Prospecting chiral multi-site interactions in prototypical magnetic systems

Abstract

Atomistic spin models have found enormous success in addressing the properties of magnetic materials, grounded on the identification of the relevant underlying magnetic interactions. The huge development in the field of magnetic skyrmions and other noncollinear magnetic structures is largely due to our understanding of the chiral Dzyaloshinskii-Moriya interaction. Recently, various works have proposed new types of chiral interactions, with seemingly different forms, but the big picture is still missing. Here, we present a systematic construction of a generalized spin model containing isotropic and chiral multi-site interactions. These are motivated by a microscopic model that incorporates local spin moments and the spin-orbit interaction, and their symmetry properties are established. We show that the chiral interactions arise solely from the spin-orbit interaction and that the multi-site interactions do not have to follow Moriya's rules, unlike the Dzyaloshinskii-Moriya and chiral biquadratic interactions. The chiral multi-site interactions do not vanish due to inversion symmetry, and comply with a generalized Moriya rule: If all sites connected by the interaction lie in the same mirror plane, the chiral interaction vector must be perpendicular to this plane. We then illustrate our theoretical considerations with density functional theory calculations for prototypical magnetic systems. These are triangular trimers built out of Cr, Mn, Fe and Co adatoms on the Re(0001), Pt(111) and Au(111) surfaces, for which $C_{3v}$ symmetry applies, and Cr and Fe square tetramers on Pt(001) with $C_{4v}$ symmetry. The multi-site interactions are substantial in magnitude and cannot be neglected when comparing the energy of different magnetic structures. Finally, we discuss the recent literature in light of our findings, and clarify several unclear or confusing points.

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References in corpus (32)

• Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials
• Restoring the density-gradient expansion for exchange in solids and surfaces
• Generalized gradient approximation for solids and their surfaces
• Advanced capabilities for materials modelling with Quantum ESPRESSO
• Anyons in an exactly solved model and beyond
• Advances in the Physics of Magnetic Skyrmions and Perspective for Technology
• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• Quantum Spin Liquids
• Skyrmion lattice with a giant topological Hall effect in a frustrated triangular-lattice magnet
• Spin waves and electronic interactions in La2CuO4
• Incommensurate magnetic order in the alpha-Fe(Te,Se) superconductor systems
• First-order magnetic and structural phase transitions in Fe${}_{1+y}$Se${}_x$Te${}_{1-x}$
• Nanometric square skyrmion lattice in a centrosymmetric tetragonal magnet
• Effective bilinear-biquadratic model for noncoplanar ordering in itinerant magnets
• Real-space observation of short-period cubic lattice of skyrmions in MnGe
• Possible Kitaev Quantum Spin Liquid State in 2D Materials with S=3/2
• Anisotropic Spin Hamiltonians due to Spin-Orbit and Coulomb Exchange Interactions
• Topological-chiral magnetic interactions driven by emergent orbital magnetism
• Microscopic origin of Heisenberg and non-Heisenberg exchange interactions in ferromagnetic bcc Fe
• Systematic derivation of realistic spin-models for beyond-Heisenberg solids
• Magnetic hedgehog lattices in noncentrosymmetric metals
• Atomistic spin-model based on a new spin-cluster expansion technique: Application to the IrMn3/Co interface
• The chiral biquadratic pair interaction
• Discovery of magnetic single- and triple-Q states in Mn/Re(0001)
• Extension of the standard Heisenberg Hamiltonian to multispin exchange interactions
• Competition of Dzyaloshinskii-Moriya and higher-order exchange interactions in Rh/Fe atomic bilayers on Ir(111)
• Trends in the magnetic properties of Fe, Co and Ni clusters and monolayers on Ir(111), Pt(111) and Au(111)
• First principles calculation of spin-interactions and magnetic ground states of Cr trimers on Au(111)
• Magnetic structure of monatomic Fe chains on Re(0001): emergence of chiral multi-spin interactions
• Metamagnetic texture in a polar antiferromagnet
• Mapping the magnetic exchange interactions from first principles: Anisotropy anomaly and application to Fe, Ni, and Co
• Stabilizing spin systems via symmetrically tailored RKKY interactions

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• Stabilization mechanisms of magnetic skyrmion crystal and multiple-$Q$ states based on momentum-resolved spin interactions
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• Mechanism of antisymmetric spin polarization in centrosymmetric multiple-$Q$ magnets based on bilinear and biquadratic spin cross products
• Multifarious skyrmion phases on a trilayer triangular lattice
• Short period magnetization texture of B20-MnGe explained by thermally fluctuating local moments
• Proper and improper chiral magnetic interactions
• Trends of higher-order exchange interactions in transition-metal trilayers
• Square skyrmion crystal in centrosymmetric systems with locally inversion-asymmetric layers
• Magnons in antiferromagnetic bcc-Cr and Cr${}_2$O${}_3$ from time-dependent density functional theory
• Exchange constants for local spin Hamiltonians from tight-binding models
• Higher order exchange driven noncoplanar magnetic state and large anomalous Hall effects in electron doped kagome magnet Mn${}_3$Sn
• Reply to 'Comment on "Proper and improper chiral magnetic interactions" '
• Phase Coexistence of Mn Trimer Clusters and Antiferromagnetic Mn Islands on Ir(111)
• Topologically-driven three-spin chiral exchange interactions treated from first principles
• Robust Wannierization including magnetization and spin-orbit coupling via projectability disentanglement
• Unraveling the connection between high-order magnetic interactions and local-to-global spin Hamiltonian in non-collinear magnetic dimers
• Generalization of the Landau-Lifshitz-Gilbert equation by multi-body contributions to Gilbert damping for non-collinear magnets
• Adiabatic spin dynamics and effective exchange interactions from constrained tight-binding electronic structure theory: Beyond the Heisenberg regime