- Open Access
Approach to Magnetocrystalline Anisotropy of Strong Magnets
Phys. Rev. X 4, 021027 – Published 15 May, 2014
DOI: https://doi.org/10.1103/PhysRevX.4.021027
Abstract
The new challenges posed by the need of finding strong rare-earth-free magnets demand methods that can predict magnetization and magnetocrystalline anisotropy energy (MAE). We argue that correlated electron effects, which are normally underestimated in band-structure calculations, play a crucial role in the development of the orbital component of the magnetic moments. Because magnetic anisotropy arises from this orbital component, the ability to include correlation effects has profound consequences on our predictive power of the MAE of strong magnets. Here, we show that incorporating the local effects of electronic correlations with dynamical mean-field theory provides reliable estimates of the orbital moment, the mass enhancement, and the MAE of .
Popular Summary
Magnetic materials are widely used in technologies ranging from wind turbines to “green” automobiles. Compounds with large magnetocrystalline anisotropies are typically difficult to demagnetize, which is technologically advantageous. Magnetocrystalline anisotropy is inherently strong in heavy, rare-earth elements, but the scarcity of these elements has led scientists to investigate using transition-metal-based compounds as replacements. We demonstrate for the first time how electronic correlations determine the magnetocrystalline anisotropy of transition metals, using the yttrium-cobalt compound as a prototypical substance.
We find that the orbital magnetic moment of differs from estimates based on covalent-band theory—we propose that this discrepancy is due to dynamical electron correlations. Spin-orbit interactions are weak in transition-metal compounds, and in general, their magnetocrystalline anisotropy depends on a delicate balance of competing interactions: Coulomb repulsion, ligand fields, spin-orbit coupling, and material-dependent hybridization. We apply a dynamical mean-field theoretical approach in combination with density-functional theory—which takes into account the competing interactions—to the representative rare-earth-free magnet . We demonstrate for the first time the important role of electronic correlations in determining the magnetocrystalline anisotropy.
Our reliable estimates of the orbital moment, mass enhancement, and the magnetocrystalline anisotropy of provide critical knowledge and new insight into the design of rare-earth-free magnets and complex magnetic functionality in general.
Article Text
References (44)
- L. Lewis and F. Jimnez-Villacorta, Perspectives on Permanent Magnetic Materials for Energy Conversion and Power Generation, Metall. Mater. Trans. A 44, 2 (2013).
- H. R. Kirchmayr and C. A. Poldy, in Handbook on the Physics and Chemistry of Rare Earths, Lecture Notes in Physics Vol. 2 (North Holland, Amsterdam, 1979).
- J. H. van Vleck, On the Anisotropy of Cubic Ferromagnetic Crystals, Phys. Rev. 52, 1178 (1937).
- E. I. Kondorskii and E. Straube, Magnetic Anisotropy of Nickel, Zh. Eksp. Teor. Fiz. 63, 356 (1972) [Sov. Phys. JETP 36, 188 (1973)].
- F. Bloch and G. Gentile, Zur Anisotropie der Magnetisierung Ferromagnetischer Einkristalle, Z. Phys. 70, 395 (1931).
- H. Brooks, Ferromagnetic Anisotropy and the Itinerant Electron Model, Phys. Rev. 58, 909 (1940).
- G. H. O. Daalderop, P. J. Kelly, and M. F. H. Schuurmans, First-Principles Calculation of the Magnetocrystalline Anisotropy Energy of Iron, Cobalt, and Nickel, Phys. Rev. B 41, 11 919 (1990).
- J. Trygg, B. Johansson, O. Eriksson, and J. M. Wills, Total Energy Calculation of the Magnetocrystalline Anisotropy Energy in the Ferromagnetic Metals, Phys. Rev. Lett. 75, 2871 (1995).
- H. J. F. Jansen, Origin of Orbital Momentum and Magnetic Anisotropy in Transition Metals, J. Appl. Phys. 67, 4555 (1990).
- L. Nordström, M. S. S. Brooks, and B. Johansson, Calculation of Orbital Magnetism and Magnetocrystalline Anisotropy Energy in , J. Phys. Condens. Matter 4, 3261 (1992).
- J. Schweizer and F. Tasset, Polarised Neutron Study of the Intermetallic Compounds. I. The Cobalt Magnetisation in , J. Phys. F 10, 2799 (1980).
- A. Heidemann, D. Richter, and K. H. J. Buschow, Investigation of the Hyperfine Fields in the Compounds , , and by Means of Inelastic Neutron Scattering, Z. Phys. B 22, 367 (1975).
- M. S. S. Brooks, Calculated Ground State Properties of Light Actinide Metals and Their Compounds, Physica (Amsterdam) 130B+C, 6 (1985).
- O. Eriksson, M. S. S. Brooks, and B. Johansson, Orbital Polarization in Narrow-Band Systems: Application to Volume Collapses in Light Lanthanides, Phys. Rev. B 41, 7311 (1990).
- J. Alameda, J. Deportes, D. Givord, R. Lemaire, and Q. Lu, Large Magnetization Anisotropy in Uniaxial Intermetallic, J. Magn. Magn. Mater. 15–18, 1257 (1980).
- H. Takahashi, S. Ohtsuka, T. Ukai, and N. Mori, On the Orbital Moment of Co in , J. Magn. Magn. Mater. 70, 189 (1987).
- A. C. Hewson, The Kondo Problem to Heavy Fermions (Cambridge University Press, Cambridge, England, 1993).
- J. B. Goodenough, Magnetism and the Chemical Bond (Interscience-Wiley, New York, 1963).
- I. Yang, S. Y. Savrasov, and G. Kotliar, Importance of Correlation Effects on Magnetic Anisotropy in Fe and Ni, Phys. Rev. Lett. 87, 216405 (2001).
- G. Kotliar, S. Y. Savrasov, K. Haule, V. S. Oudovenko, O. Parcollet, and C. A. Marianetti, Electronic Structure Calculations with Dynamical Mean-Field Theory, Rev. Mod. Phys. 78, 865 (2006).
- M. E. Pezzoli, K. Haule, and G. Kotliar, Neutron Magnetic Form Factor in Strongly Correlated Materials, Phys. Rev. Lett. 106, 016403 (2011).
- A. Grechnev, I. D. Marco, M. I. Katsnelson, A. I. Lichtenstein, J. Wills, and O. Eriksson, Theory of Bulk and Surface Quasiparticle Spectra for Fe, Co, and Ni, Phys. Rev. B 76, 035107 (2007).
- S. Chadov, J.Minár, M. I. Katsnelson, H. Ebert, D. Ködderitzsch, and A. I. Lichtenstein, Orbital Magnetism in Transition Metal Systems: The Role of Local Correlation Effects, Europhys. Lett. 82, 37001 (2008).
- R. M. Martin, Electronic Structure: Basic Theory and Practical Methods (Cambridge University Press, Cambridge, England, 2004).
- R. D. Cowan, The Theory of Atomic Structure and Spectra (University of California Press, Berkeley, 1981).
- M. Czyzyk and G. A. Sawatzky, Local-Density Functional and On-Site Correlations: The Electronic Structure of and , Phys. Rev. B 49, 14 211 (1994).
- J. H. Shim, K. Haule, and G. Kotliar, Fluctuating Valence in a Correlated Solid and the Anomalous Properties of Plutonium, Nature (London) 446, 513 (2007).
- J.-X. Zhu, R. C. Albers, K. Haule, G. Kotliar, and J. M. Wills, Site-Selective Electronic Correlation in -Plutonium Metal, Nat. Commun. 4, 2644 (2013).
- V. I. Anisimov, A. I. Poteryaev, M. A. Korotin, A. O. Anokhin, and G. Kotliar, First-Principles Calculations of the Electronic Structure and Spectra of Strongly Correlated Systems: Dynamical Mean-Field Theory, J. Phys. Condens. Matter 9, 7359 (1997).
- L. Craco, M. S. Laad, S. Leoni, and E. Müller-Hartmann, Insulator-Metal Transition in the Doped Transition Metal Oxide , Phys. Rev. B 70, 195116 (2004).
- K. Held, G. Keller, V. Eyert, D. Vollhardt, and V. I. Anisimov, Metal-Insulator Transition in Paramagnetic : An Study, Phys. Rev. Lett. 86, 5345 (2001).
- M. S. Laad, L. Craco, and E. Müller-Hartmann, Orbital Switching and the First-Order Insulator-Metal Transition in Paramagnetic , Phys. Rev. Lett. 91, 156402 (2003).
- L. V. Pourovskii, M. I. Katsnelson, and A. I. Lichtenstein, Correlation Effects in Electronic Structure of Actinide Monochalcogenides, Phys. Rev. B 72, 115106 (2005).
- J. M. Wills and B. R. Cooper, Synthesis of Band and Model Hamiltonian Theory for Hybridizing Cerium Systems, Phys. Rev. B 36, 3809 (1987).
- O. Grånäs, I. D. Marco, P. Thunström, L. Nordström, O. Eriksson, T. Björkman, and J. M. Wills, Charge Self-Consistent Dynamical Mean-Field Theory Based on the Full-Potential Linear Muffin-Tin Orbital Method: Methodology and Applications, J. Comput. Math. Sci. Teach. 55, 295 (2012).
- Full-Potential Electronic Structure Method: Energy and Force Calculations with Density Functional and Dynamical Mean Field Theory, edited by J. M. Wills, O. Eriksson, M. Alouani, and D. L. Price (Springer-Verlag, Berlin, 2010).
- Permanent Magnetism, edited by R. Skomski and J. M. D. Coey (Taylor and Francis, New York, 1999).
- J. F. Herbst, J. J. Croat, F. E. Pinkerton, and W. B. Yelon, Relationships between Crystal Structure and Magnetic Properties in , Phys. Rev. B 29, 4176 (1984).
- J. J. Croat, J. F. Herbst, R. W. Lee, and F. E. Pinkerton, PrFe and NdFe Based Materials: A New Class of High Performance Permanent Magnets, J. Appl. Phys. 55, 2078 (1984).
- M. Colarieti-Tosti, S. I. Simak, R. Ahuja, L. Nordström, O. Eriksson, D. Aberg, S. Edvardsson, and M. S. S. Brooks, Origin of Magnetic Anisotropy of Gd Metal, Phys. Rev. Lett. 91, 157201 (2003).
- J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized Gradient Approximation Made Simple, Phys. Rev. Lett. 77, 3865 (1996).
- P. Blaha, K. Schwarz, G. K. H. Madsen, D. Kvasnicka, and J. Luitz, WIEN2k: An Augmented Plane Wave+Local Orbitals Program for Calculating Crystal Properties (Technische Universitat Vienna, Vienna, 2001).
- B. T. Thole, P. Carra, F. Sette, and G. van der Lann, X-Ray Circular Dichroism as a Probe of Orbital Magnetization, Phys. Rev. Lett. 68, 1943 (1992).
- P. Carra, B. T. Thole, M. Altarelli, and X. Wang, X-Ray Circular Dichroism and Local Magnetic Fields, Phys. Rev. Lett. 70, 694 (1993).