Calculating spin-lattice interactions in ferro- and antiferromagnets: The role of symmetry, dimension, and frustration

Lange, Hannah; Mankovsky, S.; Polesya, S.; Weißenhofer, Markus; Nowak, Ulrich; Kashyap, Arti

doi:10.1103/physrevb.107.115176

Cited by 3 publications

(3 citation statements)

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“…This is again in line with the idea of the spin-spiral approach: the DM interactions give rise to the spin spirals, while the magnetic anisotropy acts against them, by deforming the spin spirals and locking them to the crystallographic lattice [47,48]. The alternative to the spin-spiral technique is to work in the real space separately for each magnetic bond [49][50][51][52]. Such methods, which have certain limitations, will be briefly considered in section 6.1.…”

Section: Spin Spirals So Coupling and Dm Interactionsmentioning

confidence: 63%

“…Then, 1 2 ( Ĵij − Ĵji ), which has only three inequivalent matrix elements, can be related to the DM vector, while the traceless part of 1 2 ( Ĵij + Ĵji ) gives rise to the exchange anisotropy. This method was successfully implemented in several computational packages, which are actively used for calculations of isotropic as well anisotropic exchange interactions [32,[49][50][51][52]. Nevertheless, one should remember that this method has limitations inherent to the scheme b, which is an approximation.…”

Section: Symmetric Anisotropic Exchange Interactionsmentioning

confidence: 99%

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Linear response theories for interatomic exchange interactions

Solovyev

2024

J. Phys.: Condens. Matter

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The linear response is a perturbation theory establishing the relationship between given physical variable and the external field inducing this variable. A well-known example of the linear response theory in magnetism is the susceptibility relating the magnetization with the magnetic field. In 1987, Liechtenstein \etal came up with the idea to formulate the problem of interatomic exchange interactions, which would describe the energy change caused by the infinitesimal rotations of spins, in terms of this susceptibility. The formulation appears to be very generic and, for isotropic systems, expresses the energy change in the form of the Heisenberg model, irrespectively on which microscopic mechanism stands behind the interaction parameters. Moreover, this approach establishes the relationship between the exchange interactions and the electronic structure obtained, for instance, in the first-principles calculations based on the density functional theory. The purpose of this review is to elaborate basic ideas of the linear response theories for the exchange interactions as well as more recent developments. The special attention is paid to the approximations underlying the original method of Liechtenstein \etal in comparison with its more recent and more rigorous extensions, the roles of the on-site Coulomb interactions and the ligand states, and calculations of antisymmetric Dzyaloshinskii-Moriya interactions, which can be performed alongside with the isotropic exchange, within one computational scheme. The abilities of the linear response theories as well as many theoretical nuances, which may arise in the analysis of interatomic exchange interactions, are illustrated on magnetic van der Walls materials Cr$X_3$ ($X$$=$ Cl, I), half-metallic ferromagnet CrO$_2$, ferromagnetic Weyl semimetal Co$_3$Sn$_2$S$_2$, and orthorhombic manganites $A$MnO$_3$ ($A$$=$ La, Ho), known for the peculiar interplay of the lattice distortion, spin, and orbital ordering.

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Section: Spin Spirals So Coupling and Dm Interactionsmentioning

confidence: 63%

Section: Symmetric Anisotropic Exchange Interactionsmentioning

confidence: 99%

Linear response theories for interatomic exchange interactions

Solovyev

2024

J. Phys.: Condens. Matter

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“…Alternative ways to calculate these coefficients, for example, using a model for the exchange parameters were proposed in [170][171][172][173]. Evaluation method for the spin-lattice coupling coefficients using the Green function method, similar to the LKAG approach [81], and embedded cluster method have been proposed recently in [174] and [175], respectively, and tested for several representative systems. For example, analysis of spin-lattice coefficients in [174] indicated the importance of Dzyaloshinskii-Moriya interactions in Fe bcc, induced by lattice vibrations, for the transfer of angular momentum between the spin and lattice subsystems.…”

Section: Spin-lattice Dynamicsmentioning

confidence: 99%

From electronic structure to magnetism and skyrmions

Borisov

2024

Electron. Struct.

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Solid state theory, density functional theory and its generalizations for correlated systems together with numerical simulations on supercomputers allow nowadays to model magnetic systems realistically and in detail and can be even used to predict new materials, paving the way for more rapid material development for applications in energy storage and conversion, information technologies, sensors, actuators etc. Modelling magnets on diﬀerent length scales (between a few Angström and several micrometers) requires, however, approaches with very diﬀerent mathematical formulations. Parameters deﬁning the material in each formulation can be determined either by ﬁtting experimental data or from theoretical calculations and there exists a well-established approach for obtaining model parameters for each length scale using the information from the smaller length scale. In this review, this approach will be explained step-by-step in textbook style with examples of successful multiscale modelling of diﬀerent classes of magnetic materials from the research literature as well as based on results newly obtained for this review.

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