Spintronics exploits the idea of using electron spin instead of charge to encode and process information. But can electrons carry more than just spin across diverse materials? Our work answers with a resounding yes, unveiling the transport of spin “shape” in solids. The word “shape” means how spin is distributed spatially about the center of mass of a single electron wave packet. In practice it can be described by the multipole moments of spin distributions. We have isolated the part of such multipole moments that does not depend on how the wave packets are constructed, thus having an absolute meaning. Similar to spin, the well-defined spin or magnetic multipole moments can then be transported by electrons driven by external fields. As one example, we showed that an electric current flowing through phosphorene subjected to a perpendicular electric field can generate magnetic octupole moments. Such octupole moments are manifested by accumulation of spins with alternating signs at square sample corners, as illustrated in the figure below. Our work propels the emergence of “multipoletronics,” a promising new phase beyond spintronics.
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