Band filling dependence of the Curie temperature in CrO<sub>2</sub>

Solovyev, I. V.; Kashin, I. V.; Мазуренко, В. В.

doi:10.1088/0953-8984/28/21/216001

Cited by 5 publications

(4 citation statements)

References 36 publications

(85 reference statements)

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“…4. The interactions remain sizable up to at least 8th coordination sphere [52,53]. Moreover, since the rutile structure is nonsymmorphic, there are two types of interactions J 7 and J 8 , which are denoted by superscripts ">" and "<".…”

Section: Half-metallic Ferromagnetic Cro2mentioning

confidence: 99%

Exchange interactions and magnetic force theorem

Solovyev

2020

Preprint

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We critically reexamine the problem of interatomic exchange interactions, which describe the total energy change caused by infinitesimal rotations of spins near some equilibrium state in the framework of constrained spin-density functional theory (cSDFT). For the small variations of the spin magnetization, such interactions can be always related to the response function (or transverse spin susceptibility). However, the form of this relation can depend on additional approximations supplementing the practical calculations. Particularly, the commonly used magnetic force theorem prescribes the linear relation between the exchange interactions and the response function, while the exact theory requires this dependence to be inverse, as it can be rigorously derived from cSDFT. We explore the origin and consequences of these differences in the definition for the wide class of materials, including ferromagnetic Ni, antiferromagnetic NiO, half-metallic ferromagnetic CrO2, multiferroic HoMnO3, and layered van der Waals magnets CrCl3 and CrI3. While in most of these cases, the magnetic force theorem produces quite reasonable results and can be rigorously justifies in the long wavelength and strong-coupling limits, the exact formulation appears to be more consistent, especially in dealing with two important issues, which typically arise in the theory of exchange interactions: (i) the treatment of the ligand states, and (ii) the choice of the suitable variable for the description of infinitesimal rotations in the system of spins within cSDFT. Both issues can be efficiently resolved by employing the ideas of adiabatic spin dynamics supplemented with the exact expression for the exchange interactions. Particularly, the ligand states can produce quite sizable contributions to the total energy change. For this case, we propose a simple "downfolding" procedure of elimination of the ligand spins from the model by transferring their effect to the interaction parameters between the localized 3d spins. Furthermore, the exchange interactions appear to be sensitive to the definition of the variable, which is used in order to describe the rotations of spins in cSDFT: generally, the rotations of spin moments and spin magnetization matrix lead to different results. In this respect, we argue that the rotations of spin moments are more suitable for the description of low-energy excitations, while the rotations of the whole magnetization matrix cause much stronger perturbation in the system of spins.I.

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Section: Half-metallic Ferromagnetic Cro2mentioning

confidence: 99%

Exchange interactions and magnetic force theorem

Solovyev

2020

Preprint

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“…This approach is especially important for metallic systems, where the static Hartree-Fock approximation is clearly insufficient and, as long as the Coulomb interactions are taken into account, they should be treated on a more rigorous footing. For instance, the dynamic correlations have a profound effect on the electronic structure of half-metallic compounds [119], which is reflected in the behavior of exchange interactions, as was demonstrated for CrO 2 [120,169]. However, as the most interesting applications of this method are beyond the strong-coupling limit, the scheme b can have serious limitations.…”

Section: Dynamic Electron Correlationsmentioning

confidence: 99%

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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“…This approach is especially important for metallic systems, where the static Hartree-Fock approximation is clearly insufficient and, as long as the Coulomb interactions are taken into account, they should be treated on a more rigorous footing. For instance, the dynamic correlations have a profound effect on the electronic structure of half-metallic compounds [115], which is reflected in the behavior of exchange interactions, as was demonstrated for CrO 2 [108,156]. However, as the most interesting applications of this method are beyond the strong-coupling limit, the scheme b can have serious limitations.…”

Section: Dynamic Electron Correlationsmentioning

confidence: 99%

Linear response based theories for Dzyaloshinskii-Moriya interactions

Solovyev

2023

Phys. Rev. B

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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 wellknown example of the linear response theory in magnetism is the susceptibility relating the magnetization with the magnetic field. In 1987, Liechtenstein et al 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 resent developments. The special attention is paid to the approximations underlying the original method of Liechtenstein et al 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 CrX 3 (X= Cl, I), half-metallic ferromagnet CrO 2 , ferromagnetic Weyl semimetal Co 3 Sn 2 S 2 , and orthorhombic manganites AMnO 3 (A= La, Ho), known for the peculiar interplay of the lattice distortion, spin, and orbital ordering.

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Band filling dependence of the Curie temperature in CrO₂

Cited by 5 publications

References 36 publications

Exchange interactions and magnetic force theorem

Exchange interactions and magnetic force theorem

Linear response theories for interatomic exchange interactions

Linear response based theories for Dzyaloshinskii-Moriya interactions

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Band filling dependence of the Curie temperature in CrO2

Cited by 5 publications

References 36 publications

Exchange interactions and magnetic force theorem

Exchange interactions and magnetic force theorem

Linear response theories for interatomic exchange interactions

Linear response based theories for Dzyaloshinskii-Moriya interactions

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Band filling dependence of the Curie temperature in CrO₂