Ab initio calculation of the Dzyaloshinskii–Moriya parameters: Spin–orbit GSO‐HF, DFT, and CI approaches

Takeda, Ryo; Yamanaka, Shusuke; Yamaguchi, Kizashi

doi:10.1002/qua.21267

Cited by 15 publications

(19 citation statements)

References 22 publications

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“…We have to admit that we are not aware of any microscopic mechanism that could mediate this interaction and tie the value of À to the identity of the 3d metals (Mn or Fe). It may be related to the recent theoretical conjecture on the local character of magnetization [21]; ab initio calculations of DM interactions are definitely needed to shed light on the microscopic origin for coupling structural and magnetic chirality [22]. It is probable that a symmetry analysis of the DM interaction in B20-type crystals can reveal a nontrivial character of tilting the Mn(Fe) moments [23].…”

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confidence: 96%

Chiral Properties of Structure and Magnetism inMn1−xFexGeCompounds: When the Left and the Right are Fighting, Who Wins?

et al. 2013

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Magnetic susceptibility measurements have shown that the compounds Mn(1-x)Fe(x)Ge are magnetically ordered through the whole range of concentrations x = [0.0,1.0]. Small-angle neutron scattering reveals the helical nature of the spin structure with a wave vector, which changes from its maximum (|k| = 2.3 nm(-1)) for pure MnGe, through its minimum (|k| → 0) at x(c) ≈ 0.75, to the value of |k| = 0.09 nm(-1) for pure FeGe. The macroscopic magnetic measurements confirm the ferromagnetic nature of the compound with x = x(c). The observed transformation of the helix structure to the ferromagnet at x = x(c) is explained by different signs of chirality for the compounds with x > x(c) and x

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confidence: 96%

Chiral Properties of Structure and Magnetism inMn1−xFexGeCompounds: When the Left and the Right are Fighting, Who Wins?

et al. 2013

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“…This makes extracting all symmetry‐allowed couplings sometimes impossible from DFT calculations. Exchange constants are typically more reliable for higher symmetry cases, e.g., Heisenberg couplings without spin–orbit coupling. Reliable results for anisotropic couplings that arise from spin–orbit coupling (such as the Dzyaloshinskii–Moriya interaction D ij · ( S i × S j )) and higher order ring‐exchange can sometimes be obtained by DFT formulations with non‐collinear moments . However, such calculations require additional care and are not always reliable …”

Section: Numerical and Analytical Methodsmentioning

confidence: 99%

“…Reliable results for anisotropic couplings that arise from spin-orbit coupling (such as the Dzyaloshinskii-Moriya interaction D ij Á (S i Â S j )) and higher order ringexchange can sometimes be obtained by DFT formulations with non-collinear moments. [50][51][52][53][54][55] However, such calculations require additional care and are not always reliable. [56][57][58] (iv) Since broken symmetry DFT correctly incorporates the essential physics of the isotropic magnetic couplings, it will typically reproduce trends in J (e.g., as a function of crystal structure), even when absolute values prove unreliable.…”

Section: Total Energy (Broken Symmetry) Dftmentioning

confidence: 99%

Ab Initio Approaches for Low‐Energy Spin Hamiltonians

Riedl

Liu

Valentí

et al. 2019

Physica Status Solidi (b)

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Implicit in the study of magnetic materials is the concept of spin Hamiltonians, which emerge as the low‐energy theories of correlation‐driven insulators. In order to predict and establish such Hamiltonians for real materials, a variety of first principles ab initio methods have been developed, based on density functional theory and wavefunction methodologies. In this Feature Article, a basic introduction to such methods and the essential concepts of low‐energy Hamiltonians is provided, with a focus on their practical capabilities and limitations. Furthermore, recent efforts toward understanding a variety of complex magnetic systems that present unique challenges from the perspective of ab initio approaches are discussed.

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“…al. 24 have used a non-collinear approach to estimate the DM interaction. Instead of the use of simple product functions, this work capitalizes on the use of generalized orbitals which are composed of a linear combination of both spinors with different and variable spatial functions.…”

Section: Comparison With Other Methodsmentioning

confidence: 99%

First-principles studies of spin-orbit and Dzyaloshinskii-Moriya interactions in the {Cu3} single-molecule magnet

et al. 2012

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Frustrated triangular molecule magnets such as {Cu3} are characterized by two degenerate S=1/2 ground-states with opposite chirality. Recently it has been proposed theoretically [PRL 101, 217201 (2008)] and verified by ab-initio calculations [PRB 82, 155446 (2010)] that an external electric field can efficiently couple these two chiral spin states, even in the absence of spin-orbit interaction (SOI). The SOI is nevertheless important, since it introduces a splitting in the ground-state manifold via the Dzyaloshinskii-Moriya interaction. In this paper we present a theoretical study of the effect of the SOI on the chiral states within spin density functional theory. We employ a recently-introduced Hubbard model approach to elucidate the connection between the SOI and the Dzyaloshinskii-Moriya interaction. This allows us to express the Dzyaloshinskii-Moriya interaction constant D in terms of the microscopic Hubbard model parameters, which we calculate from first-principles. The small splitting that we find for the {Cu3} chiral state energies (∆ ≈ 0.02 meV) is consistent with experimental results. The Hubbard model approach adopted here also yields a better estimate of the isotropic exchange constant than the ones obtained by comparing total energies of different spin configurations. The method used here for calculating the DM interaction unmasks its simple fundamental origin which is the off-diagonal spin-orbit interaction between the generally multireference vacuum state and single-electron excitations out of those states

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Ab initio calculation of the Dzyaloshinskii–Moriya parameters: Spin–orbit GSO‐HF, DFT, and CI approaches

Cited by 15 publications

References 22 publications

Chiral Properties of Structure and Magnetism inMn1−xFexGeCompounds: When the Left and the Right are Fighting, Who Wins?

Chiral Properties of Structure and Magnetism inMn1−xFexGeCompounds: When the Left and the Right are Fighting, Who Wins?

Ab Initio Approaches for Low‐Energy Spin Hamiltonians

First-principles studies of spin-orbit and Dzyaloshinskii-Moriya interactions in the {Cu3} single-molecule magnet

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