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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 ofspin-orbital bipolarons. Polaron charge trapping, favoured by the Jahn-Teller lattice activity, converts the Os 5d¹spin-orbital J_eff = 3/2 levels, characteristic of the parent compound Ba₂NaOsO₆(BNOO), into a bipolaron 5d²J_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 d¹BNOO to d²Ba₂CaOsO₆(BCOO). 

In this work, we study the effect of electron doping on the kagome superconductor CsV₃Sb₅. Single crystals and powders of CsV₃Sb_5−xTe_xare synthesized and characterized via magnetic susceptibility, nuclear quadrupole resonance, and x-ray diffraction measurements, where we observe a slight suppression of the charge density wave transition temperature and superconducting temperature with the introduction of electron dopants. In contrast to hole doping, both transitions survive relatively unperturbed up to the solubility limit of Te within the lattice. A comparison is presented between the electronic phase diagrams of electron- and hole-tuned CsV₃Sb₅. 

Nuclear magnetic resonance (NMR) experiments can reveal local properties in materials, but are often limited by the low signal-to-noise ratio. Spin squeezed states have an improved resolution below the Heisenberg limit in one of the spin components, and have been extensively used to improve the sensitivity of atomic clocks, for example [1]. Interacting and entangled spin ensembles with non-linear coupling are a natural candidate for implementing squeezing. Here, we propose measurement of the spin-squeezing parameter that itself can act as a local probe of emergent orders in quantum materials. In particular, we demonstrate how to investigate an anisotropic electric field gradient via its coupling to the nuclear quadrupole moment. While squeezed spin states are pure, the squeezing parameter can be estimated for both pure and mixed states. We evaluate the range of fields and temperatures for which a thermal-equilibrium state is sufficient to improve the resolution in an NMR experiment and probe relevant parameters of the quadrupole Hamiltonian, including its anisotropy.