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Journal of Chemical Physics / Volume 130 / Issue 19 / ARTICLES / Theoretical Methods and Algorithms

J. Chem. Phys. 130, 194109 (2009); http://dx.doi.org/10.1063/1.3134430 (14 pages)

Magnetic anisotropy from density functional calculations. Comparison of different approaches: Mn12O12 acetate as a test case

Christoph van Wüllen

Fachbereich Chemie, Technische Universität Kaiserslautern, Erwin-Schrödinger-Straße, 67663 Kaiserslautern, Germany

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(Received 18 September 2008; accepted 24 April 2009; published online 18 May 2009)

Magnetic anisotropy is the capability of a system in a triplet or higher spin state to store magnetic information. Although the source of the magnetic anisotropy is the zero-field splitting of the ground state of the system, there is a difference between these two quantities that has to be fully rationalized before one makes comparisons. This is especially important for small spins such as triplets, where the magnetic anisotropy energy is only half of the zero-field splitting. Density functional calculations of magnetic anisotropy energies correspond to a high-field limit where the spins are aligned by the external magnetic field. Data are presented for the well-studied molecular magnet Mn12O12 acetate. Both perturbative and self-consistent treatments, different quasirelativistic Hamiltonians (zeroth order regular approximation, Douglas–Kroll, effective core potentials) and exchange-correlation functionals are compared. It is shown that some effects usually considered minor, such as the inclusion of the exchange-correlation potential in the effective one-particle spin-orbit operator, lead to sizable differences when computing magnetic anisotropy energies. Higher-order contributions, that is, the difference between self-consistent and perturbative results, increase the magnetic anisotropy energy somewhat but do not introduce sizeable quartic terms or an in-plane anisotropy. In numerical experiments, on can switch off and on spin-orbit coupling at individual atomic sites. This procedure yields single-site contributions to the overall magnetic anisotropy energy that could be used as parameters in phenomenological spin Hamiltonians. If ferrimagnetic systems are treated with broken symmetry density functional methods where the Kohn–Sham reference function is not a spin eigenfunction, corrections are needed which depend on the size of the exchange couplings in the system and must therefore be evaluated case by case.

© 2009 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. ZERO-FIELD SPLITTING AND MAGNETIC ANISOTROPY ENERGY
  3. COMPUTATIONAL DETAILS AND CALIBRATION OF SPIN-ORBIT METHODS
  4. RESULTS FOR Mn12
  5. CONCLUSIONS

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KEYWORDS and PACS

Keywords

density functional theory, exchange interactions (electron), magnetic anisotropy, molecular magnetism, organic compounds, spin Hamiltonians, spin-orbit interactions

PACS

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3134430

PUBLICATION DATA

ISSN

0021-9606 (print)  
1089-7690 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

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