Ab initio calculation of magnetic exchange parameters Mojtaba Alaei Physics Department, Isfahan University of Technology Quantum Simulation materials https://qsm.iut.ac.ir/ TCCW 2019 27-28 Feb 2019  Chemistry Department, Isfahan University of Technology

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, ….

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:

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, ….

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:

Heisenberg model J1 J2 J3

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

Mapping DFT total energy to Heisenberg model An example: Sr2NiWO6

Mapping DFT total energy to Heisenberg model Different magnetic configurations:

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)

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, ….

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)

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)

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

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

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, ….

DFT+U Local Density Approximation; LDA

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

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

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)

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

DFT+U Mott insulator and Hubbard model

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

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

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, ….

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

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, ….

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

Bi-quadratic exchange interaction

Magnetic anisotropy

Spin-Spin correlation There is no correlation

AFM-II or AFM-IIb?

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:1806.09395 https://arxiv.org/abs/1806.09395

Thank for your attention