Determination of susceptibility and specific heat critical exponents for weak itinerant-electron ferromagnets from vibrating reed experiments

Abstract

We report the observation of a linear relationship between the magnetic contribution to Young's modulus, $\ensuremath{\Delta}{E/E}_{0},$ and inverse magnetic susceptibility ${\ensuremath{\chi}}^{\ensuremath{-}1}$ for amorphous weak itinerant-electron ferromagnets ${\mathrm{Fe}}_{90}{\mathrm{Zr}}_{10}$ and ${\mathrm{Fe}}_{91}{\mathrm{Zr}}_{9}$ in the asymptotic critical region near the ferromagnetic-paramagnetic phase transition. The proportionality $\ensuremath{\Delta}{E(T)/E}_{0}\ensuremath{\propto}{\ensuremath{\chi}}^{\ensuremath{-}1}(T)$ is shown to provide as accurate a means of determining the asymptotic critical exponent $\ensuremath{\gamma}$ and the leading ``correction-to-scaling'' amplitudes for susceptibilty from the $\ensuremath{\Delta}{E/E}_{0}$ data as a direct measurement of magnetic susceptibilty does. Similarly, the well-known relation between the magnetic contributions to sound velocity and specific heat is fully exploited to extract accurate estimates for the universal critical amplitude ratio ${A}^{+}{/A}^{\ensuremath{-}}$ and the asymptotic critical exponents ${\ensuremath{\alpha}}^{\ifmmode\pm\else\textpm\fi{}}$ for the specific heat from the sound velocity data. The presently determined values of ${\ensuremath{\alpha}}^{\ifmmode\pm\else\textpm\fi{}}$ and $\ensuremath{\gamma},$ together with the reported value for spontaneous magnetization critical exponent $\ensuremath{\beta},$ not only obey the scaling equalities ${\ensuremath{\alpha}}^{+}={\ensuremath{\alpha}}^{\ensuremath{-}}$ and $\ensuremath{\alpha}+2\ensuremath{\beta}+\ensuremath{\gamma}=2$ but also assert that the atomic magnetic moments in the alloys in question interact with one another through an attractive interaction which decays faster than ${1/r}^{5}$ with the interatomic spacing, r.