Toward a first-principles theory of rare-earth ions in crystals

Abstract

Density functional theory (DFT), including its extensions designed to treat strongly correlated localized electron systems such as DFT+$U$ and DFT+dynamical mean field theory, has proven exceedingly useful in studying the magnetic properties of solids. However, materials with rare earths ($R$) have remained a notable exception. The most vital rare-earth magnetic properties, such as magnetocrystalline anisotropy (MA), have been notoriously elusive due to the ubiquitous self-interaction error present in nearly all available DFT flavors. In this work, we show explicitly how the orbital dependence of self-interaction error may contradict Hund's rules and plague MA calculations, and how analyzing DFT metastable states that respect Hund's rules can alleviate the problem. We systematically investigate and discuss several rare-earth-containing families, $R$Co${}_5$, $R_2$Fe${}_{14}$B, $R$Fe${}_{12}$, and $R$Mn${}_6$Sn${}_6$, to benchmark the MA calculations in DFT+$U$. For all compounds we investigated, we found that our methodology reproduces the magnetic easy-axis, easy-plane, and non-trivial easy-cone anisotropies in full agreement with low-temperature experimental measurements. Besides the fully-numerical ab initio approach, we further illustrate an efficient semi-analytical perturbation method that treats the crystal field as a perturbation in the limit of large spin-orbit coupling. This approach evaluates the rare-earth anisotropy by assessing the dependence of crystal-field energy on spin-quantization axis rotation using $4f$ crystal-field levels obtained from non-spin-orbit calculations. Our analytical method provides a quantitative microscopic understanding of the factors that control MA and can be used for predicting new high-MA materials.

11 pages, 4 figures

References in corpus (15)

• Discovery of a quantum limit Chern magnet TbMn6Sn6
• Self-consistency over the charge-density in dynamical mean-field theory: a linear muffin-tin implementation and some physical implications
• Constituents of magnetic anisotropy and a screening of spin-orbit coupling in solids
• GW method applied to localized 4f electron systems
• Uniaxial ferromagnetism in the kagome metal TbV${}_6$Sn${}_6$
• Highly anisotropic magnetism in the vanadium-based kagome metal TbV6Sn6
• Prediction of a new efficient permanent magnet SmCoNiFe3
• Interplay between magnetism and band topology in Kagome magnets $R$Mn${}_6$Sn${}_6$
• Intrinsic magnetic properties of {$R$(Fe${}_{1-x}$Co${}_x$)${}_{11}$Ti$Z$} ($R$ = Y and Ce; $Z$ = H, C, and N)
• Temperature-dependent magnetocrystalline anisotropy of rare earth/transition metal permanent magnets from first principles: The light RCo${}_5$ (R=Y, La-Gd) intermetallics
• Intersublattice magnetocrystalline anisotropy using a realistic tight-binding method based on maximally localized Wannier functions
• Origin of the spin reorientation transitions in (Fe${}_{1-x}$Co${}_x$)${}_2$B alloys
• High-order crystal field and rare-earth magnetism in RECo5 intermetallics
• Low temperature competing magnetic energy scales in the topological ferrimagnet TbMn6Sn6
• Unification of Perdew-Zunger Self-Interaction Correction, DFT+U, and Rung 3.5 Density Functionals

Cited by in corpus (5)

• Physical properties of $R$Co${}_2$Al${}_8$ ($R=$ La, Ce, Pr, Nd and Sm) single crystals: An emerging structure-type for anisotropic Kondo lattice studies
• Single Atom Magnets on Thermally Stable Adsorption Sites: Dy on NaCl(100)
• Modeling of a twisted-Kagome HoAgGe spin ice using Reduced-Configuration-Space Search and Density Functional Theory
• Pair anisotropy in disordered magnetic systems
• Distinct effect of Kondo physics on crystal field splitting in electron and spin spectroscopies