$ab$-$initio$ 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 review, we provide a basic introduction to such methods and the essential concepts of low-energy Hamiltonians, with a focus on their practical capabilities and limitations. We further discuss our recent efforts toward understanding a variety of complex magnetic systems that present unique challenges from the perspective of $ab$-$initio$ approaches.

arXiv commentSubmitted to the SFB/TRR49 special issue of Physica Status Solidi B

References in corpus (94)

• Anyons in an exactly solved model and beyond
• Maximally-localized generalized Wannier functions for composite energy bands
• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• Maximally-localized Wannier functions for entangled energy bands
• Quantum Spin Liquid States
• Magnetic Pyrochlore Oxides
• Correlated quantum phenomena in the strong spin-orbit regime
• Spin Liquid Ground State of the $S=1/2$ Kagome Heisenberg Model
• Fractionalized excitations in the spin liquid state of a kagomé lattice antiferromagnet
• Spin Liquid State in an Organic Mott Insulator with Triangular Lattice
• Spin Dynamics of the Spin-1/2 Kagome Lattice Antiferromagnet ZnCu_3(OH)_6Cl_2
• Relevance of the Heisenberg-Kitaev model for the honeycomb lattice iridates A_2IrO_3
• Spin-Orbit Physics Giving Rise to Novel Phases in Correlated Systems: Iridates and Related Materials
• Observation of the Magnon Hall Effect
• Generic spin model for the honeycomb iridates beyond the Kitaev limit
• Identifying Topological Order by Entanglement Entropy
• Models and Materials for Generalized Kitaev Magnetism
• Spin waves and revised crystal structure of honeycomb iridate Na2IrO3
• On the Origin of Zigzag Magnetic Order in Iridium Oxide Na2IrO3
• Challenges in Design of Kitaev Materials: Magnetic Interactions from Competing Energy Scales
• The monoclinic crystal structure of $\alpha$-RuCl${}_3$ and the zigzag antiferromagnetic ground state
• Calculations of Hubbard U from first-principles
• Scattering Continuum and Possible Fractionalized Excitations in $\alpha$-RuCl${}_3$
• Magnetic order in $\alpha$-RuCl${}_3$: a honeycomb lattice quantum magnet with strong spin-orbit coupling
• Quantum Spin Ice: A Search for Gapless Quantum Spin Liquids in Pyrochlore Magnets
• Physics of the Kitaev model: fractionalization, dynamical correlations, and material connections
• Quantum magnetism in the paratacamite family: towards an ideal kagome lattice
• Variational study of triangular lattice spin-1/2 model with ring exchanges and spin liquid state in κ-(ET)_2 Cu_2 (CN)_3
• Quantum Criticality: competing ground states in low dimensions
• Predicting the Spin-Lattice Order of Frustrated Systems from First-Principles
• Orbital order and fluctuations in Mott insulators
• Direct evidence of a zigzag spin chain structure in the honeycomb lattice: A neutron and x-ray diffraction investigation on single crystal $\mathrm{N}{\mathrm{a}}_2\mathrm{Ir}{\mathrm{O}}_3$
• Topological Magnon Insulator in Insulating Ferromagnet
• Quantum Criticality
• Hyper-honeycomb iridate $\beta$-Li2IrO3 as a platform for Kitaev magnetism
• Effect of magnetic frustration on nematicity and superconductivity in Fe chalcogenides
• Kitaev magnetism in honeycomb RuCl3 with intermediate spin-orbit coupling
• Quantum frustration in organic Mott insulators: from spin liquids to unconventional superconductors
• A spin-adapted Density Matrix Renormalization Group algorithm for quantum chemistry
• A new spin-anisotropic harmonic honeycomb iridate
• Kitaev interactions between j=1/2 moments in honeycomb Na2IrO3 are large and ferromagnetic: insights from ab initio quantum chemistry calculations
• Multiferroicity in an organic charge-transfer salt: Electric-dipole-driven magnetism
• Tight-binding models for the new iron based superconductor materials
• Quantum Kagome antiferromagnet ZnCu3(OH)6Cl2
• The kagome antiferromagnet: a chiral topological spin liquid ?
• Ab initio analysis of the tight-binding parameters and magnetic interactions in Na2IrO3
• Incommensurate Counterrotating Magnetic Order Stabilized by Kitaev Interactions in the Layered Honeycomb $\alpha$-Li${}_2$IrO${}_3$
• Orbital magnetic field effects in spin liquid with spinon Fermi sea: Possible application to $\kappa$-(ET)${}_2$Cu${}_2$(CN)${}_3$
• Anisotropic Spin Hamiltonians due to Spin-Orbit and Coulomb Exchange Interactions
• Tunable magnon Weyl points in ferromagnetic pyrochlores
• Multi-step approach to microscopic models for frustrated quantum magnets - the case of the natural mineral azurite
• Ordering in the pyrochlore antiferromagnet due to Dzyaloshinsky-Moriya interactions
• Scale-free antiferromagnetic fluctuations in the S=1/2 kagome antiferromagnet herbertsmithite
• Vanishing spin gap in a competing spin-liquid phase in the kagome Heisenberg antiferromagnet
• Ground-State Energy and Spin Gap of Spin-1/2 Kagome Heisenberg Antiferromagnetic Clusters: Large Scale Exact Diagonalization Results
• First-principles determination of Heisenberg Hamiltonian parameters for the spin-1/2 kagome antiferromagnet ZnCu3(OH)6Cl2
• Rods of Neutron Scattering Intensity in Yb2Ti2O7: Compelling Evidence for Significant Anisotropic Exchange in a Magnetic Pyrochlore Oxide
• Paramagnetism in the kagome compounds (Zn,Mg,Cd)Cu${}_3$(OH)${}_6$Cl${}_2$
• Extension of the spin-1/2 frustrated square lattice model: the case of layered vanadium phosphates
• Gapless chiral spin liquid in a kagome Heisenberg model
• Pressure-Tuned Exchange Coupling of a Quantum Spin Liquid in the Molecular Triangular Lattice $\kappa$-(ET)${}_2$Ag${}_2$(CN)${}_3$
• Modified kagome physics in the natural spin-1/2 kagome lattice systems - kapellasite Cu3Zn(OH)6Cl2 and haydeeite Cu3Mg(OH)6Cl2
• Valence-bond crystal in the extended kagome spin-1/2 quantum Heisenberg antiferromagnet: A variational Monte Carlo approach
• Anisotropic Magnetic Couplings and Structure-Driven Canted to Collinear Transitions in Spin-orbit Coupled Sr2IrO4
• CORE Technology and Exact Hamiltonian Real-Space Renormalization Group Transformations
• Renormalization group analysis of competing quantum phases in the J1-J2 Heisenberg model on the kagome lattice
• Spin Bose-Metal and Valence Bond Solid phases in a spin-1/2 model with ring exchanges on a four-leg triangular ladder
• Issues with J-dependence in the LSDA+U method for non-collinear magnets
• Spin-liquid versus spiral-order phases in the anisotropic triangular lattice
• Magnetic state of pyrochlore Cd2Os2O7 emerging from strong competition of ligand distortions and longer-range crystalline anisotropy
• Importance of Spin-Orbit Coupling in Organic BEDT-TTF and BEDT-TSF Salts
• Ab initio two-dimensional multiband low-energy models of EtMe_3Sb[Pd(dmit)_2]_2 and κ-(BEDT-TTF)_2Cu(NCS)_2 with comparisons to single-band models
• Haydeeite: a spin-1/2 kagome ferromagnet
• Spin wave spectrum of the quantum ferromagnet on the pyrochlore lattice Lu2V2O7
• Microscopic origin of isotropic non-Heisenberg behavior in highly correlated systems
• Frustration and Dzyaloshinsky-Moriya anisotropy in the kagome francisites Cu${}_3$Bi(SeO${}_3{)}_2$O${}_2$X
• Core -- a New Computational Technique for Lattice Systems
• Single-ion anisotropy, Dzyaloshinskii-Moriya interaction and negative magnetoresistance of the spin-1/2 pyrochlores R2V2O7
• Anions effects on the electronic structure and electrodynamic properties of the Mott insulator $\kappa$-(BEDT-TTF)${}_2$Ag${}_2$(CN)${}_3$
• Field-induced staggered magnetic moment in the quasi-two-dimensional organic Mott insulator $\kappa$-(BEDT-TTF)${}_2$Cu[N(CN)${}_2$]Cl
• What is the minimal model of magnetic interactions in Fe-based superconductors?
• One-dimensional spin liquid, collinear, and spiral phases from uncoupled chains to the triangular lattice
• Magnetism of CuX2 frustrated chains (X = F, Cl, Br): the role of covalency
• Quantum kagome antiferromagnet: ZnCu3(OH)6Cl2
• Spin liquid phase in the semiclassical theory of the Heisenberg model on an anisotropic triangular lattice with ring exchange
• A simplified method for the computation of correlation effects on the band structure of semiconductors
• Spin liquid phase due to competing classical orders in the semiclassical theory of the Heisenberg model with ring exchange on an anisotropic triangular lattice
• Orbital Ordering in ferromagnetic Lu2V2O7
• Effective Spin Couplings in the Mott Insulator of the Honeycomb Lattice Hubbard Model
• Computational Study of the Magnetic Structure of Na${}_2$IrO${}_3$
• Comparative study of DFT+$U$ functionals for non-collinear magnetism
• Ab initio determination of spin Hamiltonians with anisotropic exchange interactions: the case of the pyrochlore ferromagnet Lu${}_2$V${}_2$O${}_7$
• Specific heat of a one-dimensional interacting Fermi system: the role of anomalies
• Microscopic theory of Dzyaloshinsky-Moriya interaction in pyrochlore oxides with spin-orbit coupling

Cited by in corpus (21)

• TB2J: a python package for computing magnetic interaction parameters
• Electronic properties of α-RuCl3 in proximity to graphene
• Microscopic origin of magnetism in monolayer $3d$ transition metal dihalides
• Ab initio guided minimal model for the "Kitaev" material BaCo${}_2$(AsO${}_4$)${}_2$: Importance of direct hopping, third-neighbor exchange and quantum fluctuations
• Magnetic anisotropy reversal driven by structural symmetry-breaking in monolayer α-RuCl3
• Symmetry Conserving Maximally Projected Wannier Functions
• Origin of Magnetic Ordering in a Structurally-Perfect Quantum Kagome Antiferromagnet
• Negative-vector-chirality 120${}^{\circ }$ spin structure in the defect- and distortion-free quantum kagome antiferromagnet YCu${}_3$(OH)${}_6$Cl${}_3$
• Magnetoelastic coupling and effects of uniaxial strain in $\alpha$-RuCl${}_3$ from first principles
• Electronic and magnetic properties of the RuX${}_3$ (X=Cl, Br, I) family: Two siblings -- and a cousin?
• Signature of a randomness-driven spin-liquid state in a frustrated magnet
• Static and dynamical signatures of Dzyaloshinskii-Moriya interactions in the Heisenberg model on the kagome lattice
• Above-room-temperature ferromagnetism in ultrathin van der Waals magnet
• A $j_{\mathrm{eff}}=1/2$ Kitaev material on the triangular lattice: The case of NaRuO${}_2$
• Ferromagnetic kinetic exchange interaction in magnetic insulators
• $t$-$J$ model for strongly correlated two-orbital systems: Application to bilayer nickelate superconductors
• Magnetism and field-induced effects in the S = 5/2 honeycomb lattice antiferromagnet FeP3SiO11
• Breakdown of broken-symmetry approach to exchange interaction
• Is Herbertsmithite far from an ideal antiferromagnet? Ab-initio answer including in-plane Dzyaloshinskii-Moriya interactions and coupling with extra-plane impurities
• From Density Functional Theory to Spin Hamiltonians: Magnetism in $d^5$ Honeycomb Compound OsCl${}_3$
• Spin-orbit driven $J_{eff}=1/2$ magnetism in a d${}^7$ triangular-lattice monolayer cobaltate