Contribution of giant spin clusters to the resistivity, neutron-scattering cross section, and specific heat in alloys: Application to Ni-Cu

Abstract

A simple model for a nondilute alloy containing giant spin clusters is used to calculate the spin contribution to the resistivity, the neutron cross section, and the specific heat $C_V$. The model is expected to be applicable to Ni-Cu alloys near the critical concentration for ferromagnetism. Intracluster interactions are treated exactly using a near-neighbor Heisenberg exchange interaction. Intercluster interactions are treated within the molecular-field approximation. It is assumed that in paramagnets there is a weak local field, which derives from the magnetic-anisotropy energy. Reasonable semiquantitative agreement with resistivity, elastic neutron scattering, and low-temperature specific-heat measurements on Ni-Cu for a range of concentrations and temperatures is obtained if the average cluster contains 50 Ni spins and if a Ni atom has a spin when eight or more of its near neighbors are also Ni. It is found that the anomalous temperature dependence of the resistivity, which behavior is common to a variety of alloy systems, can be accounted for using the present theory if the Fermi wave vector times the lattice spacing is less than ≅2. The previously unexplained behavior of the elastic neutron cross section in paramagnetic alloys can also be understood within this theoretical framework. In contrast to earlier discussions, it is shown that the spin contribution to $C_V$ is not temperature independent; in ferromagnetic alloys this contribution is found to increase with increasing temperature and in paramagnetic alloys it decreases with temperature. It is believed that this temperature dependence has, in the past, been incorrectly attributed to the electronic contribution to the specific heat. The validity of previous suggestions that the specific-heat and neutron-scattering measurements on these alloys probe different spin clusters is also questioned.