Satisfaction and Violation of the Fluctuation-Dissipation Relation in spin ice materials

TL;DR

This study investigates the fluctuation-dissipation relation in spin ice materials, revealing its validity at certain temperatures and frequencies, and identifying violations and aging effects at low temperatures and frequencies.

Contribution

It provides the first detailed experimental analysis of FDR violations and aging phenomena in spin ice materials at very low temperatures.

Findings

FDR holds at temperatures above 600 mK indicating local equilibrium.

Violations of FDR occur below 400 mK at low frequencies, similar to spin glasses.

New relaxation and aging behaviors are observed in the ac susceptibility at low frequencies.

Abstract

We test the fluctuation-dissipation relation (FDR) in spin ice materials Dy$_2$Ti$_2$O$_7$ and Ho$_2$Ti$_2$O$_7$ by measuring both the magnetic noise and the out-of-phase part of the susceptibility and comparing their ratio. We show that it is satisfied at temperatures well into the non-ergodic region below 600 mK, indicating local equilibrium. In both materials, below 400 mK, low frequency violations develop, showing an excess of noise as in spin glasses, with a frequency threshold of 0.1 Hz. New relaxation pathways and aging properties are unveiled in this frequency range in the ac susceptibility. The FDR remains valid at higher frequencies down to 150 mK.