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Spin Excitations in Solids from Many-Body Perturbation Theory

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First Principles Approaches to Spectroscopic Properties of Complex Materials

Part of the book series: Topics in Current Chemistry ((TOPCURRCHEM,volume 347))

Abstract

Collective spin excitations form a fundamental class of excitations in magnetic materials. As their energy reaches down to only a few meV, they are present at all temperatures and substantially influence the properties of magnetic systems. To study the spin excitations in solids from first principles, we have developed a computational scheme based on many-body perturbation theory within the full-potential linearized augmented plane-wave (FLAPW) method. The main quantity of interest is the dynamical transverse spin susceptibility or magnetic response function, from which magnetic excitations, including single-particle spin-flip Stoner excitations and collective spin-wave modes as well as their lifetimes, can be obtained. In order to describe spin waves we include appropriate vertex corrections in the form of a multiple-scattering T matrix, which describes the coupling of electrons and holes with different spins. The electron–hole interaction incorporates the screening of the many-body system within the random-phase approximation. To reduce the numerical cost in evaluating the four-point T matrix, we exploit a transformation to maximally localized Wannier functions that takes advantage of the short spatial range of electronic correlation in the partially filled d or f orbitals of magnetic materials. The theory and the implementation are discussed in detail. In particular, we show how the magnetic response function can be evaluated for arbitrary k points. This enables the calculation of smooth dispersion curves, allowing one to study fine details in the k dependence of the spin-wave spectra. We also demonstrate how spatial and time-reversal symmetry can be exploited to accelerate substantially the computation of the four-point quantities. As an illustration, we present spin-wave spectra and dispersions for the elementary ferromagnet bcc Fe, B2-type tetragonal FeCo, and CrO2 calculated with our scheme. The results are in good agreement with available experimental data.

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Notes

  1. 1.

    In the Bethe–Salpeter equation for the T matrix (30), the product of Green functions appears as the kernel, which is why the letter K is used to denote it (26). It should not be mistaken for the interaction kernel.

  2. 2.

    This can be achieved by avoiding that degenerate subspaces are cut in the construction of the Wannier functions, i.e., if a state is included in the Wannier construction – m summation in (33) – then all states that are degenerate with it should also be included.

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Authors and Affiliations

  1. Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425, Jülich, Germany

    Christoph Friedrich, Ersoy Şaşıoğlu, Mathias Müller & Stefan Blügel

  2. Department Physik, Universität Paderborn, 33095, Paderborn, Germany

    Arno Schindlmayr

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  1. Christoph Friedrich
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  2. Ersoy Şaşıoğlu
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  3. Mathias Müller
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  4. Arno Schindlmayr
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Correspondence to Christoph Friedrich .

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Editors and Affiliations

  1. Dipartimento di Scienza dei Materiali, Università di Milano-Bicocca, via Cozzi 55 20125, Milano, Italy

    Cristiana Di Valentin

  2. UMR5306 Université Lyon 1-CNRS Université Lyon, Institut Lumière Matière and ETSF, Villeurbanne, France

    Silvana Botti

  3. Éole polytechnique fédérale de Lausanne, Institute of Materials, Lausanne, Switzerland

    Matteo Cococcioni

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Friedrich, C., Şaşıoğlu, E., Müller, M., Schindlmayr, A., Blügel, S. (2014). Spin Excitations in Solids from Many-Body Perturbation Theory. In: Di Valentin, C., Botti, S., Cococcioni, M. (eds) First Principles Approaches to Spectroscopic Properties of Complex Materials. Topics in Current Chemistry, vol 347. Springer, Berlin, Heidelberg. https://doi.org/10.1007/128_2013_518

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