Anomalous Nernst Effects in Pyrochlore Molybdates with Spin Chirality

The transverse thermoelectric (Nernst) effect on pyrochlore molybdates is investigated experimentally. In ${\mathrm{Nd}}_2{\mathrm{Mo}}_2{\mathrm{O}}_7$ and ${\mathrm{Sm}}_2{\mathrm{Mo}}_2{\mathrm{O}}_7$ with the spin chirality, the Nernst signal, which mostly arises from the transverse heat current (or equivalently the transverse Peltier coefficient ${\alpha }_{xy}$), shows a low-temperature (20–30 K) positive extremum, whereas it is absent in $({\mathrm{Gd}}_{0.95}{\mathrm{Ca}}_{0.05}{)}_2{\mathrm{Mo}}_2{\mathrm{O}}_7$ with no single-spin anisotropy of the rare-earth ion and hence with no spin chirality. The correlation between the Hall conductivity ${\sigma }_{xy}$ and ${\alpha }_{xy}$ in ${\mathrm{Nd}}_2{\mathrm{Mo}}_2{\mathrm{O}}_7$ also indicates the spin chirality plays a significant role in the spontaneous (anomalous) Nernst effect.

Figure 1

Temperature dependence of (a) the magnetization $M$ at $B=1\mathrm{T}$ and the longitudinal transport properties; (b) resistivity $\rho$ and (c) Seebeck coefficient $S$ at $B=0\mathrm{T}$ in $R_2{\mathrm{Mo}}_2{\mathrm{O}}_7$ ($R=\mathrm{Nd}$, Sm, and ${\mathrm{Gd}}_{0.95}{\mathrm{Ca}}_{0.05}$). The horizontal thick bar on the left ordinate in (a) indicates the estimated value of the Mo spin moment from the neutron diffraction data [4, 18]. The insets of (a) and (c) display $\rho$ and $S$ in $B=0\mathrm{T}$ and 14 T (closed and open circles) for $R=\mathrm{Nd}$, respectively. The vertical thick bars in the insets indicate the ferromagnetic transition temperature ($T_c$) for $R=\mathrm{Nd}$. The magnetic field was applied along the [111] direction.

Figure 2

Magnetic-field dependence of the transverse Nernst signal $e_N$ for ${\mathrm{Nd}}_2{\mathrm{Mo}}_2{\mathrm{O}}_7$, measured in the magnetic field along the [100] direction (left panel) and the [111] direction (right panel) below $T=10\mathrm{K}$ (a) and above $T=20\mathrm{K}$ (b). The broken curves of the upper panels indicate the magnetic-field dependence of the anomalous Hall resistivity ${\rho }_H$ at 2 K, whose ordinates refer to the right-hand ones.

Figure 3

$R$-site dependence of (a) the Hall resistivity ${\rho }_H$ and (b) the Nernst signal $e_N$ in $R_2{\mathrm{Mo}}_2{\mathrm{O}}_7$ ($R=\mathrm{Nd}$, Sm, and ${\mathrm{Gd}}_{0.95}{\mathrm{Ca}}_{0.05}$). Magnetic field of $B=1\mathrm{T}$ was applied along the [111] direction. The vertical thick bars on the bottom abscissa indicate the ferromagnetic transition temperatures, $T_c=85\mathrm{K}$, 73 K, and 30 K in $R=\mathrm{Nd}$, Sm, and ${\mathrm{Gd}}_{0.95}{\mathrm{Ca}}_{0.05}$, respectively. Inset: $|{\alpha }_{xy}/T|$ as a function of $|\partial {\sigma }_{xy}/\partial H|$ at 10 K on a logarithmic scale.

Figure 4

(a) The magnetization $M$, (b) the Hall conductivity ${\sigma }_{xy}$, and (c) the transverse Peltier coefficient ${\alpha }_{xy}$ for the applied magnetic field of $B=1\mathrm{T}$ (open squares and circles) and $B=14\mathrm{T}$ (closed squares and circles) along the [100] (blue online) and [111] (red) directions in ${\mathrm{Nd}}_2{\mathrm{Mo}}_2{\mathrm{O}}_7$, respectively. The vertical thick bar on the bottom abscissa indicates the ferromagnetic transition temperature ($T_c=85\mathrm{K}$). Inset: Temperature dependence of ${\alpha }_{xy}/T$ [(red) open and closed circles] and $\partial {\sigma }_{xy}/\partial H$ [(blue) open and closed squares] for the applied magnetic field of 5 T along the [100] and [111] directions, respectively. The value of $\partial {\sigma }_{xy}/\partial H$ at 5 T was obtained by the differential procedure as $[{\sigma }_{xy}(5\mathrm{T})-{\sigma }_{xy}(4\mathrm{T})]/1\mathrm{T}$.