H−Tphase diagram for spin-glasses: An experimental study of Ag:Mn

Abstract

We present high-resolution SQUID (superconducting quantum interference device) measurements of the dc magnetization on two Ag:Mn samples containing 2.6 and 4.0 at.% Mn. We have measured in detail the temperature dependence of the magnetization on warming through the glass temperature, ${T}_{G}$, (i) after cooling to $T<{T}_{G}$ in a near-zero field and then applying the measurement field, zero-field cooled, and (ii) after cooling to $T<{T}_{G}$ in the measurement field. This has been done for fields $0.5\ensuremath{\le}H\ensuremath{\le}500$ Oe. The temperature derivative, $\frac{\mathrm{dM}(H,T)}{\mathrm{dT}}$, of the ZFC curve shows structure, allowing the identification of several characteristic temperatures associated with the paramagnetic to spin-glass transition in the presence of an external magnetic field. The temperature, ${T}_{B}$, where the crossover from a Curie-like to a nonlinear susceptibility occurs, behaves as $\ensuremath{\sim}{H}^{0.5\ifmmode\pm\else\textpm\fi{}0.1}$. Two further temperatures, $\overline{T}$ and ${T}_{P}$, where $\overline{T}<{T}_{P}<{T}_{G}^{0}(H\ensuremath{\rightarrow}0)$ are suggested as possible candidates for the theoretical-field-dependent transition temperature ${T}_{G}(H)$ given by ${1\ensuremath{-}[\frac{{T}_{G}(H)}{{T}_{G}^{0}}]}={\mathrm{Ah}}^{\frac{2}{3}}$ where $h=\frac{H}{J}=\frac{{g}_{{\ensuremath{\mu}}_{B}}H}{{k}_{B}{T}_{G}^{0}}$ and $A$ is of order unity. We find ${1\ensuremath{-}[\frac{\overline{T}(H)}{{T}_{G}^{0}}]}={\mathrm{Bh}}^{0.70\ifmmode\pm\else\textpm\fi{}0.05}$, but where $B$ is approximately ${(19)}^{2/3}$. However, the ${T}_{P}$ data are consistent with the theoretical prediction ($A\ensuremath{\simeq}1$) using no adjustable parameters, but the range of data is insufficient to enable an unambiguous verification of the theory. On the basis of recent theories, we suggest that the system entering the spin-glass phase at ${T}_{G}(H)$ should be marked experimentally by ${\ensuremath{\chi}}_{\mathrm{dc}}=\frac{M}{{H}_{\mathrm{static}}}>{\ensuremath{\chi}}_{\mathrm{ac}}(\ensuremath{\nu},{H}_{\mathrm{osc}},{H}_{\mathrm{static}})$ where $M$ is the magnetization, ${H}_{\mathrm{static}}$ the magnitude of the dc field, ${H}_{\mathrm{osc}}$ the amplitude of the ac oscillating field, and $\ensuremath{\nu}$ its frequency. This argument leads us to conclude that ${T}_{P}(H)$ should be taken as the experimental definition of ${T}_{G}(H)$.