Spin-order-dependent magneto-elastic coupling in two dimensional antiferromagnetic MnPSe$_3$ observed through Raman spectroscopy

Layered antiferromagnetic materials have emerged as a novel subset of the two-dimensional family providing a highly accessible regime with prospects for layer-number-dependent magnetism. Furthermore, transition metal phosphorous trichalcogenides, MPX3 (M = transition metal; X = chalcogen) provide a platform for investigating fundamental interactions between magnetic and lattice degrees of freedom providing new insights for developing fields of spintronics and magnonics. Here, we use a combination of temperature dependent Raman spectroscopy and density functional theory to explore magnetic-ordering-dependent interactions between the manganese spin degree of freedom and lattice vibrations of the non-magnetic sub-lattice via a Kramers-Anderson super-exchange pathway in both bulk, and few-layer, manganese phosphorous triselenide (MnPSe$_3$). We observe a nonlinear temperature dependent shift of phonon modes predominantly associated with the non-magnetic sub-lattice, revealing their non-trivial spin-phonon coupling below the N{\'e}el temperature at 74 K, allowing us to extract mode-specific spin-phonon coupling constants.