Proliferation of magnetic topological defects in a 2D square lattice

Magnetic domain walls and their crossings, which form magnetic vortices, are typical topological magnetic defects found in many magnetic materials. However, visualizing these defects and their evolution under magnetic fields at the atomic level has rarely been reported, except in the case of magnetic skyrmions. Here, I will present the proliferation of topological magnetic defects in a two-dimensional (2D) square lattice under applied magnetic fields, as revealed by neutron scattering.

By introducing Ising spins into a 2D bilayer square lattice, we realized a frustrated magnet in which no long-range magnetic order was observed down to 100 mK. Using the local magnetic susceptibility method with polarized neutrons, we identified canted Ising spins. With this information, we were able to simulate the neutron diffuse scattering patterns observed under selected magnetic fields through machine-learning-assisted spin Hamiltonian optimization. Our studies revealed a short-range-ordered 2D stripe magnetic phase enclosed by domain-wall phases. When a magnetic field was applied perpendicular to the square-lattice plane, the stripe magnetic phase melted, and the condensed domain-wall phases formed a short-range-ordered vortex lattice. Further increasing the magnetic field caused all spins to cant toward the field direction, leading to a polarized paramagnetic phase.

The evolution of the stripe and domain-wall phases can be precisely controlled by a magnetic field and tracked using neutron scattering. A Z₄ vortex was found to originate from the crossing of two domain walls. The densities of both domain walls and vortices increase with the field, reaching their maximum before the system enters the fully polarized paramagnetic phase.