Anisotropic magnetoresistance effects in ferromagnetic Anisotropic magnetoresistance effects in ferromagnetic semiconductor and metal devicessemiconductor and metal devices

Tomas Jungwirth

University of Nottingham Bryan Gallagher, Tom Foxon,

Richard Campion, Kevin Edmonds, Andrew Rushforth, Chris King et al.

Hitachi Labs., UK & Japan University of Texas and Texas A&M Jorg Wunderlich, Byong-Guk Park, Andrew Irvine, Allan MacDonald, Jairo Sinova David Williams, Akira, Sugawara, et al.

Institute of Physics ASCR Alexander Shick, Jan Mašek, Josef Kudrnovský,

František Máca, Karel Výborný, Jan Zemen, Vít Novák, Kamil Olejník, et al.

University of Wuerzburg Polish Academy of Sciences Tohoku University Laurens Molenkamp, Charles Gould Tomasz Dietl, et al. Hideo Ohno, et al.

Outline

1. Intro - basic micromagnetics in DMSs

2. DMS materials science

3. AMR effects in DMSs and metals – devices and physics

(Ga,Mn)As: an archetypical dilute moment FM semiconductor

Mn-d-like localmoments

As-p-like holes

Mn

Ga

AsMn

SW-transf. Jpd SMn . shole

Dilute Mn-doped SC: sensitive to doping; 100smaller Ms than in conventional metal FMs

Mn-Mn coupling mediated by holes in SO-coupled SC valence bands:sensitive to gating, comparable magnetocrystalline anisotropy energy and stiffness to metal FMs

For not too strong p-d hybridization:kinetic-exchange (Jpd) & host SC bands provides simple yet often semiquantitative description

MF-like M(T);square hysteresis loops

1 mm 500 nm

8 K 22 KMacro (100’s m) domains;

10-100 nm domain walls (~A/K)reflecting combined T-dependentuniaxial and cubic anisotropies

One

One

0.1-1 m

(b)Strain controlled micromagnetics andcurrent induced DW dynamics tunable 100x smaller critical currentsthan in metals

Huge hysteretic MR tunable by gate due to CBAMR spintronic transistor … plus weak dipolar crosslinks

prospect for dense integration of magnetic microelements

Outline

1. Intro - basic micromagnetics in DMSs

2. DMS materials science

3. AMR effects in DMSs and metals – devices and physics

Magnetism in systems with coupled dilute moments and delocalized band electrons

(Ga,Mn)As

cou

pli

ng

str

eng

th /

Fer

mi

ener

gy

band-electron density / local-moment density

VB-CB

VB-IB

Mn-acceptor level (IB)

Short-range ~ M . s potential

- additional Mn-hole binding - ferromagnetism - scattering

GaAs:Mn extrinsic semiconductorGaAs VB

GaMnAs disordered VB

2.2x1020 cm-3

MIT in GaAs:Mn at order of magnitude higher doping than quoted in text books

MIT in p-type GaAs:- shallow acc. (30meV) ~ 1018 cm-3

- Mn (110meV) ~1020 cm-3

Mobilities:- 3-10x larger in GaAs:C- similar in GaAs:Mg or InAs:Mn

> 2% Mn: metallic but strongly disordered

Model:SO-coupled, exch.-split Bloch VB & disorder

- conveniently simple and increasingly meaningful as metallicity increases

- no better than semi-quantitative

Mn spacing

Covalent SCs do not like doping self-compensation by interstitial Mn

Interstitial MnInt is detrimental to magnetic order

charge and moment compensation defect

Mnsub

MnInt

Mnsub

As

Ga

MnInt

+

-Can be annealed out

Tc 95K in as-grown (9% Mn)

to 173 in annealed (6% Mnsub)

but MnGa < nominal Mn

theory & exp.

MnGa solubility limit

d4

d

Weak hybrid.Delocalized holeslong-range coupl.

Strong hybrid.Impurity-band holesshort-range coupl.

d 5 d 4 no holes

InSb, InAs, GaAs

GaN

GaP, AlAs

d5

Search for optimal III-V host:

optimal combination of hole delocalization,

p-d coupling strength, low self-compensation

I-II-Mn-V ferromgantic semiconductors

III = I + II Ga = Li + Zn

• GaAs and LiZnAs are twin semiconductors

• Prediction that Mn-doped are also twin ferromagnetic semiconductors

• No limit for Mn-Zn (II-II) substitution

• Independent carrier doping by Li-Zn stoichiometry adjustment

Outline

1. Intro - basic micromagnetics in DMSs

2. DMS materials science

3. AMR effects in DMSs and metals – devices and physics

M || <111> M || <100>Anisotropic, SO-coupled, exchange-split hole bands

Chemical potential CBAMR

Tunneling DOS TAMR

M

M

I

I

Impurity scattering rates AMR

GMMGG0

20

C

C

e

)M(V&)]M(VV[CQ&

C2

)QQ(U

electric && magneticmagnetic

control of Coulomb blockade oscillations

Coulomb blockade AMR – anisotropic chemical potential

Q

0

'D

'

e

)M(Q)Q(VdQU

Source Drain

GateVG

VDQ

[010]

M[110]

[100]

[110][010]

• CBAMR if change of |CBAMR if change of |((MM)| ~ )| ~ ee22//22CC

• In our (Ga,Mn)As ~ meV (~ 10 Kelvin)In our (Ga,Mn)As ~ meV (~ 10 Kelvin)

• In room-T ferromagnet change of |In room-T ferromagnet change of |((MM)|~100K )|~100K

• Room-T conventional SET (e2/2C >300K) possible

Worth trying to look for CBAMR in SO-coupled room-Tc metal FMs

Tunneling AMR – anisotropic TDOS

TAMR in GaMnAs

GaMnAsAuAlOx Au

Res

ista

nce

Magnetisation in plane

M perp.

M in-plane

~ 1-10% in metallic GaMnAs

Huge when approaching MIT in GaMnAs

Anisotropc tunneling amplitudes

TAMR in metals

theory

experiment

Anisotropic magnetoresistance

TH

EO

RY

EX

PE

RIM

EN

TSemiquantitative numerical understanding in GaMnAs

SO & polarized scatterers

Qualitative physical (analytical) picture

anisotropic scattering