Magnetostriction of rare-earth random magnetic anisotropy spin glasses.

Abstract

A model of magnetostriction for single-ion random magnetic anisotropy (RMA) spin glasses (SG) is developed, the calculation being based on the replica technique. An overall uniform strain is assumed and coupled to the local easy axis (or easy plane) by an adequate projection. The obtained bulk magnetostriction becomes proportional to the average quadrupolar moment, which depends upon the assumed ferromagnetic uniform exchange, ${J}_{0}$, and the RMA crystal field (CEF), ${D}_{0}$, strengths. Magnetostriction measurements parallel (${\ensuremath{\lambda}}_{?}$) and perpendicular (${\ensuremath{\lambda}}_{\ensuremath{\perp}}$) to the applied magnetic field (up to 7 T) have been performed between 4.2 and 150 K (much larger than the SG temperature, ${T}_{\mathrm{SG}}$) for the amorphous spin glasses ${R}_{40}$${\mathrm{Y}}_{23}$${\mathrm{Cu}}_{37}$ (R=Tb, Dy, Ho, and Er). Anisotropic magnetostriction is a forced effect, with no sign of saturation, and is quite large well above ${T}_{\mathrm{SG}}$. The developed model fits quantitatively and remarkably well the temperature variation of the anisotropic magnetostriction, ${\ensuremath{\lambda}}_{t}$=${\ensuremath{\lambda}}_{?}$-${\ensuremath{\lambda}}_{\ensuremath{\perp}}$, in the case of Tb, Dy, and Ho alloys. The values obtained from the fit for ${D}_{0}$, respectively, are +3.0, +1.25, and +0.6 K. For Er, ${D}_{0}$ becomes -0.37 K. The signs of ${D}_{0}$ are in agreement with having local axial anisotropy for the Tb, Dy, and Ho compounds, and planar for the Er one, in good agreement with the signs of the ${\ensuremath{\alpha}}_{J}$ Stevens quadrupolar parameter. From the above comparison between our theory and the measured magnetostriction, values for ${M}_{2}$/${C}_{e}$, where ${M}_{2}$ is the magnetoelastic coupling coefficient and ${C}_{e}$ the average elastic constant, are also obtained, being in the relation +1:+0.31:+0.18:-0.28, in remarkably good agreement with the point-charge model of CEF especially developed for those amorphous alloys.