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Magnetic correlations beyond the Heisenberg model in an Fe monolayer on Rh(001)

Motivated by a recent experimental observation of a complex magnetic structure [Takada et al. 2013 J. Magn. Magn. Mater. 329 95] we present a theoretical study of the magnetic structure of an Fe monolayer deposited on Rh(001). We use a classical spin Hamiltonian with parameters obtained from ab initio calculations and go beyond the usual anisotropic Heisenberg model by including isotropic biquadratic interactions. Zero-temperature Landau--Lifshitz--Gilbert spin dynamics simulations lead to a complex collinear spin configuration that, however, contradicts experimental finding. We thus conclude that higher order multi-spin interactions are likely needed to account for the magnetic ordering of the system.