Susceptibility of theCuMnspin-glass: Frequency and field dependences

Abstract

Alternating current susceptibility measurements on powdered samples of the spin-glass $\mathrm{Cu}\mathrm{Mn}$ (Mn concentrations: $0.23<~c<~6.3$ at.%) showed relatively broad maxima as well as sharp cusps in ${\chi }^{\prime }$ as a function of temperature depending on the method of preparing the sample. In contrast to the broadly peaked ${\chi }^{\prime }\mathrm{}\left(T\right)\mathrm{}$ curves, the sharply cusped ones were more affected by small, external, static fields $H$. This field dependence was measured at various temperatures above and below $T_f$, the freezing temperature. At $T_f$ the behavior of ${\chi }^{\prime }\mathrm{}\left(H\right)\mathrm{}$ was analyzed and the critical exponent $\delta$ determined. The susceptibility data for the lower concentration alloys were independent of the measurement frequency ($1 \mathrm{Hz}<\nu <10\mathrm{} \mathrm{kHz}$) within the absolute experimental accuracy of about 1%. However, in the concentration regime of ≈ 1 at.% Mn and above, the sharply cusped, so-called "quenched" samples exhibited a small frequency dependence in ${\chi }^{\prime }\mathrm{}\left(T\right)\mathrm{}$ near $T_f$. The relative shift in freezing temperature $\Delta \frac{T_f}{T_f}$ per decade of frequency was found to be 0.0050 independent of concentration from 1 to 6.3 at.% Mn. Below $T_f$ the various ${\chi }^{\prime }\left(\nu \right)$ curves seemed to converge towards a single, nonzero ${\chi }^{\prime }$ value as $T\to 0$ K. Above $T_f$ and below about 50 K, the susceptibility obeyed a simple Curie-like law, whereas in the higher temperature region from 100 to 150 K a Curie-Weiss-like behavior was observed with a small, positive paramagnetic Curie-Weiss temperature. To analyze the behavior of ${\chi }^{\prime }\mathrm{}\left(T\right)\mathrm{}$ near $T_f$ and at the lowest temperatures of measurement 0.4 K, the superparamagnetic blocking model of Wohlfarth was used. A distribution of blocking temperatures was thus determined from the experimental ${\chi }^{\prime }$ data. This distribution function shows a rather sharp step at $T_f$, indicating that there are cooperative effects in the freezing of a spin-glass.