The susceptibility of archetypical spin glasses: A phenomenological model approach to the frequency and field dependence of χ and its implications on magnetization measurements

We present a phenomenological model to describe the frequency dependence of the differential susceptibility χ of spin glasses. It is argued that clusters of magnetically coupled spins are formed at temperatures far above the freezing temperature T_f. The frequency-dependent behaviour of χ around and below T_f arises due to the intercluster interactions. It is demonstrated that for systems with antiferromagnetic intercluster interaction ( CuMn, AuMn and AgMn) this dependence vanishes at lower temperatures in a way similar to the parallel susceptibility of an antiferromagnet. In cases of ferromagnetic intercluster interaction the frequency dependence is much larger and remains large down to low temperatures. The mutual relation between χ′ and χ″ (the in-phase and the out-of-phase components of χ) is analysed successfully on the basis of the Kramers-Kronig relations, incorporating a distribution of relaxation times. In the final part of this paper we present the dependence on the external magnetic field of both χ and the magnetization M for the above-mentioned spin-glass systems. These measurements were performed instantaneously and clearly demonstrate the occurrence of irreversible contributions in M below T_f, which are not visible for the ac driving field. These type of measurements present a new concept in the study of spin glasses and may be used for further experiments to verify our model description.