We present a combined experimental and computational study of the effect of charge doping in the osmium based double perovskite Ba 2 Na 1– x Ca x OsO 6 for 0 ≤ x ≤ 1 in order to provide a structural and electronic basis for understanding this complex Dirac–Mott insulator material. Specifically, we investigate the effects of the substitution of monovalent Na with divalent Ca, a form of charge doping or alloying that nominally tunes the system from Os 7+ with a 5d 1 configuration to Os 6+ with 5d 2 configuration. After an X-ray diffraction characterization, the local atomic and electronic structure has been experimentally probed by X-ray absorption fine structure at all the cation absorption edges at room temperature; the simulations have been performed using ab initio density functional methods. We find that the substitution of Na by Ca induces a linear volume expansion of the crystal structure which indicates an effective alloying due to the substitution process in the whole doping range. The local structure corresponds to the expected double perovskite one with rock-salt arrangement of Na/Ca in the B site and Os in the B′ one for all the compositions. X-ray absorption near edge structure measurements show a smooth decrease of the oxidation state of Os from 7+ (5d 1 ) to 6+ (5d 2 ) with increasing Ca concentration, while the oxidation states of Ba, Na, and Ca are constant. This indicates that the substitution of Na by Ca gives rise to an effective electron transfer from the B to the B′ site. The comparison between X-ray absorption measurements and ab initio simulations reveals that the expansion of the Os–O bond length induces a reduction of the crystal field splitting of unoccupied Os derived d states.

In this work we study the complex entanglement between spin interactions, electron correlation and Janh-Teller structural instabilities in the 5d 1 J ef f = 3 2 spin-orbit coupled double perovskite Ba2NaOsO6 using first principles approaches. By combining non-collinear magnetic calculations with multipolar pseudospin Hamiltonian analysis and many-body techniques we elucidate the origin of the observed quadrupolar canted antifferomagnetic. We show that the non-collinear magnetic order originates from Jahn-Teller distortions due to the cooperation of Heisenberg exchange, quadrupolar spin-spin terms and both dipolar and multipolar Dzyaloshinskii-Moriya interactions. We find a strong competition between ferromagnetic and antiferromagnetic canted and collinear quadrupolar magnetic phases: the transition from one magnetic order to another can be controlled by the strength of the electronic correlation (U ) and by the degree of Jahn-Teller distortions.

Conflicting interpretations of experimental data preclude the understanding of the quantum magnetic state of spin-orbit coupled d 2 double perovskites. Whether the ground state is a Janh-Teller-distorted order of quadrupoles or the hitherto elusive octupolar order remains debated. We resolve this uncertainty through direct calculations of all-rank intersite exchange interactions and inelastic neutron scattering cross section for the d 2 double perovskite series Ba 2 MOsO 6 (M ¼ Ca, Mg, Zn). Using advanced many-body firstprinciples methods, we show that the ground state is formed by ferro-ordered octupoles coupled by superexchange interactions within the ground-state E g doublet. Computed ordering temperature of the single second-order phase transition is consistent with experimentally observed material-dependent trends. Minuscule distortions of the parent cubic structure are shown to qualitatively modify the structure of gaped magnetic excitations.

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