Far-from-equilibrium monopole dynamics in spin ice

Abstract

Condensed matter in the low-temperature limit reveals exotic physics associated with unusual orders and excitations, with examples ranging from helium superfluidity 1 to magnetic monopoles in spin ice 2,3 . The far-from-equilibrium physics of such low-temperature states may be even more exotic, yet to access it in the laboratory remains a challenge. Here we demonstrate a simple and robust techniquethe 'magnetothermal avalanche quench'-and its use in the controlled creation of non-equilibrium populations of magnetic monopoles in spin ice at millikelvin temperatures. These populations are found to exhibit spontaneous dynamical effects that typify far-from-equilibrium systems and yet are captured by simple models. Our method thus opens new directions in the study of far-from-equilibrium states in spin ice and other exotic magnets.The normal way of controlling the temperature of a system is to connect it thermally to a second body with a much larger thermal mass, which then acts as a thermal reservoir. If it is desired to force thermal excitations out of equilibrium by a rapid temperature quench, then the simplest strategy would be to heat the sample, and then abruptly remove the heating so that the sample is cooled rapidly by the reservoir. However, direct heating of the sample will also tend to heat the reservoir, and this becomes a particular problem in low-temperature devices: for example, in a 3 He-4 He dilution refrigerator it may entail heating of the mixing chamber, and ultimately limit the speed of any thermal quench that can be practically achieved. Our technique gets round this problem by using the natural tendency of magnets to undergo magnetothermal 'avalanches' at low temperature [4][5][6][7] . It is illustrated in Fig. 1 and discussed further in Supplementary Section 1.4. The essential principle is that magnetic work done on the sample is abruptly converted into internal heat, which causes a sudden increase in temperature inside the sample (T int ). The sample then finds itself at a relatively high temperature but connected to a cold thermal bath. The ensuing quench is as efficient and rapid as possible as it involves minimal heating of the sample environment, which remains at the reservoir temperature, T .Magnetothermal avalanches typically occur at low temperature (T < 1 K), a regime also notable for the occurrence of exotic magnetic states based on long-range interactions, quantum effects and magnetic frustration [8][9][10][11][12][13][14] . Hence, the avalanche quench technique could be generally used to drive such systems out of equilibrium. We focus on the case of spin ice, a nearly ideal realization of a magnetic ice-type or vertex model 8 . The far-from-equilibrium physics of vertex models is a subject of great intrinsic interest 15 In spin-ice materials such as Dy 2 Ti 2 O 7 and Ho 2 Ti 2 O 7 , the frustrated pyrochlore lattice geometry and local crystal field combines with a self-screening dipole-dipole interaction to give a local 'ice rule' that controls low-energy spin configurations 8,16...

Out-of-equilibrium dynamics and extended textures of topological defects in spin ice

“…But in three dimensions, it has so far only been partially stabilized at equilibrium in the spin-ice model with dipolar interactions 46 , or requires four-body interactions 39 or the suppression of double charges 37,38 . The nonequilibrium magnetic-field quench proposed here provides a promising tool to realize this state and demonstrates the possibility of engineering a macroscopic state via nonequilibrium techniques 47 .…”

“…Last but not least, the apparition of the FCSL phase demonstrates the promises of engineering macroscopic states via nonequilibrium techniques 47 . We hope our work will further motivate the exploration of nonequilibrium phenomena in geometrically frustrated magnets, ranging from topological ergodicity breaking 74 to glassiness without disorder 18,23 , and with connections to kagome systems 75,76 including their realization in artificial spin ice [40][41][42][43][44] and the 16-vertex model 54,55 .…”

Vacancy defects and monopole dynamics in oxygen-deficient pyrochlores

“…Our results make it apparent that the density of oxygen vacancies in spin ice samples is of key importance in the interpretation and understanding of relaxation and response properties, and far from equilibrium behaviour in general. Many experimental results in this direction are already available 13,[17][18][19]30 , and in some cases it may be that further work is needed to distinguish the effects of oxygen vacancies from the stoichiometric behaviour.…”

Amorphous ferromagnetism and re-entrant magnetic glassiness in single-crystallineSm2Mo2O7

“…proper of magnetic monopoles has been recently claimed in spin-ices by means of both macroscopic [54][55][56][57][58] and local magnetic techniques, 59,60 even if the topic is still highly controversial and debated particularly in the case of muon spin spectroscopy (µ + SR) results.…”