Ab Initio Calculation of Intrinsic Spin Hall Effect in Semiconductors and Magnetic Nanostructures

8/3/2019 Ab Initio Calculation of Intrinsic Spin Hall Effect in Semiconductors and Magnetic Nanostructures

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GuangGuang--Yu GuoYu Guo

Physics Dept., Natl. Taiwan Univ., Taipei, TaiwanPhysics Dept., Natl. Taiwan Univ., Taipei, Taiwan

AbAb InitioInitio Studies of Intrinsic Spin Hall EffectStudies of Intrinsic Spin Hall Effect

and Magnetic Nanostructuresand Magnetic Nanostructures

(A talk in Physics Dept., Natl.(A talk in Physics Dept., Natl. TsingTsing--HuaHua Univ., April 13, 2005)Univ., April 13, 2005)


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Plan of this Talk

Part I. Intrinsic Spin Hall Effect in Semiconductors

Part II. Magnetic Nanostructures


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-- spin current generation without magnetic field or magnetic materials --

Part I:Part I: AbAb InitioInitio Calculation ofCalculation of

Intrinsic Spin Hall Effect in SemiconductorsIntrinsic Spin Hall Effect in Semiconductors


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Acknowledgements:

Co-Authors:

Qian Niu (Austin), Yugui Yao (Beijing)

Stimulating Discussions:

Ming-Che Chang (NTNU).

Financial Support:National Science Council.


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I. Introduction

Outline of this first part of the talk

II. Theory and Computational Method

1. Basic elements in spintronics.

2. Spin Hall effect.

3. Motivations

1. Kubo linear response theory.

2. Relativistic band structure methods.

III. Calculated Spin and Orbital-Angular-Momentum Hall Effects in

Semiconductors

1. dc spin Hall effect.

2. Effects of epitaxial strain.

3. ac spin Hall effect.

IV. Conclusions


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1. Basic elements of spintronics

Spin currents:

Generation,

detection,

manipulation (control).

I. Introduction


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Usual spin current generations:

Ferromagnetic leads

especially half-metals

Schematic band pictures of (a) non-magnetic

metals, (b) ferromagnetic metals and (c) half-metallic metals .

Spin filter

[Slobodskyy, et al., PRL 2003]

Problems: magnets and/or

magnetic fields needed, and

difficult to integrate withsemiconductor technologies.


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2. Spin Hall effect

1) The Hall Effect

Ordinal Hall Effect (1879)

Anomalous Hall Effect (Hall, 1880 & 1881)

(Extraordinary or spontaneous Hall effect)


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Zoo of the Hall Effects

Ordinary Hall effect (1879);

Anomalous Hall effect (1880 & 1881);

Integer quantum Hall effect (von Klitzing, et al., 1980);

Fractional quantum Hall effect (Tsui, et al., 1982);

(Extrinsic) spin Hall effect (Hirsch, 1999);

Intrinsic spin Hall effect (Murakami, et al., 2003).

(Spontaneous and dissipationless)


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2) (Extrinsic) Spin Hall Effect

[Dyakonov & Perel, JETP 1971; Hirsch, PRL 1999;

Zhang, PRL 2000]

(Extrinsic) spin Hall effect

L += )()( rVrVV soc


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3) Berry phase and semiclassical dynamics of electrons

( ) ( ){ }, nn

( ) ( )( ) ( )tidti

nn

t

n

eett

= 0

/h

=

t

nnn id0

Geometric phase:

n

Adiabatic theorem:

Parameter dependent system:

1

2

0

t

(1) Berry phase

[Berry, Proc. Roy. Soc. London A 392, 451 (1984)]


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1221

= ii

= 21 ddn1

2

C

=C

nnn

id

Well defined for a closed path

Stokes theorem

Berry Curvature


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(2) Semiclassical dynamics of Bloch electrons

Old version [e.g., Aschroft, Mermin, 1976]

.)(

,)(1

Bxr

rBxEk

k

kx

==

=

cc

nc

eeee&

hh&

hh

&

h

&

Berry phase correction [Chang & Niu, PRB (1996)]New version [Marder, 2000]

.||Im)(

,)(

),()(1

kkk

Bxr

rk

kk

k

kx

kk

=

=

=

nnn

c

nn

c

uu

ee&

hh

&

&

h

&

(Berry curvature)


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= ),()(3

krxj gekd &

(3) Semiclassical transport theory

),()(),(

)(

krkkr

Ek

kx

ffg

en

+=

+

=

hh&

k

krkkkkEj

=

)(),()( 33

2

nfde

fde

hh

(Anomalous Hall conductance) (ordinary conductance)


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Anomalous Hall conductivity [Yao, et al., PRL 2004]

=

=

nn nn

yxz

n

n

z

nnxy

nvnnvn

fde

'2

'

32

)(

||''||Im2

)(

)())((

kk

kkkk

k

kkk

h

P.N. Dheer,Phys.Rev156, 637(1967)

1032 (ohm cm)-1

G. S. Krinchik and V. S. Gushchin,

Sov. Phys.-JETP 24, 984 (1969).

FM bcc Fe


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3) Intrinsic spin Hall effect

Luttinger Hamiltonian

Spin current

nh = 1019 cm-3, = 50 cm /Vs,= enh = 80

-1cm-1;

s= 80-1cm-1

nh = 1016 cm-3, = 50 cm /Vs,= enh = 0.6

-1cm-1;

s= 7-1cm-1

(1) In p-type bulk semiconductors


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(2) In a 2-D electron gas in n-type semiconductor heterostructures

Rashba Hamiltonian

Universal spinHall conductivity


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(3) Significances of these theoretical discoveries of intrinsic spin Hall effects

Among other things,

it would enable us to generate spin currentelectrically in semiconductor microstructures

without applied magnetic fields or magnetic

materials,and hence make possible pure electric driven

spintronics in semiconductors which could be

readily integated with conventional electronics.


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(1) Non-existence of intrinsic spin Hall effect in bulkp-type

semiconductor?

[X. Wang and X.-G. Zhang, cond-mat/0407699]

3. Motivations

1) Questions concerning the intrinsic spin Hall Effects?


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(2) Will the intrinsic spin Hall effect exactly cancelled

by the intrinsic orbital-angular-momentum Halleffect?

[S. Zhang and Z. Yang, cond-mat/0407704]

for Rashba

Hamiltonian.


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2) Motivations for the present work

(1) Try to resolve the above two important problems.

(2) To go beyond thespherical 4-band

Luttinger

Hamiltonian.

(3) To understand the

effects of epitaxialstrains.


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II. Theory and Computational Method

Assume E-field alongx-axis and spin or H-field alongz-axis,

the Hall conductivity (off-diagonal element) is [e.g., Marder, 2000]

1. Linear-response-theory Kubo formalism

where Vc

is the cell volume, |kn> is the nth Bloch state with crystal

momentum k, is the photon energy.

The intrinsic Hall effect comes from the static = 0 limit:

)1(||''||

)(' ''

' ++

=

k kkkk

kkkkkk

nn nn

q

yx

nn

nn

c

q

xyi

njnnvnff

iV

e

h

)2()(

]||''||Im[)('

2

'

'

=k kk

kkkkkk

nn nn

q

yx

nn

c

q

xynjnnvnff

Ve

current operator jy = -evy (AHE),

jy = {z,vy}/4 (SHE),jy = {Lz,vy}/4 (OHE).


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Settingto zero and using ),3()(1

P1

lim0

i

i

m=

Imaginary (part) Hall conductivity

).4()(]||''||Im[)()("'

''

= kkkkk kkkk

nnnn

q

yxnn

c

q

xy njnnvnffV

e

h

Real (part) Hall conductivity is (Kramers-Kronig transformation)

).5('

)'("''P

2)('

0 22

=

xy

xy d


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Calculations must be based on a relativistic band theory because

all the intrinsic Hall effects are caused by spin-orbit coupling.

{ } cz,4

=h

j { } cLz,2

h=j

2. Relativistic band structure method

velocity operatorv = c ,

current operatorj = -ec (AHE), (SHE), (OHE)

,, are 44 Dirac matrices.

A fully relativistic extension of linear muffin-tin orbital (LMTO)method. [Ebert, PRB 1988; Guo, Ebert, PRB 1995]

)()(

2

rp

vImccHD++=

Dirac Hamiltonian


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Density functional theory with generalized gradient

approximation (DFT-GGA).


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III. Calculated intrinsic spin and orbital-angular-

momentum Hall effects

1. dc Hall conductivity


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2. Effects of lattice mismatch strains


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3. ac Hall conductivity

IV C l i


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1. Relativistic band theoretical calculations reveal that intrinsicspin Hall conductivity in hole-doped semiconductors Ge,

GaAs and AlAs is large, showing the possibility of spin Hall

effect beyond the Luttinger Hamiltonian.2. The calculated orbital Hall conductivity is one order of

magnitude smaller, indicating no cancellation between the

spin and orbital Hall effects in bulk semiconductors.3. The spin Hall effect can be strongly manipulated by strains.

4. The ac spin Hall conductivity is also large in pure as well as

doped semiconductors.5. The spin Hall effects in semiconductors have just been

observed [Kato et al. (2004), Wunderlich et al. (2004)], another

milestone in spintronics research, though the intrinsic or

extrinsic nature needs to be established.

IV. Conclusions


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[Kato et al., Science 306, 1910 (2004)]


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Part II: Magnetic NanostructuresPart II: Magnetic Nanostructures


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Acknowledgements:

Taida team:

Amel Laref (Postdoc), Yi-Wen Fu (Assistant),Jen-Chuan Tung (PhD Student)

Financial Support:

National Science Council.


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I. Free standing transition metal atomic chains

Outline of this second part of the talk

II. Metal atomic chains in/on, and wetted layers on BN nanotubes

1. Basic elements in spintronics.

2. Spin Hall effect.

3. Motivations

1. Kubo linear response theory.

2. Relativistic band structure methods.

III. Bulk, thin films, nanowires and nanopartices of FePt

1. dc spin Hall effect.

2. Effects of epitaxial strain.3. ac spin Hall effect.

Ab Initio Calculation of Intrinsic Spin Hall Effect in Semiconductors and Magnetic Nanostructures

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