Modeling of magnetic susceptibility of an antiferromagnetic system with disorder-driven quantum critical behavior

A simple model has been proposed for an antiferromagnetic system in which the quantum critical regime is induced by disorder. The proposed model makes it possible to find the magnetic susceptibility for an arbitrary ratio of the temperature $T$ to the characteristic magnitude of the exchange integral $J$ in a disordered magnet. The model analytically describes the crossover from the power dependence $\chi\sim1/T^\xi$, which is characteristic of the ground state (the Griffiths phase, $T\ll J$), to a dependence of the Curie–Weiss type $(T\ge J)$ with the effective parameters dependent on the characteristics of the distribution function of the exchange integrals. The characteristic size of spin clusters forming the Griffiths phase has been estimated. It has been demonstrated using iron-doped germanium cuprate as an example that, within the proposed approach, the experimental data can be adequately described over a wide temperature range in which the temperature changes by more than two orders of magnitude and the magnetic properties of the Griffiths phase are determined by spin clusters of nanometer size.