Pure spin currents, i.e. the transport of angular momentum without an accompanying charge current, represent a new, promising avenue in modern spintronics from both a fundamental and an application point of view. Such pure spin currents can not only flow in electrical conductors via mobile charge carriers, but also in magnetically ordered electrical insulators as a flow of spin excitation quanta. Over the course of the last years remarkable results have been obtained in heterostructures consisting of magnetically ordered insulators interfaced with a normal metal, where a pure spin current flows across the interface. This topical review article deals with the fundamental principles, experimental findings and recent developments in the field of pure spin currents in magnetically ordered insulators. We here put our focus onto four different manifestations of pure spin currents in such heterostructures: The spin pumping effect, the longitudinal spin Seebeck effect, the spin Hall magnetoresistance and the all-electrical detection of magnon transport in non-local device concepts. In this article, we utilize a common theoretical framework to explain all four effects and explain important material systems (especially rare-earth iron garnets) used in the experiments. For each effect we introduce basic measurement techniques and detection schemes and discuss their application in the experiment. We account for the remarkable progress achieved in each field by reporting the recent progress in each field and by discussing research highlights obtained in our group. Finally, we conclude the review article with an outlook on future challenges and obstacles in the field of pure spin currents in magnetically ordered insulator / normal metal heterostructures.
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