First-principles study of the magnetic exchange forces between the RuO₂ (110) surface and Fe tip

Magnetic exchange force microscopy (MExFM) is an important experimental technique for mapping the magnetic structure of surfaces with atomic resolution relying on the spin-dependent short-range exchange interaction between a magnetic tip and a magnetic surface. RuO₂ is a significant compound with applications in heterogeneous catalysis and electrocatalysis. It has been characterized recently as an antiferromagnetic (AFM) material, and its magnetism has been predicted somewhat surprisingly to play an important role in its catalytic properties. In the current study, we explore theoretically whether MExFM can visualize the magnetic surface structure of RuO₂ . We use density functional theory (DFT) calculations to extract the exchange interactions between a ferromagnetic Fe tip interacting with an AFM RuO₂ (110) surface, as a function of tip-surface distance and the position of the tip over the surface. Mimicking the MExFM experiment, these data are then used to calculate the normalized frequency shift of an oscillating cantilever tip versus the minimum tip-surface distance, and construct corrugation height line profiles. It is found that the exchange interaction between tip and surface is strongest for a parallel configuration of the spins of the tip and of the surface; it is weakest for an anti-parallel orientation. In a corrugation profile, this gives rise to a sizable height difference of 25 pm between the spin-up and spin-down Ru atoms in the RuO₂ (110) surface at a normalized frequency shift $$ =-10.12 fNm^1/2 . The O atoms in the surface are not or hardly visible in the corrugation profile.