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Multiplet structure of chromium(III) dopants in wide band gap materials

Ilya Popov, Petros-Panagis Filippatos, Shayantan Chaudhuri, Andrei L. Tchougréeff, Katherine Inzani, Elena Besley

Abstract

Transition metal doping is commonly used for altering the properties of solid-state materials to suit applications in science and technology. Partially filled $d$-shells of transition metal atoms lead to electronic states with diverse spatial and spin symmetries. Chromium(III) cations have shown great potential for designing laser materials and, more recently, for developing spin qubits in quantum applications. They also represent an intriguing class of chemical systems with strongly correlated multi-reference excited states, due to the $d^3$ electron configuration. These states are difficult to describe accurately using single-reference quantum chemical methods such as density functional theory (DFT), the most commonly used method to study the electronic structures of solid-state systems. Recently, the periodic effective Hamiltonian of crystal field (pEHCF) method has been shown to overcome some limitations arising in the calculations of excited $d$-states. In this work, we assess the suitability of DFT and pEHCF to calculate the electronic structure and $d$-$d$ excitations of chromium(III) dopants in wide band gap host materials. The results will aid computational development of novel transition metal-doped materials and provide a deeper understanding of the complex nature of transition metal dopants in solids.

Multiplet structure of chromium(III) dopants in wide band gap materials

Abstract

Transition metal doping is commonly used for altering the properties of solid-state materials to suit applications in science and technology. Partially filled -shells of transition metal atoms lead to electronic states with diverse spatial and spin symmetries. Chromium(III) cations have shown great potential for designing laser materials and, more recently, for developing spin qubits in quantum applications. They also represent an intriguing class of chemical systems with strongly correlated multi-reference excited states, due to the electron configuration. These states are difficult to describe accurately using single-reference quantum chemical methods such as density functional theory (DFT), the most commonly used method to study the electronic structures of solid-state systems. Recently, the periodic effective Hamiltonian of crystal field (pEHCF) method has been shown to overcome some limitations arising in the calculations of excited -states. In this work, we assess the suitability of DFT and pEHCF to calculate the electronic structure and - excitations of chromium(III) dopants in wide band gap host materials. The results will aid computational development of novel transition metal-doped materials and provide a deeper understanding of the complex nature of transition metal dopants in solids.

Paper Structure

This paper contains 5 sections, 6 equations, 3 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. Periodic Effective Hamiltonian of Crystal Field
  4. Density Functional Theory Calculations
  5. Results and Discussion

Figures (3)

  • Figure 1: Crystalline structures of Cr^3+-doped (a) $\upalpha$-Al$_2$O$_3$, (b) AlB$_4$O$_6$N, and BeAl$_2$O$_4$ at (c) $C_{s}$- and (d) $C_{i}$-symmetrized sites. Cell boundaries are shown with black dotted lines. All shown crystalline structures are available in Supplementary Information for both r$^{2}$SCAN and HSE06 functionals.†
  • Figure 2: Ground-state geometries of the Cr coordination sphere and the splitting diagrams of the one-electron $d$-states for (a) $\upalpha$-Al$_2$O$_3$, (b) AlB$_4$O$_6$N, and BeAl$_2$O$_4$ at (c) $C_{s}$- and (d) $C_{i}$-sites. The corresponding splitting parameters of the one-electron $d$-states calculated with r$^{2}$SCAN, HSE06, and pEHCF are presented in Table \ref{['tab:one-el']}.
  • Figure 3: The atomic orbital-projected density of states (DOS) for Cr^3+-doped (a) $\upalpha$-Al$_2$O$_3$, (b) AlB4O6N and (c) BeAl2O4 ($C_{s}$), as calculated using the r$^2$SCAN, HSE06 and pEHCF. The total density of states, chromium 3$d$, oxygen 2$p$ and aluminium 3$p$ states are shown in gray, red, green and blue, respectively. Other atomic orbitals are not shown for clarity. For the purpose of comparison across all three methods, the position of the reference point on the energy axis is chosen such that the top of the $sp$-valence band corresponds to 0eV. In pEHCF, the peaks corresponding to the $d$-states indicate the position of the one-electron $d$-orbitals. This representation does not fully reflect the complexity of the electronic structure of the $d$-system containing multi-reference many-electron multiplets described by pEHCF.