Isosbestic Point and Magnetoresistance Components in Ho\(_{0.5}\) Lu\(_{0.5}\) B\(_{12}\)

We present the results of precise magnetoresistance (MR) measurements of an antiferromagnetic cage-glass solid solution Ho\(_{0.5}\)Lu\(_{0.5}\)B\(_{12}\) in magnetic fields up to 80 kOe and at temperatures between 1.9 and 100 K. The analysis of results allows to separate the positive and negative contributions to MR. The dominant MR-term was found to be the high field positive contribution \(\Delta \rho /\rho _{(m+)} =\mu _\mathrm{D} arrow up H arrow up \) which is caused by the drift mobility \(\mu _\mathrm{D} \) of charge carriers. It was also shown that the negative MR observed at temperatures \(T \le \) 10 K may be described by the well-known relation between MR and local magnetization \(\Delta \rho /\rho _{(-)} =M_\mathrm{{loc}} arrow up \) obtained by Yosida in the framework of s-d exchange model. We discuss as well the scattering of charge carriers on antiferromagnetic nanosize domains of Ho\(3+}\) ions with effective magnetic moments 3.5-5.5 \(\mu _\mathrm{B}\) as the mechanism responsible for the appearance of the negative MR component.