Susceptibility of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Cu</mml:mi><mml:mi/><mml:mi mathvariant="normal">Mn</mml:mi></mml:math>spin-glass: Frequency and field dependences

Abstract

Alternating current susceptibility measurements on powdered samples of the spin-glass $\mathrm{Cu}\mathrm{Mn}$ (Mn concentrations: $0.23&lt;~c&lt;~6.3$ at.%) showed relatively broad maxima as well as sharp cusps in ${\ensuremath{\chi}}^{\ensuremath{'}}$ as a function of temperature depending on the method of preparing the sample. In contrast to the broadly peaked ${\ensuremath{\chi}}^{\ensuremath{'}}(T)$ 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 ${\ensuremath{\chi}}^{\ensuremath{'}}(H)$ was analyzed and the critical exponent $\ensuremath{\delta}$ determined. The susceptibility data for the lower concentration alloys were independent of the measurement frequency ($1 \mathrm{Hz}&lt;\ensuremath{\nu}&lt;10 \mathrm{kHz}$) within the absolute experimental accuracy of about 1%. However, in the concentration regime of \ensuremath{\approx} 1 at.% Mn and above, the sharply cusped, so-called "quenched" samples exhibited a small frequency dependence in ${\ensuremath{\chi}}^{\ensuremath{'}}(T)$ near ${T}_{f}$. The relative shift in freezing temperature $\ensuremath{\Delta}\frac{{T}_{f}}{{T}_{f}}$ 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 ${\ensuremath{\chi}}^{\ensuremath{'}}(\ensuremath{\nu})$ curves seemed to converge towards a single, nonzero ${\ensuremath{\chi}}^{\ensuremath{'}}$ value as $T\ensuremath{\rightarrow}0$ 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 ${\ensuremath{\chi}}^{\ensuremath{'}}(T)$ 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 ${\ensuremath{\chi}}^{\ensuremath{'}}$ 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.