1. , KITS, Beijing
　Numerical study of electron correlation effects in spintronic materials
Bo Gu (顾波)
Advanced Science Research Center (ASRC)
Japan Atomic Energy Agency (JAEA) 1 1 1

2. Self-introduction Dec. 1977 born in Hubei, China Education:
– Wuhan University, Bachelor
Peking University, M.S.
（Supervisor: 苏肇冰, Co-supervisors: 向涛, 王孝群，覃绍京）
Graduate University of Chinese Academy of Sciences, Ph.D.
（ Supervisor: 苏刚）
Employment:
– Tohoku University, Japan, Post-doc
(Supervisor: Sadamichi Maekawa)
– Japan Atomic Energy Agency, Post-doc
– Japan Atomic Energy Agency, Scientist (Permanent Staff)
– now Japan Atomic Energy Agency, Senior Scientist (Permanent Staff)

3. Outline
1. Introduction on diluted magnetic semiconductor (DMS)
2. DMS with wide band gap
3. DMS with narrow band gap
I am sorry to skip the part of spin Hall effect due to time limit.
I am happy to answer questions on spin Hall effect.

4. Spintronics Conventional electronic devices charge (e) electron
spin (μB)
Spintronic devices
Advantage:
Non-volatility (data are retained with power off)
Low electric power consumption
etc…

5. Diluted magnetic semiconductors (DMS)
e.g. GaAs
e.g. (Ga,Mn)As
Nonmagnetic semiconductors (charge)
Diluted magnetic semiconductors (charge + spin)
Classic DMS (Ga,Mn)As:
Curie Tc ~ 200 K.
(2)　p-type (hole) (Ga3+  Mn2+)
Challenges:
High Tc > Room Temperature
p-type (hole) & n-type (electron) (e.g. spin p-n junction)

6. A picture of ferromagnetism (FM) in DMS
Bulut PRB 76, (2007); Tomoda Physica B 404, 1159 (2009)
Host band gap △g = 2 eV
IBS: impurity bound state (split-off state)
~ 0.1 eV
Symmetric model at μ = △g/2 μ
Quantum Monte Carlo (QMC) method
Chemical potential μ = eV (metallic)  RKKY-type (Ruderman-Kittel-Kasuya-Yoshida)
impurity-host
impurity-impurity
β=1/T
impurity-impurity distance
impurity-host distance

7. Chemical potential μ = 0.1 eV (semiconductor)
 long-range FM
IBS: impurity bound state μ
impurity-host
impurity-impurity
Ferromagnetic
β=1/T
Antiferromagnetic
impurity-impurity distance
impurity-host distance
Impurity
Carrier-mediated ferromagnetism !
Host
IBS

8. IBS: impurity bound state ~ 0.1 eV Impurity-Impurity β=1/T
μ ~
Condition for FM
IBS
Bulut PRB 76, (2007)
Chemical potential μ (eV)
Hartree-Fock approximation
Spatial distribution of spin of host
Impurity
IBS
Host
effective mass of host
energy level of IBS
M. Ichimura et al, Proceedings of ISQM-Tokyo 2005, p ; cond-mat/

9. A picture of p-type ferromagnetism (FM) in DMS materials
FM in p-type DMS VB CB μ
p-type μ
n-type μ
Strong p-d mixing in VB  IBS near VB
Weak s-d mixing in CB  no IBS near CB
p-type: μ ~  FM
n-type: μ >>  No FM
IBS: impurity bound state (split-off state)
The picture for (Ga,Mn)As, (Zn,Mn)O, Mg(O,N), Li(Zn,Mn)P
wide band gap

10. DMS: Semiconductor host + Magnetic impurity
Carriers (electrons, holes)
Localized moment
VB: p-orbital; CB: s-orbital
Band structure
Ferromagnetism
Electron correlations
Density functional theory (DFT)
Quantum Monte Carlo (QMC)
Advantage of QMC
1. Treat electrons correlations correctly.
2. Not rely on separation between spin and charge fluctuations.

11. Anderson impurity model:
Our method for DMS
Anderson impurity model:
Host band
Mixing
Impurity level
 Density functional theory (DFT)
Coulomb correlations of impurity
 Quantum Monte Carlo (QMC) with Hirsch-Fye algorithm
DFT+QMC: Electron Correlations; Spin and Charge Fluctuations
Chemical potential μ: a free parameter, model p- or n-type carriers.
Occupation number of impurity
Magnetic correlations between impurities

12. Outline
1. Introduction on diluted magnetic semiconductor (DMS)
2. DMS with wide band gap
3. DMS with narrow band gap

13. Case 1: (Zn,Mn)O & Impurity bound state (IBS)
zincblend: ~ 0.1 eV
wurtzite: ~ 0.2 eV
wurtzite
(Shallow IBS)
(Local moment)2
zincblende
rocksalt
rocksalt: ~ 1.6 eV
IBS
IBS
(Deep IBS)
Band gap △g = 3.45 eV
Chemical potential μ (eV)
Gu, Bulut, Maeawa, J. Appl. Phys. 104, (2008). μ

14. Ferromagnetic (FM) correlation in (Zn,Mn)O
~0.2 eV
FM in p-type DMS VB CB
~0.1 eV
p-type μ
μ ~
Condition for FM
~1.6 eV
No FM
(Deep IBS)
Hartree-Fock result:
Mn-Mn distance (alattice)
Gu, Bulut, Maeawa, J. Appl. Phys. 104, (2008).

15. B. Debate on experiments
A. Many experiments declare high-temperature ferromagnetism in p-type (Zn,Mn)O
M. Ivill, et al., J. Appl. Phys. 97, (2005)
K. R. Kittilstved, et al., Nat. Mater. 5, 291 (2006)
J. R. Neal, et al., PRL 96, (2006)
B. Debate on experiments
Unexpected ferromagnetic materials (cluster etc.)
Nature of the experimentally
observed ferromagnetic signals
Intrinsic (Carrier-mediated) ferromagnetism
K. Ando, Science 312, 1883 (2006)
Our message on (Zn,Mn)O
It is possible to have intrinsic ferromagnetism in (Zn,Mn)O.
We predict that zincblende structure (stable in thin film) is better than wurtzite structure (most common phase) in terms of FM.
Gu, Bulut, Maeawa, J. Appl. Phys. 104, (2008).

16. Case 2: New generation 111-type DMS
(Ga3+, Mn2+)As
111-type
Li1+x(Zn2+, Mn2+)As
Li1+x(Zn2+, Mn2+)P
Hole & Spin
Hole/Electron
Spin
Independently dope charge and spin !
Experiments on 111-type DMS
Li(Zn,Mn)As
Tc ~ 50 K, P-type, Band gap = eV
Z. Deng et al, Nat. Commun. 2, 422 (2011)
Li(Zn,Mn)P
Tc ~ 36 K, P-type, Band gap ~ 2 eV
Z. Deng et al, PRB 88, (R) (2013).

17. Ferromagnetic (FM) correlations in Li(Zn,Mn)P
Impurity bound state (IBS).
Impurity-Impurity FM coupling
Occupation number (Mn)
~ 0 eV
IBS
Chemical potential μ (eV)
Mn-Mn distance (alattice)
Reasonable p-type μ
FM in p-type DMS VB CB μ
p-type μ

18. How to obtain n-type DMS ?
DMS with wide band gap
FM in p-type DMS
IBS: impurity bound state VB CB μ
p-type μ
n-type μ
Our idea: DMS with narrow band gap
FM in p & n-type DMS VB CB μ
p-type μ
n-type μ

19. Outline
1. Introduction on diluted magnetic semiconductor (DMS)
2. DMS with wide band gap
3. DMS with narrow band gap

20. FM in n-type (electron)
Good materials to check our idea: 　
122-type DMS: Mn-doped BaZn2As2
FM in p-type (hole)
FM in n-type (electron)
(Ba2+,K+)(Zn,Mn)2As2　　　　　Tc ~ 230 K
K. Zhao et al, Nat. Commun. (2013) ; Chin. Sci. Bull. (2014).
Ba(Zn,Mn,Co)2As2 Tc ~ 80 K
H. Man et al, arXiv (2014)
BaZn2As2 : Gap = 0.2 eV
 Mn-doped BaZn2As2 and BaZn2Sb2 !
BaZn2As2　(I4/mmm)
Gap = 0.2 eV
BaZn2Sb2　(Pnma)
Gap = 0.2 eV

21. Density of state (Mn-3d)
Case 1: Ba(Zn,Mn)2As2 VB CB
Density of state (Mn-3d)
IBS
IBS
IBS
Chemical potential μ (eV)
ARPES: H. Suzuki et al, PRB 92, (2015).
p-type μ
n-type μ

22. Ferromagnetic (FM) correlation in Ba(Zn,Mn)2As2
P-type
Long-range FM (larger <M1M2>)
Tc (exp) ~ 230 K
N-type
Long-range FM (smaller <M1M2>)
Tc (exp) ~ 80 K
Mn-Mn distance (Å)
Gu and Maekawa, PRB 94, (2016)

23. A simple estimation of exchange coupling J12 by <M1M2>
Ferromagnetic
Antiferromagnetic
Gu, Ziman, Maekawa, PRB 79, (2009)

24. Case 2: Ferromagnetic (FM) correlation in Ba(Zn,Mn)2Sb2
P-type
Long-range FM
Mn-Mn distance (Å)
p-type
FM ＜M1M2＞ (2nd n.n.)
FM range Tc
Mn in BaZn2As2
~ 0.08
~ 6 Å
230 K (Zhao, 2014)
Mn in BaZn2Sb2
~ 0.14
~ 10 Å
> 230 K (expected)
Gu and Maekawa, PRB 94, (2016)

25. Case 3: Cr vs. Mn impurities in BaZn2As2VB CB
Impurity bound state (IBS)
Cr: bottom of CB
Mn: top of VB
Density of state (3d)
IBS(Mn)
IBS(Cr)
N-type FM:
Cr : more promising
Chemical potential μ (eV)
Impurity level : Ed (Mn2+: d5) < Ed (Cr2+: d4) < EF  IBS(Mn) < IBS (Cr)
AIP Advances 7, (2017).

26. Summary of diluted magnetic semiconductor (DMS)
FM in p-type DMS
Found ferromagnetic (FM) correlations in some DMSs with wide band gap. Clarify the controversial experiments. VB CB
(Zn,Mn)O, Mg(O,N)
Contributed to a new promising direction
IBS: impurity bound state
Li(Zn,Mn)As, Li(Zn,Mn)P
p-type μ
n-type μ
Proposed a way to realize p- and n-type DMS: Narrow band gap.
FM in p & n-type DMS
Consistent with exp. in Ba(Zn,Mn)2As2 VB CB
Predict p- and n-type FM in Ba(Zn,Cr)2As2
Predict high Tc (> 230K) in Ba(Zn,Mn)2Sb2
p-type μ
n-type μ

27. Outlook & Future Conduction electrons Localized electrons
Electron correlations
Band structure
Density functional theory (DFT)
Quantum Monte Carlo (QMC)
DFT + QMC method: Useful in a wide range of materials !

28. Acknowledgments (Diluted Magnetic Semiconductor)
Theories:
S. Maekawa (ASRC, JAEA)
N. Bulut (Izmir Inst. Tec.): QMC, (Zn,Mn)O
T. Ziman (Inst. Laue Langevin): Mg(O,N)
J. Ohe (Toho U): (Ga,Mn)As
Experiments:
F. L. Ning（宁凡龙）(Zhejiang U)（浙大）: n-type Ba(Zn,Mn)2As2
C. Q. Jin （靳常青）(IOP, CAS)（物理所）: Li(Zn,Mn)As, Ba(Zn,Mn)2As2
A. Fujimori (U Tokyo): ARPES
Y. J. Uemura (Columbia U): muSR, organization

29. Thank you very much !