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arXiv · 1412.3702

Biquadratic and ring exchange interactions in orthorhombic perovskite manganites

Natalya S. Fedorova·Claude Ederer·Nicola A. Spaldin·Andrea Scaramucci
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Abstract

We use ab initio electronic structure calculations within the generalized gradient approximation (GGA+U) to density functional theory (DFT) to determine the microscopic exchange interactions in the series of orthorhombic rare-earth manganites, o-$R$MnO$_3$. Our motivation is to construct a model Hamiltonian (excluding effects due to spin-orbit coupling), which can provide an accurate description of the magnetism in these materials. First, we consider TbMnO$_3$, which exhibits a spiral magnetic order at low temperatures. We map the exchange couplings in this compound onto a Heisenberg Hamiltonian and observe a clear deviation from the Heisenberg-like behavior. We consider first the coupling between magnetic and orbital degrees of freedom as a potential source of non-Heisenberg behavior in TbMnO$_3$, but conclude that it does not explain the observed deviation. We find that higher order magnetic interactions (biquadratic and four-spin ring couplings) should be taken into account for a proper treatment of the magnetism in TbMnO$_3$ as well as in the other representatives of the o-$R$MnO$_3$ series with small radii of the $R$ cation.

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Natalya S. Fedorova, Claude Ederer, Nicola A. Spaldin, Andrea Scaramucci. 2014-12-11. Biquadratic and ring exchange interactions in orthorhombic perovskite manganites. https://doi.org/10.1103/physrevb.91.165122

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