Atomically-sharp magnetic soliton in the square-net lattice EuRhAl$_{4}$Si$_{2}$

Abstract: Topological spin textures are hallmark manifestations of competing interactions in magnetic matter. Their effective description by nonlinear field theories reflects an energetic frustration that destabilizes uniform order while selecting finite-size, topologically nontrivial configurations as stationary states. Among the most extreme realizations are atomically-sharp domain wall excitations, namely one-dimensional (1D) magnetic solitons, which represent the ultimate scaling limit of magnetic textures. Such solitons may emerge in magnetic systems where effective exchange interactions compete directly with uniaxial magnetic anisotropy. Here we show that the square-net rare earth compound EuRhAl${4}$Si${2}$ realizes a very susceptible regime where the magnetic anisotropy competes with highly frustrated exchange interactions stabilizing a rare ferrimagnetic $\uparrow\uparrow\downarrow$ state that, under applied magnetic field, supports the formation of atomically-sharp soliton defects. We confirm the bulk response of the 1D magnetic solitons via magnetization and electrical transport measurements. We establish both the zero- and in-field $\uparrow\uparrow\downarrow$ order via neutron diffraction, while magnetic force microscopy visualizes its real-space evolution into a stripe-like array. To elucidate the microscopic origin of the soliton, we relate the Ruderman-Kittel-Kasuya-Yosida (RKKY)-driven exchange interactions and the magnetic anisotropy through density functional theory, and we construct an effective 1D $J_{1}$-$J_{2}$-$K$ model whose atomistic spin dynamics simulations reproduce the observed soliton states as a function of external field. Our results demonstrate that EuRhAl${4}$Si${2}$ hosts atomically-sharp, field-driven 1D magnetic solitons, providing a new platform for studying 1D topological excitations at the atomic length scale.