We propose a longitudinal spin-Seebeck effect (SSE), in which a magnon-induced spin current is injected parallel to a temperature gradient from a ferromagnet into an attached paramagnetic metal. The longitudinal SSE is measured in a simple and versatile system composed of a ferrimagnetic insulator ${\text{Y}}_3{\text{Fe}}_5{\text{O}}_{12}$ slab and a Pt film by means of the inverse spin-Hall effect. The experimental results highlight the intriguing character of the longitudinal SSE due to its own geometric configuration.

The spin Seebeck effect refers to the generation of a spin voltage caused by a temperature gradient in a ferromagnet, which enables the thermal injection of spin currents from the ferromagnet into an attached nonmagnetic metal over a macroscopic scale of several millimeters. The inverse spin Hall effect converts the injected spin current into a transverse charge voltage, thereby producing electromotive force as in the conventional charge Seebeck device. Recent theoretical and experimental efforts have shown that the magnon and phonon degrees of freedom play crucial roles in the spin Seebeck effect. In this paper, we present the theoretical basis for understanding the spin Seebeck effect and briefly discuss other thermal spin effects.

The spin Seebeck effect (SSE) refers to the generation of a spin current as a result of a temperature gradient in magnetic materials including insulators. The SSE is applicable to thermoelectric generation because the thermally generated spin current can be converted into a charge current via spin-orbit interaction in conductive materials adjacent to the magnets. The insulator-based SSE device exhibits unconventional characteristics potentially useful for thermoelectric applications, such as simple structure, device-design flexibility, and convenient scaling capability. In this article, we review recent studies on the SSE from the viewpoint of thermoelectric applications. Firstly, we introduce the thermoelectric generation process and measurement configuration of the SSE, followed by showing fundamental characteristics of the SSE device. Secondly, a theory of the thermoelectric conversion efficiency of the SSE device is presented, which clarifies the difference between the SSE and conventional thermoelectric effects and the efficiency limit of the SSE device. Finally, we show preliminary demonstrations of the SSE in various device structures for future thermoelectric applications and discuss prospects of the SSE-based thermoelectric technologies.

We formulate a linear response theory of the spin Seebeck effect, i.e., a spin voltage generation from heat current flowing in a ferromagnet. Our approach focuses on the collective magnetic excitation of spins, i.e., magnons. We show that the linear-response formulation provides us with a qualitative as well as quantitative understanding of the spin Seebeck effect observed in a prototypical magnet, yttrium iron garnet.