Strain Anisotropy and Magnetic Domain Structures in Multiferroic Heterostructures: High-Throughput Finite-Element and Phase-Field Studies

Abstract Understanding magnetic domain structures and their responses to electric fields in multiferroic heterostructures is critical to the design of electric-field-driven spintronic devices. High-throughput finite-element and phase-field simulations are performed to probe the piezoelectric strain anisotropy and its relaxation, magnetic domain structures and their responses to applied voltages as function of the in-plane dimensions and thickness of the magnetic Ni nanoislands grown on a Pb(Mg 1/3 Nb 2/3 )O 3 -PbTiO 3 (PMN-PT) membrane. The piezoelectric strain anisotropy is found to increase with the in-plane aspect ratio, but it can be significantly relaxed, as large as >80%, in nanoislands of thickness larger than >15 nm. Magnetic domain diagrams are established to identify the domain structures for Ni nanoislands of different lengths of in-plane major and minor axis, as well as thickness. When a voltage is applied to the multiferroic heterostructure, the single-domain magnetic domain can be switched by the piezoelectric strain, whereas the vortex domain is not switched. However, for a multiferroic heterostructure with a thick nanoisland wherein most of the piezoelectric strain is relaxed, the single-domain magnetic domain shows a weak response to the voltage and cannot be switched. The effect of thickness variation in real magnets on the switching is also discussed. The present results are expected to provide guidance to the understanding and design of multiferroic nanostructures for achieving electric-field-modulated magnetic properties.