Search NASA⌕ Search

SEARCH · Search NASA

Results for “rare-earth ions”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records

Lanthanide Separations through Helicate Self-Assembly

Skyrocketing demand for rare-earth elements makes their isolation and reuse from electronic waste an increasingly attractive alternative to mining. Typically, the capture of individual lanthanides from mixtures requires the iterative design of complex, macrocyclic ligands, a sometimes successful but often laborious process. Here we show that the self-assembly of rare-earth ions with a ditopic ligand, L d , results in the selective incorporation of smaller lanthanides and gives rise to impressive separation factors. Comparison to a monotopic ligand, L m , shows that the separation performance of ditopic L d critically depends on the presence of two adjacent binding sites. Isothermal titration calorimetry (ITC) experiments show that the selectivity of L d for smaller ions is thermodynamically driven and provide evidence of positive cooperativity among the two binding sites of L d . The simplicity of the separation procedure reported here, requiring only 1 min of sonication in methanol, shows the potential applicability of this approach to real-world separations. Here, by achieving efficient rare-earth separations in small, synthetically facile helicates, this work shows the promise of self-assembly as a mechanism to drive metal separations.

Alcohols↗

Isolated spin ladders in 𝐿⁢𝑛 2 ⁢Ti 9 ⁢Sb 11 (𝐿⁢𝑛 :La–Nd) metals

Here we present the discovery and characterization of a series of antimonides 𝐿⁢𝑛 2 ⁢Ti 9⁢ Sb 11 (Ln: La–Nd) that exhibit well-isolated, 𝑛 = 2 rare-earth spin ladders. We discuss the structure of these compounds, with a particular focus on the magnetic Ln spin ladders. Nd 2 ⁢Ti 9 ⁢Sb 11 and Ce 2 ⁢Ti 9 ⁢Sb 11 exhibit antiferromagnetic interactions and a well-defined doublet ground state, whereas Pr 2 ⁡Ti 9⁢ Sb 11 exhibits a weakly magnetic singlet ground state. Nd 2 ⁢Ti 9 ⁢Sb 11 is a poor metal with an electrical resistivity of 0.1m⁢Ω cm at 300 K and weak temperature dependence. The thermal conductivity along the ladder exhibits significant field dependence even at 40 K, considerably higher than the magnetic ordering temperature of 1.1 K. Compared to compounds with transition metal spin ladders, the rare-earth elements impart much lower energy scales, making these compounds highly tunable with external stimuli like magnetic fields. In conclusion, the diverse magnetism of the rare-earth ions and Ruderman-Kittel-Kasuya-Yosida interactions further contribute to the potential for a wide array of rich magnetic ground states, positioning these materials as a rare example of an inorganic square spin-ladder platform.

Crystal growth↗

Influence of controlled disorder on the dipolar spin-ice state of Ho-based pyrochlores

Pyrochlore magnets of the form 𝑅 2 ⁢𝐵 2 ⁢O 7 , in which rare-earth ions on the 𝑅 site form a three-dimensional network of corner-sharing tetrahedra, provide a canonical setting for geometrical frustration. Ho-based pyrochlores host a dipolar spin-ice ground state, characterized by Ising moments constrained by the ice rules and elementary excitations analogous to magnetic monopoles. Here, in this work, we examine how controlled chemical disorder influences this state by introducing site mixing on the nonmagnetic 𝐵 site in two compounds. Ho 2⁢ GaSbO 7 contains only Ga 3+ /Sb 5+ charge disorder, whereas Ho 2 ⁢ScSbO 7 exhibits both charge and substantial size disorder arising from the large ionic-radius mismatch between Sc 3+ and Sb 5+ . Although both materials retain the pyrochlore structure, neutron-scattering measurements reveal a reduced correlation length for the 𝑅/𝐵-site cation ordering and enhanced local structural distortions in Ho 2 ⁢ScSbO 7 . Despite these structural differences, bulk thermodynamic measurements and magnetic diffuse scattering demonstrate that both systems exhibit the defining signatures of a dipolar spin-ice state. Low-energy inelastic neutron spectroscopy further uncovers broad magnetic excitations that develop within the dipolar spin-ice regime, a feature absent in pristine Ho pyrochlores and indicative of disorder-induced splitting of the non-Kramers ground-state doublet. Together, these results show that controlled disorder generates tunable transverse-field-driven quantum fluctuations in Ho-based pyrochlores, although the dipolar spin-ice state is remarkably robust to this disorder.

magnetic anisotropy↗

Ramification of complex magnetism in Nd 2 Ir 2 O 7 observed by Raman scattering spectroscopy

Using Raman scattering spectroscopy, we uncover a complex magnetic behavior of Nd2Ir2O7, which stands out among magnetic pyrochlores by the lowest temperature of the all-in-all-out (AIAO) Ir moments ordering (${T}_{{\rm{Ir}}}^{{\rm{N}}} = 33$ K) and the highest temperature at which AIAO order of rare-earth Nd ions is detected (${T}_{{\rm{Nd}}}^{{\rm{* }}}$ = 15 K). Detected magnetic Raman scattering and calculations of expected response allow us to demonstrate that the ordering of Ir magnetic moments is accompanied by an appearance of one-magnon Raman modes at 26.3 and 29.6 meV compatible with the AIAO order and allowing to estimate the energies of Ir-Ir interactions. An additional two-magnon excitation of the AIAO Nd order at around 33 meV appears in the spectra below the ordering temperature of Nd moments ${T}_{{\rm{Nd}}}^{{\rm{* }}}$ = 15 K. In the temperature range between 15 K and 33 K we observe a broad mode, which demonstrates strong temperature dependence and shifts on cooling below 20 K from 14 meV to higher frequencies, and disappears at 5 K, when two-magnon excitation of Nd moments becomes prominent. We suggest an interpretation of this excitation in terms of continuum arising from collective fluctuations of Nd moments above the transition. This complex behavior emerges from the interplay of strong spin-orbit coupling, electronic correlations, and geometric frustration on two magnetic pyrochlore sublattices of Nd and Ir ions.

magnetic properties and materials↗

Enhancement of microwave to optical spin-based quantum transduction via a magnon mode

We propose a method for converting single microwave photons to single optical sideband photons based on spinful impurities in magnetic materials. This hybrid system is advantageous over previous proposals because (i) the implementation allows much higher transduction rates (10 3 times faster at the same optical pump Rabi frequency) than state-of-the-art devices, (ii) high-efficiency transduction is found to happen in a significantly larger space of device parameters (in particular, over 1 GHz microwave detuning), and (iii) it does not require mode volume matching between optical and microwave resonators. We identify the needed magnetic interactions as well as potential materials systems to enable this speed up using erbium dopants for telecom compatibility. This is an important step towards realizing high-fidelity entangling operations between remote qubits and will provide additional control of the transduction through perturbation of the magnet.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Ion-Specific Precipitation of Extractants Enables Rare-Earth Separation and Wastewater Remediation from Solvent Extraction of Critical Elements

The increasing demand for rare-earth elements (REEs) necessitates sustainable recovery strategies, particularly from secondary sources, such as electronic waste. Solvent extraction is the primary industrial method for REE separation; however, the unintentional dissolution of extractants into wastewater poses serious environmental risks, leading to organic contamination and process inefficiencies. Existing wastewater treatment methods struggle to remove these persistent pollutants, underscoring the need for innovative recovery approaches. Herein, we present a ligand-mediated precipitation strategy that simultaneously recovers REEs and removes dissolved extractants from solvent extraction wastewater. We show that residual extractants in the aqueous phase can selectively bind REEs, inducing their precipitation while leaving transition metals in solution. By integrating FTIR spectroscopy, EDS, XPS, EXAFS, and SAXS, we elucidate the mechanism of ion-specific precipitation and the local coordination environment of metal ions in the precipitate. Importantly, we demonstrate that the precipitated extractants can be efficiently recovered and reused, providing a closed-loop solution that enhances sustainability. Applying this method to leachates from samarium–cobalt (Sm–Co) and neodymium–iron–boron (NdFeB) mixed magnets, we achieve highly selective REE precipitation under mild conditions, demonstrating a scalable and cost-effective pathway for REE recovery, wastewater purification, and extractant recycling. In conclusion, by integrating element-specific ligand-mediated precipitation with extractant reuse, this work offers a transformative approach to REE separation that reduces the environmental impact while improving resource efficiency.

E-waste↗

Advanced Analysis of X-ray Fluorescence Measurements of the Interfacial Density of Eu Ions at Liquid–Liquid Interfaces for Solvent Back-Extraction

X-ray fluorescence near total reflection (XFNTR) is the primary technique used to measure the element-specific interfacial density of ions at liquid−liquid interfaces. Fluorescence from ions in the bulk liquids can complicate the determination of the interfacial density; consequently, measurements have been previously limited to samples without ions in the upper phase and with concentrations on the order of 10 μM or less in the lower phase. We modify the analysis of XFNTR data to account for ions in both bulk phases, then demonstrate its use in the context of rare-earth separations processes. In a model of ion stripping (i.e., back-extraction), dodecane solutions of di(2-ethylhexyl)- phosphoric acid (HDEHP) loaded with Eu(III) at the 1 mM level are placed in contact with either pure water or aqueous solutions of nitric or citric acid at pH 3. XFNTR measurements of equilibrated, quiescent samples reveal that citric acid solutions produce a disproportionately large depletion of ions from the interface compared to that from the bulk organic solution, whereas stripping by pure water or nitric acid solutions is negligible. As a result, this advance in the methodology of XFNTR may have broad applicability to the investigation of metal ions in chemical and biological processes at liquid−liquid interfaces.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Irradiation-induced gas production in REBCO-based magnet materials used for future compact fusion reactors

Nuclear fusion is an enticing alternative to current sources of energy, with multilayered Rare-Earth Barium Copper Oxide (REBCO) coated conductors deemed pivotal in the race toward fully realized, commercially viable, and magnetic confinement fusion reactors. In this study, we simulated the ion spectrum expected to evolve from REBCO's nickel-based Hastelloy C-276 substrate and copper stabilizer in an affordable robust compact-like reactor. We then emulated this gas production through helium implantation to investigate changes in materials and superconducting properties. Our results revealed that the substrate and stabilizer are capable of producing protons energetic enough to recoil throughout the tape thickness in appreciable doses, and alphas energetic enough to deposit 7.54 × 1014 ions/cm2 or 50.1 helium appm in the superconducting layer over a 30-year reactor lifetime. The superconducting layer of SuperPower® tapes exhibited at least double the swelling rate of the other major layers, and both SuperPower and Fujikura Ltd. tapes displayed microstructural changes in the REBCO layer not observed in isotropic metals. For the estimated lifetime fluence, the Fujikura tapes showed a ∼1 K reduction in critical temperature and a 32% degradation in critical current for compact reactor-relevant conditions (16 T, 20 K). Nuclear transmutation, low-temperature solder implantations, gas-ion evolution, the influence of gas production on vortex dynamics, and other related considerations are also discussed.

Reis, Chris↗

Structurally Frustrated Remeika Phases: Tolerance Factor and Non-Kramers’ Ion Effects

Quantum materials that are found on the verge of structural, magnetic, and electronic instabilities are deep reservoirs for exotic phenomena. Our criteria to study the reported Ln 5 Ru 6 Sn 18 (Ln = Gd, Tb) are guided by the tolerance factor for Remeika phases─a class of intermetallic compounds with the general formula A 3 M 4 X 13 (where A = rare-earth element, M = transition metal, and X = tetrel), which can be viewed as structural analogues of pseudoperovskites (4 × ABX 3 ), with one of the tetrel atoms occupying the A-site. We have grown single crystals, up to 0.5 cm on the largest facet, of Gd 5 Ru 6 Sn 18 (a = 13.8052(12) Å) and Tb 5 Ru 6 Sn 18 (a = 13.7825(9) Å), which we expect to be on the verge of a formation instability. Bulk magnetic, heat capacity, and electrical transport measurements reveal unusual behavior that originates from the trivalent Gd and Tb ions, with deviations from typical metallic behavior and magnetic ordering that is short-range or disrupted in some other way. Furthermore, to better understand these phenomena, single-crystal neutron diffraction is investigated, which reveals short-range correlations among the partially occupied Tb and Sn sublattices, with 3D-ΔPDF analysis supporting direction-dependent local order. Taken together, these measurements show the utility of using tolerance factors in identifying materials that are likely to exhibit complex phenomena and uncover environments where a formation instability may strongly impact emergent bulk magnetic and electronic phenomena.

36 MATERIALS SCIENCE↗

Re-entrant unconventional superconductivity induced by rare-earth substitution in Nd 1-x Eu x NiO 2 thin films

High temperature superconductivity is typically associated with strong coupling and a large superconducting gap, yet these characteristics have not been demonstrated in the nickelates. Here, we provide experimental evidence that Eu substitution in the spacer layer of Nd 1-x Eu x NiO 2 (NENO) thin films enhances the superconducting gap, driving the system toward a strong-coupling regime. This is accompanied by a magnetic-exchange-driven magnetic-field-enhanced superconductivity. We investigate the upper critical magnetic field, H c2 , and the superconducting gap of superconducting NENO thin films with x = 0.2 to 0.35. Magnetoresistance measurements reveal magnetic-field-enhanced superconductivity in NENO films. We interpret this phenomenon as a result of an interaction between magnetic Eu ions and superconducting states in the Ni d x2-y2 orbital. The upper critical magnetic field strongly violates the weak-coupling Pauli limit. Infrared spectroscopy confirms a large gap-to-Tc ratio $2\Delta /{k}_{B}{T}_{{\rm{c}}}\simeq 5-6$, indicating a stronger coupling pairing mechanism in NENO relative to the Sr-doped NdNiO 2 . The substitution of Eu in the rare-earth layer causes pronounced modifications of the superconducting gap and magnetic interactions in Nd-based nickelates, opening new pathways to engineer high- T c superconductivity in infinite-layer nickelates.

36 MATERIALS SCIENCE↗

REBOUND: Reverse Engineering Bidirectional Outflow Under Non-Equilibrium Diffusion

Rare-earth elements (REEs) are essential for electronics, renewable energy, and defense technologies. However, the current supply of REEs relies on mining concentrated in a few countries and energy-intensive separations. DOE’s Basic Energy Sciences (BES) program has launched a grand challenge which aims to ensure a sustainable supply of critical REEs by developing innovative and environmentally friendly separation methods. As an alternative to costly and harmful traditional methods, the Non-Equilibrium Transport Driven Separations (NETS) initiative has created a microfluidic Y-channel co-flow method that applies external fields to exploit magneto- and electrohydrodynamic effects for separating dilute REE ions from complex feedstocks. Computational fluid dynamics (CFD) studies have identified a few operating conditions with promising ion selectivity and separation efficiency. However, challenges remain regarding Y-channel versatility across feedstocks and accurate incorporation of physical phenomena into CFD models. In this work, we develop a multi-fidelity modelling approach which integrates experimental results with CFD simulation to build a surrogate model for the dependence of separation efficiency to variation of design parameters. The surrogate model enables a reinforcement learning (RL) method to adaptively launch CFD and experimental runs, improving model fidelity around optimal Y-channel parameters.

36 MATERIALS SCIENCE↗

Metal-Dependent Photodissociation of Hydrazone Photoswitches from Rare-Earth Complexes

Rare-earth element separation processes often rely on a small decrease in ionic radii along the series of elements. Separation processes based on the distinct optical properties of REs remain less explored, although photochemical methods may offer a viable alternative. Accurate selection of the synthetic precursors of a photoswitchable acylhydrazonic ligand led to a system that could quantitatively isomerize (E−to−Z) upon irradiation with commercial LED lights. Coordination of the photoswitch with RE III nitrates (RE = La−Lu except Pm and Y) resulted in the retention of the photoswitching properties observed in solution. The lower binding affinity of the generated Z−isomer with RE III ions yielded the dissociation of the complexes upon irradiation (photodissociation) with the release of RE−nitrates in solution. The rate of the reaction was found to be dependent on the optical properties of the RE III ions, with nonemissive complexes (no 4f excited states) dissociating faster than emissive ones (having accessible 4f excited states). A thorough solid-state characterization of the complexes was performed by using crystallographic and photochemical methods. Ultimately, the accessibility of the 4f excited states of the metals following light irradiation and excitation of the ligand led to a decrease in the rate of the reaction due to quenching of the ligand excited state. These results demonstrate that the direct modulation of the metal coordination environment, combined with the metal-dependent reaction rate, could provide a strategy for the development of RE−separation processes based on differences in their optical properties.

Ions↗

Emergent quasi-one-dimensional antiferromagnetism in the distorted kagome magnet CePtPb

CePtPb hosts a distorted kagome lattice of Ce 3+ ions, providing a clean platform to investigate how reduced local symmetry and strong spin-orbit coupling reshape frustrated magnetism. Magnetization, specific heat, and magnetocaloric effect measurements, combined with a symmetry analysis of the single-ion anisotropy, demonstrate that the local 𝑚⁢2⁢𝑚 site symmetry selects a nearly Ising-like Kramers doublet with easy axes lying within the 𝑎⁢𝑏 plane. This results in three distinct in-plane Ising directions and an overall easy-plane anisotropy. The low-energy magnetic response is well captured by a three-sublattice Ising model, which quantitatively reproduces the saturation magnetization for arbitrary in-plane field orientations, including $[110]$ and $[1\bar{⁢1}⁢0]$, as well as the ratio of the field-induced critical fields. For 𝐵∥$[110]$, the phase diagram exhibits two quantum critical points at 𝐵 c⁢1 = 0.25T and 𝐵 c⁢2 = 0.55T, arising from the sequential polarization of the three Ising sublattices. In conclusion, these results reveal that the system develops quasi-one-dimensional spin chains along the 𝑐 axis, emerging from the nominally three-dimensional crystal structure composed of stacked kagome layers, and illustrate how reduced local symmetry can drive effective dimensional reduction in rare-earth Ising magnets.

Li, Fangli [Southern University of Science and Tec↗

Effect of Fluoride Anions on Nd(III) Electrode Processes and Nd Metal Recovery in LiCl–KCl–NdCl 3

Here, this work investigated the impact of fluoride anions on Nd metal recovery in LiCl–KCl–NdCl 3 electrolytes by introducing LiF at a molar F/Nd ratio of 9 at 773 K. The voltammetric measurements confirmed that the fluoride ions facilitated single-step Nd(III)/Nd reduction by promoting the stability of the Nd(III) state compared to two-step reduction (Nd(III)/Nd(II) and Nd(II)/Nd) in all-chloride electrolytes. The stabilized Nd(III) state in the LiF-containing electrolyte effectively suppressed partial Nd(III)/Nd(II) reduction and the back-dissolution of Nd metal via comproportionation. By suppressing these reactions, high round-trip Coulombic efficiencies of 77–86% were achieved in the LiF-containing electrolyte during selective Nd deposition–removal cycles compared to 53–59% in all-chloride electrolytes. The Faradaic yield for Nd metal recovery was estimated at 38.6% in the LiF-containing electrolyte following long-term electrolysis, more than three times higher than 11.3% in all-chloride electrolytes. These results confirm the beneficial effect of fluoride ions on Nd metal recovery in low-melting chloride-based electrolytes, promising efficient Nd recovery at low temperatures.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Structural Investigation of Six Quinary Sulfides Synthesized via the Flux-Assisted Boron-Chalcogen Mixture (BCM) Method: Eu 2+ Containing Members of the RE 3 MTQ 7 (M and T = Transition or Main Group Metals, Q = Chalcogens) Family

For this work, a series of six quinary rare-earth sulfides Ce 4+ 1.85 Eu 2+ 1.15 Na 0.30 SiS 7 , Ce 4+ 1.91 Eu 2+ 1.09 K 0.18 SiS 7 , Ce 4+ 1.96 Eu 2+ 1.04 Rb 0.08 SiS 7 , Ce 4+ 1.98 Eu 2+ 1.02 Cs 0.05 SiS 7 , Ce 4+ 1.97 Eu 2+ 1.03 Ag 0.06 SiS 7 , and Ce 4+ 1.50 Eu 2+ 1.50 CuSiS 7 were obtained in an alkali iodide flux using the boron-chalcogen mixture (BCM) method. Single crystal X-ray diffraction was used to determine the structures of the high quality single crystals that were grown; their elemental compositions were confirmed by energy-dispersive spectroscopy (EDS). The compounds crystallize in the hexagonal crystal system in the noncentrosymmetric space group P63. The crystal structure consists of a three-dimensional network composed of mixed cerium and europium bicapped trigonal prisms, isolated SiS4 tetrahedra, and monovalent metals (Na, K, Rb, Cs, Ag, and Cu) located in cavities created by linked Ce/EuS 8 polyhedra. The structures are charge-balanced when Ce and Eu are in their +4 and +2 oxidation states, respectively. The effective magnetic moment of Ce 1.50 4+ Eu 1.50 2+ CuSiS 7 determined from the temperature dependence of the magnetic susceptibility data is consistent with the presence of Ce 4+ and Eu 2+ . Clear correlations between the alkali ion site occupancy, the ionic radius of the alkali cations, and the average bond length of Ce 4+ /Eu 2+ –S, were established. UV–vis diffuse reflectance data were collected for Ce 1.50 4+ Eu 1.50 2+ CuSiS 7 and a band gap of 1.9(1) eV was established.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Erbium quantum memory platform with long optical coherence via back-end-of-line deposition on foundry-fabricated photonics

Realizing scalable quantum interconnects necessitates the integration of solid-state quantum memories with foundry photonics processes. While prior photonic integration efforts have relied upon specialized, laboratory-scale fabrication techniques, this work demonstrates the monolithic integration of a quantum memory platform with low-loss foundry photonic circuits via back-end-of-line deposition. We deposited thin films of titanium dioxide (Ti⁢O 2 ) doped with erbium (Er) onto silicon nitride nanophotonic waveguides and studied Er optical coherence at subkelvin temperatures with photon echo techniques. Furthermore, we suppressed optical dephasing through ex-situ oxygen annealing and optimized measurement conditions, which yielded an optical coherence time of 64 μ⁢s (a 5-kHz homogeneous linewidth) and slow spectral diffusion of 27 kHz over 4 ms, results that are comparable to state-of-the-art Er nanophotonic devices. Combined with second-long electron spin lifetimes and demonstrated electrical control of Er emission, our findings establish Er:Ti⁢O 2 on foundry photonics as a manufacturable platform for ensemble and single-ion quantum memories.

Electro-optic effects↗

Crystal fields, exchange and dipolar interactions, and noncollinear magnons of erbium oxide

Here, we simulate the properties of magnons in erbium oxide, a noncollinear antiferromagnet, from an effective single-ion Hamiltonian, including exchange and long-range dipolar interactions. We parametrize the crystal-field splitting of Er 2 ⁢O 3 using Steven's operators and obtain the effective symmetry-dependent exchange constants between different erbium ions quenched by the crystal field at different symmetry sites. We apply the Holstein-Primakoff transformation to the noncollinear spin system and employ paraunitary diagonalization for the effective spin Hamiltonian. The addition of the dipolar interaction to the exchange magnon dispersion changes the magnon bands drastically. The long-range nature of the dipolar interaction provides challenges to convergence, however, we find that the averaged and normalized difference in the magnon dispersion is less than an averaged factor of 10 −6 if the dipolar interaction is included out to the 40th nearest neighbor.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

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↗