Coarsening dynamics of Ising-nematic order in a frustrated Heisenberg antiferromagnet

Abstract

We study the phase ordering dynamics of the classical antiferromagnetic $J_1$-$J_2$ (nearest-neighbor and next-nearest-neighbor couplings) Heisenberg model on the square lattice in the strong frustration regime ($J_2/J_1>1/2$). While thermal fluctuations preclude any long-range magnetic order at finite temperatures, the system exhibits a long-range spin-driven nematic phase at low temperatures. The transition into the nematic phase is further shown to belong to the two-dimensional Ising universality class based on the critical exponents near the phase transition. Our large-scale stochastic Landau-Lifshitz-Gilbert simulations find a two-stage phase ordering when the system is quenched from a high-temperature paramagnetic state into the nematic phase. In the early stage, collinear alignments of spins lead to a locally saturated Ising-nematic order. Once domains of well-defined Ising order are developed, the late-stage relaxation is dominated by curvature-driven domain coarsening, as described by the Allen-Cahn equation. The characteristic size of Ising-nematic domains scales as the square root of time, similar to the kinetic Ising model described by the time-dependent Ginzburg-Landau theory. Our results confirm that the late-stage ordering kinetics of the spin-driven nematic, which is a vestigial order of the frustrated Heisenberg model, belongs to the dynamical universality class of a non-conserved Ising order. Interestingly, the system shows no violation of the superuniversality hypothesis under weak bond disorder. The dynamic scaling invariance is preserved in the presence of weak bond disorder. We also discuss possible applications of our results to materials for which vestigial Ising-nematic order is realized.

13 pages, 13 figures

References in corpus (22)

• Evidence for an electron nematic phase transition in underdoped iron pnictide superconductors
• Strong Correlations and Magnetic Frustration in the High Tc Iron Pnictides
• Theory of Electron Nematic Order in LaOFeAs
• Ising and Spin orders in Iron-based Superconductors
• Pairing Symmetry in a Two-Orbital Exchange Coupling Model of Oxypnictides
• Ironing out the details of unconventional superconductivity
• Plaquette valence bond solid in the frustrated Heisenberg quantum antiferromagnet on the square lattice
• Ground-state phases of the spin-1/2 J_1-J_2 Heisenberg antiferromagnet on the square lattice: A high-order coupled cluster treatment
• Domain growth morphology in curvature driven two dimensional coarsening
• Crossover in Growth Law and Violation of Superuniversality in the Random Field Ising Model
• Semiclassical dynamics of spin density waves
• Where is the Quantum Spin Nematic?
• Langevin dynamics of generalized spins as SU($N$) coherent states
• Coarsening in inhomogeneous systems
• Nematic state in CeAuSb${}_2$
• Dimensionality crossover to 2D vestigial nematicity from 3D zigzag antiferromagnetism in an XY-type honeycomb van der Waals magnet
• Photoinduced ultrafast dynamics of local nematicity and lattice distortions in FeSe crystals
• Observation of three-state nematicity and domain evolution in atomically-thin antiferromagnetic NiPS3
• Thermal Ising transition in the spin-1/2 J1-J2 Heisenberg model
• The phase diagram of a frustrated Heisenberg model: from disorder to order and back again
• Strain-tuned quantum criticality in electronic Potts-nematic systems
• Magnetic and Quasiparticle Excitation Spectra of an Itinerant $J_1-J_2$ Model for Iron Pnictide Superconductors

Cited by in corpus (1)

• Compatible Instability: Gauge Constraints of Elasticity Inherited by Electronic Nematic Criticality