First-principles materials design forsemiconductor spintronics
Application of MACHIKANEYAMA
to materials design

K. Sato, Osaka Univ.
CMD35 workshop
3, Sep. 2019. Osaka Univ. Toyonaka

OUTLINE¢ Introduction

Spintronics, dilute magnetic semiconductors (DMS) Why we need MACHIKANEYAMA ?
Disordered systems¢ Finite temperature magnetism¢¢ Dilute magnetic semiconductors

Origin of the ferromagnetism in DMS
 Magnetic interactions in DMS
 Practical and accurate TC calculation for DMS
 Why high-TC is so difficult ?
¢ Inhomogeneity in DMS
K. Sato et al.,First-principles theory of dilute magnetic semiconductors, Rev. Mod. Phys., 82 (2010) 1633.
T. Dietl et al.,Spinodal nanodecomposition in semiconductors doped with magnetic impurities, Rev. Mod. Phys. 87 (2015) 1311.

SPINTRONICS AND DILUTE MAGNETICSEMICONDUCTORS(Ga, Mn)As
Se-hn¢ Dilute magnetic semiconductor (DMS)¢ Carrier induced ferromagnetism(In, Mn)As; TC = 60 (K)¢ (Ga, Mn)As; TC = 190 (K)¢‘Properties of ferromagnetic III-V semiconductors’
H. Ohno, J. Magn. Magn. Matt. 200 (1999) 110.

ELECTRIC-FIELD CONTROL OF
FERROMAGNETISM IN (In, Mn)As‘Electric-field control of ferromagnetism’
H. Ohno et al. Nature 408 (2000) 944.

ELECTRICAL SPIN INJECTION

Y. Ohno et al., ‘Electrical spin injection
in a ferromagnetic semiconductor
heterostructure’,
Nature 402 (1999) 790.

APPLICATION TO REAL MATERIALS¢ Crystal:

Translation symmetry
 Band structure¢ Alloying and doping

Magnetic impurities occupy
cation sites randomly.
 p-type or n-type carrierdoping¢ Magnetic disorderIn the paramagnetic state,magnetic moments arerandomly oriented.

Coherent potential
approximation (CPA)APPLICATION TO DMS SYSTEMS¢ Local spin density approximation (LSDA)¢ Korringa-Kohn-Rostoker method (KKR)¢ Coherent-potential-approximation (CPA)èMACHIKANEYAMA2002 by Akai

http://kkr.issp.u-tokyo.ac.jp/jp/

Disordered local moment stateDTCMFA OF Mn-DOPED III-V DMS(Ga, Mn)N; Tc ~ √c(Ga, Mn)Sb; Tc ~ cElectronic structure¢ Origin of theferromagnetism
 double exchange p-d exchange

K. Sato et al., J. Phys. Cond. Matt. 16 (2004) S5491

ELECTRONIC STRUCTURE OF
III-V+Mn DMS
K. Sato et al.,Impurity bandin the gap → double exchange

J. Phys. Cond. Matt. 16 (2004) S5491

Localized d-states
below valence band → p-d exchange

FERROMAGNETISM IN DMSCALCULATION OF EXCHANGE
INTERACTIONSJij: exchange interaction
ei: direction of the moment

EXCHANGE INTERACTIONS IN
K. Sato et al., PRB 70 (2004)201202
DMS double exchange system (Ga, Mn)N → strong, but short-range interactions
 p-d exchange system (Ga, Mn)Sb → weak, but long-range interactions

MAGNETIC PERCOLATION PROBLEML. Bergqvist et al. PRL (2004)
K. Sato et al., PRB 70 (2004)201202

D. Stauffer and A. Aharony,‘Introduction to Percolation Theory’
Taylor & Francis, London, 1994

                NEAREST NEIGHBOR HEISENBERGMODEL                

MONTE CARLO SIMULATION

K. Binder and D. W. Heermann,‘Monte Carlo simulation in statistical Physics’
Berlin, Springer, 1992

Exact TC values taking disorder effect fully into accountTC BY MONTE CARLO

L. Bergqvist et al., PRL (2004)
K. Sato et al., PRB 70 (2004)201202,
T. Fukushima et al., JJAP 43 (2004) L1416

Reasonable agreement with experiments.
For low concentration, high-TC can not be expected.(magnetic percolation)
Origin of high-TC phases → Inhomogeneity

OUTLINE¢ Introduction

Spintronics, dilute magnetic semiconductors (DMS) Why we need MACHIKANEYAMA ?
Disordered systems¢ Finite temperature magnetism¢¢ Dilute magnetic semiconductors

Origin of the ferromagnetism in DMS
 Magnetic interactions in DMS
 Practical and accurate TC calculation for DMS
 Why high-TC is so difficult ? … magnetic percolation¢ Inhomogeneity in DMS
K. Sato et al.,First-principles theory of dilute magnetic semiconductors, Rev. Mod. Phys., 82 (2010) 1633.
T. Dietl et al.,Spinodal nanodecomposition in semiconductors doped with magnetic impurities, Rev. Mod. Phys. 87 (2015) 1311.

INHOMOGENEOUS IMPURITY DISTRIBUTION IN
Review: A. Bonnani,DMS
Semicond. Sci. Technol. 22 (2007) R41((%(((Gu et al., JMMM 290-291(2005)1395.

((%) %((%) () %(%Singh et al.,APL 86(2005)12504

SELF-ORGANIZED NANO-COLUMN IN
GeMn¢ Mn-doped Ge¢ MBE crystal growth¢ TEM, EELS analysis¢ Average: Mn = 6%
¢ Self-organized nano-column

3nm diameter 10nm interval Mn concentration ~ 35%¢ TC > 400 K

M. Jamet et al., Nature materials 5 (2006) 653
T. Devillers et al., PRB 76 (2007) 205306

GENERALIZED PERTURBATIONMETHOD
Ducastelle and Gautier: ‘Generalized perturbation method’J. Phys. F6 (1976) 2039

Turchi et al., PRL 67 (1991) 1779.

EFFECTIVE PAIR INTERACTIONSK. Sato et al., JJAP 44 (2005) L948,IN DMS
45 (2006) L 416

Effective attractive interactions
between nearest neighbors→ phase separation✿ Similar results✿–––

M. van Schilfgaarde et al., PRB 63 (2001)
233205
H. Raebiger et al., JMMM 290-291 (2005)
1398
J. Osorio-Guillen et al., PRB 74 (2006) 35305

LAYER BY LAYER GROWTHCONDITION

T. Fukushima et al.,Jpn. J. Appl. Phys. 45 (2006) L416

¢ Quasi-one dimensional structure due to the spinodal nano-decomposition under the layer-by-layer growth condition¢ Large clusters for low concentrations

LAYER BY LAYER GROWTH SIMULATION(Zn, Cr)Te, Cr 5%

T. Fukushima et al., Jpn. J. Appl. Phys. 45 (2006) L416
¢ Spinodal nano-decomposition in 3D
Small clusters
 No percolation
 Super paramagnetism¢ Layer-by-layer

condition

One dimensional
fragments
 Large clusters
 Large blocking
temperature(Ga, Mn)N, Mn 5%

SUPER-PARAMAGNETIC BLOCKING
PHENOMENA
Finite relaxation time to flip themagnetization due to the energy
barrier caused by the anisotropy→ Hysteretic behavior

K. Sato et al., Jpn. J. Appl. Phys. 46 (2007) L682

D. A. Dimitrov et al.,
PRB 54 (1996) 9237

K: Anisotropy, V: volume,
M: moment, B: external field¢ Hysteresis¢ Anisotropy constant → parameter

SIMULATION OF BLOCKING PHENOMENAIN DMS
K. Sato et al., Jpn. J. Appl. Phys. 46 (2007) L682

¢ Homogeneous distributionAbove TC → no hysteresis¢ Large cluster → ferromagnetic behavior at hightemperature

SUMMARY¢ Application of MACHIKANEYAMA to DMSDisordered state … KKR-CPAFinite temperature magnetism→ DLM state, Mapping on Heisenberg model¢ Ferromagnetism in DMS

Impurity band in the gap→ double exchange → short range interaction
 Localized moment→ p-d exchange → long range interaction
 Low concentration, Low TC (Magnetic percolationproblem)¢ Inhomogeneous DMSPhase separation in DMS
Super-paramagnetism, blocking phenomena