Ab Initio study of strongly correlated systems: rare earth hosted solids and molecule and two dimensional MXene

Yogendra Limbu

In this thesis, we investigated the phase stability, electronic structure, and magnetic properties of strongly correlated systems containing rare-earth (RE) elements, as well as transition metal (TM) based systems, using density functional theory (DFT) calculations. In RE-containing systems, we additionally calculated the crystal field parameters (CFPs) and the corresponding crystal field splitting of the 4f states. Standard DFT methods using generalized gradient approximation (GGA) often fall to accurately describing the localized and strongly correlated nature of the 3d and 4f electrons. To overcome this limitation, we incorporated the Hubbard U correction on top of GGA and also employed hybrid functionals, which more reliably capture electronic and magnetic properties, including band gaps and magnetic moments. The following abstracts summarize ourfindings across the various systems. In chapter 2, we present an effective ab initio method to calculate the CFPs of an erbium (Er3+) ion experiencing different local site symmetries in several wide band gap oxides (MgO, ZnO, TiO2, CaWO4, and PbWO4), and then evaluate crystal field splittings of these Er3+ ions for their ground and excited states. The optical transitions between the ground state (Z) and excited state (Y ) manifolds of the environmentally shielded 4f states of these Er3+ ions have wavelengths ∼ 1.5 μm and thus have potential applications to quantum communications and quantum memories. These results are in excellent agreement with recent low-temperature measurements, provided the inadequate calculation of the 4f shell screening is adjusted by reducing the radial extent of the 4f wavefunctions by approximately a factor of 2. In chapter 3, 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 Er-doped wide band gap α-and β-gallium oxides (Ga2O3), applicable to optoelectronic and quantum devices. 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 defect formation energy analysis also confirms that both Er-doped α-and β-Ga2O3 prefer Er3+ (neutral) state. The underestimated band gaps of the pristine phases from standard DFT calculations as compared to experimental values are corrected by employing the hybrid functional calculations, resulting to indirect band gaps of 5.21 eV in α-Ga2O3 and 4.94 eV in β-Ga2O3. The site preference energy analysis indicates partial occupation of Er in the octahedral site of Ga. Anisotropic nature of hyperfine tensor coefficients of Er are similar in both phases which may be due to the occupation of Er in the same octahedral Ga site. On the other-hand, calculated magnetic exchange interaction between two Er dopants is negative for α and positive for β, indicating AFM ground state in the former and the FM ground state in the latter. Large values of DMIs are obtained along the x-direction in the α and along the y-direction in the β. 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 CFPs calculated from DFT are used to analyze 4f multiplets and 4f – 4f transitions. Thus calculated lowest energy level of the first excited state to the lowest energy level of the ground state is about 1.53 μm, which is in a good agreement with available experiment and it falls within the quantum telecommunication wavelength range. In chapter 4, we present an ab initio understanding of electronic quantum states, interactions, and excitations, forming a foundation for the quantum advancement of this system. The stability of Er3+:YAG is confirmed by defect formation and phonon dispersions. The hybrid functional calculations improve its band gap prediction, retaining insulating characteristic and Hund’s rule Er-4f spin and orbital magnetic moments. The nearest-neighbor Er atoms favor FM spin alignment and low spin-phonon coupling, and produce a large DMI along the x-direction. Er3+:YAG possesses magneto-optic Kerr, anisotropic hyperfine, and magnetic anisotropy effects, exhibiting eight excited states (Z1 – Z8) and seven ground states (Y1 – Y7) Kramer pairs of Er-4f . The 4f – 4f transition (6660.26 cm−1) from the first excited state Y1 to the first ground state Z1 falls within the telecommunication range. In chapter 5, we report an ab initio understanding of the electronic quantum states, interactions, and excitations in Er:CeO2 that forms a foundation for its quantum advancement. The stability of the dopant host configuration, and valence state and partially quenched orbital 4f magnetic moment of Er are confirmed by defect formation and electronic structure calculations. The defect formation energy reveals that the Er-doped system favors the incorporation of two Er dopants accompanied by the creation of an oxygen vacancy near Er, stabilizing the system in Er3+ and Ce4+ oxidation states. These two Er dopants prefer a ferromagnetic configuration, as confirmed by the lower total energy compared to the antiferromagnetic state. The hybrid functional theory corrected band gap of Er:CeO2, confirms the insulating characteristic. The strong crystal field environmentforces the Er atom to have a partially quenched 4f orbital magnetic moment due to the splitting of energy levels and the shielding effect of the outer electrons. The CFPs responsible for the 4f splitting are extracted from the crystal field potential calculated using DFT. For the Oh symmetry in Er:CeO2, four non-zero CFPs are identified, giving rise to five multiplet levels in both the ground and first excited states. The presence of oxygen vacancies lowers the local symmetry, increasing the number of non-zero CFPs and resulting in eight and seven energy levels in the ground and first excited states, respectively. Additionally, we compute the g-tensor for the lowest-energy Kramers doublets of the both ground and first excited states in Er:CeO2 and the energetically most stable configuration of two Er:CeO2 with an O-vacancy. A large principal value of g-tensor is identified along the x (= y)-direction for the former and along the z-direction for the later cases, suggesting that the magnetic response of the Kramers pair can be tuned via defect engineering. In chapter 6, we present an ab initio study of the defect formation, electronic structure, magnetic interactions, and crystal filed splitting of Er-doped yttrium orthosilicate (Y2SiO5:YSO), employing DFT calculations. The underestimated band gaps with the standard density functional (GGA) are resolved with hybrid functional (HSE), producing the band gaps closer to the experi-ments. The defect formation energy shows that Er-doped phases favor a neutral charge state at the middle of the band gap, preserving an insulating in nature. The 4f states appear below the Fermi level, providing ∼ 6 μB orbital and ∼ 3 μB spin moments per Er. The two Er dopants favor an AFM configuration in both phases. In C2/c phase, the DMI is prominent along the y (x)-direction for Er doping at the Y1 (Y2) site, whereas in the P21/c phase it is significant along the y (z)-direction for Er doping at the Y1 (Y2) site. In both phases, Er:YSO exhibits in-plane anisotropy due to the large a-axis lattice parameter. The calculated dielectric constants further reveal strong optical anisotropy, reflecting the low-symmetry crystal structure. This low symmetry gives rise to fifteen non-zero CFPs, yielding eight manifolds (Z1 – Z8) in the ground state and seven manifolds (Y1 – Y7) in the first excited state. The calculated 4f – 4f optical transition from Y1 to Z1 is ∼ 1.5 μm, making it a promising candidate for telecommunication applications. In chapter 7, using DFT calculations, we investigate the electronic and magnetic properties of pristine and Er-doped yttrium iron garnet (Y3Fe5O12:YIG), focusing on the crystal-field excitations of Er3+ ions. YIG is a FIM insulator with a band gap of 2.83 eV, obtained by treating the strongly correlated Fe-3d electrons using the Hubbard U correction, where Fe atoms occupying octahedral and tetrahedral sites are aligned antiparallel, as confirmed by calculating the magnetic exchange interactions. These exchange interactions are then used to compute the magnon spectrum, in reasonable agreement with available results. Defect formation energy calculations confirm the chemical stability of Er:YIG, which remains insulating and aligns Er spins parallel to tetrahedral Fe. We identified fifteen non-zero CFPs (Bkq ), resulting in eight (Z1 – Z8) and seven (Y1 – Y7) multiplets in the ground and first excited states. The g-tensor shows a large z-component for Z1 and Y1 Kramers doublets, with the Y1 → Z1 transition lies within the telecommunication range, making Er:YIG as a promising platform for quantum information processing, including telecommunication applications. In chapter 8, alongside RE-doped wide band gap host materials, we also present an ab initio investigation of functionalized and 3d-electrons doped Cr2C MXenes. Upon functionalization, the Cr2C becomes chemically, dynamically, and mechanically stable, and it exhibits magnetic semiconducting behavior. Cr2CF2 stands out as a wide band gap semiconductor, possessing super exchange interaction mediated by F atoms within the layer, however, the applied strain transforms it from an indirect to a direct band gap semiconductor. Strong spin-phonon coupling found in Cr2CH2 is supported by the distorted Cr spin density due to hydrogen environment. Two magnon branches, associated with two sub-lattice spins, are found in the FM Cr2CO2 and AFM Cr2CF2. Depending on the types of 3d-electron dopants and functionalization, Cr2C MXenes (except for Cr2CO2)change from the indirect band gap magnetic semiconductor to different states of electronic and magnetic matter including exotic direct band gap magnetic bipolar semiconductor. In addition, we reveal that spin orbit coupling (SOC) open a band gap in the two highest valence bands in the Fe-doped Cr2CCl2. Finally, in Chapter 9, we extend our method for calculating the CFPs of RE ions in wide band gap host materials to molecular systems. We develop an ab initio method to calculate the CFPs of Er in mononuclear anionic erbium complex [Er(hfac)4]− (hfac = hexafluoroacetylacetone), without relying on any fitting parameters. The CFPs are obtained using a local orbital basis set from two separate calculations: one employing the 4f -core approximation to generate the crystal field potential, and the other treating the 4f electrons as valence states to extract the corresponding 4f wave functions. The resulting 4f wave function spreading within the system and interacts with the surrounding crystal field potential, giving rise to non-zero CFPs that are responsible for the 4f splitting of rare-earth ions. Using the calculated CFPs, we solve the effective semi-empiricalHamiltonian to generate the multiplet energy levels. We identified eight and seven energy levels in the ground and first excited states, respectively, with an 4f – 4f optical transition from Y1 to Z1 at ∼1.5 μm, which lies within the telecommunication wavelength regime.

Ab Initio study of strongly correlated systems: rare earth hosted solids and molecule and two dimensional MXene

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