Transition to Irreversibility in Insulating Spin Glasses.

We have made detailed measurements in spin-glasses of the in-phase and quadrature component of the ac magnetic susceptibility as a function of dc magnetic field near the freezing temperature in order to investigate the nature of the spin-glass transition. We carried out measurements on two insulating spin-glass systems, crystalline Eu(,0.4)Sr(,0.6)S and glassy Al(,2)Mn(,3)Si(,3)O(,12), with a high sensitivity SQUID magnetometer. These data were analyzed to obtain a phase boundary in the field-temperature plane that marks the high-temperature limit for hysteretic behavior. This transition temperature is found to be reduced with increasing dc field once the field exceeds a frequency dependent threshold value H(,th). These results have been compared with predictions of various theories and Monte Carlo calculations. In particular, scaling relations for both zero and finite transition temperatures are consistent with our data provided we take the exponents as free parameters. Zero temperature scaling gives exponents which differ from the Monte Carlo simulation results for 3d Ising systems. The finite transition temperature scaling on the other hand gives the scaling exponent (DELTA) that is consistent with the standard relation among dynamic and static critical exponents. It also gives the relaxation time exponent z(nu) which agrees well with recent computer simulations on 3d Ising systems. Finally we have proposed an empirical generalization of the scaling theory which is sample independent. The threshold field of the transition line sets a characteristic energy scale which has not previously been included in theories for spin glasses.