Biquadratic and ring exchange interactions in orthorhombic perovskite manganites

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.

13 pages, 12 figures

References in corpus (4)

• Spin-Orbit Coupling and Ion Displacements in Multiferroic TbMnO3
• Magnetically-induced ferroelectricity in orthorhombic manganites: microscopic origin and chemical trends
• Long-Range Magnetic Interactions Induced by the Lattice Distortions and the Origin of the E-type Antiferromagnetic Phase in the Undoped Orthorhombic Manganites
• Structural distortions and model Hamiltonian parameters: from LSDA to a tight-binding description of LaMnO_3

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