Temperature dependence of the nonlinear susceptibility in spin glasses

In most metallic spin glasses the nonlinear susceptibility χ2 =d3M/dH3‖H→0 exhibits a singular behavior at the freezing temperature Tf. Within the framework of the molecular field theory, χ2 is proportional to (T−Tf)−1. However, several experimental results show that χ2 is proportional to (T−Tf)−γs(T) over a wide range of temperature, with temperature dependent values of γs greater than 1. A similar discrepancy is observed for the paramagnetic susceptibility χ0=dM/dH‖H→O of amorphous ferromagnets. We have shown earlier that this anomaly in amorphous ferromagnets results from the noncritical interplay between the magnetic correlations and the spatial fluctuations of the exchange interaction, and it was described by a spatially correlated molecular field theory. We now apply this theory to spin glasses and show that the staggered susceptibility exhibits an anomalous (T−Tf)−γψ(T), (γψ≳1) behaviour in a wide range of temperature, and argue that the nonlinear susceptibility χ2 shows a similar behaviour. We suggest, therefore, that the anomalous behaviour of χ2 does not represent a critical phenomenon, thus the value of γs(T) can be dependent both on the system and temperature.