Thermally and field-driven mobility of emergent magnetic charges in square artificial spin ice

Sophie A Morley,Jose Maria Porro,Diego Alba Venero,Gavin Burnell,Peter Fischer,Aleš Hrabec,Mark C Rosamond,Mi-Young Im,Christopher H Marrows,Edmund H Linfield,Sean Langridge

doi:10.1038/s41598-019-52460-7

Abstract

Designing and constructing model systems that embody the statistical mechanics of frustration is now possible using nanotechnology. We have arranged nanomagnets on a two-dimensional square lattice to form an artificial spin ice, and studied its fractional excitations, emergent magnetic monopoles, and how they respond to a driving field using X-ray magnetic microscopy. We observe a regime in which the monopole drift velocity is linear in field above a critical field for the onset of motion. The temperature dependence of the critical field can be described by introducing an interaction term into the Bean-Livingston model of field-assisted barrier hopping. By analogy with electrical charge drift motion, we define and measure a monopole mobility that is larger both for higher temperatures and stronger interactions between nanomagnets. The mobility in this linear regime is described by a creep model of zero-dimensional charges moving within a network of quasi-one-dimensional objects.

Highlights

Artificial spin ices (ASI) are arrays of nanomagnetic islands that are effectively single domain and so have bistable Ising-like macrospin states
Due to the high temperatures or low moment materials required for thermal behaviour, magnetic force microscopy (MFM) has not been suitable for dynamic studies of thermally active arrays, since the stray field of the tip would perturb the fluctuating states
Just as electrons and holes in a semiconductor are driven in opposite directions by an electric field, here we can drive apart the opposite magnetic charges in a pair created from the ice rule state with a magnetic field

Summary

Introduction

Artificial spin ices (ASI) are arrays of nanomagnetic islands that are effectively single domain and so have bistable Ising-like macrospin states. Starting from an ice-rule obeying state, shown on the left-hand side of Fig. 1a,b, it is possible to flip the macrospin of a nanomagnet in order to change the vertex configurations to Type 3 (T3) and violate the “two-in/two-out” ice rule This results in three-in and one-out state for one vertex (red circle) and three-out one-in for the other (blue circle), as shown on the right-hand side of Fig. 1a,b,which possess opposite net magnetic charges at the vertex and can be considered an emergent monopole-antimonopole pair. Just as electrons and holes in a semiconductor are driven in opposite directions by an electric field, here we can drive apart the opposite magnetic charges in a pair created from the ice rule state with a magnetic field By directly imaging this motion using MTXM, we have observed increased mobility of these charges with temperature and coupling strength of the islands, similar to the properties of ionic hopping conduction of electrons in solids[29]. This linear creep regime reveals a reduction in the dimensionality of the system

Methods

Results

Conclusion