Magnetostriction of rare-earth random magnetic anisotropy spin glasses

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, J0, and the RMA crystal field (CEF), D0, strengths. Magnetostriction measurements parallel (λ/sub X/) and perpendicular (λ/sub perpendicular/) 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/sub SG/) for the amorphous spin glasses R/sub 40/Y/sub 23/Cu/sub 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/sub SG/. The developed model fits quantitatively and remarkably well the temperature variation of the anisotropic magnetostriction, λ/sub t/ = λ/sub X/-λ/sub perpendicular/, in the case of Tb, Dy, and Ho alloys. The values obtained from the fit for D0, respectively, are +3.0, +1.25, and +0.6 K. For Er, D0 becomes -0.37 K. The signs of D0 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 α/sub J/ Stevens quadrupolar parameter