Ab Initio Approaches for Low‐Energy Spin Hamiltonians

Abstract

Implicit in the study of magnetic materials is the concept of spin Hamiltonians, which emerge as the low‐energy theories of correlation‐driven insulators. In order to predict and establish such Hamiltonians for real materials, a variety of first principles ab initio methods have been developed, based on density functional theory and wavefunction methodologies. In this Feature Article, a basic introduction to such methods and the essential concepts of low‐energy Hamiltonians is provided, with a focus on their practical capabilities and limitations. Furthermore, recent efforts toward understanding a variety of complex magnetic systems that present unique challenges from the perspective of ab initio approaches are discussed.

Magnetoelastic coupling and effects of uniaxial strain in α−RuCl3 from first principles

“…For the exchange interactions J ij ( ), we first computed non-relativistic hopping parameters for each relaxed structure in non-spin-polarized configurations within GGA using Full Potential Local Orbital (FPLO) code [51]. Magnetic interactions were then estimated via exact diagonalization (ED) of the two-site five-orbital Hubbard Hamiltonian and projection of the low-energy states onto the j eff = 1/2 subspace [52,53]. Here, we considered both t 2g and e g orbitals explicitly, extending on previous approaches of some of the authors [53].…”

Origin of Magnetic Ordering in a Structurally Perfect Quantum Kagome Antiferromagnet

“…To understand the magnetism of YCu 3 ðOHÞ 6 Cl 3 , the first task is to determine its dominant isotropic exchange interactions. As in other kagome compounds [37][38][39][40], we tackle this problem using total-energy (broken-symmetry) DFT þ U calculations [41] (for details see Ref. [18]).…”

Ferromagnetic kinetic exchange interaction in magnetic insulators

“…Moreover, the AMOs have been used in the analysis of exchange interactions derived from first-principles calculations [5,[17][18][19]. The physics of Anderson's model lies in the basis of the derivation of exchange parameters through spin-unrestricted broken-symmetry density functional theory (DFT) widely employed nowadays [20][21][22][23][24]. The superexchange theory [1,6] has been extended to treat exchange interactions between orbitally degenerate sites [25][26][27][28][29], in the presence of spin-orbit coupling on the metal ions [30][31][32][33][34][35][36][37], and beyond the second-order perturbation theory after b, leading to biquadratic [6,30,38,39] and ring [40][41][42] exchange interactions.…”