Issues with J-dependence in the LSDA+U method for non-collinear magnets

Eric Bousquet1,2 and Nicola Spaldin3

1 Materials Department, University of California, Santa Barbara, CA 93106, USA

2 Physique Théorique des Matériaux, Université de Liège, B-4000 Sart Tilman, Belgium and

3 Department of Materials, ETH Zurich, Wolfgang-Pauli-Strasse 10 CH-8093 Zurich, Switzerland

Abstract:

We re-examine the commonly used density functional theory plus Hubbard U (DFT+U) method for the case of non-collinear magnets. While many studies neglect to explicitly include the exchange correction parameter J, or consider its exact value to be unimportant, here we show that in the case of non-collinear magnetism calculations the J parameter can strongly affect the magnetic ground state. We illustrate the strong J -dependence of magnetic canting and magnetocrystalline anisotropy by calculating trends in the magnetic lithium orthophosphate family LiMPO4 (M = Fe and Ni) and difluorite family MF2 (M = Mn, Fe, Co and Ni). Our results can be readily understood by expanding the usual DFT+U equations within the spinor scheme, in which the J parameter acts directly on the off-diagonal components which determine the spin canting.

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https://arxiv.org/pdf/1011.0939.pdf 

Density functional theory (DFT) within the local density (LDA) and generalized gradient (GGA) approximations is widely used to describe a large variety of materials with good accuracy. The LDA and GGA functionals often fail, however, to correctly reproduce the properties of strongly correlated materials containing d and f electrons. The LDA+U approach – in which a Hubbard U repulsion term is added to the LDA functional for selected orbitals – was introduced in response to this problem, and often improves drastically over the LDA or GGA. Indeed, it provides a good description of the electronic properties of a range of exotic magnetic materials, such as the Mott insulator KCuF3 1 and the metallic oxide LaNiO2 2 .

Two main LDA+U schemes are in widespread use today: The Dudarev approach in which an isotropic screened on-site Coulomb interaction Uef f = U − J is added, and the Liechtenstein1 approach in which the U and exchange (J) parameters are treated separately. The Dudarev approach is equivalent to the Liechtenstein approach with J = 0 . Both the effect of the choice of LDA+U scheme on the orbital occupation and subsequent properties 5 , as well as the dependence of the magnetic properties on the value of U 6 , have recently been analyzed. There has been no previous systematic study, however, of the effect of the J parameter of the Liechtenstein approach in non-collinear magnetic materials. Here we show that neither the approach of not explicitly considering the J parameter (as in the Dudarev implementation), nor the assumption that its importance is borderline – a common approximation is to use J ' 10% U without careful testing – within the Liechtenstein implementation are justified in the case of non-collinear magnets. We demonstrate that in the case of non-collinear antiferromagnets, the choice of J can strongly change the amplitude of the spin canting angle (LiNiPO4) or even modify the easy axis of the system (LiFePO4 and FeF2), with consequent drastic effects on the magnetic susceptibilities and magnetoelectric responses.