Magnetostriction of Dilute Magnetic Alloys

Measurements of the magnetostriction and magnetization of two ferromagnetic $\mathrm{Pt}\mathrm{Fe}$ alloys and a paramagnetic $\mathrm{Pd}\mathrm{Ni}$ alloy are presented. The Belov equation for the free energy of a weak itinerant ferromagnet including magnetoelastic terms is used to estimate the volume dependence of the Curie temperature $T_C$. For the alloy ${\mathrm{Pt}}_{0.99}$ ${\mathrm{Fe}}_{0.01}$, the resultant value is $\frac{\partial \ln T_C}{\partial \omega }=-47\mathrm{}$, where $\omega$, is the volume strain. The volume dependence of the magnetization $M$, determined from the magnetostriction, is field dependent and decreases monotonically from $\frac{\partial \ln M}{\partial \omega }=-1.6\mathrm{}$ at 35 kOe to $\frac{\partial \ln M}{\partial \omega }=-37\mathrm{}$ at 2 kOe, where it is still decreasing rapidly. This behavior is in disagreement with the $s-d$ interaction model, which was found to explain satisfactorily the behavior of $\mathrm{Pd}\mathrm{Fe}$ alloys. The model predicts that $\frac{\partial \ln M}{\partial \omega }$ should be field independent and of the same order of magnitude as $\frac{\partial \ln T_C}{\partial \omega }$. In the alloy ${\mathrm{Pt}}_{0.97}$ ${\mathrm{Fe}}_{0.03}$, it is not possible to estimate $\frac{\partial \ln T_C}{\partial \omega }$ from the Belov plots, because of domain effects. The value of $\frac{\partial \ln M}{\partial \omega }$ is constant and equal to - 0.5 above about 15 kOe, but increases considerably at lower fields, as in ${\mathrm{Pt}}_{0.99}$ ${\mathrm{Fe}}_{0.01}$, before domain effects intervene. The Belov equation is modified to describe the magnetostriction and magnetization of the paramagnetic alloy ${\mathrm{Pd}}_{0.9811}$ ${\mathrm{Ni}}_{0.0189}$, and thereby to estimate the value, $\frac{\partial \ln {\chi }_A}{\partial \omega }=-19\mathrm{}$, of the volume dependence of its susceptibility ${\chi }_A$. The Belov equation and its modification for a strongly paramagnetic metal describe satisfactorily the field dependence of the magnetostriction, but not the magnetization, both for the ferromagnetic $\mathrm{Pt}\mathrm{Fe}$ alloys and the $\mathrm{Pd}\mathrm{Ni}$ alloy.