Acoustic susceptibility of an insulating spin-glass in an applied magnetic field

(Received 8 November 1990, accepted 16 November 1990)

Abstract
The propagation of longitudinal acoustic waves of frequency between 30 MHz and 800 MHz has been studied in the insulating spin-glass (CoF ₂) _0.5(BaF ₂) _0.2(NaPO ₃) _0.3. This was achieved in the temperature range 1.2 to 4.2 K which includes the critical temperature  K, with an applied magnetic field up to 9 Teslas. The results are the following. i) The velocity shows an anisotropic bahaviour. It depends on the angle between the field and the acoustic wavevector. ii) The initial slope of the velocity versus the square of the magnetic field which measures a non-linear magneto-elastic coefficient presents a very rapid variation (a jump) at . iii) Below the velocity presents a minimum, whereas the attenuation has a maximum for H around 1 T. iv) Above the velocity shows a complicated behaviour : a maximum followed by a minimum and finally an increase with the field. v) For high fields the velocity increases with the field, the lower the temperature the steeper the slope, and a trend towards saturation is observed at the lowest temperatures for the highest fields. In the same field range the attenuation decreases with the field. All these data are interpreted within the framework of the static Sherrington-Kirkpatrick model including two spin-strain coupling mechanisms : a Waller mechanism and a field induced mechanism. It is shown that, besides terms coming directly from the two coupling mechanisms, crossed terms not previously taken into account are important. The value of the jump of the non-linear magneto-elastic coefficient, the minimum of the velocity below , and the succession of a maximum and a minimum above for the velocity are well explained. The dynamical effects are briefly considered for the paramagnetic phase in low field.