First-principles study on the electronic structure transition of β-UH3 under high pressure

Juefei Wu; Wang Yue-Chao; Yu Liu; Bo Sun; Yanhong Zhao; Jiawei Xian; Xingyu Gao; Haifeng Liu; Haifeng Song

doi:10.1063/5.0091969

Abstract

We investigate the electronic properties of stable β-UH₃ under high pressure up to 75 GPa within the first-principles DFT + U formalism with pressure-dependent U in a self-consistent calculation, and we find an electronic structure transition at about 20 GPa due to the quantum process of localization and itinerancy for partially filled uranium 5f electrons. The electronic structure transition is examined from four perspectives: magnetization, band structure, density of states, and 5f electron energy. On the basis of the density of states of 5f electrons, we propose an order parameter, namely, the 5f electron energy, to quantify the electronic structure transition under pressure. Analogously to the isostructural transition in 3d systems, β-UH₃ retains its magnetic order after the electronic structure transition; however, this is not accompanied by volume collapse at the transition point. Our calculation is helpful for understanding the electronic properties of β-UH₃ under high pressure.

I. INTRODUCTION

Hydrogen-rich materials synthesized under high pressure such as H₃S,1 LaH₁₀,2 and the C–S–H system3 have opened possible routes to high-temperature superconductivity. The uranium–hydrogen binary system is among the potential candidates for such materials.4 Kruglov et al.4 synthesizied the predicted UH₇ and UH₈ in laser-heating diamond anvil cell (DAC) experiments, using UH₃ as the precursor material. UH₃ is a stable composition under ambient conditions5–8 and has important roles in nuclear technology and as a chemical hydrogen storage material.9–13 Therefore, exploring the high-pressure properties of UH₃ is important for both fundamental research and industrial applications.5

At present, there is a fairly comprehensive understanding of UH₃ under ambient condition. UH₃ crystallizes in two structures: α-UH₃ and β-UH₃.14 The α-UH₃ structure is metastable and can only be found at low temperatures.15 It transforms into stable β-UH₃ at temperatures between 373 and 523 K.16 Taylor et al.15 simulated the phase transformation paths from α-UH₃ to β-UH₃. Tkach et al.17 stabilized α-UH₃ with Zr and conducted experiments to study its electronic properties. β-UH₃ transforms from a ferromagnetic (FM) state18 to a paramagnetic (PM) state at a Curie temperature of about 180 K.19 Zhang et al.16 calculated the electronic, mechanical, and thermodynamic properties of both UH₃ phases under ambient conditions.

Zhang et al.20 calculated the mechanical and thermodynamic properties of α-UH₃ under high pressures. According to DAC experiments,4,21α-UH₃ transforms to β-UH₃ when the pressure is increased to 5 GPa, and the x-ray diffraction signature of β-UH₃ is preserved up 69 GPa.4 According to theoretical calculations by Taylor,22 ferromagnetism in β-UH₃ vanishes when the unit-cell volume becomes about 50% of the equilibrium volume. In particular, the magnetization exhibits a sharp decrease from about 2.8 to 2.0 μ_B/U as the volume of the system increases from 32 to 36 Å³.22 These characteristics of the magnetization appear to be analogous to the isostructural transitions in 3d materials such as FeCO₃23 and LiFePO₄.24 In Refs. 23 and 24, the structure was retained, while the spin state was transformed from a high-spin (HS, S = 2) to a low-spin (LS, S = 0) state under pressure, accompanied by volume collapse at the transition point. Actually, the magnetic order of β-UH₃ remains ferromagnetic, and the impact of the transition on the volume is not known at present. Besides, β-UH₃ contains 5f electrons,25,26 and this gives rise to exotic physics.27 Thus, it is intriguing to study the electronic structures of β-UH₃ under high pressure.

In this work, we conduct first-principles calculations of the electronic structure of β-UH₃ under high pressure. A local screened Coulomb correction (LSCC) approach28 is employed to evaluate the pressure-dependent local Coulomb interaction parameters in a self-consistent way. We predict an electronic structure transition of β-UH₃ under high pressure and illustrate it from four perspectives. First, we find that the magnetization has a discontinuity around 32 Å³, suggesting a possible electronic structure transition. Second, we find that the calculated band structure of β-UH₃ is reconstructed after 18 GPa. Third, after the transition, the density of states (DOS) becomes more dispersed. Fourth, we present an order parameter to quantify the electronic structure transition by calculating the 5f electron energy of the occupied states under pressure. Finally, we analyze the charge density difference to reveal the enhanced metallicity and calculate the volume drop after the transition.

II. COMPUTATIONAL METHODS

The space group of the stable β-UH₃ structure is Pm $\bar{3}$ n (223),29,30 with the uranium atoms occupying the 2(a) (0, 0, 0) [U(I)] and 6(c) (0.25, 0, 0.5) [U(II)] sites, and the hydrogen atoms occupying the 24(k) (0, 0.156, 0.313) sites.21,31

In the present ab initio calculations, we employ the Vienna Ab initio Simulation Package (VASP) based on density functional theory (DFT).32,33 The exchange-correlation functional is treated using the generalized gradient approximation (GGA) of Perdew, Burke, and Ernzerhof.34 The calculations use the projector-augmented wave (PAW)35 approach to describe the core electrons and their effects on valence orbitals. Spin–orbit coupling (SOC) is taken into account, with the direction of magnetic axis along (111). Ferromagnetic (FM) ordering is assumed in the simulation [Fig. 1(a)].

Figure 1.(a) and (b) Magnetic structures of the FM and AFM states, respectively, with the red and blue arrows denoting the magnetic axes. (c) Energy–volume relations of the FM, AFM, and PM states. The inset shows U_eff as determined by the LSCC approach under different pressures. (d) Pressure–volume relations of FM and AFM states.

DFT + U36 calculations are performed using the formulation of Dudarev et al.37 to account for the on-site Coulomb repulsion among the localized uranium 5f electrons. The total energy is of the form $E_{LSDA + U} = E_{LSDA} + \frac{U - J}{2} \sum_{σ} [Tr ρ^{σ} - Tr (ρ^{σ} ρ^{σ})],$ (1)where ρ is the local density matrix of the f states, and the Hubbard U and Hund exchange J correspond to the spherically averaged screened Coulomb interaction and the exchange interaction, respectively. The difference between U and J is significant in this formalism and is denoted by U_eff for simplicity. The dependence of U on pressure or volume is evaluated by the LSCC approach,28 which provides accurate descriptions of electronic and magnetic properties in strongly correlated systems.

To estimate the Curie temperature T_C, we use the classical Heisenberg model in mean-field theory (MFA).38 The Curie temperature is given by $T_{C} = \frac{2 z J S (S + 1)}{3 k_{B}} = \frac{E_{AFM} - E_{FM}}{6 k_{B}},$ (2)where k_B is the Boltzmann constant, and E_FM and E_AFM are the total energies (per formula unit) of the FM and antiferromagnetic (AFM) states [Fig. 1(b)], respectively. To verify the feasibility of the AFM state, we construct a magnetic disorder 2 × 2 × 2 supercell using the similar atomic environment (SAE) method.39 Five components [H][U(-1-11)][U(11-1)][U(-111)][U(1-1-1)] are considered and are randomly distributed in the supercell.

We recheck our electronic structure calculations using the orbital polarization (OP) limit of GGA + U.16

We set the plane-wave kinetic-energy cutoff to 650 eV, and the Brillouin zone is sampled with a special k-mesh generated by the Monkhorst–Pack scheme with a k-point spacing of 2π × 0.03 Å⁻¹. The convergence tolerance is 10⁻⁶ eV for total energy, and all forces are converged to be less than 0.003 eV/Å.

III. RESULTS AND DISCUSSION

High-pressure experimental4,21 and theoretical5 studies suggest that there is no structural transition in β-UH₃ up to 69 GPa. In our calculation, the structure remains Pm $\bar{3}$ n in the structural relaxation process. The calculated spontaneous magnetization under ambient conditions is 0.68 μ_B/U. This is close to the experimental value of ∼1 μ_B/U17 and is in line with the results calculated using the OP limit method.16 As plotted in Fig. 1, the total energy of the FM state is below that of the AFM state, and U_eff gradually decreases from about 2.4 to 1.9 eV with increasing pressure (inset of Fig. 1). The E–V relation indicates that the ground state retains FM order in the calculated pressure range. The supercell constructed by the SAE method is able to describe the PM state, and the total energy difference between the PM and AFM states is less than 0.1%. This indicates that the AFM order is a good approximation to the PM state.40 To estimate the Curie temperature T_C, we calculate the total energies of the FM and AFM states with a fixed U_eff = 2.3 estimated at ambient pressure. The calculated Curie temperature is 158.8 K, which is in reasonable agreement with the experimental value of 180 K.16 Thus, our method is suitable for simulating the properties of β-UH₃.

We present the electron magnetization per uranium atom in Fig. 2. The discontinuity in magnetization is around 20 GPa, and the magnitude is about 0.14 μ_B/U. The pressure of 20 GPa corresponds to about 33 Å³. The reduction in magnetization indicates a possible electronic structure transition, and the abrupt change around 33 Å³ suggests an immediate elevation of metallicity.

Figure 2.Electron magnetization per uranium atom as a function of pressure for β-UH₃.

To illustrate the transition, we calculate the band structures of β-UH₃ at pressures up to 75 GPa, as plotted in Fig. 3. The band structures below 18 GPa have analogous characteristics, such as a “bandgap” along the Brillouin path X–R. We can also observe a gradual variation in the band structure from 24 to 75 GPa. Here, we characterize two types of electronic structure. One, E1, exhibits a “bandgap” along X–R, as exemplified by the band structures at pressures below 18 GPa [Figs. 3(a)–3(c)]. The other, E2, lacks this “bandgap,” as exemplified by the band structures at pressures above 24 GPa [Figs. 3(d)–3(f)]. From a comparison of E1 at 18 GPa [Fig. 3(c)] with E2 at 24 GPa [Fig. 3(d)], it can be seen that the “bandgap” along X–R undergoes a sudden collapse. The band structure is reconstructed along other Brillouin paths as well. This suggests the existence of a transition in electronic structure between 18 and 24 GPa.

Figure 3.Band structures of β-UH₃ under different pressures.

We then calculate the DOS of β-UH₃ under different pressures [Fig. 4(a)]. At each pressure, the DOS is relative to the Fermi energy. As can be seen from Fig. 4(a), the distribution below 18 GPa is relatively localized, while that above 24 GPa becomes more dispersed. In Figs. 4(b) and 4(c), the f electrons make the greatest contribution in both the E1 and E2 states around the Fermi energy. Hence, the dispersed behavior above 24 GPa, such as the emerging peaks around −1.5 eV at 24 GPa [Fig. 4(a)], can be attributed to the redistribution of 5f electrons.

Figure 4.(a) DOS of β-UH₃ under different pressures relative to the Fermi energy. (b) and (c) Total f-electron DOS at 75 and 5 GPa, respectively.

To quantify the electronic structure transition, we propose the following order parameter: $E_{5 f} = \frac{\int_{- \infty}^{E_{F}} E N_{f} (E) d E}{\int_{- \infty}^{E_{F}} N_{f} (E) d E} - E_{F},$ (3)where N_f(E) is the DOS of 5f electrons and E_F is the Fermi energy. This order parameter is also referred to as the 5f electron energy. As depicted in Fig. 5, there is a cliff in the 5f electron energy around 20 GPa. The height of this cliff is about 0.36 eV, which is comparable to the value of the energy at 18 GPa (−1.03 eV) and 24 GPa (−1.39 eV). This sharp drop is related to the sudden broadening of the 5f bands, indicating enhancement of the itinerancy. The order parameter based on the 5f electron energy can be an appropriate descriptor for the electronic structure transition.

Figure 5.5f electron energy of occupied states under different pressures.

We calculate the enthalpy of the distinct electronic states and determine the transition point at 21 GPa. At this pressure, we analyze the charge density difference between E1 and E2 states. As illustrated in Fig. 6, we select the (200) plane, the isosurface value is ±0.001 e/bohr,3 and blue and red colors represent areas losing and gaining electrons, respectively. The areas losing electrons are localized around uranium and hydrogen atoms, while the areas gaining most electrons are connected via the H–U(II)–U(II)–H channel. Hence, the E2 state is more itinerant than the E1 state; in other words, the metallicity is elevated after the electronic structure transition.

Figure 6.Charge density difference of β-UH₃ relative to E1 state on the (200) plane at 21 GPa.

We recheck the electronic structure calculations with the OP limit of GGA + U.16 The ground state retains FM order within 70 GPa, and we can observe an electronic structure transition around 13 GPa (33 Å³) as well. This confirms the validity of the electronic structure transition under high pressure for β-UH₃. Besides, the volume drops about 0.7% at the transition point, which is significantly less than the 10% drop for FeCO₃23 and the 3% drop for LiFePO₄.24 This may explain why volume collapse has not reported in previous high-pressure experiments.4,21

To further verify the electronic structure transition in β-UH₃, we suggest that detailed partial fluorescence yield x-ray absorption spectroscopy (PFY XAS) or resonant inelastic x-ray scattering (RIXS) spectra under pressure be performed in the future.

IV. CONCLUSIONS

In summary, using first-principles calculations, we have predicted an electronic structure transition in β-UH₃ at about 20 GPa, and we have illustrated this from the perspectives of magnetization, band structure, DOS, and 5f electron energy. On the basis of the 5f electron energy, we propose an order parameter as a descriptor for the electronic structure transition. After the electronic structure transition, the itinerancy of the 5f electrons exhibits a sudden enhancement, accompanied by an abrupt elevation in metallicity. β-UH₃ remains ferromagnetic after the electronic structure transition, and this transition has only a slight impact on the structure volume. Our calculations provide further understanding of the electronic properties of β-UH₃ under high pressure.

ACKNOWLEDGMENTS

Acknowledgment. We acknowledge support from the National Key Research and Development Program of China under Grant No. 2021YFB3501503 and from the National Natural Science Foundation of China under Grant Nos. 12004048 and U1930401.

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