Conserved momenta of ferromagnetic solitons through the prism of differential geometry

The relation between symmetries and conservation laws for solitons in a ferromagnet is complicated by the presence of gyroscopic (precessional) forces, whose description in the Lagrangian framework involves a background gauge field. This makes canonical momenta gauge-dependent and requires a careful application of Noether’s theorem. We show that Cartan’s theory of differential forms is a natural language for this task. We use it to derive conserved momenta of the Belavin–Polyakov skyrmion, whose symmetries include translation, global spin rotation, and dilation.

Coherent spin rotation-induced zero thermal expansion in MnCoSi-based spiral magnets

Materials exhibiting zero thermal expansion (ZTE), namely, volume invariance with temperature change, can resist thermal shock and are highly desired in modern industries for high-precision components. However, pure ZTE materials are rare, especially those that are metallic. Here, we report the discovery of a pure metallic ZTE material: an orthorhombic Mn1-xNixCoSi spiral magnet. The introduction of Ni can efficiently enhance the ferromagnetic exchange interaction and construct the transition from a spiral magnetic state to a ferromagnetic-like state in MnCoSi-based alloys. Systematic in situ neutron powder diffraction revealed a new cycloidal spiral magnetic structure in the bc plane in the ground state, which transformed to a helical spiral in the ab plane with increasing temperature. Combined with Lorentz transmission electron microscopy techniques, the cycloidal and helical spin order coherently rotated at varying periods along the c-axis during the magnetic transition. This spin rotation drove the continuous movement of the coupled crystalline lattice and induced a large negative thermal expansion along the a-axis, eventually leading to a wide-temperature ZTE effect. Our work not only introduces a new ZTE alloy but also presents a new mechanism by which to discover or design ZTE magnets.