Extraction of the Spin Glass Correlation Length

TL;DR

This paper investigates the relationship between the spin glass relaxation rate peak and the correlation length, using experimental data and fitting to dynamic models to understand barrier heights and spin correlations.

Contribution

It introduces a method to extract the spin glass correlation length from the peak shift of the relaxation rate, comparing power law and activated dynamic models with experimental data.

Findings

Power law and activated models fit the data well

Activated dynamics have a too small prefactor

Correlation length scales with time according to the models

Abstract

The peak of the spin glass relaxation rate, S(t)=d{-M_{TRM}(t,t_w)}/H/{d ln t}, is directly related to the typical value of the free energy barrier which can be explored over experimental time scales. A change in magnetic field H generates an energy E_z={N_s}{X_fc}{H^2} by which the barrier heights are reduced, where X_{fc} is the field cooled susceptibility per spin, and N_s is the number of correlated spins. The shift of the peak of S(t) gives E_z, generating the correlation length, Ksi(t,T), for Cu:Mn 6at.% and CdCr_{1.7}In_{0.3}S_4. Fits to power law dynamics, Ksi(t,T)\propto {t}^{\alpha(T)} and activated dynamics Ksi(t,T) \propto {ln t}^{1/psi} compare well with simulation fits, but possess too small a prefactor for activated dynamics.