Ferromagnetic Semiconductors

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Ferromagnetic Semiconductors

• Gergely Zaránd
• Budapest Univ. Technology

Collaborators Greg Fiete (Santa Barbara)
Boldizsár Jankó (Notre Dame) Pawel Redlinski
(Notre Dame) Jacek Furdyna (Notre Dame) Pascu
Moca Catalin (Nagyvarad/Oradea)
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Outline

• Introduction / Motivation
• (Ga,Mn)As and its simple picture
• (Ga,Mn)As in reality
• band structure SO coupling
• impurity band formation
• frustration effects
• localization effects

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Motivation
Combine semiconductor technology with MAGNETISM
Spintronics
Control magnetism through electricity (e.g.,
write bits through electric current) transfer
information through spin current ? Spin-base
quantum computation ????....
Physics
localization magnetism anomalous Hall
effect strong spin-orbit effects
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Goal produce a semiconductor that can be
integrated with standard technology and is a soft
magnet, but has high TC
Difficulty III-V low solubility of Mn ions

• Low-temperature growth of (Ga,Mn)As
• Ohno, Science 281, 951 (1998)

Solution

• Annealing methods
• Hayashi et al., APL 78, 1691 (2001),

Wang et al., AIP Conf. Proc. 772, 333 (2005)
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III-V Materials
???
Carrier-mediated ferromagnetism
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Examples of applications

• Spin polarized light emitting diode
• R. Fiederling et al., Nature 402, 787 (1999)
• Field effect control of ferromagnetism
• H. Ohno et al., Nature 408, 944 (2000)
• Light induced ferromagnetism
• Koshihara et al., PRL 78, 1019 (2000)

Ruester et al. PRL 91, 216602 (2003)
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(Ga,Mn)As The simplest picture
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Crystal structure Mn ions
Many holes in it !!!

• Mn ions
• MnGa replace Ga ions

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Crystal structure Mn ions
Many holes in it !!!

• Mn ions
• MnGa replace Ga ions

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Good MnGa ions
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Bad MnI ions
One can anneal them away !
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Annealing
One can anneal away !
Potashnik et al. APL 79, 1495 (2001)
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Simplest model
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(Ga,Mn)As The reality
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Complications

• Several p-bands
• complicated band structure
• Large spin-orbit coupling
• magnetic anisotropies, spin relaxation etc.
• Very large disorder
• localization effects, impurity band,
• acceptor states
• Random spin positions
• Large electron-electron interaction

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Band structure and SO coupling
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Electron structure I
SO-coupling
hopping
conduction band
j 3/2
p ( l 1 )
j 1/2
s ( l 0 )
j 1/2
j 3/2
p ( l 1 )
valence band
j 1/2
8 e-
s ( l 0 )
j 1/2
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Electron structure of GaAs SO effects
J.S. Blakemore, J. Appl. Phys. 53, R123 (1982)

• Strong spin-orbit interaction
• Holes have spin j3/2 character
• GaMnAs is degenerate Fermi system

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Kohn-Luttinger Hamiltonian
Holes have J 3/2 spin that couples strongly to
their orbital motion

• Luttinger parameters
• J.M. Luttinger, W. Kohn, PR 97, 869 (1955)

Cubic symmetry determines
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Spherical approximation
Approximate
A. Baldereschi and N.O. Lipari, Phys. Rev. B 8,
2697 (1973)
SU(2) invariant
Eigenstates are chiral
n heavy hole 10 nlight hole
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Dilute limit
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Single Mn ion
Hamiltonian
Spectrum for
Valence holes
Localized hole with spin J3/2
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For
Mn spin and couple to form a spin
triplet
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Polaron hopping picture
Berciu, M., and R. N. Bhatt, PRL. 87, 107203
(2002) G. Fiete, GZ, K. Damle, PRL 91, 097202
(2003) Kaminski, A., and S. Das Sarma, Phys.
Rev. Lett. 88, 2472002 (2002) Durst, A. C., R.
N. Bhatt, and P. A. Wolff, PRB 65, 235205 (2002)
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Study Mn2 ion
Compute low-lying spectrum of 2 Mn ions
Obtain effective Hamiltonian (spherical approx)

P. Redlinski, GZ, B Janko, cond-mat/0505038 G.
Fiete, GZ, K. Damle, PRL 91, 097202 (2003)
Spin-dependent hopping
Local spin-anisotropy for holes
Energy shift
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Computed parameters
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Minimum model (dilute limit)
Hopping F3/2 fermions coupled to local classical
spins

• Spin-hopping direction coupled matrix elements

spin 3/2 rotation matrix
diagonal matrix
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Band structure of a relaxed Mn system
( xactive0.01, f0.1 )
ARPES H. Asklund, et al., PRB 66, 115319
(2002). J. Okabayashi, et al. PR B 64, 125304
(2001) Physica E 10, 192 (2001). STM B.
Grandidier, et al., APL 77, 4001 (2000) T.
Tsuruoka, et al. APL 81, 2800 (2002) OPTICAL
CONDUCTIVITY E. J. Singley, et al PRL, 89,
097203 (2002) Phys. Rev. B 68,
165204 (2003). ELLIPSOMETRY K. S. Burch, et al.
PRB 70, 205208 (2004).
Impurity band in small concentration limit
( xactive lt 0.01 )
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Non-collinear magnetic states
( xactive0.01, f0.3 )
Distribution of angles
G. Fiete, G.Z., and K. Damle, 2003, PRL 91,
097202 (2003)
Experiments small fields induce substantial
increase of magnetization in small concentration
unannealed samples
see, e.g. B. Grandidier, et al. APL 77, 4001
(2000).
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Metallic limit
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RKKY interaction non-collinear states ?
Neglect disorder, and compute effective spin-spin
interaction
GZ, and B. Janko, PRL 89, 047201 (2002)
Non-collinear States ?
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RKKY interaction
Almost collinear states for x gt 0.03
Brey, L., and G. Gomez-Santos, PRB 68, 115206
(2003) G. Fiete, GZ, B. Janko, et al., PR B 71,
115202 (2005) Timm, C., and A. H. MacDonald, PRB
71, 155206 (2005)
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Ab initio calculations
Bergqvist, et al. PRL 93, 137202 (2004)
Hilbert, S., and W. Nolting, PR B 71, 113204
(2005) Xu, J. L., M. van Schilfgaarde, and G. D.
Samolyuk, PRL 94, 097201 (2005) G. Bouzerar,
G., T. Ziman, and J. Kudrnovsky, Europhys. Lett.
69, 812 (2005)
G. Bouzerar, G., T. Ziman, and J. Kudrnovsky,
Europhys. Lett. 69, 812 (2005)
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Transport properties
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Resistivity anomalies in
GaMnAs data from P. Schiffers group
Sea also Potashnik et al., APL 79, 1495
(2001) Matsukura et al., PRB 57, R2037
(1998) Edmonds et al, APL 81, 4991 (2002)
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Possible explanations for the peak?
Spin disorder scattering
Diverges at TC
Only a kink at TC Fischer-Langer
Critical fluctuations ?
Magnetic polarons ? Kasuya, Dietl and Spalek, P.
Littlewood
Maximum way above TC P. Littlewood
Selfconsistent potantials ? Nagaevs theory
Curves cross
None of these works
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Proposal Interplay of magnetization and
localization
Magnetic-ordering decreases effective disorder
Resistance changes at microscopic scale
Interplay with localization produces peak at

GZ, P. Moca, and B. Janko, PRL 94, 247202
(2005).

• Similar ideas emerged for Manganites Viret et
  al. PRB 55, 8067 (1997)
• There Jahn-Teller effect provides localization
• Some conceptual difficulties

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Influence of spin on disorder possible mechanisms

• Spin splitting of bands

Lopez-Sancho and Brey, PRB 68, 113201 (2003)
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Finite conductivity
Insulating Phase
Motts variable range formula
Metallic Phase
We need to know
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Single parameter scaling theory of localization
(T0)
Typical dimensionless conductance of slab L
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Spin distribution changes disorder !
Insulator
Metal
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Beta function, Phase diagram
To compute we need to solve a
differential equation
beta function extracted from model calculations
GZ, P. Moca, and B. Janko, PRL 94, 247202
(2005).
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Experimentally observed anomalies, localized fits
Some fine-tuning is needed to fit the metallic
data through variable range hopping
GaMnAs data from P. Schiffers group
GZ, P. Moca, and B. Janko, PRL 94, 247202
(2005).
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Fitting through metallic expression
GZ, P. Moca, and B. Janko, PRL 94, 247202
(2005), and unpublished
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More fits
Best fit !
Experiments on (Ga,Mn)As metal rings find similar
behavior ! K. Wagner, et al. PRL 97, 056803
(2006)
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Conclusions
REVIEWS
General review, GaMnAs Jungwirth et al.
cond-mat/0603380 Carrier-mediated mechanism in
GaMnAs Dietl, T., 2003, condmat/0306479. First
principles calculations Sanvito, S., G. Theurich,
and N. A. Hill, Journal of Superconductivity 15,
85 (2002) Sato, K., and H. Katayama-Yoshida,
Semicond. Sci. Technol. 17, 367 (2002) II-VI
materials Furdyna, J. K., and J. Kossut, Diluted
Magnetic Semiconductors, volume 25 of
Semiconductor and Semimetals (Academic Press, New
York, 1988). Spintronics Zutic, J. Fabian, and S.
Das Sarma, Rev. Mod. Phys. 76, 323 (2004).
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Transfer matrix / scaling analysis of Lyapunov
exponents
slabs
Single parameter scaling
Lyapunov exponent
Microscopic length scale
Universal function
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Single parameter scaling theory of localization II
Consider a slab of size and
conductance
increases as we increase
decreases as we increase
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Test these ideas for a toy model
Disordered Kondo lattice
Take
classical spins
Spins at mean field level
Transfer Matrix Analysis
(MacKinnon and Kramers, PRL, 1981)
Similar analysis in the context of manganites
Li et al., PRB 56, 4541 (1997)
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Beta function, Phase diagram