1. Ab initio calculation of magnetic exchange parameters
Mojtaba Alaei
Physics Department, Isfahan University of Technology
Quantum Simulation materials
TCCW 2019
27-28 Feb 2019  Chemistry Department, Isfahan University of Technology

2. Bird’s-eye view ab initio Spin polarized DFT Non-collinear DFT DFT+U
Experiment
Spin model Hamiltonian
Elastic neutron scattering ,
Inelastic neutron scattering,
Magnetic susceptibility,
Neel temperature,
Curie-weiss temperature,
...
Heisenberg term,
Bi-quadratic term,
Single-ion term,
...
Monte Carlo Simulation,
Spin-wave theory, ….

3. Model Hamiltonian and ab initio methods
Physics of a system
There are two strategies to get physics from Quantum mechanic of many electron systems:
One is to simplify H .i.e. to get rid non-relevant freedom to specific problem: for example Ising model:
One is to take account all freedom and use the complete
Hamiltonian. These methods are called ab initio:

4. ab initio
Spin polarized DFT
Non-collinear DFT
DFT+U
Experiment
Spin model Hamiltonian
Elastic neutron scattering ,
Inelastic neutron scattering,
Magnetic susceptibility,
Neel temperature,
Curie-weiss temperature,
...
Heisenberg term,
Bi-quadratic term,
Single-ion term,
...
Monte Carlo Simulation,
Spin-wave theory, ….

5. Mapping ab initio Hamiltonian to model Hamiltonian
The simple idea:
Using different electronic configurations to build model Hamiltonian
Pauli’s Principle:
An effective model Hamiltonian:

6. Heisenberg model J1 J2 J3

7. Extensions of Heisenberg Model
Biquadratic interaction:
4-spin exchange interaction:
Dzyaloshinsky-Moriya (DM) interaction:
Single-ion anisotropy: …

8. Mapping DFT total energy to Heisenberg model
An example: Sr2NiWO6

9. Mapping DFT total energy to Heisenberg model
Different magnetic configurations:

10. Mapping DFT total energy to Heisenberg model
DFT energy exchange parameters
-0.16
-0.12
-3.06
-3.45
Least square
method
(meV)
(meV)
(meV)
(meV)

11. ab initio
Spin polarized DFT
Non-collinear DFT
DFT+U
Experiment
Spin model Hamiltonian
Elastic neutron scattering ,
Inelastic neutron scattering,
Magnetic susceptibility,
Neel temperature,
Curie-weiss temperature,
...
Heisenberg term,
Bi-quadratic term,
Single-ion term,
...
Monte Carlo Simulation,
Spin-wave theory, ….

12. How to evaluate microscopic exchange parameters?
1-Transition Temperature
TN=54 K
C. G. F. Blum et al., Journal of Crystal Growth 421, 39 (2015)

13. How to evaluate microscopic exchange parameters?
2-Curie-Weiss temperature
Curie-Weiss law
-150
-100
-50
C. G. F. Blum et al., Journal of Crystal Growth 421, 39 (2015)

14. How to evaluate microscopic exchange parameters?
3-Inelastic neutron scattering
Y. Todate, Journal of Physics and Chemistry of Solids 60, 1173(1999).

15. How to calculate TN, ѲCW...from exchange parameters?
Using (Classical) Spin Monte Carlo (MC) Simulation
An illustration of MC simulation (T < TN) for J1 > 0:
N MC steps
MC step

16. ab initio
Spin polarized DFT
Non-collinear DFT
DFT+U
Experiment
Spin model Hamiltonian
Elastic neutron scattering ,
Inelastic neutron scattering,
Magnetic susceptibility,
Neel temperature,
Curie-weiss temperature,
...
Heisenberg term,
Bi-quadratic term,
Single-ion term,
...
Monte Carlo Simulation,
Spin-wave theory, ….

17. DFT+U
Local Density Approximation; LDA

18. DFT+U Achievements of LDA: Homogeneous Systems
Phys. Rev. Lett. 45, 1004, 1980

19. DFT+U Failures of LDA: Nonhomogeneous systems
CeO2 crystal with an oxygen vacancy
Int. J. Quantum Chem. 114, 14, 2014

20. DFT+U
Integer preference; delocalization vs. localization
”In a collection of separated objects, nature prefers to locate an integer number
of electrons on each object, and will do so except in the presence of unusual
degeneracies between two or more integer configurations.”
Advances in Quantum Chemistry, 21, 113 (1990)

21. DFT+U Integer preference; delocalization vs. localization
Science, 321, 792 (2008)

22. DFT+U
Mott insulator and Hubbard model

23. DFT+U Idea: Combination of DFT (LDA, GGA, …) with Hubbard model:
Delocalization
Localization
Repulsive potential
Attractive potential

24. DFT+U Delocalization (error) to localization (correction):
Int. J. Quantum Chem. 114, 14, 2014

25. ab initio
Spin polarized DFT
Non-collinear DFT
DFT+U
Experiment
Spin model Hamiltonian
Elastic neutron scattering ,
Inelastic neutron scattering,
Magnetic susceptibility,
Neel temperature,
Curie-weiss temperature,
...
Heisenberg term,
Bi-quadratic term,
Single-ion term,
...
Monte Carlo Simulation,
Spin-wave theory, ….

26. Tuning the Hubbard U U(eV) J1(meV) J1c(meV) J2(meV) J2c(meV) TN(K)
0.36
0.34
8.06
9.07
139 5
0.16
0.12
3.06
3.45 52 6
0.14
0.10
2.52
2.73 43 7
0.11
0.08
2.05
2.30 35
MC simulation
Exp: TN=54

27. ab initio
Spin polarized DFT
Non-collinear DFT
DFT+U
Experiment
Spin model Hamiltonian
Elastic neutron scattering ,
Inelastic neutron scattering,
Magnetic susceptibility,
Neel temperature,
Curie-weiss temperature,
...
Heisenberg term,
Bi-quadratic term,
Single-ion term,
...
Monte Carlo Simulation,
Spin-wave theory, ….

28. Still there is a magnetic entropy!
Snapshot of spin configuration at T=4 K
Anti-ferromagnetic

29. Bi-quadratic exchange interaction

30. Magnetic anisotropy

31. Spin-Spin correlation
There is no correlation

32. AFM-II or AFM-IIb?

33. Spin Hamiltonian and Magnetic Ordering of the Double Perovskite SrNiWO
To see more details:
Spin Hamiltonian and Magnetic Ordering of the Double Perovskite SrNiWO
Authors:
Nafise Rezaei, Tayebehsadat Hashemifar, Mojtaba Alaei, Farhad Shahbazi, S Javad Hashemifar, Hadi Akbarzadeh
arXiv:

34. Thank for your attention