Phase transitions and critical phenomena in alloys with random anisotropy.

Abstract

The effects of random magnetic anisotropy on ferromagnetic critical behavior in four rare-earth-based amorphous alloys, ${\mathrm{Gd}}_{65}$${\mathrm{Co}}_{35}$, ${\mathrm{Nd}}_{50}$${\mathrm{Co}}_{50}$, ${\mathrm{Nd}}_{65}$${\mathrm{Co}}_{35}$, and ${\mathrm{Tb}}_{65}$${\mathrm{Co}}_{35}$, are reported. The ratio of anisotropy to exchange, D/${\mathit{J}}_{0}$, ranges from 0.004(1) to 0.323(35) in these alloys. The zero-field state of the anisotropic alloys (Nd and Tb based) is spin-glass-like below ${\mathit{T}}_{\mathit{c}}$. In order to determine the extent of the critical regime as a function of reduced temperature, \ensuremath{\epsilon}=(T-${\mathit{T}}_{\mathit{c}}$)/${\mathit{T}}_{\mathit{c}}$, and to determine if the asymptotic critical regime is probed, a wide range of \ensuremath{\epsilon} is covered. Evidence for crossovers as a function of applied field and as a function of D/${\mathit{J}}_{0}$ are observed. As a function of applied field, the alloys containing anisotropic rare-earth atoms cross over with increasing field from a state that shows the characteristics of a speromagnet to a state where the magnetic isotherms follow a ferromagnetic-scaling equation of state. The field above which good ferromagnetic scaling is observed increases monotonically with D/${\mathit{J}}_{0}$. No deviations from scaling were found at small \ensuremath{\epsilon} giving confidence that the asymptotic critical regime is probed. Deviations from scaling were seen at large values of \ensuremath{\epsilon} (\ensuremath{\epsilon}>0.06) which gives the limit of the critical regime. We find systematic variations in the measured ferromagnetic critical exponents \ensuremath{\gamma} and \ensuremath{\delta} with D/${\mathit{J}}_{0}$ indicating a crossover in critical behavior presumably from an isotropic to a random anisotropy class with increasing D/${\mathit{J}}_{0}$. Finally, we point out that there are some theoretical hints of a ferromagneticlike state below ${\mathit{T}}_{\mathit{c}}$ in random-anisotropy models.