Surface Magnetization in Antiferromagnets: Classification, Example Materials, and Relation to Magnetoelectric Responses

We use symmetry analysis and density-functional theory to determine and characterize surface terminations that have a finite equilibrium magnetization density in antiferromagnetic materials. A nonzero magnetic dipole moment per unit area or “surface magnetization” can arise on particular surfaces of many antiferromagnets due to the bulk magnetic symmetries. Such surface magnetization underlies intriguing physical phenomena like interfacial magnetic coupling and can be used as a readout method of antiferromagnetic domains. However, a universal description of antiferromagnetic surface magnetization is lacking. We first introduce a classification system based on whether the surface magnetization is either sensitive or robust to roughness and on whether the magnetic dipoles at surface of interest are compensated or uncompensated when the bulk magnetic order is retained at the surface. We show that roughness-sensitive categories can be identified by a simple extension of a previously established group-theory formalism for identifying roughness-robust surface magnetization. We then map the group-theory method of identifying surface magnetization to a novel description in terms of bulk magnetic multipoles, which are already established as symmetry indicators for bulk magnetoelectric responses at both linear and higher orders. We use density-functional calculations to illustrate that nominally compensated surfaces in magnetoelectric ${\mathrm{Cr}}_2{\mathrm{O}}_3$ and centrosymmetric altermagnetic ${\mathrm{FeF}}_2$ develop a finite magnetization density at the surface, in agreement with our predictions based on both group theory and the ordering of the bulk multipoles. Our analysis provides a comprehensive basis for understanding the surface magnetic properties and their intimate correspondence to bulk magnetoelectric effects in antiferromagnets and has important implications for technologically relevant phenomena such as exchange-bias coupling.