Intrinsic Spin-Dependent Thermal Transport

Most studies of spin caloritronic effects to date, including spin-Seebeck effect, utilize thin films on substrates. We use patterned ferromagnetic thin film to demonstrate the profound effect of a substrate on the spin-dependent thermal transport. With different sample patterns and on varying the direction of temperature gradient, both longitudinal and transverse thermal voltages exhibit asymmetric instead of symmetric spin dependence. This unexpected behavior is due to an out-of-plane temperature gradient imposed by the thermal conduction through the substrate and the mixture of anomalous Nernst effects. Only with substrate-free samples have we determined the intrinsic spin-dependent thermal transport with characteristics and field sensitivity similar to those of the anisotropic magnetoresistance effect.

Figure 1

(a) Schematic diagram of a Py wire sample for the thermal measurement with voltage leads on two sides, heat source indicated by the large oval, and magnetic field direction at angle $\theta$. (b) field dependence of thermal voltage at different angle $\theta$. Angular dependence of thermal voltage when heater is on the (c) left, and (d) right of the wire. Insets show power dependence of thermal voltage.

Figure 2

(a) Schematic diagram of the Hall bar sample used for the thermal transport measurement with the heater on one side, transverse voltages measured at three locations (hot, cold, middle). (b) Field dependence of thermal voltage at the hot side and the cold side at $\theta =0°$. (c) Angular dependence of thermal voltage at cold side. (d) Field dependence of thermal voltage at the hot side and the cold side with a closer heater position at $\theta =0°$.

Figure 3

Field dependence of thermal voltage on the hot side (top panel) and cold side (bottom panel) of Hall bar Py sample with heater placed on (a) top; and (b) bottom of the sample. Results of same measurements with a 10-nm Pt layer on top of 300-nm Py are shown in (c) and (d).

Figure 4

(a) Schematic sideview of a suspended Fe foil sample for the intrinsic spin-dependent thermal transport measurement (b) Field dependence of thermal voltage when the field is applied at different angle $\theta$. (c) Angular dependence of saturated thermal voltage with the solid curve of ${cos}^2\theta$.