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Workshop de Nanomagnetismo – 24 e 25/6/2004 Rede Virtual de Nanoci ência e Nanotecnologia do Estado do Rio de Janeiro/FAPERJ. Parametrization of Mn-Mn interactions in Ga 1-x Mn x As semiconductors. Antônio J. Roque da Silva (IFUSP), Adalberto Fazzio (IFUSP), - PowerPoint PPT Presentation
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Antônio J. Roque da Silva (IFUSP), Adalberto Fazzio (IFUSP), Raimundo R. dos Santos (UFRJ), and Luiz Eduardo Oliveira
(UNICAMP)
Parametrization of Mn-Mn interactions in
Ga1-xMnxAs semiconductors
Workshop de Nanomagnetismo – 24 e 25/6/2004
Rede Virtual de Nanociência e Nanotecnologia do Estado do Rio de Janeiro/FAPERJ
Financiamento: •CNPq •FAPERJ•FAPESP •Inst Milênio de Nanociências, •Rede Nacional de Materiais Nanoestruturados
Motivation
Combination of semiconductor technology with magnetism should give rise to new devices: Spin-polarized electronic transport
long spin-coherence times (~ 100 ns) have been observed in semiconductors
manipulation of quantum states at a nanoscopic level
Magnetic semiconductors
• Early 60’s: EuO and CdCr2S4 very hard to grow
• Mid-80’s: Diluted Magnetic Semiconductors II-VI (e.g., CdTe and ZnS) II Mn difficult to dope direct Mn-Mn AFM exchange interaction
PM, AFM, or SG (spin glass) behavior
• 90’s: Low T MBE (In,Mn)AsUniform (Ga,Mn)As films on GaAs substrates: FM; heterostructures- Possibility of useful devices
Ga: [Ar] 3d10 4s2 4p1
Mn: [Ar] 3d5 4s2
Mn atoms: provide both magnetic moments and holes hole-mediated ferromagnetism
Ga
As
Ga1-xMnxAs
Resistance measurements on samples with different Mn concentrations:
Metal R as T Insulator R as T
Reentrant MIT
[Ohno, JMMM 200, 110(1999)]
Ga1-xMnxAs
0.00 0.02 0.04 0.06 0.08 0.1020
40
60
80
100
120
circles: Matsukura et al, PRB57, R2037 (1998) squares: Edmonds et al, APL 81, 3010 (2002)up triangles: Seong et al, PRB 66, 033202 (2002) and Potashnik et al, APL 79, 1495 (2001)diamonds: van Esch et al, PRB 56, 13103 (1997)down triangles: Asklund et al, PRB 66, 115319 (2002)
open star = Yu et al, PRB 65, 201303 (2002); APL81, 844 (2002)full star = Moriya-Munekata, JAP 93, 4603 (2003)full squares = Potashnik et al, PRB66, 012408 (2002)
Tc(
K)
Mn composition (x)
Reproducibility?
0.00 0.02 0.04 0.06 0.08 0.100
2
4
6
8
open star = Yu et al, PRB 65, 201303 (2002); APL81, 844 (2002)full star = Moriya-Munekata, JAP 93, 4603 (2003)
circle: Ohno et al, JMMM 200, 110 (1999)squares: Edmonds et al, APL 81, 3010 (2002)up triangles: Seong et al, PRB 66, 033202 (2002) Potashnik et al, APL 79, 1495 (2001)
ho
le c
on
cen
trat
ion
(10
20 c
m-3)
Mn composition x
Hole concentration vs Mn concentration
1 hole/Mn atom
A simple mean field treatment† yields
1h/MnNotice maximum of p(x) within the M phase correlate with MIT
Early predictions
[Matsukura et al., PRB 57, R2037 (1999)]
log!
†[RRdS, LE Oliveira, and J d’Albuquerque e Castro, JPCM (2002)]
First principles calculations should shed light into these issues
Experimental data very sensitive to growth conditions
what are the dominant mechanisms behind the origin of ferromagnetism in DMS?
• how delocalized are the holes (are effective mass theories meaningful)?
• what is the effective Mn-Mn interaction? RKKY?
• what is the role of disorder?
Method
Ab initio total energy calculations – DFT -VASP
Ultra-soft pseudopotential
Supercell calculations – 128/250 atoms (fcc)• Spin polarized• GGA (Perdew, Burke, Ernzerhof) for exchge-correl’n• Plane waves basis set – (cutoff of 230eV, k = L)
• Final forces smaller than 0.02 eV/Å
MnAs
Ga
Single Mn atom
20.3 Å
Isosurfaces for the net local magnetization MnGa )()()( rrrm
Ground state: quite localized hole interacting antiferromagnetically with S=5/2 of Mn(d 5 )
Green=0.004e/A3
Blue= -0.004e/A3
We now consider two Mn atoms per unit cell
Assume all possible non-equivalent positions
For a given relative position, we consider FM and AFM relative Mn orientations, and work out the energy difference
Fit this energy difference to a Heisenberg interaction:
21MnMn SS JH
thus estimates for J (r1– r2)
Ferromagnetic
Mn Mn
As As
Mn-Mn 1st NN
Antiferromagnetic
Ferromagnetic
Mn MnMn Mn
As AsAs As
Mn-Mn 1st NN
Antiferromagnetic
Ferromagnetic
Mn MnMn Mn
As AsAs As
As
As
Mn
Mn
Mn-Mn 1st NN
Mn-Mn 2nd NN
Antiferromagnetic
Ferromagnetic
Mn MnMn Mn
Mn
Mn
As AsAs As
As
As
Mn
MnAs
As
Mn-Mn 1st NN
Mn-Mn 2nd NN
Antiferromagnetic
Again, note quite localized character of the holes
12<110>
6<100>
24<211>
12<110>
24<310>
8<111>
The ferro-antiferro total energy differences yield...
12
6
24
12
248
the effective coupling between Mn spins (JMn-
MnSMn·SMn)
Therefore:
• impurity levels are localized
effective-mass picture for holes may be quite inadequate
• Mn-Mn interaction mediated by AFM coupling Mn-hole
• J Mn-Mn always ferromagnetic non-RKKY
• estimates for anisotropy and direction dependences for effective J Mn-Mn
Our current agenda:
1) Effects of disorder?
2) Effects of concentration?
Preliminary results
Strategy (in principle): Randomly place Mn atoms in the Ga sublattice and use a look up table for J’s
Ga
MnJ1
J4
J2
We start with 4 Mn in our 128 atoms supercell:
Roadmap1) Randomly place 4 Mn atoms in the Ga sublattice
2) Calculate, using same ab initio scheme, the total energies for:
a) (Mn1,Mn2,Mn3,Mn4)=(up,up,up,up) – Ferro
b) (Mn1,Mn2,Mn3,Mn4)=(down,up,up,up) – Flip Mn1
c) (Mn1,Mn2,Mn3,Mn4)=(up,down,up,up) – Flip Mn2
d) Etc.
3) Calculate energy differences E(Flip-Mn1)-Ferro, etc.
4) Write up same energy differences using an effective Heisenberg Hamiltonian, and extract effective Jn
5) Compare with previous results with only two Mn
4 Mn in 128 cell: - disorder inside unit cell - images are taken care of (unwanted
order!) - Mn concentration – 0.0625 (6.25 %)
- Different from 1 Mn in 32 atoms unit cell or
2 Mn in 64 atoms unit cellGa
Mn
J1
Ji
4 Mn in 128 atoms unit cell
Ab initio results
Ferro = -553.737 eV
Flip 1 = -553.547 eV
Flip 2 = -553.586 eV
Flip 3 = -553.302 eV
Flip 4 = -553.508 eV
Ferro - lowest energy configuration
1-Ferro = 0.190 eV
2-Ferro = 0.151 eV
3-Ferro = 0.435 eV
4-Ferro = 0.229 eV
4 Mn in 128 atoms unit cellHeisenberg Hamiltonian results
Ferro =
Flip 1 = Flip 2 =
Flip 3 =
Flip 4 =
1-Ferro =
2-Ferro =
3-Ferro =
4-Ferro =
For the particular realization, the Hamiltonian is
434232
413121
134
315
2
2
MnMnMnMnMnMn
MnMnMnMnMnMn
SSJSSJSSJ
SSJSSJSSJH
4
25
ji MnMn SS
5431 22224
25JJJJ
54 224
25JJ
5431 22224
25JJJJ
5431 22224
25JJJJ
543 2224
25JJJ
531 4224
25JJJ
543 4424
25JJJ
41 444
25JJ
31 424
25JJ
2 Mn in 128 atoms unit cellClassical x Quantum Heisenberg Hamiltonian results
4
25
ji MnMn SS
ji SSJH ˆˆ
Classical Quantum
J1 -23.2 -19.3
J2 -10.4 -8.7
J3 -13.6 -11.3
J4 -5.6 -4.7
J5 -2.6 -2.2
J6 -4.4 -3.7
ji SSJH
J (meV)
Same trend,
Classical or
Quantum
2 Mn x 4 Mn in 128 atoms unit cellClassical Heisenberg Hamiltonian
4
25
ji MnMn SS
2Mn 4Mn
J1 -23.2 -12.6
J2 -10.4 -
J3 -13.6 -2.8
J4 -5.6 -4.8
J5 -2.6 0.1
J6 -4.4 -
ji SSJH
J (meV)
2 Mn x 4 Mn in 128 atoms unit cellClassical Heisenberg Hamiltonian
4
25
ji MnMn SS
2Mn (4Mn)1 (4Mn)2
J1 -23.2 -12.6 -13.0
J2 -10.4 - -4.7
J3 -13.6 -2.8 -6.0
J4 -5.6 -4.8 -
J5 -2.6 0.1 -1.3
J6 -4.4 - -
ji SSJH
J (meV)
2 Mn x 3Mn x 4 Mn in 128 atoms unit cellClassical Heisenberg Hamiltonian
4
25
ji MnMn SS
2Mn 3Mn (4Mn)1 (4Mn)2
J1 -23.2 -19.2 -12.6 -13.0
J2 -10.4 - - -4.7
J3 -13.6 -8.4 -2.8 -6.0
J4 -5.6 - -4.8 -
J5 -2.6 -1.0 0.1 -1.3
J6 -4.4 - - -
ji SSJH
J (meV)
2Mn: x = 0.03125
3Mn: x = 0.046875
4Mn: x = 0.0625
2 Mn x 3Mn x 4 Mn in 128 atoms unit cell
Large reduction in the values of some of the J’s
– Possible reasons:
-Effective Heisenberg Hamiltonian may not be appropriate to describe “magnetic” excitations
-Effective Hamiltonian ok to describe low-energy magnetic excitations, but our spin flip excitations may have too high an energy (non-collinear spin ab initio calculations?)
-Disorder and/or concentration may have an important effect in the effective J couplings
Next steps (1):• Perform more calculations with random structures – obtain a distribution for effective J’s
• Perform similar calculations for different Mn concentrations
• Non-collinear spin calculations
•If we conclude that we have a physically correct description through effective J’s + classical Heisenberg Hamiltonian, perform calculations for T > 0 (Monte Carlo)Next steps (2):
• Study (ab initio) how defects (e.g., interstitial Mn) change this picture by placing them in the, for example, 4 Mn in 128 atoms supercell – local disorder + defects
Conclusions:
• Effective mass descriptions (and improvements thereof) not reliable
• Effective Mn-Mn interactions not RKKY
• Disorder strongly influences effective Mn-Mn interactions; simple model?
• Heterostructures: -doping, Be co-doping
Mn-hole exchange coupling
Jhd = 0.083 eV; 250 atoms, x = 0.008
Jhd = 0.11 eV; 128 atoms, x = 0.0156
• We have performed total energy calculations based on the density-functional theory (DFT) within the generalized-gradient approximation (GCA) for the exchange-correlation potential.
• The electron-ion interactions are described using ultra-soft pseudopotentials and plane wave expansion up to 200 eV as implemented in the VASP code.
• We used a 128-atom and 250-atom fcc supercell and the L-point for the Brillouin sampling. The positions of all atoms in the supercell were relaxed until all the force components were smaller than 0.05 eV/Å.
)()( rr
Isosurfaces for the difference between
calculated for the MnGa ground state and the GaAs host
m(r) = (r)-(r)
m(r) = +0.5 e-/Å3
Sub-Si n=p
n.5p.oo5
As
As
As
As Ga
a1
t2
As
As
As
As
a1
t2
As
As
As
As Mn
a1
t2
t2
e
•F. Matsukura, H. Ohno, A. Shen, and Y. Sugawara, Phys. Rev. B 57, R2037 (1998)
MBE at low growth T (200 - 300 OC) on GaAs (001) substrates
x = 0.015 – 0.071
200 nm thick Ga1-xMnxAs samples
•A. van Esch et al, PRB 56, 13103 (1997)
Ga1-xMnx As layers grown on GaAs (100) substrates
GaAs grown by MBE at low temperatures (200 – 300 OC)
samples of 3 m thick with Mn concentrations up to 9%
•K. W. Edmonds et al, APL 81, 3010 (2002)
metallic behavior for 0.015 x 0.08
Ga1-xMnxAs layers grown on semi-insulating GaAs (001) substrates by low-temperature (180 – 300 OC) MBE using As2
samples: 45 nm thick
•S. J. Potashnik et al, APL 79, 1495 (2001)
temperature during growth: 250 OC
Ga1-xMnxAs layers: thicknesses in range 110 – 140 nm
•M. J. Seong et al, PRB 66, 033202 (2002)
samples grown as in Potashnik et al: 250 OC and 120 nm
used a Raman-scattering intensity analysis of the coupled plasmon-LO phonon mode
and the unscreened LO phonon.
•H. Asklund et al, PRB 66, 115319 (2002)
angle-resolved photoemission; 1% - 6%
growth temperature of LT-GaAs and GaMnAs was typically 220 0C
Mn concentrations accurate within 0.5 %
NOTE THAT
•T. Hayashi et al, APL 78, 1691 (2001)
“a 10 oC difference in the substrate temperature during growth can lead to a
considerable difference in the transport properties as well as in magnetism even
though there is no difference in the growth mode as observed by electron diffraction
2 Mn atoms as nearest-neighbors (Ga sub-lattice)
Antiferromagnetic couplingm(r) = +0.004 e-/Å3
m(r) = -0.004 e-/Å3
• VERY DILUTED DOPING LIMIT: Mn FORMS ACCEPTOR LEVEL 110 meV ABOVE VALENCE BAND
• ANGLE-RESOLVED PHOTOEMISSION SPECTROSCOPY OBSERVES IMPURITY BAND NEAR EF.
• INFRARED MEASUREMENTS OF THE ABSORPTION COEFFICIENT ALSO REVEAL A STRONG RESONANCE NEAR THE ENERGY OF THE Mn ACCEPTOR IN GaAs.
• E. J. Singley, R. Kawakami, D. D. Awschalom, and D. N. Basov, PRL 89, 097203 (02)
conductivity data: estimate the effective mass to be 0.7 mo < m* < 15 mo for the x = 0.052 sample, and larger at all other dopings, which suggest that the carriers do not simply reside in the unaltered GaAs valence band
favor a picture of the electronic structure involving
impurity states at EF rather than of holes doped into
an unaltered GaAs valence band
work obtained by using “complete” Kohn-Luttinger
formalism (magnetic anisotropy, strain, etc):
• M. Abolfath, T. Jungwirth, J. Brum, and A. H. MacDonald, PRB 63, 054418 (2001).
• T. Dietl, H. Ohno, and F. Matsukura, PRB 63, 195205 (2001).
Isosurfaces for the net local magnetization: two MnGa defects
In (a) and (b) the two Mn are nearest neighbors with their S=5/2 spins alligned parallel and antiparallel, respectively
Mn Mn
As As
Mn-Mn 1st nn
Mn Mn
As As
)()()( rrrm
Green=0.004e/A
Blue= -0.004e/A