Degenerate manifolds, helimagnets, and multi-$\mathbf{Q}$ chiral phases in the classical Heisenberg antiferromagnet on the face-centered-cubic lattice

Abstract

We present a detailed study of the ground state phase diagram of the classical frustrated Heisenberg model on the face-centered-cubic lattice. By considering exchange interactions up till third nearest neighbors, we find commensurate, helimagnetic, as well as noncollinear multi-{\bf Q} orders which include noncoplanar and chiral spin structures. We reveal the presence of subextensively degenerate manifolds that appear at triple points and certain phase boundaries in the phase diagram. Within these manifolds, the spin Hamiltonian can be recast as a complete square of spins on finite motifs, permitting us to identify families of exact ground state spin configurations in real space -- these include randomly stacked ferro- or antiferromagnetically ordered planes and interacting ferromagnetic chains, among others. Finally, we critically investigate the ramifications of our findings on the example of the Ising model, where we exactly enumerate all the states numerically for finite clusters.

arXiv comment26 pages, 10 figures, 10 tables, small corrections and clarifications

References in corpus (39)

• Properties of a classical spin liquid: the Heisenberg pyrochlore antiferromagnet
• Low-temperature properties of classical, geometrically frustrated antiferromagnets
• Nematic order in square lattice frustrated ferromagnets
• Order by disorder and spiral spin liquid in frustrated diamond lattice antiferromagnets
• An investigation of the quantum $J_1-J_2-J_3$ model on the honeycomb lattice
• Spiral order by disorder and lattice nematic order in a frustrated Heisenberg antiferromagnet on the honeycomb lattice
• Lattice symmetries and regular states in classical frustrated antiferromagnets
• Spiral spin-liquid and the emergence of a vortex-like state in MnSc${}_2$S${}_4$
• Finite temperature properties and frustrated ferromagnetism in a square lattice Heisenberg model
• Possible chiral phase transition in two-dimensional solid ${}^3$He
• Octupolar ordering of classical kagome antiferromagnets in two and three dimensions
• Evidence for a three-dimensional quantum spin liquid in PbCuTe${}_2$O${}_6$
• Quantum and Classical Phases of the Pyrochlore Heisenberg Model with Competing Interactions
• Twelve sublattice ordered phase in the J1-J2 model on the kagome lattice
• Functional renormalization group for three-dimensional quantum magnetism
• Nematic, vector-multipole, and plateau-liquid states in the classical O(3) pyrochlore antiferromagnet with biquadratic interactions in applied magnetic field
• Ground State of a Spin System with Two- and Four-spin Exchange Interactions on the Triangular Lattice
• The frustrated spin-1/2 J1-J2 Heisenberg ferromagnet on the square lattice: Exact diagonalization and Coupled-Cluster study
• SU(2) slave-boson formulation of spin nematic states in S=1/2 frustrated ferromagnets
• Spin-orbit entangled j=1/2 moments in Ba${}_2$CeIrO${}_6$ -- a frustrated fcc quantum magnet
• Intertwined nematic orders in a frustrated ferromagnet
• Stability of the spiral spin liquid in MnSc${}_2$S${}_4$
• Quantum stabilization of classically unstable plateau structures
• Novel phases in a square-lattice frustrated ferromagnet : 1/3-magnetisation plateau, helicoidal spin-liquid and vortex crystal
• Phase diagram of the spin-1/2 $J_1$-$J_2$-$J_3$ Heisenberg model on the square lattice
• Of chain-based order and quantum spin liquids in dipolar spin ice
• Classical spiral spin liquids as a possible route to quantum spin liquids
• Monte Carlo study of first-order transition in Heisenberg fcc antiferromagnet
• Projective studies of spin nematics in a quantum frustrated ferromagnet
• Order by quenched disorder in the model triangular antiferromagnet RbFe(MoO4)2
• Three-Dimensional Crystallization of Vortex Strings in Frustrated Quantum Magnets
• Classical Spin Spirals in Frustrated Magnets from Free-Fermion Band Topology
• Quantum paramagnetism and helimagnetic orders in the Heisenberg model on the body centered cubic lattice
• Quantum disordered insulating phase in the frustrated cubic-lattice Hubbard model
• Magnon spectrum of the Weyl semimetal half-Heusler compound GdPtBi
• Affine lattice construction of spiral surfaces in classical Heisenberg models
• Projective symmetry group classifications of quantum spin liquids on the simple cubic, body centered cubic, and face centered cubic lattices
• Intrinsic peculiarities of real material realizations of a spin-1/2 kagome lattice
• Frustrated Heisenberg Antiferromagnets on Cubic Lattices: Magnetic Structures, Exchange Gaps, and Non-Conventional Critical Behaviour

Cited by in corpus (26)

• Multiloop functional renormalization group approach to quantum spin systems
• Spiral spin-liquid on a honeycomb lattice
• Generic Spiral Spin Liquids
• Low energy structure of spiral spin liquids
• Non-Coplanar Magnetic Orders in Classical Square-Kagome Antiferromagnets
• Ground state selection by magnon interactions in the fcc antiferromagnet
• Antiferromagnetic resonance in the cubic iridium hexahalides (NH${}_4$)${}_2$IrCl${}_6$ and K${}_2$IrCl${}_6$
• Anisotropic spin model and multiple-$Q$ states in cubic systems
• Stability of Skyrmion Crystal Phase in Centrosymmetric Distorted Triangular-Lattice Antiferromagnets
• Anisotropic exchange and non-collinear antiferromagnets on a noncentrosymmetric fcc structure as in the half-Heuslers
• Hierarchical excitations from correlated spin tetrahedra on the breathing pyrochlore lattice
• Line-Graph Approach to Spiral Spin Liquids
• Helical superfluid in a frustrated honeycomb Bose-Hubbard model
• Competing orders in a frustrated Heisenberg model on the Fisher lattice
• Complex magnetic phase diagram with a small phase pocket in a three-dimensional frustrated magnet CuInCr${}_4$S${}_8$
• Spin-orbital-lattice entanglement in the ideal j=1/2 compound K${}_2$IrCl${}_6$
• Pulling order back from the brink of disorder: Observation of a nodal line spin liquid and fluctuation stabilized order in K${}_2$IrCl${}_6$
• Classical spin models of the windmill lattice and their relevance for PbCuTe${}_2$O${}_6$
• Disordered ground state in the three-dimensional face-centred frustrated spin-$\frac{5}{2}$ system MnSn(OH)${}_{\text{6}}$
• Spin-orbital order and excitons in magnetoresistive HoBi
• Double-$Q$ and quadruple-$Q$ instabilities at low-symmetric ordering wave vectors under tetragonal symmetry
• Fully-frustrated octahedral antiferromagnets: emergent complexity in external field
• Collinear Magnetic Structure in the Diamond Network Magnet EuTi${}_2$Al${}_{20}$
• Frustrated magnets in the limit of infinite dimensions: dynamics and disorder-free glass transition
• L-point quadrupole order under magnetic field in cubic PrIr${}_2$Zn${}_{20}$
• Codimension-Two Spiral Spin-Liquid in the Effective Honeycomb-Lattice Compound Cs${}_3$Fe${}_2$Cl${}_9$