Spin-orbital Jahn-Teller bipolarons

Abstract

Polarons and spin-orbit (SO) coupling are distinct quantum effects that play a critical role in charge transport and spin-orbitronics. Polarons originate from strong electron-phonon interaction and are ubiquitous in polarizable materials featuring electron localization, in particular 3d transition metal oxides (TMOs). On the other hand, the relativistic coupling between the spin and orbital angular momentum is notable in lattices with heavy atoms and develops in 5d TMOs, where electrons are spatially delocalized. Here we combine ab initio calculations and magnetic measurements to show that these two seemingly mutually exclusive interactions are entangled in the electron-doped SO-coupled Mott insulator Ba₂Na_1-xCa_xOsO₆ (0 < x < 1), unveiling the formation of spin-orbital bipolarons. Polaron charge trapping, favoured by the Jahn-Teller lattice activity, converts the Os 5d¹ spin-orbital J_eff = 3/2 levels, characteristic of the parent compound Ba₂NaOsO₆ (BNOO), into a bipolaron 5d² J_eff = 2 manifold, leading to the coexistence of different J-effective states in a single-phase material. The gradual increase of bipolarons with increasing doping creates robust in-gap states that prevents the transition to a metal phase even at ultrahigh doping, thus preserving the Mott gap across the entire doping range from d¹ BNOO to d² Ba₂CaOsO₆ (BCOO).

Fig. 1. Spin-orbit d² bipolaron in Ba₂Na_0.875Ca_0.125OsO₆.

a DFT charge density isosurface of the occupied Os t_2g bands, showing the formation of d² a J_eff = 2 bipolaron coexisting with d¹ ${\mathrm{J}}_{\mathrm{eff}}=\frac{3}{2}$ sites characteristic of pristine x = 0 BNOO. Blue and red lobes refers to the entangled bipolaronic PB1 and PB2 bands displayed in (b). The J_eff spin-orbital levels are obtained from DFT+HI. b Band structure and relative density of states of pristine BNOO (x = 0, left) characterized by a multiband manifold of d¹ states, and bipolaronic Ba₂Na_0.875Ca_0.125OsO₆ (right) with a localized d² bipolaronic level below the Fermi level composed by two entangled d¹ bands (PB1 and PB2). The green line represents the occupied d states of a single Os site in the pristine phase.

Fig. 2. Polaron hopping: experiment and DFT.

a NMR spin-lattice (square) and spin-spin (triangles) relaxation rates showing an anomalous peak at 130 K and 50 K due to a dynamical process. The 1/T₁ anomalous peak is detailed in the right plot. The curve fit (red solid line) to a thermally activated BPP model provides an activation energy E_a = 74(2) meV. b μSR data showing only a peak due to the magnetic transition but no high temperature anomalous feature corresponding to the NMR one. c Evolution of the density of states around the Fermi level for selected snapshots across the hopping path displayed in (d), projected onto the initial (I, dark blue) and final (F, orange) Os sites. The five plots correspond to reaction coordinate equal to 0.0 (I), 0.3 (IT), 0.5 (T), 0.7 (TF) and 1.0 (F). The d² bipolaron charge is gradually transferred from the initial and final hosting sites. At the transition state (T, at 0.5) the charge is equally distributed between both Os sites giving rise to an adiabatic weakly metallic transient state (brown). d Potential energy for a bipolaron migrating from I to F with the charge density projected on the two neighboring Os atoms, using a color gradient from blue (bipolaron fully localized in I) to orange (bipolaron fully localized in F). The insets show the charge density isosurface decomposed over the bipolaron bands PB1 (blue) and PB2 (red). The resulting hopping barrier, 66 meV, is in excellent agreement with the experimentally-derived activation energy. e band structure around the Fermi level at the initial (I), transition (T) and final (F) point of the hopping process.

Fig. 3. Role of Jahn-Teller and SOC on polaron stability.

a Polaron energy E_pol as a function of the SO coupling scaling factor c_λ (For c_λ = 0 SO is completely suppressed, whereas c_λ=1 refers to the full SO regime). E_pol is progressively less negative for increasing SO coupling. b JT tetragonal distortion amplitude Q₃ as a function of c_λ. The color scale and circle’s size indicate the variation of E_pol relative to the c_λ = 1 case: SO coupling rapidly quenches Q₃ and reduces the polaron stability. c JT energy E_JT at the polaron trapping site as a function of c_λ for all three JT modes. Q₃ is the only mode influenced by SO coupling. d–f Geometrical interpretation of the JT non-zero modes Q₂, Q₃ and Q_xy respectively.

Fig. 4. Polaron dynamics in Ba₂Na_1−xCa_xOsO6: DFT+NMR.

a DFT energy gap (black diamonds) and number of bipolarons (red filled squares) as a function of doping. Chemically doped BNOO remains insulating for any doping concentration. The number of d² bipolaron sites grows linearly with doping. At full doping (x = 1, corresponding to BCOO) all Os sites are doubly occupied (d²) and polaron formation is completely quenched (empty square). b Polaronic 1/T₁ anomalous peak data and fitting curves calculated with the quadrupole relaxation model of Eq. (1). For all investigated doping concentration doped BNOO exhibits a polaronic peak at approximately the same temperature T. c Second moment Δ² of the fluctuating field as extracted from the experimental data (black squares) compared with our predicted data obtained from the DFT polaron phonon field (red circles). The dashed lines connect to pristine BNOO (x = 0) and BCOO (x = 1) where the absence of polaron leads to Δ² = 0.