Field-tuned skyrmion crystals and anomalous quantum oscillations in magnetic metals

Skyrmions are topological magnetic swirls which have been discovered in a variety of itinerant magnets. They are stabilized by anisotropic exchange interactions induced by relativistic spin-orbit coupling. Recent activity in this field has focused on the Berry-flux-induced topological Hall effect in ferromagnetic (FM) skyrmion crystals, and on the hunt for skyrmions and skyrmion crystals in frustrated antiferromagnets. In this work, we study the impact of quartic spin interactions in such systems, and find that it can lead to strong mode-mode coupling which depends on an applied Zeeman magnetic field. This effect combined with the anisotropic exchange couplings leads to the formation of triple-$\mathbf{Q}$ skyrmion crystals which are shown to have a field-tunable lattice constant. We discuss this effect in triangular-lattice ferromagnets with broken inversion symmetry, which host Dzyaloshinkii-Moriya interactions, as well as in frustrated antiferromagnets such as Gd$_2$PdSi$_3$ which have been explored in recent experiments. For FM skyrmion crystals, we show that coupling itinerant electrons to this spin texture leads to a tunable Hofstadter-type model, resulting in Chern bands which strongly depend on a Zeeman field coupled to the local moments. Such magnetic metals are argued to be candidates for observing Zeeman-field-induced anomalous quantum oscillations.