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

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.

💡 Research Summary

The authors report the discovery of atomically‑sharp one‑dimensional magnetic solitons in the square‑net rare‑earth intermetallic EuRhAl₄Si₂. The material crystallizes in the tetragonal BaMg₄Si₃‑type structure (space group P4/mmm) and hosts localized Eu²⁺ (4f⁷, S = 7/2) moments. Although Eu²⁺ lacks strong single‑ion anisotropy, the system exhibits a pronounced uniaxial anisotropy K that competes directly with the Ruderman‑Kittel‑Kasuya‑Yosida (RKKY) exchange interactions. First‑principles calculations reveal oscillatory, sign‑changing exchange couplings extending up to three lattice spacings, with a nearest‑neighbour ferromagnetic J₁ ≈ ‑0.5 meV and a next‑nearest‑neighbour antiferromagnetic J₂ ≈ +0.2 meV. The competition between J₁, J₂ and K stabilizes a collinear ferrimagnetic ↑↑↓ (up‑up‑down) configuration with a propagation vector q = 1/3 along either the a or b axis.

Bulk magnetization measured with the field applied along the crystallographic c‑axis displays a robust 1/3 M_sat plateau (≈2.3 µ_B per Eu) over a wide field range (≈0.3–1.5 T). Within this plateau two very fine steps appear on either side, corresponding to magnetization values M = M_sat/