How to Make Semiconductors Ferromagnetic: A First Course in Spintronics

Dr. Sankar Das Sarma, Univ of Maryland (KITP Correlated Electrons 10/17/02) 1

Theories of ferromagnetic semiconductors (S. Das Sarma)

• Weiss Mean Field Theory: Localized and Delocalized

• Percolation Theory: Insulating DMS• Dynamical Mean Field Theory: Impurity

Band extended and Localized

• PRL87,227202(2001);PRL 88,247202(2002);PRB65,233206(2002)

How to Make Semiconductors Ferromagnetic: A First Course in Spintronics

Dr. Sankar Das Sarma, Univ of Maryland (KITP Correlated Electrons 10/17/02) 2

Signatures of charge carrier localization

Ge1-xMnxGa1-xMnxAs

Bound magnetic polaron

localized hole

−−∝Ψ

Ba

rrr 0exp)(

magnetic impurities+

( )hi nn >>

hihi

ih sSJH�

�

∑=,

ˆ

−−=

B

hiih

a

rrJJ

2exp0

⇒lower T

T

AJar B

p0ln

2=

polaronradius:

How to Make Semiconductors Ferromagnetic: A First Course in Spintronics

Dr. Sankar Das Sarma, Univ of Maryland (KITP Correlated Electrons 10/17/02) 3

Polaron percolation

Interaction of two polarons

)2/("")2/(1

12(1,2)int.reg. rJNJrJ

TNM ≈⇒≈

+=

T

Jna

T

Jar iB

B 030polaron lnln

2

1ln

2""

How to Make Semiconductors Ferromagnetic: A First Course in Spintronics

Dr. Sankar Das Sarma, Univ of Maryland (KITP Correlated Electrons 10/17/02) 4

Percolation theory:the model of overlapping spheres

only one parameter: 3 nr

known characteristics: ( ) ( )333 ,,86.0)( nrVnrNnr crit =

Results

( )

−=

30

386.0

exphBh

ihBc

naJ

n

nnaT

matches mean-field result

0Jn

nT

h

ic = at 13 ≈hB na

+=

T

TnaV

M

TM chB ln86.0

)0(

)(3

How to Make Semiconductors Ferromagnetic: A First Course in Spintronics

Dr. Sankar Das Sarma, Univ of Maryland (KITP Correlated Electrons 10/17/02) 5

Comparison with experimentsand numeric experiments

Ge1-xMnx (Park et al. (2002))

Also In1-xMnxAs, Ga1-xMnxSb, Ga1-xMnxAs (for x < 3%)

Monte-Carlo (Bhatt et al. (2000))

0.4�

;)()( � ≈−∝→ TTTTM cc

)0(1)0( 6

� 3

MTTMBian

−≈→

1.7�;)()(� � ≈−∝→ cc TTTT

Magnetization and susceptibility

How to Make Semiconductors Ferromagnetic: A First Course in Spintronics

Dr. Sankar Das Sarma, Univ of Maryland (KITP Correlated Electrons 10/17/02) 6

M(T,B) and χ(T,B)

How to Make Semiconductors Ferromagnetic: A First Course in Spintronics

Dr. Sankar Das Sarma, Univ of Maryland (KITP Correlated Electrons 10/17/02) 7

How to Make Semiconductors Ferromagnetic: A First Course in Spintronics

Dr. Sankar Das Sarma, Univ of Maryland (KITP Correlated Electrons 10/17/02) 8

How to Make Semiconductors Ferromagnetic: A First Course in Spintronics

Dr. Sankar Das Sarma, Univ of Maryland (KITP Correlated Electrons 10/17/02) 9

How to Make Semiconductors Ferromagnetic: A First Course in Spintronics

Dr. Sankar Das Sarma, Univ of Maryland (KITP Correlated Electrons 10/17/02) 10

How to Make Semiconductors Ferromagnetic: A First Course in Spintronics

Dr. Sankar Das Sarma, Univ of Maryland (KITP Correlated Electrons 10/17/02) 11