Theory of Ca${}_{10}$Cr${}_7$O${}_{28}$ as a bilayer breathing-kagome magnet: Classical thermodynamics and semi-classical dynamics

Abstract

Ca${}_{10}$Cr${}_7$O${}_{28}$ is a novel spin-$1/2$ magnet exhibiting spin liquid behaviour which sets it apart from any previously studied model or material. However, understanding Ca${}_{10}$Cr${}_7$O${}_{28}$ presents a significant challenge, because the low symmetry of the crystal structure leads to very complex interactions, with up to seven inequivalent coupling parameters in the unit cell. Here we explore the origin of the spin-liquid behaviour in Ca${}_{10}$Cr${}_7$O${}_{28}$, starting from the simplest microscopic model consistent with experiment - a Heisenberg model on a single bilayer of the breathing-kagome (BBK) lattice. We use a combination of classical Monte Carlo (MC) simulation and (semi-)classical Molecular Dynamics (MD) simulation to explore the thermodynamic and dynamic properties of this model, and compare these with experimental results for Ca${}_{10}$Cr${}_7$O${}_{28}$. We uncover qualitatively different behaviours on different timescales, and argue that the ground state of Ca${}_{10}$Cr${}_7$O${}_{28}$ is born out of a slowly-fluctuating "spiral spin liquid", while faster fluctuations echo the U(1) spin liquid found in the kagome antiferromagnet. We also identify key differences between longitudinal and transverse spin excitations in applied magnetic field, and argue that these are a distinguishing feature of the spin liquid in the BBK model.

arXiv comment32 pages, 22 figures; two animation videos as supplementary files, see https://www.youtube.com/watch?v=GGug4w4MiKQ and https://www.youtube.com/watch?v=jSRF7MZTiNM

References in corpus (66)

• Anyons in an exactly solved model and beyond
• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• Quantum Spin Liquids
• Quantum Spin Liquid States
• Parallel Tempering: Theory, Applications, and New Perspectives
• Fractionalized excitations in the spin liquid state of a kagomé lattice antiferromagnet
• Spin Liquid State in an Organic Mott Insulator with Triangular Lattice
• Proximate Kitaev Quantum Spin Liquid Behaviour in α-RuCl${}_3$
• Z_2 Gauge Theory of Electron Fractionalization in Strongly Correlated Systems
• Pyrochlore Photons: The U(1) Spin Liquid in a S=1/2 Three-Dimensional Frustrated Magnet
• Models and Materials for Generalized Kitaev Magnetism
• Multiple-q states and skyrmion lattice of the triangular-lattice Heisenberg antiferromagnet under magnetic fields
• Weak magnetism and non-Fermi liquids near heavy-fermion critical points
• A Field Guide to Spin Liquids
• Properties of a classical spin liquid: the Heisenberg pyrochlore antiferromagnet
• Physics of the Kitaev model: fractionalization, dynamical correlations, and material connections
• Low-temperature properties of classical, geometrically frustrated antiferromagnets
• Variational study of triangular lattice spin-1/2 model with ring exchanges and spin liquid state in κ-(ET)_2 Cu_2 (CN)_3
• The "Coulomb phase" in frustrated systems
• Evidence for a Field-induced Quantum Spin Liquid in $\alpha$-RuCl${}_3$
• On the low energy properies of fermions with singular interactions
• 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
• Non-Fermi Liquid Fixed Point in 2+1 Dimensions
• Low Energy Dynamics of the Spinon-Gauge System
• Seeing the light : experimental signatures of emergent electromagnetism in a quantum spin ice
• Power-law spin correlations in pyrochlore antiferromagnets
• Gauge-invariant response functions of fermions coupled to a gauge field
• Spiral order by disorder and lattice nematic order in a frustrated Heisenberg antiferromagnet on the honeycomb lattice
• Physical realization of a quantum spin liquid based on a novel frustration mechanism
• Unusual liquid state of hard-core bosons on the pyrochlore lattice
• Octupolar ordering of classical kagome antiferromagnets in two and three dimensions
• Classical Spin Liquid: Exact Solution for the Infinite-Component Antiferromagnetic Model on the Kagomé Lattice
• Magnetoelastic excitations in the pyrochlore spin liquid Tb${}_2$Ti${}_2$O${}_7$
• Novel spin-liquid states in the frustrated Heisenberg antiferromagnet on the honeycomb lattice
• Quantum spin liquids in frustrated spin-1 diamond antiferromagnets
• Dynamical structure factor of the three-dimensional quantum spin liquid candidate NaCaNi${}_2$F${}_7$
• Absent pinch points and emergent clusters: further neighbour interactions in the pyrochlore Heisenberg antiferromagnet
• Nematic, vector-multipole, and plateau-liquid states in the classical O(3) pyrochlore antiferromagnet with biquadratic interactions in applied magnetic field
• Candidate quantum spin ice in the pyrochlore Pr${}_2$Hf${}_2$O${}_7$
• Comprehensive study of the dynamics of a classical Kitaev spin liquid
• Competing spin liquids and hidden nematic order in spin ice with frustrated transverse exchange
• The quantum origins of moment fragmentation in Nd2Zr2O7
• Spontaneous formation of a non-uniform chiral spin liquid in moat-band lattices
• Order and excitations in large-$S$ kagomé-lattice antiferromagnets
• Spin slush in an extended spin ice model
• Quantum spin ice with frustrated transverse exchange: from pi-flux phase to nematic quantum spin liquid
• Semi-classical spin dynamics of the antiferromagnetic Heisenberg model on the kagome lattice
• Magnetic excitations of the gapped quantum spin dimer antiferromagnet Sr${}_3$Cr${}_2$O${}_8$
• Ground-state selection and spin-liquid behaviour in the classical Heisenberg model on the breathing pyrochlore lattice
• Propagation and Ghosts in the Classical Kagome Antiferromagnet
• Novel phases in a square-lattice frustrated ferromagnet : 1/3-magnetisation plateau, helicoidal spin-liquid and vortex crystal
• Generic Spiral Spin Liquids
• Semiclassical dynamics of spin density waves
• When opposites repel: from metastability to extended chiral spin textures in spin ice with short-range topological-defect interactions
• Magnetic clustering, half-moons, and shadow pinch points as signals of a proximate Coulomb phase in frustrated Heisenberg magnets
• The magnetic Hamiltonian and phase diagram of the quantum spin liquid Ca10Cr7O28
• Clustering of Topological Charges in a Kagome Classical Spin Liquid
• Half moons are pinch points with dispersion
• Dynamic quantum kagome ice
• Crystal growth, structure and magnetic properties of Ca10Cr7O28
• Negative thermal expansion in the plateau state of a magnetically-frustrated spinel
• Semiclassical theory for liquid-like behaviour of the frustrated magnet ${\mathrm{Ca}}_{10}{\mathrm{Cr}}_7{\mathrm{O}}_{28}$
• The double life of electrons in magnetic iron pnictides, as revealed by NMR
• Signatures for spinons in the quantum spin liquid candidate Ca${}_{10}$Cr${}_7$O${}_{28}$
• Synthesis and pressure and field dependent magnetic properties of the Kagome-bilayer spin liquid Ca${}_{10}$Cr${}_7$O${}_{28}$

Cited by in corpus (22)

• Spiral spin-liquid on a honeycomb lattice
• Multifarious skyrmion phases on a trilayer triangular lattice
• Semi-classical simulation of spin-1 magnets
• Low energy structure of spiral spin liquids
• Skyrmion fluid and bimeron glass protected by a chiral spin liquid on a kagome lattice
• Curie-law crossover in spin liquids
• Spiral-spin-liquid behaviors and persistent reciprocal kagomé structure in frustrated van der Waals magnets and beyond
• Stability of Skyrmion Crystal Phase in Centrosymmetric Distorted Triangular-Lattice Antiferromagnets
• Line-Graph Approach to Spiral Spin Liquids
• Spiral spin liquid in a frustrated honeycomb antiferromagnet: A single-crystal study of GdZnPO
• Spiral Spin Liquid Noise
• Observation of the spiral spin liquid in a triangular-lattice material
• Magnetic properties of the spiral spin liquid and surrounding phases in the square lattice XY model
• Thermodynamics of the dipole-octupole pyrochlore magnet Ce${}_2$Hf${}_2$O${}_7$ in applied magnetic fields
• Giant Magnetocaloric Effect in a Honeycomb Spiral Spin-Liquid Candidate
• Classical spin models of the windmill lattice and their relevance for PbCuTe${}_2$O${}_6$
• Dynamic Spin-Lattice Coupling and Statistical Interpretation for the Molecular-Like Excitations in Frustrated Pyrochlores
• Finite temperature tensor network algorithm for frustrated two-dimensional quantum materials
• Pinch points and half moons encode Berry curvature
• Strong coupling of lattice and orbital excitations in quantum magnet Ca${}_{10}$Cr${}_7$O${}_{28}$: Anomalous temperature dependence of Raman phonons
• Codimension-Two Spiral Spin-Liquid in the Effective Honeycomb-Lattice Compound Cs${}_3$Fe${}_2$Cl${}_9$
• Origin of the intermediate-temperature magnetic specific heat capacity in the spin-liquid candidate Ca${}_{10}$Cr${}_7$O${}_{28}$