Physics of Carrier Induced Ferromagnetism

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Physics of Carrier Induced Ferromagnetism
in Diluted Magnetic Semiconductors
Tomas Jungwirth Juergen Koenig Byounghak Lee Qian
Niu John Schliemann Eric Yang UT
Austin Supported by DARPA Bill Atkinson
Southern Illinois University Ramin Abolfath
University of Oklahoma Hsiu-Hau Lin Tsing Hua
University Tomas Dietl Polish Academy of
Sciences
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Models of Carrier Induced Ferromagnetism
in Diluted Magnetic Semiconductors

• First Principles LSDA

Ab Initio LDSA ? (Self-Interaction) Computational
Limitations
Too hot!

• Impurity Band Models

Dilute Limit OK Predictive power? Itinerant Limit
Too cold!

• k.p ? Local Moment

Just right!
Fudges Atomic Scale Physics
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Fedorich et al. cond-mat/0106227 ?
k.p ? Local Moment - Degrees of Freedom
One S5/2 spin for each Mn J 3/2 (and
J1/2) valence band holes
Successful for (II,Mn)V semiconductors
Kossut Phys. Stat. Solidi 78 p.537 (1976)
Reviews Dietl Handbook of Semiconductors, 17
(1994)
Furdyna J. App. Phys. 64, R29 (1988)
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k.p ? Local Moment - Hamiltonian
ESSENTIALS

• Luttinger Band Hamiltonian
• Exchange Coupling
• External Fields
• Coulomb interactions been holes and Mn ions
• Coulomb interactions among holes
• Interactions with (antisite?) defects
• Chemical shift
• Near-neighbor antiferromagnetic interactions

EXTRAS
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Two Approximations
Virtual Crystal Approximation
Bastard, J. de Physique, 39 p. 87 (1978) Gaj,
Phys. Stat. Solidi 89 p.655 (1978)
Mean Field Approximation
? Field felt by band electrons

• Field felt by local moments
• ?Dietl, Ohno et al., MacDonald et al.

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Apparent Successes of VCA Mean-Field Theory
Dietl, Ohno, Matsukura et al. PRB 55 Science 297
PRB 63 MacDonald, Lee, Abolfath, et al. PRB 59
PRB 61 PRB 63 Fernandez, Sham et al.
Dietl, Ohno et al. ?

• Critical Temperature
• Magnetization
• Magnetic Anisotropy Scale
• Strain/Magnetic Anisotropy Correlation
• Optical Properties MCD
• Anomalous Hall Effect
• Spin Stiffness
• 2D Ferromagnetism

Abolfath et al. PRB 2000
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Anomalous Hall Effect K-space Berry Phase
? Anomalous Velocity
? Berry Curvature
Jungwirth, Niu, and AHM, unpublished
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Magnetic Excitations and Curie Temperature

• Spin waves VCA
• Koenig PRL 2000

Schliemann et. al, APL 78, 1550 (2001)
PRB (to appear) Monte Carlo for Parabolic
Band Model
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Regimes of Ferromagnetism
Schliemann, et. al, APL 78, 1550 (2001)
Parabolic Band Model
Tc? Ef (n/N)1/3
Tc? ?2/ Ef n/N Range ??F gtgt N-1/3
Tc? ?2/ Ef (n/N)1/3 Range ??F N-1/3 A ?2F
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Realistic Collective Excitations
Single Parabolic Band Model
Realistic Valence Bands
p 0.35 nm-3
Comparison vs. Density
König et al., cond-mat/0103116
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Spin Excitations Discrete Mn

• Schliemann and AHM, unpublished
• Non-collinear Ferromagnetism
• and Glassy Physics

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(III,Mn)V Ferromagnetism

• VCA Mean-Field Theory OK
• Carrier-mediated Ferromagnetism ? RKKY
• Strategy of increasing DOS to increase Curie
• temperature has limits
• Glassy Ferromagnets