Cascade of Spin Moiré Superlattices with In-Plane Field in Triangle Lattice Semimetal EuAg$_4$Sb$_2$

Abstract

EuAg$_4$Sb$_2$ is a rhombohedral europium triangle lattice material that exhibits a rich phase diagram of spin moiré superlattices (SMS) and single-$q$ magnetic phases. In this paper, we characterize the incommensurate phases accessible with field applied in the plane with small angle neutron scattering (SANS). A variety of phases with unusual SANS patterns are accessible with magnetic field applied along the $a$ and $a^*$ directions. Many of these phases can be understood to be multi-$q$ phases. One phase in particular, ICM2b (ICM=incommensurate magnetic phase), is rather unconventional in that it is an anisotropic multi-$q$ phase that can rotate freely within the $ab$-plane, dependent on magnetic field direction and history. The stabilization of tunable multi-$q$ incommensurate spin textures \textit{via} in-plane field sets this class of materials apart from conventional skyrmion materials. We further identify that the propagation vectors of the in-plane phases have a significant commensuration with the diameter of the smallest pocket of the Fermi surface ($2k_{\text{F}}$). The multi/single-$q$ nature is also correlated with the enhancement of resistivity, suggesting that a gap opens in the electron bands at $q=2k_{\text{F}}$. We also compare with a phenomenological model of the phase diagram. The richness of phases revealed in this study hint at the frustrated nature of the incommensurate magnetism present in EuAg$_4$Sb$_2$ and motivate further probes of these phases and the origin of the stability of spin moiré superlattices. Finally, the coupling of the multi-$q$ nature and $q=2k_{\text{F}}$ commensuration condition reveals the key requirements for a strong SMS transport response.