Probing the spin-glass freezing transition in $\mathrm{C}{\mathrm{u}}_{1-x}\mathrm{M}{\mathrm{n}}_x$ alloy by spin current

In this study, we used the thermally driven spin current to investigate the spin frustrations and spin fluctuations in spin-glass (SG) $\mathrm{C}{\mathrm{u}}_{1-x}\mathrm{M}{\mathrm{n}}_x$ alloys. Tuning the $\mathrm{C}{\mathrm{u}}_{1-x}\mathrm{M}{\mathrm{n}}_x$ composition results in a transition of the alloys from the SG state to the antiferromagnetic state; these states have different spin-freezing temperatures $\left(T_f\right)$. Most spins randomly freeze at temperatures lower than the $T_f$ of the alloy. For each alloy composition, we obtained a temperature-dependent inverse spin Hall voltage with a peak at $T_p$. Crucially, $T_p$ had nearly identical composition dependence as that of $T_f,$, with $T_p$ being nine times larger than $T_f$. Similar behavior was captured using the SG insulator, amorphous ${\mathrm{Y}}_3\mathrm{F}{\mathrm{e}}_5{\mathrm{O}}_{12}$. These results indicated that the maximum spin fluctuation in both conducting and insulating SGs occurred at temperatures considerably higher than the $T_f$ of each. In addition, we demonstrated the importance of the effective number of valence electrons in tailoring the spin Hall angle in binary alloys.

Figure 1

(a) Schematic of the magnetic ordering from spin glass to the antiferromagnetic state by increasing composition of Mn and from the magnetically ordered state to the spin-fluctuation state by increasing temperature. Schematic of the spin-current transmission through (b) SG metal and (c) SG insulator using the ISHE/SSE measurement.

Figure 2

(a) ZFC (dashed curve) and FC (solid curve) temperature-dependent magnetization for $\mathrm{C}{\mathrm{u}}_{1-x}\mathrm{M}{\mathrm{n}}_x$(300)/Si with $x=0.14$ (black), 0.34 (red), 0.54 (green), 0.79 (blue), and 1 (yellow). Arrows indicate the corresponding spin-freezing temperat- ure ($T_f$) for each composition. (b) Field-dependent ISHE voltage for $\mathrm{C}{\mathrm{u}}_{86}\mathrm{M}{\mathrm{n}}_{14}\left(5\right)/\mathrm{YIG}$ (upper red), $\mathrm{C}{\mathrm{u}}_{86}\mathrm{M}{\mathrm{n}}_{14}\left(5\right)/\mathrm{Si}$ (upper black), Mn(5)/YIG (lower red), and Mn(5)/Si (lower black) at room temperature.

Figure 3

(a) Temperature-dependent spin Seebeck coefficient for 5-nm- (black), 8-nm- (red), and 15-nm-thick (blue) $\mathrm{C}{\mathrm{u}}_{86}\mathrm{M}{\mathrm{n}}_{14}$. (b) Temperature-dependent spin Seebeck coefficient for $\mathrm{C}{\mathrm{u}}_{1-x}\mathrm{M}{\mathrm{n}}_x$ with $x=0.14$ (black), 0.34 (red), 0.54 (green), 0.79 (blue), and 1 (yellow). Arrows indicate the voltage peak at $T_p$. (c) Plots of $T_p$ (green star), $T_f$ (red triangle), and $T_p/T_f$ (yellow square) on $\mathrm{C}{\mathrm{u}}_{1-x}\mathrm{M}{\mathrm{n}}_x$ compositions.

Figure 4

Scaling plot of the normalized spin Seebeck coefficient by the 3D Ising critical exponent with (a) $T_{\mathrm{critical}}=T_p$ and (b) $T_{\mathrm{critical}}=T_f$ for $\mathrm{C}{\mathrm{u}}_{1-x}\mathrm{M}{\mathrm{n}}_x$ over the entire range of compositions.

Figure 5

Thickness-dependent $|\mathrm{\Delta }{V}_{\mathrm{ISHE}}|/\rho$ for (a) $\mathrm{C}{\mathrm{u}}_{86}\mathrm{M}{\mathrm{n}}_{14}\left(t\right)/\mathrm{YIG}$ and (b) $\mathrm{Mn}\left(t\right)/\mathrm{YIG}$. Red dashed line is the fitting curve determined by Eq. (2). Plot of (c)$|\mathrm{\Delta }{V}_{\mathrm{ISHE}}|/\rho$ and (d) resistivity as a function of $\mathrm{C}{\mathrm{u}}_{1-x}\mathrm{M}{\mathrm{n}}_x$ composition.

Figure 6

(a) Temperature-dependent magnetization under ZFC (black) and FC (red) for $a$-YIG(300)/Si. (b) Field-dependent $V_{\mathrm{ISHE}}$ for $\mathrm{Pt}/a\text{−}\mathrm{YIG}\left(t\right)/\mathrm{YIG}$. (c) Normalized $V_{\mathrm{ISHE}}$ for $\mathrm{Pt}/a\text{−}\mathrm{YIG}\left(t\right)/\mathrm{YIG}$ as a function of $a\text{−}\mathrm{YIG}$ thicknesses. Inset depicts normalized $V_{\mathrm{ISHE}}$ for $\mathrm{Pt}/\mathrm{Si}{\mathrm{O}}_2\left(t\right)/\mathrm{YIG}$ as a function of $\mathrm{Si}{\mathrm{O}}_2$ thicknesses. Red curves are fittings from Eq. (4). (d) Temperature-dependent spin Seebeck coefficient for Pt(3)/YIG (red), Pt(5)/YIG (yellow), and $\mathrm{Pt}\left(3\right)/a\text{−}\mathrm{YIG}\left(t\right)/\mathrm{YIG}$ with $t=0$ (red), 5 (green), and 10 nm (blue).