Presentation by Boldizsár Nagy at the 4th Cuenca Collquium, 1 October 2009.
Ferromagnetic Semiconductors Gergely Zaránd Budapest Univ. Technology Collaborators: Greg Fiete...
-
Upload
myrtle-allen -
Category
Documents
-
view
213 -
download
0
Transcript of Ferromagnetic Semiconductors Gergely Zaránd Budapest Univ. Technology Collaborators: Greg Fiete...
![Page 1: Ferromagnetic Semiconductors Gergely Zaránd Budapest Univ. Technology Collaborators: Greg Fiete (Santa Barbara) Boldizsár Jankó (Notre Dame) Pawel Redlinski.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e5e5503460f94b584fd/html5/thumbnails/1.jpg)
Ferromagnetic SemiconductorsFerromagnetic 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)
![Page 2: Ferromagnetic Semiconductors Gergely Zaránd Budapest Univ. Technology Collaborators: Greg Fiete (Santa Barbara) Boldizsár Jankó (Notre Dame) Pawel Redlinski.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e5e5503460f94b584fd/html5/thumbnails/2.jpg)
• Introduction / Motivation
• (Ga,Mn)As and its simple picture
• (Ga,Mn)As in realityband structure + SO couplingimpurity band formationfrustration effectslocalization effects
OutlineOutline
![Page 3: Ferromagnetic Semiconductors Gergely Zaránd Budapest Univ. Technology Collaborators: Greg Fiete (Santa Barbara) Boldizsár Jankó (Notre Dame) Pawel Redlinski.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e5e5503460f94b584fd/html5/thumbnails/3.jpg)
Motivation:Motivation:
Combine semiconductor technology with MAGNETISM
Control magnetism through electricity(e.g., write bits through electric current)
transfer information through spin current ? Spin-base quantum computation ????....
Physics:
“Spintronics”:
localization + magnetism… anomalous Hall effect…
strong spin-orbit effects…
![Page 4: Ferromagnetic Semiconductors Gergely Zaránd Budapest Univ. Technology Collaborators: Greg Fiete (Santa Barbara) Boldizsár Jankó (Notre Dame) Pawel Redlinski.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e5e5503460f94b584fd/html5/thumbnails/4.jpg)
Difficulty: III-V: low solubility of Mn ions …
Solution:
•Annealing methods[Hayashi et al., APL 78, 1691 (2001),
…]
Wang et al., AIP Conf. Proc. 772, 333 (2005)
• Low-temperature growth of (Ga,Mn)As [Ohno, Science 281, 951 (1998)]
Goal: produce a semiconductor that can be integrated with standard technology and is a soft magnet, but has high TC
![Page 5: Ferromagnetic Semiconductors Gergely Zaránd Budapest Univ. Technology Collaborators: Greg Fiete (Santa Barbara) Boldizsár Jankó (Notre Dame) Pawel Redlinski.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e5e5503460f94b584fd/html5/thumbnails/5.jpg)
III-V MaterialsIII-V Materials
AsMnIn
SbMnGa
SbMnIn
xx
xx
xx
1
1
1
Ga1 xMnx AsNMnIII ),(
PMnIII ),(Carrier-mediated ferromagnetism
???
![Page 6: Ferromagnetic Semiconductors Gergely Zaránd Budapest Univ. Technology Collaborators: Greg Fiete (Santa Barbara) Boldizsár Jankó (Notre Dame) Pawel Redlinski.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e5e5503460f94b584fd/html5/thumbnails/6.jpg)
Examples of applicationsExamples of applications
[Ruester et al. PRL 91, 216602 (2003)]
• 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)]
![Page 7: Ferromagnetic Semiconductors Gergely Zaránd Budapest Univ. Technology Collaborators: Greg Fiete (Santa Barbara) Boldizsár Jankó (Notre Dame) Pawel Redlinski.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e5e5503460f94b584fd/html5/thumbnails/7.jpg)
(Ga,Mn)As: The simplest picture (Ga,Mn)As: The simplest picture
![Page 8: Ferromagnetic Semiconductors Gergely Zaránd Budapest Univ. Technology Collaborators: Greg Fiete (Santa Barbara) Boldizsár Jankó (Notre Dame) Pawel Redlinski.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e5e5503460f94b584fd/html5/thumbnails/8.jpg)
Mn ions • MnGa replace Ga ions
Crystal structure + Mn ionsCrystal structure + Mn ions
Ga
As
Many holes in it … !!!
![Page 9: Ferromagnetic Semiconductors Gergely Zaránd Budapest Univ. Technology Collaborators: Greg Fiete (Santa Barbara) Boldizsár Jankó (Notre Dame) Pawel Redlinski.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e5e5503460f94b584fd/html5/thumbnails/9.jpg)
Mn ions • MnGa replace Ga ions
Crystal structure + Mn ionsCrystal structure + Mn ions
Ga
As
Many holes in it … !!!
Mn ions • MnGa replace Ga ions • MnI sit in holes…
![Page 10: Ferromagnetic Semiconductors Gergely Zaránd Budapest Univ. Technology Collaborators: Greg Fiete (Santa Barbara) Boldizsár Jankó (Notre Dame) Pawel Redlinski.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e5e5503460f94b584fd/html5/thumbnails/10.jpg)
Good MnGa ionsGood MnGa ions
MnGa ions:
12 44: psGa
25 43: sdMn heMn 32
eGa 33
• gives SPIN: S = 5/2, g=2 d 5 configuration• dopes hole
• negatively charged (strong scatterer!!!)• couples antiferromagnetically to holes
Sea of happyholes
![Page 11: Ferromagnetic Semiconductors Gergely Zaránd Budapest Univ. Technology Collaborators: Greg Fiete (Santa Barbara) Boldizsár Jankó (Notre Dame) Pawel Redlinski.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e5e5503460f94b584fd/html5/thumbnails/11.jpg)
Bad MnI ionsBad MnI ions
• Kill MnGa spins !• take away 2 holes !• expands lattice
• positively charged Bind to MnGa ions !
[Jungwirth et al. PRB 72, 165204 (2005)]
Sea of (partially)
happy holes
One can anneal them away !
![Page 12: Ferromagnetic Semiconductors Gergely Zaránd Budapest Univ. Technology Collaborators: Greg Fiete (Santa Barbara) Boldizsár Jankó (Notre Dame) Pawel Redlinski.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e5e5503460f94b584fd/html5/thumbnails/12.jpg)
One can anneal away !
AnnealingAnnealing
[Potashnik et al. APL 79, 1495 (2001)]
![Page 13: Ferromagnetic Semiconductors Gergely Zaránd Budapest Univ. Technology Collaborators: Greg Fiete (Santa Barbara) Boldizsár Jankó (Notre Dame) Pawel Redlinski.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e5e5503460f94b584fd/html5/thumbnails/13.jpg)
Simplest modelSimplest model
Mn
MnR
RMnpd SRr
J
mp
H )(22 *
23nmmeV54pdJ
Scaling not satisfied experimentally(exchange corrections,
spin fluctuations, disorder …)
Mean field theory (neglecting disorder):
0S
SJNh pdMneff
holesMnpdspin SNJH
2
SNJT
SSS holesMnpd
2
3)1( 3/1~~ pxNT holesMn
MFC
[Dietl et al. Science 287, 1019 (2000); Konig et al. PRL 84, 5628 (2000)]
![Page 14: Ferromagnetic Semiconductors Gergely Zaránd Budapest Univ. Technology Collaborators: Greg Fiete (Santa Barbara) Boldizsár Jankó (Notre Dame) Pawel Redlinski.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e5e5503460f94b584fd/html5/thumbnails/14.jpg)
(Ga,Mn)As: The reality (Ga,Mn)As: The reality
![Page 15: Ferromagnetic Semiconductors Gergely Zaránd Budapest Univ. Technology Collaborators: Greg Fiete (Santa Barbara) Boldizsár Jankó (Notre Dame) Pawel Redlinski.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e5e5503460f94b584fd/html5/thumbnails/15.jpg)
Complications Complications
• Several p-bandscomplicated band structure
• Large spin-orbit coupling magnetic anisotropies, spin relaxation etc.
• Very large disorderlocalization effects, impurity band, acceptor states
• Random spin positions• Large electron-electron interaction
![Page 16: Ferromagnetic Semiconductors Gergely Zaránd Budapest Univ. Technology Collaborators: Greg Fiete (Santa Barbara) Boldizsár Jankó (Notre Dame) Pawel Redlinski.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e5e5503460f94b584fd/html5/thumbnails/16.jpg)
Band structure and SO couplingBand structure and SO coupling
![Page 17: Ferromagnetic Semiconductors Gergely Zaránd Budapest Univ. Technology Collaborators: Greg Fiete (Santa Barbara) Boldizsár Jankó (Notre Dame) Pawel Redlinski.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e5e5503460f94b584fd/html5/thumbnails/17.jpg)
Electron structure IElectron structure I
123 44 psGaGa 325 44 psAsAs
s ( l = 0 )
p ( l = 1 )
s ( l = 0 )
j = 3/2
hoppingSO-
coupling
p ( l = 1 ) j = 1/2
j = 3/2
j = 1/2
j = 1/2
j = 1/2 valenceband
conductionbandGa
As 8 e-
![Page 18: Ferromagnetic Semiconductors Gergely Zaránd Budapest Univ. Technology Collaborators: Greg Fiete (Santa Barbara) Boldizsár Jankó (Notre Dame) Pawel Redlinski.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e5e5503460f94b584fd/html5/thumbnails/18.jpg)
[J.S. Blakemore, J. Appl. Phys. 53, R123 (1982)]
• Strong spin-orbit interaction• Holes have spin j=3/2 character• GaMnAs is degenerate Fermi system
Electron structure of GaAs: SO effectsElectron structure of GaAs: SO effects
eV42.1gapE
eV34.0SO
![Page 19: Ferromagnetic Semiconductors Gergely Zaránd Budapest Univ. Technology Collaborators: Greg Fiete (Santa Barbara) Boldizsár Jankó (Notre Dame) Pawel Redlinski.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e5e5503460f94b584fd/html5/thumbnails/19.jpg)
Cubic symmetry determines
,3/2abbaab pppp
•
•
• Luttinger parameters
[J.M. Luttinger, W. Kohn, PR 97, 869 (1955)]
,3/)1()(21 jjjjjjJ ababbaab
i
Holes have J = 3/2 spin that couples strongly to their orbital motion:
0H
H0 1
p2
2m
1
m[ 2 Jaa paa
a 3 Jab pab
ab ]
Kohn-Luttinger HamiltonianKohn-Luttinger Hamiltonian
![Page 20: Ferromagnetic Semiconductors Gergely Zaránd Budapest Univ. Technology Collaborators: Greg Fiete (Santa Barbara) Boldizsár Jankó (Notre Dame) Pawel Redlinski.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e5e5503460f94b584fd/html5/thumbnails/20.jpg)
Approximate: .)(2
)4(2210 Hpjp
mH
Eigenstates are chiral:
)5.02
2/3ˆ2
mmmk
pj hh
( ,
)07.02
2/1ˆ2
mmmk
pj ll
( ,
k
n heavy hole ≈ 10 nlight hole
[A. Baldereschi and N.O. Lipari,
Phys. Rev. B 8, 2697 (1973)]SU(2) invariant
Spherical approximationSpherical approximation
![Page 21: Ferromagnetic Semiconductors Gergely Zaránd Budapest Univ. Technology Collaborators: Greg Fiete (Santa Barbara) Boldizsár Jankó (Notre Dame) Pawel Redlinski.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e5e5503460f94b584fd/html5/thumbnails/21.jpg)
Dilute limit Dilute limit
![Page 22: Ferromagnetic Semiconductors Gergely Zaránd Budapest Univ. Technology Collaborators: Greg Fiete (Santa Barbara) Boldizsár Jankó (Notre Dame) Pawel Redlinski.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e5e5503460f94b584fd/html5/thumbnails/22.jpg)
.)(||
)(2
0int V S CC rr
ersJH
Single Mn ionSingle Mn ion
int0 HHH Hamiltonian:
Spectrum for :
meVEb 110 4
00 J
Valenceholes
Localized hole with spin J=3/2
![Page 23: Ferromagnetic Semiconductors Gergely Zaránd Budapest Univ. Technology Collaborators: Greg Fiete (Santa Barbara) Boldizsár Jankó (Notre Dame) Pawel Redlinski.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e5e5503460f94b584fd/html5/thumbnails/23.jpg)
For :00 J
Mn spin and couple to form a spin triplet
S
J
1 SJF
A10~
![Page 24: Ferromagnetic Semiconductors Gergely Zaránd Budapest Univ. Technology Collaborators: Greg Fiete (Santa Barbara) Boldizsár Jankó (Notre Dame) Pawel Redlinski.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e5e5503460f94b584fd/html5/thumbnails/24.jpg)
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)]
![Page 25: Ferromagnetic Semiconductors Gergely Zaránd Budapest Univ. Technology Collaborators: Greg Fiete (Santa Barbara) Boldizsár Jankó (Notre Dame) Pawel Redlinski.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e5e5503460f94b584fd/html5/thumbnails/25.jpg)
Study Mn2 ion Study Mn2 ion
2211
,,;2,1
452
,2,1
)()(
.].[)(2
FSGFSG
ccREFRK
chccRtH
ZZ
Z
ZZ
Z
Z
FiFiFi
Z
FFF
FeffMn
Energy shift
Spin-dependent hopping
Local spin-anisotropy for holes
Obtain effective Hamiltonian (spherical approx): Compute low-lying spectrum of 2 Mn ions
[P. Redlinski, GZ, B Janko, cond-mat/0505038 ; G. Fiete, GZ, K. Damle, PRL 91, 097202 (2003)]
![Page 26: Ferromagnetic Semiconductors Gergely Zaránd Budapest Univ. Technology Collaborators: Greg Fiete (Santa Barbara) Boldizsár Jankó (Notre Dame) Pawel Redlinski.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e5e5503460f94b584fd/html5/thumbnails/26.jpg)
Computed parameters:Computed parameters:
![Page 27: Ferromagnetic Semiconductors Gergely Zaránd Budapest Univ. Technology Collaborators: Greg Fiete (Santa Barbara) Boldizsár Jankó (Notre Dame) Pawel Redlinski.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e5e5503460f94b584fd/html5/thumbnails/27.jpg)
Hopping F=3/2 fermions coupled to local classical spins:
,',
,,',,,
2/3
2/3,min )'()( RR
RRRRR
MnR
hhRRthJhSGH
sites
• Spin-hopping direction coupled matrix elements:
)()()()( )2/3()2/3(ijijijji nDrCnDrrt
diagonalmatrix
spin 3/2 rotation matrix
Minimum model (dilute limit)Minimum model (dilute limit)
![Page 28: Ferromagnetic Semiconductors Gergely Zaránd Budapest Univ. Technology Collaborators: Greg Fiete (Santa Barbara) Boldizsár Jankó (Notre Dame) Pawel Redlinski.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e5e5503460f94b584fd/html5/thumbnails/28.jpg)
Band structure of a relaxed Mn systemBand structure of a relaxed Mn system
( xactive=0.01, f=0.1 )
Impurity band in small concentration limit
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).
( xactive < 0.01 )
![Page 29: Ferromagnetic Semiconductors Gergely Zaránd Budapest Univ. Technology Collaborators: Greg Fiete (Santa Barbara) Boldizsár Jankó (Notre Dame) Pawel Redlinski.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e5e5503460f94b584fd/html5/thumbnails/29.jpg)
Non-collinear magnetic statesNon-collinear magnetic states
( xactive=0.01, f=0.3 )
[G. Fiete, G.Z., and K. Damle, 2003, PRL 91, 097202 (2003)]
Distribution of angles
[see, e.g. : B. Grandidier, et al. APL 77, 4001 (2000).]
Experiments: small fields induce substantial increase of magnetization in small concentration unannealed samples
![Page 30: Ferromagnetic Semiconductors Gergely Zaránd Budapest Univ. Technology Collaborators: Greg Fiete (Santa Barbara) Boldizsár Jankó (Notre Dame) Pawel Redlinski.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e5e5503460f94b584fd/html5/thumbnails/30.jpg)
Metallic limit Metallic limit
![Page 31: Ferromagnetic Semiconductors Gergely Zaránd Budapest Univ. Technology Collaborators: Greg Fiete (Santa Barbara) Boldizsár Jankó (Notre Dame) Pawel Redlinski.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e5e5503460f94b584fd/html5/thumbnails/31.jpg)
RKKY interaction: non-collinear states ?RKKY interaction: non-collinear states ?
Neglect disorder, and compute effective spin-spin interaction
[GZ, and B. Janko, PRL 89, 047201 (2002)]
21
||2
||1|| )()()( SSRKSSRKRH eff
Non-collinear States ?
![Page 32: Ferromagnetic Semiconductors Gergely Zaránd Budapest Univ. Technology Collaborators: Greg Fiete (Santa Barbara) Boldizsár Jankó (Notre Dame) Pawel Redlinski.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e5e5503460f94b584fd/html5/thumbnails/32.jpg)
RKKY interaction RKKY interaction
[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)]
Almost collinear states for x > 0.03
![Page 33: Ferromagnetic Semiconductors Gergely Zaránd Budapest Univ. Technology Collaborators: Greg Fiete (Santa Barbara) Boldizsár Jankó (Notre Dame) Pawel Redlinski.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e5e5503460f94b584fd/html5/thumbnails/33.jpg)
Ab initio calculations Ab initio calculations
[G. Bouzerar, G., T. Ziman, and J. Kudrnovsky, Europhys. Lett. 69, 812 (2005)]
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)
![Page 34: Ferromagnetic Semiconductors Gergely Zaránd Budapest Univ. Technology Collaborators: Greg Fiete (Santa Barbara) Boldizsár Jankó (Notre Dame) Pawel Redlinski.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e5e5503460f94b584fd/html5/thumbnails/34.jpg)
Transport properties Transport properties
![Page 35: Ferromagnetic Semiconductors Gergely Zaránd Budapest Univ. Technology Collaborators: Greg Fiete (Santa Barbara) Boldizsár Jankó (Notre Dame) Pawel Redlinski.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e5e5503460f94b584fd/html5/thumbnails/35.jpg)
Resistivity anomalies in Resistivity anomalies in
GaMnAs data from P. Schiffer’s group
Sea also Potashnik et al., APL 79, 1495 (2001)Matsukura et al., PRB 57, R2037 (1998)Edmonds et al, APL 81, 4991 (2002)
AsMnGa xx1
21~ lkF
![Page 36: Ferromagnetic Semiconductors Gergely Zaránd Budapest Univ. Technology Collaborators: Greg Fiete (Santa Barbara) Boldizsár Jankó (Notre Dame) Pawel Redlinski.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e5e5503460f94b584fd/html5/thumbnails/36.jpg)
Possible explanations for the peak?Possible explanations for the peak?
Critical fluctuations ?
Magnetic polarons ?[Kasuya, Dietl and Spalek, P. Littlewood]
Selfconsistent potantials ? [Nagaev’s theory]
Only a kink at TC
[Fischer-Langer]
Maximum way above TC[P. Littlewood]Curves cross…
“Spin disorder scattering”
Diverges at TC …?)1( Fk
None of these works …
![Page 37: Ferromagnetic Semiconductors Gergely Zaránd Budapest Univ. Technology Collaborators: Greg Fiete (Santa Barbara) Boldizsár Jankó (Notre Dame) Pawel Redlinski.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e5e5503460f94b584fd/html5/thumbnails/37.jpg)
Proposal: Interplay of magnetization and localizationProposal: Interplay of magnetization and localization
Interplay with localization produces peak at
CT
Magnetic-ordering decreases effective disorder
Resistance changes at microscopic scale
[Similar ideas emerged for Manganites [Viret et al. PRB 55, 8067 (1997)]
• There Jahn-Teller effect provides localization• Some conceptual difficulties ]
[GZ, P. Moca, and B. Janko, PRL 94, 247202 (2005).]
![Page 38: Ferromagnetic Semiconductors Gergely Zaránd Budapest Univ. Technology Collaborators: Greg Fiete (Santa Barbara) Boldizsár Jankó (Notre Dame) Pawel Redlinski.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e5e5503460f94b584fd/html5/thumbnails/38.jpg)
Influence of spin on disorder: possible mechanismsInfluence of spin on disorder: possible mechanisms
•Static spins, double exchange mechanism )cos(1~ ijijt
• Spin splitting of bands
F
FF n
eke 4
4
4
~~1
])([21
~~ 2222 nnnnnnn
[Lopez-Sancho and Brey, PRB 68, 113201 (2003)]
• Interference between magnetic and static scattering pSVJJV z2~
1 22
[Csontos et al, Nature Mat. 2005]
![Page 39: Ferromagnetic Semiconductors Gergely Zaránd Budapest Univ. Technology Collaborators: Greg Fiete (Santa Barbara) Boldizsár Jankó (Notre Dame) Pawel Redlinski.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e5e5503460f94b584fd/html5/thumbnails/39.jpg)
We need to know )(TL
Metallic Phase:L
]),([)(),( 02
2
GTLgTLhe
HT d
pinin TDTL ~,~)(
Finite conductivity Finite conductivity T
Mott’s variable range formula )1/(1
0~ln dd TN
Insulating Phase:
)]([ 00 lGG
![Page 40: Ferromagnetic Semiconductors Gergely Zaránd Budapest Univ. Technology Collaborators: Greg Fiete (Santa Barbara) Boldizsár Jankó (Notre Dame) Pawel Redlinski.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e5e5503460f94b584fd/html5/thumbnails/40.jpg)
Single parameter scaling theory of localization (T=0) Single parameter scaling theory of localization (T=0)
)(Lg Typical dimensionless conductance of slab ~ L
L
LL 2'
LL
LgfLg'
),()'(
)(ln
)(lnLg
LdLgd
)(g
gln
cgln
0T
![Page 41: Ferromagnetic Semiconductors Gergely Zaránd Budapest Univ. Technology Collaborators: Greg Fiete (Santa Barbara) Boldizsár Jankó (Notre Dame) Pawel Redlinski.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e5e5503460f94b584fd/html5/thumbnails/41.jpg)
Spin distribution changes disorder !
),(}){( ThSP i
),(}){( 000 ThGSPGG i
)1/(1
0),(~ln dd TNTh
)],(),([)(),( 02 ThGTLGTLHT d
Insulator:
Metal:
![Page 42: Ferromagnetic Semiconductors Gergely Zaránd Budapest Univ. Technology Collaborators: Greg Fiete (Santa Barbara) Boldizsár Jankó (Notre Dame) Pawel Redlinski.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e5e5503460f94b584fd/html5/thumbnails/42.jpg)
Beta function, Phase diagramBeta function, Phase diagram
To compute we need to solve a differential
equation
)(ln
)(lnLG
LdLGd
beta function extracted from model calculations
G
[GZ, P. Moca, and B. Janko, PRL 94, 247202 (2005).]
![Page 43: Ferromagnetic Semiconductors Gergely Zaránd Budapest Univ. Technology Collaborators: Greg Fiete (Santa Barbara) Boldizsár Jankó (Notre Dame) Pawel Redlinski.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e5e5503460f94b584fd/html5/thumbnails/43.jpg)
Experimentally observed anomalies, localized fitsExperimentally observed anomalies, localized fits
GaMnAs data from P. Schiffer’s group
Some fine-tuning is needed to fit
the metallic data through variable range hopping[GZ, P. Moca, and B. Janko, PRL 94, 247202 (2005).]
![Page 44: Ferromagnetic Semiconductors Gergely Zaránd Budapest Univ. Technology Collaborators: Greg Fiete (Santa Barbara) Boldizsár Jankó (Notre Dame) Pawel Redlinski.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e5e5503460f94b584fd/html5/thumbnails/44.jpg)
Fitting through metallic expressionFitting through metallic expression
p
inin TDTL ~,~)(
)],(),([)(),( 02
2
THgTLgTLhe
HT d
)1(~ 200 mgg
[GZ, P. Moca, and B. Janko, PRL 94, 247202 (2005), and unpublished]
![Page 45: Ferromagnetic Semiconductors Gergely Zaránd Budapest Univ. Technology Collaborators: Greg Fiete (Santa Barbara) Boldizsár Jankó (Notre Dame) Pawel Redlinski.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e5e5503460f94b584fd/html5/thumbnails/45.jpg)
Best fit !
More fits…More fits…
Tin ~/1 Experiments on (Ga,Mn)As metal rings find similar behavior !
K. Wagner, et al. PRL 97, 056803 (2006)
![Page 46: Ferromagnetic Semiconductors Gergely Zaránd Budapest Univ. Technology Collaborators: Greg Fiete (Santa Barbara) Boldizsár Jankó (Notre Dame) Pawel Redlinski.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e5e5503460f94b584fd/html5/thumbnails/46.jpg)
Conclusions Conclusions
General review, GaMnAs:Jungwirth et al. cond-mat/0603380
Carrier-mediated mechanism in GaMnAs:Dietl, T., 2003, condmat/0306479.
First principles calculationsSanvito, 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 materialsFurdyna, J. K., and J. Kossut, Diluted Magnetic Semiconductors, volume 25 of Semiconductor and Semimetals (Academic Press, New York, 1988).
SpintronicsZutic, J. Fabian, and S. Das Sarma, Rev. Mod. Phys. 76, 323 (2004).
REVIEWS:
![Page 47: Ferromagnetic Semiconductors Gergely Zaránd Budapest Univ. Technology Collaborators: Greg Fiete (Santa Barbara) Boldizsár Jankó (Notre Dame) Pawel Redlinski.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e5e5503460f94b584fd/html5/thumbnails/47.jpg)
![Page 48: Ferromagnetic Semiconductors Gergely Zaránd Budapest Univ. Technology Collaborators: Greg Fiete (Santa Barbara) Boldizsár Jankó (Notre Dame) Pawel Redlinski.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e5e5503460f94b584fd/html5/thumbnails/48.jpg)
Transfer matrix / scaling analysis of Lyapunov exponentsTransfer matrix / scaling analysis of Lyapunov exponents
Lyapunov exponent
,..)](/[ 0 WMGM
Single parameter scaling:
slabs
MM M
M
Universal function
Microscopic length scale
![Page 49: Ferromagnetic Semiconductors Gergely Zaránd Budapest Univ. Technology Collaborators: Greg Fiete (Santa Barbara) Boldizsár Jankó (Notre Dame) Pawel Redlinski.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e5e5503460f94b584fd/html5/thumbnails/49.jpg)
Single parameter scaling theory of localization IISingle parameter scaling theory of localization II
400lConsider a slab of size and conductance 0g
cgg 0g increases as we
increase L
2dL~)L(g
cgg 0g decreases as we
increase L
)/2exp(~)( LLg
![Page 50: Ferromagnetic Semiconductors Gergely Zaránd Budapest Univ. Technology Collaborators: Greg Fiete (Santa Barbara) Boldizsár Jankó (Notre Dame) Pawel Redlinski.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e5e5503460f94b584fd/html5/thumbnails/50.jpg)
Test these ideas for a toy modelTest these ideas for a toy model
Disordered Kondo lattice:
,,,,
),,(,,
iii
iiii
jiji SJcccctH
Take J + classical spinsSpins 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)]
![Page 51: Ferromagnetic Semiconductors Gergely Zaránd Budapest Univ. Technology Collaborators: Greg Fiete (Santa Barbara) Boldizsár Jankó (Notre Dame) Pawel Redlinski.](https://reader030.fdocuments.in/reader030/viewer/2022032604/56649e5e5503460f94b584fd/html5/thumbnails/51.jpg)
Beta function, Phase diagramBeta function, Phase diagram
)1(~ 200 mgg