Ultrasonic measurement of the critical exponent β for the spin glass C uMn

Abstract

Ultrasonic measurements are presented providing direct measurement of the critical exponent β for a spin glass. Sound velocity measurements were made on Cu0.95Mn0.05 and Cu0.976Mn0.024 single crystals which exhibited the characteristic spin glass cusp in low-field ac susceptibility. A sound velocity anomaly was observed in the vicinity of the susceptibility peak temperature. We attribute this anomaly to critical fluctuations. Using perturbation theory we show that for a spin glass such as CuMn, the critical part of sound velocity is related to that of the Edwards–Anderson spin glass order parameter q. We are able to determine the critical exponent β associated with this order parameter by fitting the theory to the measured critical change in sound velocity in CuMn samples. By combining our values of β with the values of α′ associated with the critical change in specific heat below the spin glass transition temperature, and Suzuki’s scaling laws,we find the values of exponent γ, αs, and γs, associated with the zero field susceptibility, the magnetic field dependent part of specific heat, and the field dependent part of susceptibility.