Electronic structure calculations in a uniform magnetic field using periodic supercells

Lee, Eunseok; Cai, Wei; Galli, Giulia

doi:10.1016/j.jcp.2007.05.022

Cited by 8 publications

(7 citation statements)

References 26 publications

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“…, 其中不再满足原胞的周期性边界条件, 我们称其为磁周期性边界条件(MPBC) [112] . 该定理说明波函数在磁场下的平移会带来一个依赖于规范的相位, 这是磁平移对称性的体现 [114,115] .…”

Section: 含磁矢势的周期性体系计算unclassified

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First-principles calculation method for periodic system under external electromagnetic field

Lü,

Chen,

Xie

et al. 2023

Acta Phys. Sin.

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The exploration of electromagnetic field influences on material characteristics remains a pivotal concern within scientific investigations. Nonetheless, in the realm of computational condensed matter physics, traditional density functional theory's extrapolation to scenarios inclusive of external electromagentic fields poses considerable challenges. These issues largely stem from the disruption of translational symmetry by external fields inherent in periodic systems, rendering Bloch's theorem inoperative. Consequently, the employment of first-principles methodologies in calculating material properties in the presence of external fields becomes an intricate task, especially in circumstances where the external field cannot be approximated as a minor perturbation. Over the past two decades, a significant number of scholars within the field of computational condensed matter physics have dedicated their work towards the formulation and refinement of first-principles computational methodologies adept at handling periodic systems subjected to finite external fields. This paper endeavors to systematically recapitulate these theoretical methodologies and their application across a broad spectrum including, but not limited to, ferroelectric, piezoelectric, ferromagnetic, and multiferroic domains. In the initial segment of this paper, we provide a succinct exposition on modern theory of polarization and delineate the process of constructing two methodologies for computations in finite electric fields predicated on this theory in conjunction with density functional theory. The succeeding segment delves into the integration of external magnetic fields into density functional theory and examines the accompanying computational procedures alongside the challenges they present. In the third segment, we firstly reflect on the first-principles effective Hamiltonian method, prevalent in the study of magnetic, ferroelectric and multiferroic systems, along with its adaptations for situations involving external fields. Concluding the paper, we introduce the exciting developments in constructing effective Hamiltonian models using neural network methods from machine learning, and their extensions under consideration of external fields.

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Section: 含磁矢势的周期性体系计算unclassified

“…图 5 实空间波函数通过两次傅里叶变换到倒空间函数 [112] 性自旋旋转近似", 这在自旋较大时是合理的, 对该近似的进一步讨论见引文 [117] . 一旦得到了磁性有效哈密顿量, 便可以轻易计算出磁构型对应的能量, 并借助蒙特卡罗(MC)模拟 [118] 或者利用Lan-…”

Section: Intermediate Spaceunclassified

First-principles calculation method for periodic system under external electromagnetic field

Lü,

Chen,

Xie

et al. 2023

Acta Phys. Sin.

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“…In the PAW simulations performed for the present work, this backdrop is mimicked by constraining the ground-state spin-polarized electronic structure to converge with an equivalent total magnetization ( m s ), which is an input of the calculation. This is nothing but an approach to emulate the presence of B ext and not an explicit incorporation of it in the simulation using a periodic supercell, which has already been proposed in the literature , and is a matter of current research. The point is that this is one more approximation that will be assessed later on in this report.…”

Section: Theory and Computational Detailsmentioning

confidence: 99%

DFT-GIPAW ²⁷Al NMR Simulations for Intermetallics: Accuracy Issues and Magnetic Screening Mechanisms

Ferreira

2019

J. Phys. Chem. C

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This study reports first-principles simulations of 27Al solid-state nuclear magnetic resonance (ssNMR) shifts (δiso exp) carried out for a set of seven Al-containing intermetallic compounds. With the aim of assessing accuracy issues in such calculations using the gauge-including projector augmented waves method, the referred set was sought to cover the wide range of experimental 27Al δiso exp shifts reported in the literature for this type of compound in a representative way (from about −200 to 1600 ppm). From a technical/computational perspective, the findings allowed the detection of critical sources of inaccuracy and they were addressed to different approximations inherent in the computational methods. Among those, it is possible to highlight the formulation of the exchange-correlation energy functional in density functional theory, which at least for the 27Al nuclide has proved to be more critical than the frozen-core approximation, especially in the case of weakly magnetic aluminides. From a practical point of view, particularly regarding a possible use of such simulations for a more efficient interpretation of experimental ssNMR spectra, key physical insights into the magnetic screening mechanisms underlying the 27Al δiso exp shifts are reported, in which theory supports that in addition to the contributions of closed orbitals, those coming from unpaired electronic spins arise from two main competing hyperfine interactions: the first one with local magnetic moments at specific sites, resulting in a shielding effect and even negative shifts, and the second mechanism in which large Knight shifts to downfield gradually dominate in those compounds having a rather metallic character.

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“…The reason is that previous approaches required performing calculation in the presence of a finite external magnetic field (B), which is a challenge to incorporate with periodic boundary conditions. Though there has been theoretical work in this direction [16,17], so far a widespread implementation is lacking. This situation is in stark contrast with the case of isolated molecules, where finite-B methods are well established in existing codes [18,19].…”

Section: Introductionmentioning

confidence: 99%

Rotational g factors and Lorentz forces of molecules and solids from density functional perturbation theory

2022

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Applied magnetic fields can couple to atomic displacements via generalized Lorentz forces, which are commonly expressed as gyromagnetic g factors. We develop an efficient first-principles methodology based on density functional perturbation theory to calculate this effect in both molecules and solids to linear order in the applied field. Our methodology is based on two linear-response quantities: the macroscopic polarization response to an atomic displacement (i.e., Born effective charge tensor), and the antisymmetric part of its first real-space moment (the symmetric part corresponding to the dynamical quadrupole tensor). The latter quantity is calculated via an analytical expansion of the current induced by a long-wavelength phonon perturbation, and compared to numerical derivatives of finite-wave-vector calculations. We validate our methodology in finite systems by computing the gyromagnetic g factor of several simple molecules, demonstrating excellent agreement with experiment and previous density functional theory and quantum chemistry calculations. In addition, we demonstrate the utility of our method in extended systems by computing the energy splitting of the low-frequency transverse-optical phonon mode of cubic SrTiO 3 in the presence of a magnetic field.

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Electronic structure calculations in a uniform magnetic field using periodic supercells

Cited by 8 publications

References 26 publications

First-principles calculation method for periodic system under external electromagnetic field

First-principles calculation method for periodic system under external electromagnetic field

DFT-GIPAW ²⁷Al NMR Simulations for Intermetallics: Accuracy Issues and Magnetic Screening Mechanisms

Rotational g factors and Lorentz forces of molecules and solids from density functional perturbation theory

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Electronic structure calculations in a uniform magnetic field using periodic supercells

Cited by 8 publications

References 26 publications

First-principles calculation method for periodic system under external electromagnetic field

First-principles calculation method for periodic system under external electromagnetic field

DFT-GIPAW 27Al NMR Simulations for Intermetallics: Accuracy Issues and Magnetic Screening Mechanisms

Rotational g factors and Lorentz forces of molecules and solids from density functional perturbation theory

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Product

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DFT-GIPAW ²⁷Al NMR Simulations for Intermetallics: Accuracy Issues and Magnetic Screening Mechanisms