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

TL;DR

This paper investigates the phase ordering dynamics of Ising-nematic order in a frustrated Heisenberg antiferromagnet, revealing a two-stage coarsening process and confirming the universality class of the late-stage ordering.

Contribution

It provides a detailed simulation study of the nonequilibrium dynamics of Ising-nematic order in a frustrated magnetic system, establishing the universality class and effects of disorder.

Findings

Late-stage domain growth follows the square root of time scaling.

The ordering belongs to the dynamical universality class of non-conserved Ising order.

Weak bond disorder does not break superuniversality in the system.

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.