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Quadrupole formation and coupling to magnetic and structural degrees of freedom in the $5 d^{1}$ double perovskites ${Ba}_{2} {MgReO}_{6}$ and ${Ba}_{2} {NaOsO}_{6}$

Francesco Martinelli ^* and Claude Ederer

Materials Theory, ETH Zürich, Wolfgang-Pauli-Strasse 27, 8093 Zürich, Switzerland

^*Contact author: fmartinelli@ethz.ch

Phys. Rev. Research 8, 033163 – Published 10 August, 2026

DOI: https://doi.org/10.1103/chtv-nvsq

Abstract

We investigate the interplay between charge, magnetic, and structural degrees of freedom in the isostructural and isoelectronic $5 d^{1}$ double perovskites ${Ba}_{2} {MgReO}_{6}$ and ${Ba}_{2} {NaOsO}_{6}$ . Using first-principles-based electronic structure calculations, we show that both materials exhibit a tendency toward spontaneous quadrupolar order in the cubic paramagnetic phase, which is slightly weaker in ${Ba}_{2} {NaOsO}_{6}$ than in ${Ba}_{2} {MgReO}_{6}$ . Our analysis further reveals an intimate coupling between the local magnetic moments and charge quadrupoles, mediated by the strong spin-orbit interaction, that leads to the unusual canted configuration of magnetic moments observed in these systems. When structural degrees of freedom are included, the two materials exhibit pronounced differences. In ${Ba}_{2} {MgReO}_{6}$ , the strong coupling to Jahn-Teller distortions stabilizes the antiferroic $Q_{x^{2} - y^{2}}$ order, yielding excellent agreement with available experimental data. In contrast, the Jahn-Teller coupling is significantly weaker in ${Ba}_{2} {NaOsO}_{6}$ and appears insufficient to stabilize the antiferroic quadrupolar order. While this is consistent with the absence of any measurable long-range structural distortion above the magnetic transition temperature, it contrasts with experimental results indicating a strong canting of the magnetic moments. Our analysis thus successfully describes the mechanisms shaping the properties of the Re compound while a full quantitative description of the magnetic ground state of ${Ba}_{2} {NaOsO}_{6}$ is still elusive.

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F. Martinelli and C. Ederer, Quadrupole formation and coupling to magnetic and structural degrees of freedom in the $5 d^{1}$ double perovskites ${Ba}_{2} {MgReO}_{6}$ and ${Ba}_{2} {NaOsO}_{6}$ , Materials Cloud Archive, 2026, https://doi.org/10.24435/materialscloud:ar-wg.

Phys. Rev. Research 8, 033163– Published 10 August, 2026

Vol. 8, Iss. 3 — August - October 2026

Received 27 February 2026
Accepted 29 June 2026

DOI: https://doi.org/10.1103/chtv-nvsq

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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Quadrupole formation and coupling to magnetic and structural degrees of freedom in the $5 d^{1}$ double perovskites ${Ba}_{2} {MgReO}_{6}$ and ${Ba}_{2} {NaOsO}_{6}$

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Quadrupole formation and coupling to magnetic and structural degrees of freedom in the 5d1 double perovskites Ba2MgReO6 and Ba2NaOsO6

Abstract

Physics Subject Headings (PhySH)

Article Text

References (55)

Quadrupole formation and coupling to magnetic and structural degrees of freedom in the $5 d^{1}$ double perovskites ${Ba}_{2} {MgReO}_{6}$ and ${Ba}_{2} {NaOsO}_{6}$