Proliferation of topological magnetic defects under field*

Magnetic domain walls and their crossings as magnetic vortices are typical magnetic topological defects existing in many magnetic materials. While visualizing them and their evolution under field at the atomic level are rarely reported except for magnetic skyrmions. Here I will present the proliferation of topological magnetic defects under field, seen by neutrons.

By introducing Ising spins on a 2-dimensional bi-layer square lattice Tb₂SrAl₂O₇, we realized a frustrated magnet where no long-range magnetic order was found upon cooling to 100 mK. Using the local magnetic susceptibility method with polarized neutrons, we revealed 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 stripe magnetic phase wrapped by domain-wall phases. By applying magnetic field perpendicular to the square-lattice plane, the stripe magnetic phase melts and the condensed domain wall phases form a short-range ordered vortex lattice, so-called magnetic vortex liquid state, at a critical field of 2 T. Further application of the magnetic  field to 4 T, makes all of the spins canted to the field direction, i.e., a polarized paramagnetic phase. Here the evolution of stripe phase and domain wall phase can be precisely controlled by a magnetic field and tracked by neutron scattering.  A Z4 vortex was found to be originated from two crossed domain walls. While the density of the domain wall and vortices increase with the field and reach their maximum before entering the fully polarized paramagnetic phase.