High-magnetic-field magnetization and magnetoresistance of a transition-metal-base spin glass: Zr-Mn

The magnetization $M$ and electrical resistivity $\rho$ have been measured at $0\le H\le 135$ kG and $1.2\le T\le 27$ K for the transition metal hcp Zr containing Mn at concentrations $520\le c\le 3100$ ppm. The primary results are (a) the measurements confirm earlier indications that Mn displays a localized magnetic moment when in solution in hcp Zr and suggest a Kondo temperature $T_K<1.0\mathrm{}$ K; (b) both the high-$H$ saturation magnetization and the low-$H$ susceptibility show that the spin $S$ associated with Mn in Zr is 2.0 ± 0.2; (c) the impurity magnetization $\Delta M\equiv M\left(\mathrm{alloy}\right)-M\left(\mathrm{Zr}\right)$ obeys the Blandin-Souletie-Tournier scaling $\frac{\Delta M}{c}=F(\frac{H}{c}, \frac{T}{c})$, suggesting the dominance of a long-range oscillating Ruderman-Kittel-Kasuya-Yosida (RKKY)-like moment-moment interaction, as appears to exist in the more widely investigated non-transition-metal-host spin glasses; (d) the behavior of the resistivity, susceptibility, and reversible magnetization indicates that spin-freezing temperatures $T_0\mathrm{}\left(c\right)\mathrm{}$ (if such exist in Zr-Mn) are below the present 1.2-K temperature limit; (e) the high $T>\mathrm{}{T}_0$, high $H\gg \frac{k_{B}T}{g{\mu }_B}$, Larkin-Khmel'nitskii (LK) prediction $\Delta M\left(\mathrm{LK}\right)=\Delta M_s(1-\frac{H_0}{H})$ ($\Delta M_s$ is the impurity saturation magnetization, $H_0\propto c{V}_0$, $V_0$ is the RKKY coefficient) does not account for the (i) $T$-dependence of $\Delta M$, (ii) relatively low fields $40\lesssim H_s\lesssim 130$ kG (at $520\le c\le 3100-\mathrm{ppm}$ Mn) required for saturation of the impurity magnetization at 1.2 K; (f) fits of the measured $\Delta M\left(H\right)\mathrm{}$ to the theoretical $\Delta M\left(\mathrm{LK}\right)$ at $H<\mathrm{}{H}_s$, $c\ge 1690-\mathrm{ppm}$ Mn, yield $V_0=2.7\mathrm{}\times {10}^{-37\mathrm{}}$ erg ${\mathrm{cm}}^3$ and hence an exchange parameter $\left|J_{\mathrm{RKKY}}\right|\approx 0.5$ eV; (g) at $c=520\mathrm{}-\mathrm{ppm}$ Mn, $\Delta M\left(H\right)\mathrm{}$ is close to the free-spin Brillouin magnetization and $\rho (H,T)$ can be fit to single-impurity theory: (i) $\Delta \rho \mathrm{}(T,H=0\mathrm{})\mathrm{}\equiv \rho \left(\mathrm{alloy}\right)-\rho \left(\mathrm{Zr}\right)$ to the Hamann-Fischer formula with $T_K\le 1.0$ K, (ii) the spin-component magnetoresistance $\delta {\rho }_s(H>\mathrm{}{H}_s)$ to the Béal-Monod and Weiner third-order perturbation formula with an exchange parameter $J_m=-0.2\mathrm{}$ eV. In general, the present work indicates that localized-magnetic-moment ($S, T_K,J_m$) and high-$T>\mathrm{}{T}_0$ spin-glass (BST scaling, $V_0$, $J_{\mathrm{RKKY}}$) behavior of Mn in the transition-metal hcp Zr is rather similar to that of Mn in the noble metals. However, the present observations of relatively low fields $H_s$ required for saturation of the impurity magnetization suggest cutoffs on the order of $H_s\mathrm{}\left(c\right)\mathrm{}$ in the internal molecular-field distribution and do not appear to agree with current $T>\mathrm{}{T}_0$ theory. It is unclear whether the disagreement is a general property of metallic spin glasses, or is peculiar to transition-metal host systems or to alloys (such as the present) with relatively short electron mean free paths which might cause some damping of the RKKY oscillations.