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While anomalous diffusion coefficients with non-Arrhenius-like temperature dependence are observed in a number of metals, a conclusive comprehensive framework of explanation has not been brought forward to date. Here, we use first-principles calculations based on density functional theory to calculate self-diffusion coefficients in the bcc metals Mo and β-Ti by coupling quasiharmonic transition state theory and large-displacement phonon calculations and show that anharmonicity from thermal expansion is the major reason for the anomalous temperature dependence. We use a modified Debye approach to quantify the thermal expansion over the entire temperature range and introduce a method to relax the vacancy structure in a mechanically unstable crystal such as β-Ti. The effect of thermal expansion is found to be crucial for the nonlinear, non-Arrhenius “anomalous” self-diffusion in both bcc systems, with β-Ti showing a 60% larger relative nonlinearity parameter than Mo. Our results point to temperature dependence in the diffusion prefactor from thermal expansion as the major origin of anomalous self-diffusion. The methodology proposed for β-Ti is general and simple enough to be applicable to other mechanically unstable crystals. 

Spin-orbit coupling (SOC) is a relativistic effect, where an electron moving in an electric field experiences an effective magnetic field in its rest frame. In crystals without inversion symmetry, it lifts the spin degeneracy and leads to many magnetic, spintronic, and topological phenomena and applications. In bulk materials, SOC strength is a constant. Here, we demonstrate SOC and intrinsic spin splitting in atomically thin InSe, which can be modified over a broad range. From quantum oscillations, we establish that the SOC parameter α is thickness dependent; it can be continuously modulated by an out-of-plane electric field, achieving intrinsic spin splitting tunable between 0 and 20 meV. Unexpectedly, α could be enhanced by an order of magnitude in some devices, suggesting that SOC can be further manipulated. Our work highlights the extraordinary tunability of SOC in 2D materials, which can be harnessed for in operando spintronic and topological devices and applications.