Conduction-electron<i>g</i>-factor measurements in platinum

Gustafsson, Peter; Ohlsén, H.; Nordborg, L.

doi:10.1103/physrevb.33.3749

Cited by 14 publications

(5 citation statements)

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“…In the alkali metals [1] the Zeeman splitting is found to be isotropic, but the g factor deviates from the free-electron value of 2. On the other hand, in Rh [2], Pd [3,4], Ir [5], and Pt [6,7] the cyclotron-orbit g factor (g c ) is found to be strongly anisotropic, and it is also known that in Pd and Pt the average g factor is large. The g c factor in the noble metals [8] also shows a strong anisotropy.…”

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Zeeman splitting in Pd and Pt calculated from self-consistent band structure including an external magnetic field

Hjelm

Calais

1991

Phys. Rev. Lett.

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Fully self-consistent band-structure calculations have been performed for palladium and platinum. The effective Hamiltonian contains exchange, correlation, and relativistic effects as well as the external magnetic field. The anisotropy of the cyclotron-orbit Zeeman splitting agrees well with experimental data from de Haas-van Alphen measurements. The calculated total susceptibilities also agree with the experimental values.PACS numbers: 71.70.Ej, 71.25.Jd, 75.20.En The Zeeman splitting of cyclotron orbits has been thoroughly investigated by means of the de Haas-van Alphen (dHvA) effect. In the alkali metals [1] the Zeeman splitting is found to be isotropic, but the g factor deviates from the free-electron value of 2. On the other hand, in Rh [2], Pd [3,4], Ir [5], and Pt [6,7] the cyclotron-orbit g factor (g c ) is found to be strongly anisotropic, and it is also known that in Pd and Pt the average g factor is large. The g c factor in the noble metals [8] also shows a strong anisotropy. Previous experience indicates that simple band-structure models with the magnetic field taken into account by first-order perturbation theory cannot explain this behavior.To our knowledge, no calculations aiming at a total picture of the Zeeman splitting have been performed. MacDonald [9] has calculated average g factors for the transition metals including spin-orbit coupling, but without exchange and correlation effects. Jarlborg and Freeman [10] have calculated g factors for certain k points on the Fermi surface of Pd, neglecting spin-orbit coupling. For comparison with dHvA experiments, cyclotron-orbit values must be calculated. This has been done, including spin-orbit coupling but without enhancement of the Zeeman splitting from exchange and correlation, for the platinum group metals [11], noble metals [12], and alkali metals [13]. These studies show that spin-orbit coupling is the dominant source of the anisotropy for most Fermisurface sheets and indicate that exchange and correlation enhancement must be included in the model in order to also get the right order of magnitude of the Zeeman splitting. In the present paper results for Pd and Pt are presented using a calculational scheme where the external magnetic field is included in the self-consistent cycle, which allows the spin-dependent exchange-correlation potential and the spin-orbit coupling to affect the Zeeman splitting.In an external magnetic field, a Fermi-surface sheet in a paramagnetic or diamagnetic metal is split into two slightly different surfaces. The interference between the two dHvA signals of these sheets will then appear as a modulation of the amplitude, according to a cosine function with argument xR, where A\ and A 2 are the extremal cross-sectional areas of the two split surfaces perpendicular to the magnetic field, and B is the applied field strength. In moderate fields (i.e., for small splittings) R can be approximated bywhere m c is the effective cyclotron mass in units of the free-electron mass. In this paper, R is calculated and compared to exp...

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“…Experimental results are from Ref. [6]. term, the LSDA with spherically averaged densities, and the parametrized exchange-correlation potential from von Barth and Hedin [16] serves as a useful tool for calculating the electronic structure of metals in external magnetic fields.…”

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Zeeman splitting in Pd and Pt calculated from self-consistent band structure including an external magnetic field

Hjelm

Calais

1991

Phys. Rev. Lett.

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“…In the corresponding ODF scheme traditionally used in older stellar atmosphere computations, the problem is the same and was discussed for example in Saxner & Gustafsson (1984), where it was concluded that the cost in increased computing time as function of the number of individual opacity species made it unfeasible to continue the ODF scheme for cooler stars. Newer stellar models are therefore usually computed based on the opacity sampling scheme, as discussed for example in Jorgensen (1992), Gustafsson & Jorgensen (1994), and Helling & Jorgensen (1998). It is, however, not obvious how one should treat the strong atomic lines correctly in the opacity sampling scheme, and if these are important in exoplanetary atmospheres alongside with the multitude of molecular lines, the correlated-k method may turn out to be superior, or a new hybrid method may be needed.…”

Section: Introductionmentioning

confidence: 99%

Harnessing machine learning for accurate treatment of overlapping opacity species in general circulation models

Schneider,

Mollière,

Louppe

et al. 2024

A&A

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To understand high precision observations of exoplanets and brown dwarfs, we need detailed and complex general circulation models (GCMs) that incorporate hydrodynamics, chemistry, and radiation. For this study, we specifically examined the coupling between chemistry and radiation in GCMs and compared different methods for the mixing of opacities of different chemical species in the correlated-k assumption, when equilibrium chemistry cannot be assumed. We propose a fast machine learning method based on DeepSets (DS), which effectively combines individual correlated-k opacities (k-tables). We evaluated the DS method alongside other published methods such as adaptive equivalent extinction (AEE) and random overlap with rebinning and resorting (RORR). We integrated these mixing methods into our GCM (expeRT/MITgcm) and assessed their accuracy and performance for the example of the hot Jupiter HD 209458 b. Our findings indicate that the DS method is both accurate and efficient for GCM usage, whereas RORR is too slow. Additionally, we observed that the accuracy of AEE depends on its specific implementation and may introduce numerical issues in achieving radiative transfer solution convergence. We then applied the DS mixing method in a simplified chemical disequilibrium situation, where we modeled the rainout of TiO and VO, and confirmed that the rainout of TiO and VO would hinder the formation of a stratosphere. To further expedite the development of consistent disequilibrium chemistry calculations in GCMs, we provide documentation and code for coupling the DS mixing method with correlated-k radiative transfer solvers. The DS method has been extensively tested to be accurate enough for GCMs; however, other methods might be needed for accelerating atmospheric retrievals.

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“…Noteworthy are the works by Krishna Swamy (1969) and Gustafsson et al (1975); the latter in particular constitutes the first extended grid of theoretical 1D model atmospheres of giant stars with metallicities ranging from solar down to [Fe/H]= −3. ‡ Since then, 1D model stellar atmospheres have been continuously developed and improved (see, e.g., reviews by Gustafsson & Jorgensen 1994, Asplund 2005, especially with regard to input physics and opacities, and are still nowadays the most widely used models in stellar abundance analyses.…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional models of metal-poor stars

Collet

2008

Phys. Scr.

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I present here the main results of recent realistic, 3D, hydrodynamical simulations of convection at the surface of metal-poor red giant stars. I discuss the application of these convection simulations as time-dependent, 3D, hydrodynamical model atmospheres to spectral line formation calculations and abundance analyses. The impact of 3D models on derived elemental abundances is investigated by means of a differential comparison of the line strengths predicted in 3D under the assumption of local thermodynamic equilibrium (LTE) with the results of analogous line formation calculations performed with classical, 1D, hydrostatic model atmospheres. The low surface temperatures encountered in the upper photospheric layers of 3D model atmospheres of very metal-poor stars cause spectral lines of neutral metals and molecules to appear stronger in 3D than in 1D calculations. Hence, 3D elemental abundances derived from such lines are significantly lower than estimated by analyses with 1D models. In particular, differential 3D−1D LTE abundances for C, N, and O derived from CH, NH, and OH lines are found to be in the range −0.5 to −1 dex. Large negative differential 3D−1D corrections to the Fe abundance are also computed for weak low-excitation Fe i lines. The application of metal-poor 3D models to the spectroscopic analysis of extremely iron-poor halo stars is discussed.

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Conduction-electrong-factor measurements in platinum

Cited by 14 publications

References 19 publications

Zeeman splitting in Pd and Pt calculated from self-consistent band structure including an external magnetic field

Zeeman splitting in Pd and Pt calculated from self-consistent band structure including an external magnetic field

Harnessing machine learning for accurate treatment of overlapping opacity species in general circulation models

Three-dimensional models of metal-poor stars

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