2 sites) as well as different magneticorders for the cations at A, B1 and B2 sites [12]. The B-site cationdistribution presented in this report corresponds to the SC3 inRef. [12] as its energy is always found being the lowest among thefour distributions (SC1-SC4) having the same magnetic orderbetween the A-site, B1-site and B2-site cations. Table 1 lists allthe phases considered in this study.

In the present study, the electronic calculations are based onthe spin polarized density functional theory [13–15] implemen-ted in the plane-wave-based Vienna ab initio simulation program(VASP) which was developed at the Institute fur Material Physikof the Universitat Wien [16,17]. The generalized gradient approx-imation (GGA) developed by Perdew et al. [18] is used for theexchange-correlation energy functional. In transition metals, theon-site Coulomb repulsion is included to account for the strongcorrelation of the d-orbital electrons [19,20]. The values of U and J

for Fe, as generally adopted in iron spinel, are taken from theprevious studies as 4.5 eV and 0.89 eV, respectively [19–21]. For

Table 1The notation, with their corresponding cation distributions and magnetic orders,

used for the phases considered in this study. The magnetic orders are represented

by the parallel (þþ or ��) or antiparallel (þ�) magnetic moments between the

cations.

Site Inverse spinel Normal spinel

Ion Ipnn Ipnp Ippn Ippp Ion Npnn Nppn Nppp

A Fe þ þ þ þ Ni þ þ þ

B1 Fe � � þ þ Fe � þ þ

B2 Ni � þ � þ Fe � � þ

Fig. 1. The total energies of the phases in Table 1 relative to the lowest-energy

phase of Ipnn at different U (Ni).

Table 2The band gaps (in unit of eV) of the studied phases at different U cases. HM and M

denote half metal and metal respectively. The notation of � HM indicates a nearly

half metal (details in text). Also listed are the calculated saturation magnetic

moments.

U (Ni) (eV) Ipnn Ipnp Ippn Ippp Npnn Nppn Nppp

2 1.47 1.47 0.92 0.77 �HM 0.66 HM

4 1.76 1.77 1.29 1.08 M 1.46 HM

6 1.92 2.02 1.33 1.17 M 1.86 HM

mB=fu 2 2 8 12 8 2 12

C. Cheng / Journal of Magnetism and Magnetic Materials 325 (2013) 144–146 145

Ni, the values of 2, 4, and 6 eV for U, all with J¼1.0 eV, areincluded in order to explore the U effect of Ni in this materialwhich is not well established yet [22]. The interaction betweenions and valence electrons is described by the projector augmen-ted wave (PAW) method [23] which was implemented by Kresseand Joubert [24]. The valence electrons included are 10, 8, and6 for Ni, Fe, and oxygen respectively. Throughout this study, thecubic unit cell consisting of eight formulas is used in order toexamine the chemical and magnetic interactions between cations.The energy cutoff that determines the number of the plane wavesis 500 eV and the k-point sampling according to Monkhorst–Pack[25] is (6 6 6) for the 8-formula cubic cell. Atomic and volumerelaxations are implemented in turn until the atomic forces aresmaller than 0:02 eV=A and the total energy (per 8 formulas) isconverged to 10�4 eV while keeping the cubic unit cell. The higherenergy cutoffs (600 eV) and denser k-point sets (8 8 8) wouldchange the total energy differences between different phases byno more than 1 meV/fu [12].

The calculated relative energies of all the studied phases inTable 1 are plotted in Fig. 1 and the magnetic moments, which donot depend on the U (Ni) values, are listed in Table 2. For all theon-site Coulomb interactions considered in the present study, themost stable phase is always the Ipnn phase and its magnetization,i.e. 2 mB=fu, is consistent with the experimental value for the bulkNFO [1]. In this phase, the antiparallel moments of the Fe ions at Aand B sites are cancelled out with each other and the net momentof the phase comes from the moment of the Ni ions at B site. Thetheoretical lattice constant is 8.40 A, with less than 1% differencebetween results of all the considered U (Ni) cases, which com-pares closely to the experimental lattice constant of 8.34 A [1].The space group of this phase, taking into account of both the

cation distribution and magnetic order, is P4322 of the tetragonalspace group. Note that the previously examined structure [26–30]is the SC1 of Ref. [12] which corresponds to the Imma in theorthorhombic space group. A recent experimental paper hasreported evidence for a short-range B-site order in NiFe2O4 withpossible tetragonal P4122/P4322 symmetry, though the phasewith Imma space group was not ruled out [31]. Our calculationsalways lead to an energetic preference of P4322 over Imma,though by various amounts in different U cases, all within therange between 10 and 20 meV/fu. The different physical proper-ties between these two phases also show up in the electronicstructure. For example, in the case without including U (Ni) and U

(Fe), the SC1 phase (Imma symmetry) is a conductor while theSC3 phase (P4322 symmetry) has a band gap of 0.20 eV.

Of the four inverse spinel phases studied here which have thesame cation distribution but different magnetic orders, twophases have magnetizations much more enhanced than the low-est-energy Ipnn phase, i.e. Ippn and Ippp. The Ippn phase has amagnetization which is four times that of the Ipnn. As both theparallel moment of the A-site and B-site Fe contribute 5 B/Fe,together with the antiparallel moment of Ni ð2 mB=NiÞ they lead toa total of 8 mB=fu. The Ippn phase is the energetically most likelyphase in the bulk form which might contribute to the muchenhanced magnetization observed in the thin film or nanoparti-cles of NFO. This enhanced magnetization is achieved by havingdifferent magnetic orders from the lowest-energy Ipnn phase andaccordingly involves no cation inversion, contrary to the popularproposal previously [2–6]. Its origin lies mainly on the muchsmaller magnetic moment of Ni cations ð2 mBÞ than that of Fecations ð5 mBÞ. Whenever the two Fe ions (per formula) haveparallel moments, the system would results in a much enhancedmagnetization. Similarly, of the three magnetic orders in thenormal spinel structure, both the Npnn and Nppp phases exhibitenhanced magnetizations. However, the energies of Npnn andNppp are larger than Ippn (and Ippp too) and display a muchstronger U (Ni) dependence than the Nppn and the inverse spinelphases. These results were found to come in parallel with themetallic property of the Nppn and Nppp phases.

The calculated electronic properties are summarized inTable 2. All the inverse spinel phases are insulators. As the bulkNFO has a room-temperature resistivity of 1 kO cm, the band gapis expected to be close to that of the bulk Si (1.22 eV at 0 K). Thiscorresponds most closely to the ground state phase Ipnn at U

(Ni)¼2 eV case. The case with U (Ni)¼2 eV is therefore expectedto be the most likely physical picture for NFO. The two normalphases with much enhanced magnetization, i.e. Npnn and Nppp,are either half metals or metals. The Nppp phase is always found ahalf metal, irrespective of U (Ni) values. For the Npnn phase in thecases of U (Ni)¼2 eV, the density of states (DOS) is close to a halfmetal except for a short tail ð � 0:2 eVÞ of low DOS in theminority-spin component extending below Fermi level (Fig. 2).The Npnn phase is therefore expected to be conductive withhighly spin-polarized current. Including both the results in

Fig. 2. The electronic density of state (DOS) and the cation projected DOS of the

Npnn phase at U (Ni)¼2 eV case in the energy range around the fermi energy. The

positive and negative components correspond to the majority and minority spin

components of the electrons respectively.

Table 3The exchange interactions (in unit of meV) for the inverse and normal spinel NFO

at different U (Ni). The negative sign represents an antiferromagnetic interaction.

U (Ni) (eV) Inverse spinel (meV) Normal spinel (meV)

JAB1 JAB2 JB1B2 JAB JBB

2 �38.3 �23.6 �3.8 �12.7 �46.0

4 �38.9 �19.4 �2.9 �9.8 �95.7

6 �39.3 �15.5 �2.4 �7.3 �158.9

C. Cheng / Journal of Magnetism and Magnetic Materials 325 (2013) 144–146146

energetics and magnetization, the energetically most likely insu-lating and conductive phase with much enhanced magnetizationare the Ippn and Npnn phase respectively while the Npnn is anearly half metal (Table 3).

Using the Heisenberg model to describe the magnetic interac-tions between cations, we can obtain the three nearest-neighborinteractions for the inverse spinel phases, i.e. JAB1, JAB2, and JB1B2,from the calculated energies of the four inverse phases in Table I.Note that the cation distributions for the four inverse phasesconsidered here are identical and their differences are solely fromthe different magnetic orders. The exchange interactions for allthe considered U cases are in similar magnitude. All the threeinteractions are antiferromagnetic. However, the interactionsbetween the B-site cations are one order in magnitude smallerthan those between the A-site and B-site cations. This result is themain reason why the most stable phase Ipnn has the magneticorder of pnn, a configuration sacrifices the weak antiferromag-netic interaction among B-site cations for the strong antiferro-magnetic interaction between A-site and B-site cations. Thestrong A–B interactions are due to the around 1201 A-O-B anglewhose connecting structure provides the strong couplingbetween d orbitals of the A-site and B-site cations through thep orbital of oxygen anions while, on the other hand, the B-Binteractions are connected through the around 901 B-O-B angle.The nearest-neighbor interactions in the normal spinel structuresare also found to be antiferromagnetic. However, the JBB interac-tion is found stronger than the JAB interaction. The unexpectedlarge size of JBB is likely due to the metallic properties of the Npnnand Nppp phases.

In conclusion, we show that the ground-state phase of NFO hasa tetragonal symmetry space group of P4322. The energetics,magnetic and electronic properties of bulk NiFe2O4 with different

cation distributions and magnetic orders are investigated by thedensity-functional-based methods. The energetically most likelyphase exhibiting enhanced magnetization is the Ippn phase whichis insulating and an inverse spinel structure. The experimentallyobserved conducting phase with highly spin-polarized currentlikely originates from the normal Npnn phase which is a nearlyhalf metal.

Acknowledgments

This work was supported by the National Science Council ofTaiwan. Part of the computer resources is provided by the NCHC(National Center of High-performance Computing). We also thankthe support of NCTS (National Center of Theoretical Sciences)through the CMR (Computational Material Research) focus group.

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