Making semiconductors magnetic: new materials properties, devices, and future

JAIRO SINOVA Texas A&M University

Institute of Physics ASCR

Hitachi Cambridge Jorg Wunderlich, A. Irvine, et al

Institute of Physics ASCR Tomas Jungwirth, Vít Novák, et al Texas A&M L. Zarbo

University of Utah November 9th 2010

University of Nottingham Bryan Gallagher, Tom Foxon,

Richard Campion, et al.

NRI SWAN

OUTLINE

•  Motivation •  Ferromagnetic semiconductor materials:

–  (Ga,Mn)As - general picture –  Growth, physical limits on Tc –  Related FS materials (searching for room temperature) –  Understanding critical behavior in transport

•  Ferromagnetic semiconductors & spintronics –  Tunneling anisotropic magnetoresistive device –  Transistors (4 types)

Technologically motivated and scientifically fueled

Incorporate magnetic properties with

semiconductor tunability (MRAM, etc)

Understanding complex phenomena: • Spherical cow of ferromagnetic systems (still very complicated) • Engineered control of collective phenomena

Generates new physics: • Tunneling AMR • Coulomb blockade AMR • Nanostructure magnetic anisotropy engineering

ENGINEERING OF QUANTUM MATERIALS

More knobs than usual in semiconductors: density, strain, chemistry/pressure, SO coupling engineering

1. Create a material that marriages the tunability of semiconductors and the collective behavior of ferromagnets; once created search for room temperature systems

2. Study new effects in this new material and utilize in metal-based spintronics

3. Develop a three-terminal gated spintronic device to progress from sensors & memories to transistors & logic

Ferromagnetic semiconductor research : strategies

(Ga,Mn)As GENERAL PICTURE

Ferromagnetic semiconductors

GaAs - standard III-V semiconductor

Group-II Mn - dilute magnetic moments & holes

(Ga,Mn)As - ferromagnetic semiconductor

Need true FSs not FM inclusions in SCs

Mn

Ga As

Mn

+

Mn

Ga

As

What happens when a Mn is placed in Ga sites: Mn–hole spin-spin interaction

hybridization

Hybridization → like-spin level repulsion → Jpd SMn ⋅ shole interaction

Mn-d

As-p

In addition to the Kinetic-exchange coupling, for a single Mn ion, the coulomb interaction gives a trapped hole (polaron) which resides just above the valence band

5 d-electrons with L=0 → S=5/2 local moment

intermediate acceptor (110 meV) → hole

Mn

Ga

As Mn

EF

DO

S

Energy

spin ↓

spin ↑

Transition to a ferromagnet when Mn concentration increases GaAs:Mn – extrinsic p-type semiconductor

FM due to p-d hybridization (Zener local-itinerant kinetic-exchange)

valence band As-p-like holes

As-p-like holes localized on Mn acceptors

<< 1% Mn ~1% Mn >2% Mn

onset of ferromagnetism near MIT

Mn

Ga

As

Mn

Ga As

Mn

• Low-T MBE to avoid precipitation

• High enough T to maintain 2D growth

→  need to optimize T & stoichiometry for each Mn-doping

• Inevitable formation of interstitial Mn-double-donors compensating holes and moments → need to anneal out but without loosing MnGa

high-T growth

optimal-T growth

(Ga,Mn)As GROWTH

Interstitial Mn out-diffusion limited by surface-oxide

GaMnAs

GaMnAs-oxide

Polyscrystalline 20% shorter bonds

MnI++

O

Optimizing annealing-T another key factor Rushforth et al, ‘08

x-ray photoemission

Olejnik et al, ‘08

10x shorther annealing with etch

(Ga,Mn)As GENERAL THEORY

HOW DOES ONE GO ABOUT UNDERSTANDING SUCH SYSTEMS

1.  One could solve the full many body S.E.: not possible AND not fun

2.  Combining phenomenological models (low degrees of freedom) and approximations and comparison to other computational technieques while checking against experiments

“This is the art of condensed matter science, an intricate tango between theory and experiment whose conclusion can only be guessed at while the dance is in progress”

A.H.M et al., in “Electronic Structure and Magnetism in Complex Materials” (2002).

Theoretical Approaches to DMSs •  First Principles LSDA

PROS: No initial assumptions, effective Heisenberg model can be extracted, good for determining chemical trends

CONS: Size limitation, difficulty dealing with long range interactions, lack of quantitative predictability, neglects SO coupling (usually)

•  Microscopic TB models

• k.p ⊕ Local Moment

PROS: “Unbiased” microscopic approach, correct capture of band structure and hybridization, treats disorder microscopically (combined with CPA), very good agreement with LDA+U calculations

CONS: neglects (usually) coulomb interaction effects, difficult to capture non-tabulated chemical trends, hard to reach large system sizes

PROS: simplicity of description, lots of computational ability, SO coupling can be incorporated, CONS: applicable only for metallic weakly hybridized systems (e.g. optimally doped GaMnAs), over simplicity (e.g. constant Jpd), no good for deep impurity levels (e.g. GaMnN)

Jungwirth, Sinova, Masek, Kucera, MacDonald, Rev. of Mod. Phys. 78, 809 (2006)

Magnetism in systems with coupled dilute moments and delocalized band electrons

(Ga,Mn)As

coup

ling

stre

ngth

/ Fe

rmi e

nerg

y

band-electron density / local-moment density

Which theory is right?

KP Eastwood Fast principles Jack

Impurity bandit vs Valence Joe

How well do we understand (Ga,Mn)As? In the metallic optimally doped regime GaMnAs is well described by a disordered-valence band picture: both dc-data and ac-data are consistent with this scenario.

The effective Hamiltonian (MF) and weak scattering theory (no free parameters) describe (III,Mn)V metallic DMSs very well in the optimally annealed regime:

•  Ferromagnetic transition temperatures √ • Magneto-crystalline anisotropy and coercively √ • Domain structure √ • Anisotropic magneto-resistance √ • Anomalous Hall effect √ • MO in the visible range √ • Non-Drude peak in longitudinal ac-conductivity √ •  Ferromagnetic resonance √ •  Domain wall resistance √ •  TAMR √ • Transport critical behaviour √ • Infrared MO effects √

TB+CPA and LDA+U/SIC-LSDA calculations describe well chemical trends, impurity formation energies, lattice constant variations upon doping

EXAMPLE: MAGNETO-OPTICAL EFFECTS IN THE INFRARED

EXAMPLE: INFRARED ABSORPTIN – not so red shifted after all

PRL 2010

Tc LIMITS AND STRATEGIES

  Curie temperature limited to ~110K.!

  Only metallic for ~3% to 6% Mn!

  High degree of compensation!

  Unusual magnetization (temperature dep.)!

  Significant magnetization deficit!

But are these intrinsic properties of GaMnAs ??!

“110K could be a fundamental limit on TC” !As

Ga Mn

Mn Mn

Problems for GaMnAs (late 2002)

Can a dilute moment ferromagnet have a high Curie temperature ?

The questions that we need to answer are:

1.  Is there an intrinsic limit in the theory models (from the physics of the phase diagram) ?

2.  Is there an extrinsic limit from the ability to create the material and its growth (prevents one to reach the optimal spot in the phase diagram)?

EXAMPLE OF THE PHYSICS TANGO

COMBINATION OF THEORY APPROACHES PREDICTS:!Tc linear in MnGa local moment concentration; falls

rapidly with decreasing hole density in more than 50% compensated samples; nearly independent of hole

density for compensation < 50%.!

Jungwirth, Wang, et al. Phys. Rev. B 72, 165204 (2005)

Intrinsic properties of (Ga,Mn)As

Extrinsic effects: Interstitial Mn - a magnetism killer"

Yu et al., PRB ’02:

~10-20% of total Mn concentration is incorporated as interstitials!Increased TC on annealing corresponds to removal of these defects.!

Mn

As

Interstitial Mn is detrimental to magnetic order:!

hcompensating double-donor – reduces carrier density!

hcouples antiferromagnetically to substitutional Mn even in!

low compensation samples Blinowski PRB ‘03, Mašek, Máca PRB '03

MnGa and MnI partial concentrations!

Microscopic defect formation energy calculations:!

No signs of saturation in the dependence of MnGa concentration!on total Mn doping!

Jungwirth, Wang, et al.!Phys. Rev. B 72, 165204 (2005) !

As grown "Materials calculation"

Annealing can vary significantly increases hole densities.

Low Compensation Obtain Mnsub

assuming change in hole density due to

Mn out diffusion

Open symbols & half closed as grown. Closed symbols annealed !

High compensation

Jungwirth, Wang, et al.!Phys. Rev. B 72, 165204 (2005) !

Experimental hole densities: measured by ordinary Hall effect

Theoretical linear dependence of Mnsub on total Mn confirmed experimentally!

Mnsub MnInt

Obtain Mnsub & MnInt assuming change in hole density due to

Mn out diffusion

Jungwirth, Wang, et al.!Phys. Rev. B 72, 165204 (2005) !

SIMS: measures total Mn concentration. "Interstitials only compensation assumed "

Experimental partial concentrations of MnGa and MnI in as grown samples

Can we have high Tc in Diluted Magnetic Semicondcutors?

Tc linear in MnGa local (uncompensated) moment concentration; falls rapidly with decreasing hole density in heavily compensated samples.!

Define Mneff = Mnsub-MnInt!

NO INTRINSIC LIMIT NO EXTRINSIC LIMIT

There is no observable limit to the amount of substitutional Mn we can put in!

8% Mn

Open symbols as grown. Closed symbols annealed

High compensation

Linear increase of Tc with Mneff = Mnsub-MnInt

Tc as grown and annealed samples

●  Concentration of uncompensated MnGa moments has to reach ~10%. Only 6.2% in the current record Tc=173K sample

●  Charge compensation not so important unless > 40%

●  No indication from theory or experiment that the problem is other than technological - better control of growth-T, stoichiometry

“... Ohno’s ‘98 Tc=110 K is the fundamental upper limit ..” Yu et al. ‘03

“…Tc =150-165 K independent of xMn>10% contradicting Zener kinetic exchange ...” Mack et al. ‘08

“Combinatorial” approach to growth with fixed growth and annealing T’s

Tc limit in (Ga,Mn)As remains open

`

2008 Olejnik et al

188K!!

- Effective concentration of uncompensated MnGa moments has to increase" beyond 6% of the current record Tc=173K sample. A factor of 2 needed" → 12% Mn would still be a DMS"

- Low solubility of group-II Mn in III-V-host GaAs makes growth difficult"

Low-temperature MBE"Strategy A: stick to (Ga,Mn)As"

- alternative growth modes (i.e. with proper "

substrate/interface material) allowing for larger"and still uniform incorporation of Mn in zincblende GaAs!

More Mn - problem with solubility

Getting to higher Tc: Strategy A

Find DMS system as closely related to (Ga,Mn)As as possible with"

•  larger hole-Mn spin-spin interaction"

•  lower tendency to self-compensation by interstitial Mn"

•  larger Mn solubility"

•  independent control of local-moment and carrier doping (p- & n-type) "

Getting to higher Tc: Strategy B

Weak hybrid. Delocalized holes long-range coupl.

Strong hybrid. Impurity-band holes short-range coupl.

InSb

GaP

d5

(Al,Ga,In)(As,P) good candidates, GaAs seems close to the optimal III-V host

Other (III,Mn)V’s DMSs

Mean-field but low Tc

MF

Large TcMF but

low stiffness

Kudrnovsky et al. PRB 07

Using DEEP mathematics to find a new material

3=1+2

Steps so far in strategy B:"

•  larger hole-Mn spin-spin interaction : DONE BUT DANGER IN PHASE DIAGRAM"

•  lower tendency to self-compensation by interstitial Mn: DONE"•  larger Mn solubility ?"•  independent control of local-moment and carrier doping (p- & n-type)?"

III = I + II → Ga = Li + Zn!

GaAs and LiZnAs are twin SC!

Masek, et al. PRB (2006)!

LDA+U says that Mn-doped are also twin DMSs!

L!

As p-orb.!

Ga s-orb.!As p-orb.!

EF!

It can be n and p doped!!!!

No solubility limit for group-II Mn

substituting for group-II Zn !!!!

UNDERSTANDING CRITICAL BEHAVIOUR

IN TRANSPORT

Towards spintronics in (Ga,Mn)As: FM & transport

Dense-moment MS λF<< d↑-↑

Eu↑ - chalcogenides

Dilute-moment MS λF~ d↑-↑

Critical contribution to resistivity at Tc ~ magnetic susceptibility

Broad peak near Tc disappeares with annealing (higher uniformity)???

↑

Tc

EuCdSe

When density of carriers is smaller than density of local moments what matters is the long range behavior of Γ (which goes as susceptibility)

When density of carriers is similar to density of local moments what matters is the short range behavior of Γ (which goes as the energy)

Ni

Tc

Optimized materials with x=4-12.5% and Tc=80-185K

Remarkably universal both below and above Tc

Annealing sequence

dρ/dT singularity at Tc – consistent with kF~d↑-↑

V. Novak, et al “Singularity in temperature derivative of resistivity in (Ga,Mn)As at the Curie point”, Phys. Rev. Lett. 101, 077201 (2008).

OUTLINE

•  Motivation •  Ferromagnetic semiconductor materials:

–  (Ga,Mn)As - general picture –  Growth, physical limits on Tc –  Related FS materials (searching for room temperature) –  Understanding critical behavior in transport

•  Ferromagnetic semiconductors & spintronics –  Tunneling anisotropic magnetoresistive device –  Transistors (4 types)

Exchange split & SO-coupled bands:

Exchange split bands:

Au

discovered in (Ga,Mn)As Gold et al. PRLʼ04!

ab intio theory Shick, et al, PRB '06, Park, et al, PRL '08

TAMR in metal structures

experiment Park, et al, PRL '08

Also studied by Parkin et al., Weiss et al., etc.

DMS DEVICES

Gating of highly doped (Ga,Mn)As: p-n junction FET

p-n junction depletion estimates

Olejnik et al., ‘08

~25% depletion feasible at low voltages

(Ga,Mn)As/AlOx FET with large gate voltages, Chiba et al. ‘06

AM

R

Increasing ρ and decreasing AMR and Tc with depletion

Tc Tc

Persistent variations of magnetic properties with ferroelectric gates

Stolichnov et al., Nat. Mat.‘08

Electro-mechanical gating with piezo-stressors

Rushforth et al., ‘08

Strain & SO →

Electrically controlled magnetic anisotropies via strain

Single-electron transistor

Two "gates": electric and magnetic

(Ga,Mn)As spintronic single-electron transistor

Huge, gatable, and hysteretic MR

Wunderlich et al. PRL ‘06

control of Coulomb blockade oscillations

Q0

Q0

e2/2CΣ

[010]

Φ

M [110]

[100]

[110] [010]

SO-coupling →µ(M)

Source Drain

Gate VG

VD Q

Single-electron charging energy controlled by Vg and M

Theory confirms chemical potential anisotropies in (Ga,Mn)As & predicts CBAMR in SO-coupled room-Tc metal FMs

Variant p- or n-type FET-like transistor in one single nano-sized CBAMR device

0

ON OFF

1

0

ON OFF

1

V DD

V A V B

V A

V B

Vout

0

0

0 OFF ON

ON

OFF

0

0

1

1

ON OFF

A B Vout 0 0 0 1 0 1 0 1 1 1 1 1

0

01

ON

OFF

0

0

OFF

1

ON

1

1

1

1

OFF

ON

1

1 ON

OFF

1

“OR”

Nonvolatile programmable logic

V DD

V A V B

V A

V B

Vout

Variant p- or n-type FET-like transistor in one single nano-sized CBAMR device

0

ON OFF

1

0

ON OFF

1

A B Vout 0 0 0 1 0 1 0 1 1 1 1 1

“OR”

Nonvolatile programmable logic

Physics of SO & exchange

SET

Resistor

Tunneling device

Chemical potential → CBAMR

Tunneling DOS → TAMR

Group velocity & lifetime → AMR

Device design Materials

metal FMs

FSs

FSs and metal FS with strong SO

Conclusion No intrinsic or extrinsic limit to Tc so far: it is a materials growth issue

In the metallic optimally doped regime GaMnAs is well described by a disordered-valence band picture: both dc-data and ac-data are consistent with this scenario.

The effective Hamiltonian (MF) and weak scattering theory (no free parameters) describe (III,Mn)V metallic DMSs very well in the optimally annealed regime:

BUT it is only a peace of the theoretical mosaic with many remaining challenges!!

TB+CPA and LDA+U/SIC-LSDA calculations describe well chemical trends, impurity formation energies, lattice constant variations upon doping

•  Ferromagnetic transition temperatures √ • Magneto-crystalline anisotropy and coercively √ • Domain structure √ • Anisotropic magneto-resistance √ • Anomalous Hall effect √ • MO in the visible range √ • Non-Drude peak in longitudinal ac-conductivity √ •  Ferromagnetic resonance √ •  Domain wall resistance √ •  TAMR √ • Transport critical behaviour √ • Infrared MO effects √

Allan MacDonald U of Texas

Tomas Jungwirth Inst. of Phys. ASCR

U. of Nottingham

Joerg Wunderlich Cambridge-Hitachi

Bryan Gallagher U. Of Nottingham

Tomesz Dietl Institute of Physics, Polish Academy of

Sciences

Other collaborators: John Cerne, Jan Masek, Karel Vyborny, Bernd Kästner, Carten Timm, Charles Gould, Tom Fox, Richard Campion,

Laurence Eaves, Eric Yang, Andy Rushforth, Viet Novak

Hideo Ohno Tohoku Univ.

Laurens Molenkamp Wuerzburg

Ewelina Hankiewicz Fordham Univesrsity

· Model Anderson Hamiltonian: (s - orbitals: conduction band; p - orbitals: valence band)

+ (Mn d - orbitals: strong on-site Hubbard int. →local moment)

+ (s,p - d hybridization)

· Semi-phenomenological Kohn-Luttinger model for heavy, light, and spin-orbit split-off band holes

· Local exchange coupling: Mn: S=5/2; valence-band hole: s=1/2; Jpd > 0

k.p ⊕ Local Moment - Hamiltonian

ELECTRONS

Mn

ELECTRONS-Mn

Large S: treat classically

Tc LIMITS AND STRATEGIES

Can we have high Tc in Diluted Magnetic Semicondcutors?

Define Mneff = Mnsub-MnInt!

(lines – theory, Masek et al 05)

NO EXTRINSIC LIMIT

Relative Mn concentrations obtained through hole density measurements and saturation moment densities measurements.

Tc linear in MnGa local (uncompensated) moment concentration; falls rapidly with decreasing hole density in heavily compensated samples.!

NO IDENTIFICATION OF AN INTRINSIC LIMIT

Qualitative consistent picture within LDA, TB, and k.p

8% Mn

Open symbols as grown. Closed symbols annealed

High compensation

Linear increase of Tc with Mneff = Mnsub-MnInt

Tc as grown and annealed samples

●  Concentration of uncompensated MnGa moments has to reach ~10%. Only 6.2% in the current record Tc=173K sample

●  Charge compensation not so important unless > 40%

●  No indication from theory or experiment that the problem is other than technological - better control of growth-T, stoichiometry

III = I + II → Ga = Li + Zn

GaAs and LiZnAs are twin SC!

Masek, et al. PRB (2006)!

LDA+U says that Mn-doped are also twin DMSs!

n and p type doping through Li/Zn stoichiometry!

No solubility limit for group-II Mn

substituting for group-II Zn !!!!

Indiana & California (‘03): “ .. Ohno’s ‘98 Tc=110 K is the fundamental upper limit ..” Yu et al. ‘03

California (‘08): “…Tc =150-165 K independent of xMn>10% contradicting Zener kinetic exchange ...”

Nottingham & Prague (’08): Tc up to 185K so far

“Combinatorial” approach to growth with fixed growth and annealing T’s

? Mack et al. ‘08

Tc limit in (Ga,Mn)As remains open