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Results for “crystal field multiplet theory”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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DOE OSTI2025

Kβ X-ray Emission Spectra Analysis Using Bayesian Optimization

The Kβ X-ray emission spectrum of 3 d transition metals is rich with electronic and structural information due to strong exchange interactions with the valence shell of the metal, and has become crucial for understanding their spin and oxidation states. The spectrum is commonly treated using crystal-field multiplet theory, a semi-empirical theory that uses tunable parameters to control the strength of the effects present in X-ray emission spectroscopy (XES). However, determining the experimental values of these parameters remains a challenge. We present a methodology that applies Bayesian optimization to crystal-field multiplet theory to determine parameter values. The algorithm is tested on the X-ray emission spectra of a collection of Mn, Co, and Ni oxides. We are able to find optimal values for the four most impactful parameters: Slater−Condon reduction factors F dd , F pd , and G pd , and crystal field splitting 10 Dq . The algorithm produces significantly improved accuracy compared to current analysis methods, and probes interparameter dependencies by modeling the error landscape. This advancement enhances XES analysis by offering an approach of obtaining quantitative electronic structural information on 3 d transition metal valence shells, facilitating applications across various scientific fields.

Bayesian optimization↗

DOE OSTI2025

Satellites, core hole excitations, and spin-resolved electronic structure in the spectroscopy of half-metallic CrO 2

Photoelectron satellites—the structures appearing on the low kinetic or high binding-energy side of the “main” or “elastic” photopeak—betray the complex many-body interactions set in motion by the sudden creation of the core hole. In this work, we demonstrate, using the technologically important ferromagnetic half-metal CrO 2 , how such satellites can manifest themselves in other core-level spectroscopies of the material and how they can reveal important details pertinent to its electronic structure. Specifically, we identify a fluorescence satellite in the Cr 𝐿 3 resonant x-ray-emission spectra that radiates at a constant emission energy across the Cr 𝐿 3 x-ray edge with energy ≈1.3 eV above the ordinary valence fluorescence. Here, we provide evidence that this feature arises from the valence recombination of the Cr 2⁢𝑝 core hole “dressed” by the same shakeup charge-transfer process present in both the Cr x-ray photoelectron and the Cr x-ray absorption spectra with its energy uniquely measuring the exchange splitting of the Cr 3⁢𝑑 level. Further analysis of the x-ray emission data reveals three additional features that radiate at constant loss energy that are attributed to combinations of Cr 3⁢𝑑⁢(𝑡 2⁢𝑔 ) → Cr 3⁢𝑑⁢(𝑡 2⁢𝑔 ), charge-transfer O 2⁢𝑝→Cr 3⁢𝑑, and crystal-field Cr⁢ 3⁢𝑑⁡(𝑡 2⁢𝑔 )→Cr⁢ 3⁢𝑑⁡(𝑒 𝑔 ) excitations. These assignments and their energies are supported by density-functional theory calculations, the accuracy of which we demonstrate by hard x-ray valence-photoemission measurements. Atomic multiplet calculations, which include crystal-field effects, help interpret x-ray photoelectron and x-ray absorption spectra of the covalently mixed Cr ion. Resonant Cr K-𝐿 2,3 ⁢𝐿 2,3 Auger-electron emission spectra support a ligand-to-metal nature of the charge-transfer process while highlighting the charge sensitivity differences between photon-in/electron-out and photon-in/photon-out spectroscopies.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Stability, electronic quantum states, and magnetic interactions of Er 3+ ions in Ga 2 ⁢O 3

Here, we report an ab initio study of phase stability, defect formation, electronic structure, and multiple magnetic, Dzyaloshinskii-Moriya, optical, hyperfine, and crystal field interactions in erbium (Er)-doped wide band gap 𝛼- and 𝛽-gallium oxides (Ga 2 ⁢O 3 ), critically important to make a foundation for both optoelectronic and quantum information applications. The chemical, structural, mechanical, and dynamical stabilities of the pristine phases are confirmed from respective negative formation energies, negative cohesive energies, favorable elastic constants, and positive phonon frequencies. The phonon dispersions indicate that the Ga-O bonds are uniform in the 𝛼-phase, while they vary in the 𝛽-phase due to the anisotropic polyhedral movement. The defect formation energy analysis confirms that both Er-doped 𝛼- and 𝛽−Ga 2 ⁢O 3 prefer Er 3+ (neutral) state. The underestimated band gaps of the pristine phases from standard density functional theory (DFT) calculations as compared to experimental values are corrected by employing the hybrid functional calculations, resulting in the indirect band gaps of 5.21 eV in 𝛼−Ga 2 ⁢O 3 and 4.94 eV in 𝛽−Ga 2 ⁢O 3 . The site preference energy analysis indicates partial occupation of Er in the octahedral site of Ga. The anisotropic nature of hyperfine tensor coefficients of Er is similar in both phases, which may be due to the occupation of Er in the same octahedral Ga site. On the other hand, the calculated magnetic exchange interaction between two Er dopants is negative for 𝛼 and positive for 𝛽, indicating an antiferromagnetic (AFM) ground state in the former and a ferromagnetic (FM) ground state in the latter. Large values of Dzyaloshinskii-Moriya interactions (DMIs) are obtained along the 𝑥 direction in the 𝛼 and along the 𝑦 direction in the 𝛽. The large DMI may support exotic magnetic textures, a promising direction for spintronic applications. The analysis of dielectric constants and refractive indices of both pristine and Er-doped phases shows a good agreement with available experimental values. The calculated optical anisotropy is slightly higher in 𝛽 than those in 𝛼, which is due to the involvement of lower symmetry in 𝛽. The crystal field coefficients (CFCs) calculated from DFT are used to analyze 4⁢𝑓 multiplets and 4⁢𝑓 −4⁢𝑓 transitions. Thus calculated lowest energy level of the first excited state to the lowest energy level of the ground state is about 1.53 µ⁢m, which is in a good agreement with available experiments, and it falls within the quantum telecommunication wavelength range.

3-dimensional systems↗