Vogel-Fulcher-Tammann Freezing of a Thermally Fluctuating Artificial Spin Ice Probed by X-ray Photon Correlation Spectroscopy

TL;DR

This study investigates the glassy freezing behavior of a thermally fluctuating artificial spin ice using X-ray photon correlation spectroscopy, revealing a Vogel-Fulcher-Tammann law and a transition to a non-traditional frozen state.

Contribution

It demonstrates the first observation of Vogel-Fulcher-Tammann freezing in artificial spin ice, linking magnetic fluctuations to glassy dynamics and magnetostatic interactions.

Findings

Magnetic fluctuations slow abruptly near 178 K, indicating a freezing transition.

The freezing follows a Vogel-Fulcher-Tammann law, suggesting glassy behavior.

Fluctuations within islands increase above 40 K due to local anisotropy variations.

Abstract

We report on the crossover from the thermal to athermal regime of an artificial spin ice formed from a square array of magnetic islands whose lateral size, 30~nm~$\times$~70~nm, is small enough that they are superparamagnetic at room temperature. We used resonant magnetic soft x-ray photon correlation spectroscopy (XPCS) as a method to observe the time-time correlations of the fluctuating magnetic configurations of spin ice during cooling, which are found to slow abruptly as a freezing temperature $T_0 = 178 \pm 5$~K is approached. This slowing is well-described by a Vogel-Fulcher-Tammann law, implying that the frozen state is glassy, with the freezing temperature being commensurate with the strength of magnetostatic interaction energies in the array. The activation temperature, $T_\mathrm{A} = 40 \pm 10$~K, is much less than that expected from a Stoner-Wohlfarth coherent rotation model. Zero-field-cooled/field-cooled magnetometry reveals a freeing up of fluctuations of states within islands above this temperature, caused by variation in the local anisotropy axes at the oxidised edges. This Vogel-Fulcher-Tammann behavior implies that the system enters a glassy state on freezing, which is unexpected for a system with a well-defined ground state.