Spin treacle in a frustrated magnet observed with spin current

By means of spin current, the flow of spin angular momentum, we find a regime of “spin treacle” in a frustrated magnetic system. To establish its existence, we have performed spin transport measurements in nanometer-scale spin glasses. At temperatures high enough that the magnetic moments fluctuate at high frequencies, the spin Hall angle, the conversion yield between spin current and charge current, is independent of temperature. The spin Hall angle starts to decrease at a certain temperature $T^{*}$ and completely vanishes at a lower temperature. We argue that the latter corresponds to the spin freezing temperature $T_{\mathrm{f}}$ of the nanometer-scale spin glass, where the direction of conduction electron spin is randomized by the exchange coupling with the localized moments. The present experiment quantitatively verifies the existence of a distinct spin treacle between $T_{\mathrm{f}}$ and $T^{*}$. We have also quantified a timescale of fluctuation of local magnetic moments in the spin treacle from the spin relaxation time of conduction electrons.

Figure 1

Illustrations of ISHE in CuMnBi at three different temperature regimes: (a) $T>T^{*}$ (PM), (b) $T_{\mathrm{f}}<T<T^{*}$ (ST), and (c) $T<T_{\mathrm{f}}$ (SG). Black arrows with red and blue spheres are conduction electrons with spin-up and spin-down, respectively, and red and blue arrows show those trajectories. The shadows indicate fluctuations of conduction electron spins and magnetic moments of Mn. Yellow and gray arrows indicate the charge current density ${\mathit{j}}_{\mathrm{c}}$ generated at the Bi site (green sphere) due to the ISHE and a magnetic interaction between the Mn sites, respectively. The $x, y$, and $z$ axes in (a) correspond to the directions of ${\mathit{j}}_{\mathrm{c}}, {\mathit{j}}_{\mathrm{s}}$, and $\mathit{\sigma }$ above $T^{*}$, respectively.

Figure 2

Magnetizations $M$ of (a) bulk ${\mathrm{Cu}}_{88.9}{\mathrm{Mn}}_{10.6}{\mathrm{Bi}}_{0.5}$ and (b) 140 nm thick ${\mathrm{Cu}}_{88.9}{\mathrm{Mn}}_{10.6}{\mathrm{Bi}}_{0.5}$ film. The open and closed circles indicate $M$ under ZFC and FC, respectively. The arrows in (a) and (b) indicate $T_{\mathrm{f}}$ of bulk and film samples, respectively.

Figure 3

ISHE resistances ($R_{\mathrm{ISHE}}\equiv V/I$) of ${\mathrm{Cu}}_{99.5-x}{\mathrm{Mn}}_x{\mathrm{Bi}}_{0.5}$ measured at typical temperatures ((a) $x=4.2$, (b) $x=10.6$). The amplitude of the ISHE resistance $\mathrm{\Delta }{R}_{\mathrm{ISHE}}$ is defined in (a). The inset of (a) shows a scanning electron micrograph of typical spin Hall device and a schematic of the ISHE measurement circuit. The white bar in the inset corresponds to $1\mu \mathrm{m}$. The $x$ and $z$ axes in (a) are the same as those in Fig. 1.

Figure 4

Temperature dependence of the amplitudes of ISHE resistances ($|\mathrm{\Delta }{R}_{\mathrm{ISHE}}|$) of ${\mathrm{Cu}}_{95.3}{\mathrm{Mn}}_{4.2}{\mathrm{Bi}}_{0.5}$ and ${\mathrm{Cu}}_{88.9}{\mathrm{Mn}}_{10.6}{\mathrm{Bi}}_{0.5}$.

Figure 5

Temperature dependence of $\eta$, the spin Hall angle of ${\mathrm{Cu}}_{99.5-x}{\mathrm{Mn}}_x{\mathrm{Bi}}_{0.5}$ ($x=4.2$ and 10.6) normalized by that of ${\mathrm{Cu}}_{99.5}{\mathrm{Bi}}_{0.5}$. The solid and open arrows indicate $T^{*}$ and $T_{\mathrm{f}}$, respectively.

Figure 6

NLSV signals with and without the ${\mathrm{Cu}}_{95.3}{\mathrm{Mn}}_{4.2}{\mathrm{Bi}}_{0.5}$ wire measured at $T=10\mathrm{K}$.

Figure 7

Temperature dependence of ${\lambda }_{\mathrm{CuMnBi}}$ for ${\mathrm{Cu}}_{99.5-x}{\mathrm{Mn}}_x{\mathrm{Bi}}_{0.5}$ ($x=4.2$ and 10.6).

Figure 8

Phase diagram of SG proposed in the present work. $T_{\mathrm{f}}$ and $T^{*}$ of CuMnBi nanowires are indicated by the solid blue triangle and the solid red square, respectively. The data for ${T_{\mathrm{f}}}^{\mathrm{Bulk}}$ and $T^{*}$ at lower values of $x$ than our samples, are taken from Refs. [12, 17, 21, 31, 32, 33] and Ref. [14], respectively.

Figure 9

(a) Temperature dependence of the spin relaxation rate $1/{\tau }_{\mathrm{CuMnBi}}$ of ${\mathrm{Cu}}_{99.5-x}{\mathrm{Mn}}_x{\mathrm{Bi}}_{0.5}$ ($x=4.2$, 8.2 and 10.6). (b) Correlation time ${\tau }_{\mathrm{c}}$ of Mn moments above $T_{\mathrm{f}}$ determined by spin relaxation time measurements with $\mathrm{\Delta }\approx 4k_{\mathrm{B}}{T}_{\mathrm{f}}$ in Eq. (2). ${\tau }_{\mathrm{c}}$ determined by zero-field $\mu \mathrm{SR}$ [17] and neutron spin echo measurements [23] for samples of similar concentrations of Mn, but without Bi, are superimposed onto the same graph. The broken line shows a power law ${(1-T_{\mathrm{f}}/T)}^{-b}$ with $b\approx 2.5$ [see Eq. (3)].