Kibble-Zurek Mechanism for Nonequilibrium Generation of Magnetic Monopoles in Spin Ices

TL;DR

This paper investigates how magnetic monopoles in spin ices are generated and annihilated during cooling, applying and generalizing the Kibble-Zurek mechanism to describe their nonequilibrium dynamics.

Contribution

The study extends the Kibble-Zurek mechanism to spin ice systems, providing a kinetic reaction theory and identifying the power-law dependence of monopole density on cooling rate.

Findings

Residual monopole density follows a power law with cooling rate.

Developed a kinetic reaction theory matching Monte Carlo simulations.

Generalized KZM to spin ice with specific critical exponents.

Abstract

The proliferation of topological defects is a common out-of-equilibrium phenomenon when a system is driven into a phase of broken symmetry. The Kibble-Zurek mechanism (KZM) provides a theoretical framework for the critical dynamics and generation of topological defects in such scenarios. One of the early applications of KZM is the estimation of heavy magnetic monopoles left behind by the cosmological phase transitions in the early universe. The scarcity of such relic monopoles, which contradicts the prediction of KZM, is one of the main motivations for cosmological inflationary theories. On the other hand, magnetic monopoles as emergent quasi-particles have been observed in spin ices, a peculiar class of frustrated magnets that remain disordered at temperatures well below the energy scale of exchange interaction. Here we study the annihilation dynamics of magnetic monopoles when spin ice is cooled to zero temperature in a finite time. Through extensive Glauber dynamics simulations, we find that the density of residual monopole follows a power law dependence on the annealing rate. A kinetic reaction theory that precisely captures the annihilation process from Monte Carlo simulations is developed. We further show that the KZM can be generalized to describe the critical dynamics of spin ice, where the exponent of the power-law behavior is determined by the dynamic critical exponent $z$ and the cooling protocol.