On the maximum of the field-dependent susceptibility in ferromagnetic materials

We propose two new methods to describe the ferromagnetic field-dependent susceptibility within the mean-field theory. A parametric approach valid for any value of temperature, applied field, and spin quantum number is developed; within this approach, the scaling functions for magnetization and susceptibility are determined for values of the reduced field, smaller than 10(-3). A simple analytic derivation of the scaling functions is also given. As the susceptibility maximum is found to occur at a value of the relevant scaling variable which is of the order of unity, it cannot be accurately described by series expansions of the scaling function. A nonlocal parabolic approximant to the scaling function is constructed which reproduces its main features exactly. The methods of this paper are relevant to the study of the field-dependent susceptibility of any ferromagnet in which long-range forces are known to dominate. It is suggested that the analysis be tested on the examples of the 'mean-field' ferromagnets HoRh4B4 and ZrZn2. The whole scheme should be regarded as contributing to the elaboration of the advantageous procedure for the determination of two independent critical exponents, which is based on general scaling analysis for the field-dependent susceptibility and which avoids painstaking measurements of the exact Curie temperature.