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At least 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

On the origin of magnetic anisotropy in 4f-free ferromagnets based on the CaCu 5 structure *

Using first-principles calculations, we investigate the origin of magnetocrystalline anisotropy in a series of 4f-electron-free intermetallics with CaCu 5 -based structures: YCo 5 , YCo 4 B, and Y 3 Co 13 B 2 . The electronic structure of these compounds is characterized by a set of narrow 3d bands near the Fermi level. In YCo 5 the easy-axis anisotropy originates primarily in the spin–orbit coupling-induced mixing of the electronic states with Co d x 2 -y 2 and d xy character. The analysis of k-resolved anisotropy shows that positive contributions accumulate from the entire Brillouin zone but are particularly large near the k z = 0 plane. The analysis of the single-site and two-site terms reveals a large positive single-site contribution to the magnetocrystalline anisotropy from the Co atoms on the honeycomb sublattice, along with two-site contributions from both honeycomb and kagome sublattices.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

High-throughput studies of novel magnetic materials in borides

Borides are a versatile material family with various properties for valuable applications. Conventional magnetism, such as ferromagnetism and antiferromagnetism in borides, have been extensively studied. However, research on unconventional magnetism in borides where quantum effects are dominant is scarce. Here, we implement a high-throughput workflow combining first-principles calculations, materials prediction, and magnetic properties calculations to discover novel magnetism and magnetic materials in borides. Successfully applying the workflow, we report three families of novel magnetic borides, including two families of borides exhibiting quantum magnetism. One is a family of dimerized quantum magnets among YCrB 4 -type borides, which provides a rare platform for studying the spin-gap quantum critical point. The other is a family of altermagnets among FeMo2B 2 -type borides, extending the magnetic orderings exhibited by borides beyond conventional ferromagnetism and antiferromagnetism. We also predict a family of magnetic laminate transition metal borides, known as the MAB phases, in the AlFe 2 B 2 -type family, which provide pure-phase or alloying candidates for studying magnetocaloric materials and the associated magnetic transitions. The workflow is expected to be used in further studies of novel magnetism and magnetic materials.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Evidence for Ga clusters in β-Ga 2 O 3 from Raman spectroscopy and density functional theory

Monoclinic gallium oxide (β-Ga 2 O 3 ) single crystals have a Raman mode at ∼250 cm −1 that is strongly correlated with free-electron density. Prior work attributed this peak to an electronic excitation of a shallow donor impurity band. However, heavily n-type thin films grown by metalorganic chemical vapor deposition or molecular beam epitaxy do not have the peak. In the present work, an alternate model is proposed: the 250 cm −1 Raman peak arises from Ga clusters, defined as two or more Ga atoms that form Ga–Ga bonds. Raman mapping reveals variations in the frequency that are consistent with a distribution of cluster sizes. The intensity of the peak decreases as the temperature is raised, attributed to melting of the Ga clusters. First-principles calculations indicate that the 250 cm −1 mode is due to Ga–Ga bond-stretching vibrations. As the Fermi energy is raised, the formation of Ga–Ga dimers becomes energetically favorable, explaining the correlation between n-type conductivity and the appearance of the Raman peak.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Monolayer 1T-LaN 2 : Dirac spin-gapless semiconductor of p -state and Chern insulator with a high Chern number

Two-dimensional transition-metal dinitrides have attracted considerable attention in recent years due to their rich magnetic properties. Here, we focus on rare-earth-metal elements and propose a monolayer of lanthanum dinitride with a 1T structural phase, 1T-LaN 2 . Using first-principles calculations, we systematically investigated the structure, stability, magnetism, and band structure of this material. It is a flexible and stable monolayer exhibiting a low lattice thermal conductivity, which is promising for future thermoelectric devices. Here, the monolayer shows the ferromagnetic ground state with a spin-polarized band structure. Two linear spin-polarized bands cross at the Fermi level forming a Dirac point, which is formed by the p atomic orbitals of the N atoms, indicating that monolayer 1T-LaN 2 is a Dirac spin-gapless semiconductor of p-state. When the spin–orbit coupling is taken into account, a large nontrivial indirect bandgap (86/354 meV) can be opened at the Dirac point, and three chiral edge states are obtained, corresponding to a high Chern number of C = 3, implying that monolayer 1T-LaN 2 is a Chern insulator. Importantly, this kind of band structure is expected to occur in more monolayers of rare-earth-metal dinitride with a 1T structural phase.

2D materials↗
DOE OSTI2022

Role of defects in ultra-high gain in fast planar tin gallium oxide UV-C photodetector by MBE

Here we report ultra-high responsivity of epitaxial (Sn x Ga 1–x ) 2 O 3 (TGO) Schottky UV-C photodetectors and experimentally identified the source of gain as deep-level defects, supported by first principles calculations. Epitaxial TGO films were grown by plasma-assisted molecular beam epitaxy on (–201) oriented n-type β-Ga 2 O 3 substrates. Fabricated vertical Schottky devices exhibited peak responsivities as high as 3.5 ×10 4 A/W at –5 V applied bias under 250 nm illumination with sharp cutoff shorter than 280 nm and fast rise/fall time in milliseconds order. Hyperspectral imaging cathodoluminescence (CL) spectra were examined to find the mid-bandgap defects, the source of this high gain. Irrespective of different tin mole fractions, the TGO epilayer exhibited extra CL peaks at the green band (~2.20 eV) not seen in β-Ga 2 O 3 along with enhancement of the blue emission-band (~2.64 eV) and suppression of the UV emission-band. Based on hybrid functional calculations of the optical emission expected for defects involving Sn in β-Ga 2 O 3 , V Ga –Sn complexes are proposed as potential defect origins of the observed green and blue emission-bands. Such complexes behave as acceptors that can efficiently trap photogenerated holes and are predicted to be predominantly responsible for the ultra-high photoconductive gain in the Sn-alloyed Ga 2 O 3 devices by means of thermionic emission and electron tunneling. Regenerating the V Ga –Sn defect complexes by optimizing the growth techniques, we have demonstrated a planar Schottky UV-C photodetector of the highest peak responsivity.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Optical properties of vacancies in aluminum oxide (𝛼−Al 2 ⁢O 3 ) from first principles

We employ first-principles calculations based on hybrid density functional theory to investigate the structural and optical properties of the oxygen vacancy (𝑉 O ) and aluminum vacancy (𝑉 Al ) in 𝛼−Al 2 ⁢O 3 , the most stable (corundum) phase of alumina. Our calculations facilitate the identification of experimental excitation and luminescence spectra with specific electronic transitions at the vacancy sites. The absorption line shape for excitation of an electron at 𝑉$^0_O$ to the conduction-band minimum (CBM) is in excellent agreement with the 6.1 eV band detected by optical absorption spectroscopy, and we find that the 5.9 eV absorption band is generated by an internal electron transition at 𝑉$^0_O$. We confirm that the slowly decaying 3.0 eV emission band of the 𝐹 center is due to a triplet-singlet transition at 𝑉$^0_O$. Our calculations also reveal that the 4.8 eV/5.4 eV absorption and 3.8 eV emission bands assigned to the 𝐹 + center are generated by internal transitions at 𝑉$^{+1}_O$. The line shape for the excitation of an electron from 𝑉$^{+1}_O$ to the CBM agrees well with an absorption band at 6.4 eV, while the recombination of an electron with 𝑉$^{+2}_O$ also produces luminescence around 3.8 eV, but with a considerably broader line shape. For Al vacancies, we confirm that the most prevalent configuration in 𝛼−Al 2 ⁢O 3 is a split-vacancy configuration 𝑉 Al,s , and we calculate migration barriers for different directions in the corundum crystal. We predict absorption and emission spectra for the excitation and recombination of an electron localized at 𝑉$^{−3}_{Al}$ and 𝑉$^{−3}_{Al,s}$ sites with the CBM. The line shapes of the two 𝑉 Al configurations overlap and are considerably broader than the spectra corresponding to 𝑉 O .

36 MATERIALS SCIENCE↗
DOE OSTI2025

Competing magnetic phases in Li-Fe-Ge kagome systems

Competing interlayer magnetic interactions in kagome magnets can lead to diverse magnetic phases, which enable promising topological or quantum material properties. In this work, the electronic structure and magnetic properties are studied using first-principles calculations for the Li⁢Fe6⁢G⁡e6, Li⁢Fe6⁢G⁡e4, and Li⁢Fe6⁢G⁡e5 compounds sharing the kagome F⁡e3⁢Ge layer motif but with different interlayer arrangements. For Li⁢Fe6⁢G⁡e4 and Li⁢Fe6⁢G⁡e5, the predicted magnetic ground states are collinear antiferromagnetic (AFM) states involving a mix of ferromagnetic (FM) and AFM interlayer orientations. In contrast, for Li⁢Fe6⁢G⁡e6, an incommensurate cycloidal spin spiral ground state is stabilized, although its energy is close to a collinear A-type AFM state. The analysis of magnetic RKKY exchange coupling confirms the results of calculations. The values of atomic magnetic moments are in good agreement with existing experimental estimations. Our experiments on Li⁢Fe6⁢G⁡e6 single crystals reveals AFM ordering at ∼540 K and transition to another magnetic phase with a small FM component, possibly with spin canting, below ∼270 K.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Enhanced mobility of cations and anions in the redox state: The polaronium mechanism

Hugely enhanced slow-ion diffusivity has been widely observed under extreme redox conditions and for unclear reasons. Aided by first-principles calculations on model systems of ZrO 2 , CeO 2 , BaTiO 3 and Li 4/3 Mn 2/3 O 2 , here we successfully explained the intriguing phenomenon by a polaronium mechanism. We found a polaronium, defined as a transitory complex of a polaronic electron or hole and a migrating counterion, becomes highly mobile when the counterion comes from a d 0 or f 0 cation (e.g., Zr 4+ , Ti 4+ and Ce 4 ) or a p 6 anion (e.g., O 2- ) in the host compound. Upon a redox reaction, the complex attains a d 1 /f 1 or p 5 configuration, which spontaneously forms because it is favored by an electron-phonon interaction (manifest as the Jahn-Teller effect in high symmetry systems) that enables local relaxation and lowers the system energy. Here our calculations found such interaction reaching its peak at the saddle point where the local environment is softest, so soft that it allows a reorientation of the anisotropic d/f/p orbital to minimize the electron repulsion locally. Since the complex may dissolve after a successful ion-migration event, the redox electron/hole can be recycled to form another free-radical-like polaronium elsewhere, thereby enhancing ion migration repeatedly. The proposed polaronium mechanism, which also operates in ceramics doped with mixed-valence cations, is most relevant under dynamic and extreme thermal/field/irradiation conditions where extra electrons/holes are abundantly generated by non-equilibrium redox reactions. For such operations, some with emerging applications, our diffusion-enhancing mechanism may provide new theoretical insight to help understand their material/microstructure stability and performance.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Highly Anisotropic Quasi‐Direct Organic Metal Halide Hybrids: A Platform for Polarization‐Sensitive Optoelectronics

Low-dimensional organic–inorganic metal halide hybrids (OMHHs) exhibit remarkable optical properties and enhanced environmental stability. We investigate a 1D OMHH with formula C 4 N 2 H 14 PbBr 4 , consisting of Pb–Br chains separated by organic cations, which shows a large Stokes shift (0.83 eV) and broadband emission. Through first-principles calculations and polarized Raman spectroscopy, we characterize the material's vibrational properties and identify the specific phonon modes that drive exciton self-trapping. Our novel GW/Bethe-Salpeter equation force formalism reveals that low-frequency phonons (∼ 100 cm −1 , primarily involving Pb–Br motions) couple strongly with excitons, with a remarkably high Huang-Rhys factor of 137 ± 4, and gives a pathway for ultrafast structural analysis during the absorption process. This phonon-exciton coupling mechanism explains the material's broadband emission and provides a pathway for controlling optical properties through vibrations and for tuning vibrations through optical excitations. The material also exhibits highly anisotropic optical properties and electronic transport, with bands that are dispersive along the Pb–Br chains but nearly flat in perpendicular directions, resulting in direction-dependent electrical conductivity that is calculated to be an order of magnitude higher along the chain direction and consistent with measurements. These combined properties make this system an excellent platform for polarization-sensitive optoelectronic devices.

36 MATERIALS SCIENCE↗
DOE OSTI2021

The critical role of synthesis conditions on small polaron carrier concentrations in hematite—A first-principles study

Achieving highly efficient energy conversion with transition metal oxides necessitates overcoming conductivity limitations due to the formation of small polarons. Detailed understanding of the interplay among intrinsic defects, dopants, and electron polarons can help devise strategies for achieving higher carrier concentrations, therefore improving carrier conductivity. This work employs first-principles calculations to reliably predict electron polaron concentrations in a prominent polaronic oxide, hematite (Fe 2 O 3 ), by resolving interactions between charged defects and electron polarons and keeping charge neutrality condition among all charged species. This work addresses that both V O and Fe i can be primary donors in undoped hematite depending on the synthesis conditions, such as synthesis temperature and oxygen partial pressure, despite the fact that V O owns an extremely high ionization energy compared to k B T. Furthermore, from calculations of a plethora of n-type dopants (group IV and V elements), we find that Ti, Ge, Sb, and Nb are able to raise electron polaron concentrations in hematite significantly without considering dopant clustering. However, the magnitude of electron polaron concentration increase would be smaller if the dopant has a high tendency of clustering, such as Ti. Here we reveal the critical role of synthesis conditions on tuning electron polaron concentrations of both undoped and doped hematite. Our theoretical analysis provides important insights and general design principles for engineering more conductive polaronic oxides.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Computationally guided experimental validation of divacancy defect formation in 4H-SiC

Recent research into solid-state qubits for quantum information science has focused on optically addressable spin defects such as the negatively charged nitrogen-vacancy center in diamond and the neutrally charged divacancy (VV) in 4H-SiC as scalable quantum sensors and networking qubits. Within this context, direct investigations of the structural origin and defect formation dynamics of a sub-set of the VV center in 4H-SiC remain lacking. Here, we take a systematic experimental approach guided by predictions from first-principles simulations to gain a thorough mechanistic understanding of the VV defect formation and control in 4H-SiC. We study the effect of annealing time and temperature on VV formation in high-purity semi-insulating 4H-SiC samples following electron irradiation. Three different temperatures (1123, 1273, and 1473 K) and annealing duration (from 0.5 to 72 h) are chosen to explore VV formation in different regions. We find that samples annealed at 1273 K give the highest VV-related photoluminescence (PL) intensities, in agreement with the prediction from first-principles calculations. Furthermore, the logarithmic dependence of VV-related PL intensities on the annealing duration at 1273 K indicates that 1273 K provides sufficient thermal energy for silicon vacancy migration but not for VV migration. Together, these results suggest that efficient VV formation occurs above the V Si migration temperature and below the VV migration threshold.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2025

Nanoscale modulation of flat bands via controllable charge density wave defects in 4⁢𝐻⁡𝑏−Ta⁢S 2

Electron correlation is a main driver of exotic quantum phases and their interplay. The 4H b-TaS 2 system, possessing an intrinsic heterostructure of 1T- and 1H -TaS 2 monolayers, offers a unique opportunity to control electron correlation by distorting the atomic lattice or tuning interlayer coupling. Here, we investigated intrinsically deformed charge-density waves (CDWs) in the 1T layer of 4H b-TaS 2 to elucidate and control their effects on flat bands using scanning tunneling microscopy and spectroscopy (STM/S) combined with first-principles calculations. We identified two types of CDW defects: Type 1 has structural distortion and locally suppressed flat bands, while Type 2 features an increased flat band filling factor of intact CDW structure. Density functional theory calculations indicate that a sulfur vacancy in the 1T layer distorts the CDW structure and gives rise to a Type 1, whereas a sulfur vacancy in the 1H layer reduces the interlayer charge transfer and leads to a Type 2. Furthermore, we demonstrated creating and erasing individual CDW defects via STM manipulation. Here, our findings provide a pathway to not only tune flat bands but also selectively manipulate the interaction between CDW, the atomic lattice, and interlayer coupling in strongly correlated systems with atomic precision.

Charge density waves↗
DOE OSTI2021

Mexican-hat potential energy surface in two-dimensional III 2 -VI 3 materials and the importance of entropy barrier in ultrafast reversible ferroelectric phase change

First-principles calculations reveal a Mexican-hat potential energy surface (PES) for two-dimensional (2D) In 2 Se 3 . This unique PES leads to a pseudo-centrosymmetric paraelectric β phase that resolves the current controversy between theory and experiment. We further show that while the α-to-β (ferroelectric-to-paraelectric) phase transition is fast and coherent, assisted by an in-plane shear phonon mode, a random distribution of the atoms in the trough of the PES acts as an entropy barrier against the reverse β-to-α transition. This will be the origin of the speed limitation of current In 2 Se 3 ferroelectric devices. Furthermore, if one orders the β phase (due to the formation of in-plane ferroelectric domains), the reverse transition can take place within tens of picoseconds in the presence of a perpendicular electric field. Finally, the Mexican-hat PES is a general feature for the entire family of 2D III 2 -VI 3 materials. Our finding offers a critical physical picture in controlling the ultrafast reversible phase transition in 2D In 2 Se 3 and other III 2 -VI 3 materials, which will benefit their practical industrial development for advanced ferroelectric devices.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Tuning the Magnetic Properties of CrI 3 Using Ni Thin Film Deposition for Applications in Spintronic Devices

Chromium triiodide (CrI 3 ), a van der Waals magnet, has recently been shown to host Ising ferromagnetism down to the monolayer limit. It is a potentially important material in 2D magnet-based applications, such as magnetic sensors and spintronic devices. Prior studies have revealed the coexistence of two different types of interlayer magnetic coupling, the antiferromagnetic (AFM) coupling near the surface and ferromagnetic (FM) coupling in the deep bulk layers, in pristine CrI 3 crystals below the Curie temperature. In this study, we used Ni thin film deposition to tune the surface magnetic states in bulk CrI 3 . A nanometer thickness (4 nm thick) of Ni was deposited on the surface of CrI 3 using electron-beam evaporation to form a Ni/CrI 3 heterostructure. The deposited Ni thin layer forms nanoclusters that completely cover the CrI 3 surface. Magnetic states of CrI 3 before and after Ni deposition are probed by ultralow-frequency magneto-Raman spectroscopy. Instead of seeing three spin wave branches in Raman scattering below 2 T, as in pristine bulk CrI 3 , in Ni/CrI 3 , we observe only a single spin wave branch, which is softened compared to that in pristine CrI 3 and displays a Zeeman shift under an out-of-plane magnetic field up to 7 T. This observation reveals that the AFM layers on pristine CrI 3 crystal surfaces transit into FM layers, so the entire CrI 3 crystal is in the FM state after Ni deposition. First-principles calculations show that Ni atoms tend to diffuse into the CrI 3 lattice, and the FM interlayer coupling has a much lower energy than AFM coupling in the presence of Ni atoms. As a result, our studies show that the magnetic state of CrI 3 can be modified through deposition of a thin metal layer on the surface, offering a route for controlling the spin degree of freedom in van der Waals magnets.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Topological Phases in Graphene Nanoribbons Tuned by Electric Fields

Graphene nanoribbons (GNRs) possess distinct symmetry-protected topological phases. Here we show, through first-principles calculations, that by applying an experimentally accessible transverse electric field, certain boron and nitrogen periodically codoped GNRs have tunable topological phases. The tunability arises from a field-induced band inversion due to an opposite response of the conduction- and valence-band states to the electric field. With a spatially varying applied field, segments of GNRs of distinct topological phases are created, resulting in a field-programmable array of topological junction states, each may be occupied with charge or spin. Our findings not only show that electric field may be used as an easy tuning knob for topological phases in quasi-one-dimensional systems, but also provide new design principles for future GNR-based quantum electronic devices through their topological characters.

1-dimensional systems↗
DOE OSTI2021

Structural, electronic, and polarization properties of YN and LaN

ScN has attracted great attention for its electronic properties and its ability to enhance polarization of AlN; however, its sister compounds, YN and LaN, remain much less studied. Here, we use first-principles calculations to evaluate YN and LaN in their cubic and hexagonal phases. Rocksalt YN and LaN are semiconductors, although we show that LaN differs from ScN and YN in having a direct band gap, which we attribute to its weaker p-p coupling. Both have low electron effective masses. In addition to their rocksalt structures, we evaluate the layered hexagonal and wurtzite phases of YN and LaN. For YN, the wurtzite phase cannot be stabilized, and hexagonal YN is higher in energy than rocksalt YN. In contrast, for LaN, the wurtzite phase is favored, and it is comparable in energy to rocksalt LaN. Wurtzite LaN has a polarization of 0.608 C/m 2 (referenced to the centrosymmetric layered hexagonal phase), and a high piezoelectric coefficient e 33 = 1.78 C/m 2 . Interestingly, we find that the polarization of wurtzite LaN may be reversible; we find a relatively small switching barrier of 0.06 eV per formula unit, offering the potential for its use as a ferroelectric. Since wurtzite LaN is closely lattice matched to InP, we investigate a heterostructure between (0001) wurtzite LaN and (111) zinc-blende InP, and find the polarization discontinuity would yield a bound charge of 1.3 × 10 14 e/cm 2 , offering the potential for novel electronic applications such as tunnel junctions. Furthermore, our results compare and contrast ScN, YN, and LaN, and highlight the potential of these materials for adoption in electronic and ferroelectric devices.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Unraveling the transformation pathway of the 𝛽 to 𝛾 phase transition in Ga 2 ⁢O 3 from atomistic simulations

Defect spinel 𝛾−Ga 2 ⁢O 3 is the least stable polymorph of Ga 2 ⁢O 3 , so its frequent appearance as a structural defect within or on the surface of monoclinic 𝛽−Ga 2 ⁢O 3 remains a mystery. Through first-principles calculations, we explore potential pathways for the phase transition from 𝛽−Ga 2⁢ O 3 to 𝛾−Ga 2 ⁢O 3 , and examine two key driving forces: tensile strain and Ga deficiency. When configurational entropy contributions to phase energies are included, the 𝛾 phase becomes energetically competitive with the 𝛽 phase, with the free energy difference between these phases diminishing even further under Ga-deficient conditions. Notably, a stability crossover occurs at room temperature at high vacancy concentrations ([V$^{3−}_{Ga}$]>3%) . A simple model 𝛽 → 𝛾 transformation pathway is identified, comprising two primary reactions, that enables the formation of the 𝛾 phase via simultaneous migration of Ga atoms from tetrahedral lattice sites to octahedral interstitial positions. The transformation barriers are prohibitively large in pristine Ga 2 ⁢O 3 , but can be substantially reduced by: (1) the presence of Ga vacancies, (2) elongational strains along the crystallographic 𝑎-axis, and (3) when volumetric relaxations are possible during transformation. These results elucidate prior experimental observations, where 𝛾−Ga 2⁢ O 3 is seen on damaged surfaces or in highly 𝑛-type 𝛽−Ga 2⁢ O 3 environments, which support Ga deficiency and mechanical strain. The insights into the driving forces and mechanisms of 𝛾−Ga 2⁢ O 3 formation enhance understanding of how localized strain and nonequilibrium defect concentrations may facilitate its formation from the 𝛽 phase.

Defects↗
DOE OSTI2025

Diffusion of acceptor dopants in monoclinic 𝛽−Ga 2⁢ O 3

𝛽−Ga 2 ⁢O 3 is a promising material for next-generation power electronics because of its ultrawide band gap and high critical breakdown voltage. However, realizing its full potential requires precise control over dopant incorporation and stability. In this work, we use first-principles calculations to systematically assess the diffusion behavior of eight potential deep-level substitutional acceptors (Au, Ca, Co, Cu, Fe, Mg, Mn, and Ni) in 𝛽−Ga 2 ⁢O 3 . We consider two key diffusion mechanisms: (i) interstitial diffusion under nonequilibrium conditions relevant to ion implantation, and (ii) trap-limited diffusion (TLD) under near-equilibrium thermal annealing conditions. Our results reveal a strong diffusion anisotropy along the 𝑏 and 𝑐 axes, with dopant behavior governed by competition between diffusion and incorporation (or dissociation) activation energies. Under interstitial diffusion, Ca$^{2+}_{i}$ and Mg$^{2+}_{i}$ show the most favorable combination of low migration and incorporation barriers, making them promising candidates for efficient doping along the 𝑏 and 𝑐 axes, respectively. In contrast, Au$^{+}_{i}$ diffuses readily, but exhibits an incorporation barrier that exceeds 5 eV, rendering it ineffective as a dopant. From a thermal stability perspective, Co$^{2+}_{i}$ shows poor activation but high diffusion barriers, which may suppress undesirable migration at elevated temperatures. Under trap-limited diffusion, the dissociation of dopant-host complexes controls mobility. Mg$^{2+}_{i}$ again emerges as a leading candidate, exhibiting the lowest dissociation barriers along both axes, whereas Co$^{2+}_{i}$ and Fe$^{2+}_{i}$ display the highest barriers, suggesting improved dopant retention under thermal stress. In conclusion, our findings guide dopant selection by balancing activation and thermal stability, essential for robust semi-insulating substrates.

Defects↗