Thermal Generation of Spin Current in an Antiferromagnet

The longitudinal spin Seebeck effect has been investigated for a uniaxial antiferromagnetic insulator ${\mathrm{Cr}}_2{\mathrm{O}}_3$, characterized by a spin-flop transition under magnetic field along the $c$ axis. We have found that a temperature gradient applied normal to the ${\mathrm{Cr}}_2{\mathrm{O}}_3/\mathrm{Pt}$ interface induces inverse spin Hall voltage of spin-current origin in Pt, whose magnitude turns out to be always proportional to magnetization in ${\mathrm{Cr}}_2{\mathrm{O}}_3$. The possible contribution of the anomalous Nernst effect is confirmed to be negligibly small. The above results establish that an antiferromagnetic spin wave can be an effective carrier of spin current.

Figure 1

(a) Experimental setup for the measurement of the longitudinal spin Seebeck effect, with magnetic field ($H$) applied along the [001] axis of ${\mathrm{Cr}}_2{\mathrm{O}}_3$. Arrows in ${\mathrm{Cr}}_2{\mathrm{O}}_3$ represent the local magnetic moments, and bold blue (thin red) arrows in paramagnetic metal correspond to the propagation direction (carried spin angular momentum) of the associated spin current $J_s$. $L_T$ (thickness of bulk ${\mathrm{Cr}}_2{\mathrm{O}}_3$ along the temperature gradient direction) and $L_V$ [distance between the electrodes (black circles) on the metal layer] are 0.5 and 4 mm, respectively. Unless specified, Pt is employed as the paramagnetic metal. (b),(c) The magnetic structures of ${\mathrm{Cr}}_2{\mathrm{O}}_3$ for the ground state (i.e., $H=0$) and the $H$-induced spin-flopped state, respectively. (d) $H$ dependence of induced electric voltage $V$ for Pt and magnetization $M$ for ${\mathrm{Cr}}_2{\mathrm{O}}_3$. The similar voltage profiles are also measured with (e) a different paramagnetic metal (Cu) and (f) different magnitudes of temperature gradient $\mathrm{\Delta }T$. (g) $\mathrm{\Delta }T$ dependence of Pt voltage at 14 T.

Figure 2

(a) Magnetic field dependence of the normalized Pt voltage $\overline{V}$ ($=V{L}_T/L_V$) for $H$ applied along the [001] axis of ${\mathrm{Cr}}_2{\mathrm{O}}_3$, measured with setup $A$ [i.e., Fig. 1] and setup $B$ as shown in (b). For the latter case, $L_T$ and $L_V$ are 2 and 4 mm, respectively, and only the anomalous Nernst effect can contribute to the induced voltage.

Figure 3

(a),(b) Magnetic field dependence of Pt voltage measured at various temperatures $T$ for setup $A$ [i.e., Fig. 1], with the constant temperature gradient $\mathrm{\Delta }T=10\mathrm{K}$. (c) The corresponding magnetic field dependence of magnetization for ${\mathrm{Cr}}_2{\mathrm{O}}_3$ with $H\parallel [001]$. (d) $H-T$ phase diagram for ${\mathrm{Cr}}_2{\mathrm{O}}_3$ with $H\parallel [001]$, deduced from anomalies in magnetization profile (red closed circles). Above $T_N\sim 308\mathrm{K}$, ${\mathrm{Cr}}_2{\mathrm{O}}_3$ becomes paramagnetic. The steplike anomalies for Pt voltage observed in (a) and (b) are also plotted as blue open diamonds.

Figure 4

Temperature dependence of the inverse spin Hall voltage for the ${\mathrm{Cr}}_2{\mathrm{O}}_3/\mathrm{Pt}$ system at 14 T, obtained from the data in Figs. 3 and 3 measured with $\mathrm{\Delta }T=10\mathrm{K}$ (black closed circles). The additional set of data obtained with $\mathrm{\Delta }T=5\mathrm{K}$, which is scaled using the relationship $V\propto \mathrm{\Delta }T{L}_V/L_T$, is shown as black open circles. Corresponding magnetization values for ${\mathrm{Cr}}_2{\mathrm{O}}_3$ at 14 T, obtained from the data in Fig. 3, are also plotted as red triangles.