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Magnetic Exchange Interactions

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Handbook of Magnetism and Magnetic Materials

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Abstract

The electrostatic repulsion between electrons, combined with quantum mechanics and the Pauli principle, yields the atomic-scale exchange interaction. Intra-atomic exchange determines the size of the atomic magnetic moments. Interatomic exchange ensures long-range magnetic order and determines the ordering (Curie or Néel) temperature. It also yields spin waves and the exchange stiffness responsible for the finite extension of magnetic domains and domain walls. Intra-atomic exchange determines the size of the atomic magnetic moments. Positive and negative exchange constants mean parallel (ferromagnetic) and antiparallel (antiferromagnetic) spin alignments. As a rule, direct exchange and Coulomb interaction favor ferromagnetic spin structures, whereas interatomic hopping tends to be ferromagnetic and is often the main consideration. The basic interatomic exchange mechanisms include superexchange, double exchange, Ruderman-Kittel exchange, and itinerant exchange. Exchange interactions may also be classified according to specific models or phenomena. Examples are Heisenberg exchange, Stoner exchange, Hubbard interactions, anisotropic exchange, Dzyaloshinski-Moriya exchange, and antiferromagnetic spin fluctuations responsible for high-temperature superconductivity. From the viewpoint of fundamental physics, exchange interactions differ by the role of electron correlations, the strongly correlated Heisenberg exchange and weakly correlated itinerant exchange at the opposite ends of the spectrum. Correlations are also important for the understanding of some exotic exchange phenomena, such as frustration and quantum spin liquid behavior.

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Acknowledgments

This chapter has benefited from help in details by P. Manchanda and R. Pathak and from discussions with B. Balamurugan, C. Binek, X. Hong, Y. Idzerda, A. Kashyap, P. S. Kumar, D. Paudyal, T. Schrefl, D. J. Sellmyer, and A. Ullah. The underlying research in Nebraska has been supported by DOE BES (DE-FG02-04ER46152) NSF EQUATE (OIA-2044049), the NU Collaborative Initiative, HCC and NCMN.

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  1. University of Nebraska, Lincoln, NE, USA

    Ralph Skomski

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  1. Ralph Skomski
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  1. School of Physics, Trinity College, Dublin, Ireland

    J. M. D. Coey

  2. Max Planck Institute of Microstructure Physics, Halle (Saale), Germany

    Stuart S.P. Parkin

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Skomski, R. (2021). Magnetic Exchange Interactions. In: Coey, J.M.D., Parkin, S.S. (eds) Handbook of Magnetism and Magnetic Materials. Springer, Cham. https://doi.org/10.1007/978-3-030-63210-6_2

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