Magnetoelastic octahedral breathing mode in the ferrimagnetic La2CoIrO6 double perovskite

Distortion of transition-metal ion-oxygen octahedra in perovskite structure has been a long standing subject for exploring the physics of charge-orbital--spin-lattice couplings. Recent findings in nickelates or $\mathrm{BaBi}{\mathrm{O}}₃$ have suggested that a charge disproportionation in the transition-metal ions can evoke certain cooperative breathing distortions (CBD), constituted by the symmetric expansion and shrinkage of the octahedra in contrast to the Jahn-Teller-type asymmetric distortion. A double perovskite ferrimagnet, $\mathrm{L}{\mathrm{a}}₂\mathrm{CoIr}{\mathrm{O}}₆$ bears inherently the charge disproportionation in the cationic sites with $\mathrm{C}{\mathrm{o}}²⁺$ and $\mathrm{I}{\mathrm{r}}⁴⁺$ sublattices. In light of seeking the clues for the CBD and its coupling to the magnetic order, the crystal structure and magnetic structure of $\mathrm{L}{\mathrm{a}}₂\mathrm{CoIr}{\mathrm{O}}₆$ were examined at various temperatures by using neutron diffraction. Structure refinements and mode decomposition analyses revealed that, indeed, a CBD mode exists substantially in $\mathrm{L}{\mathrm{a}}₂\mathrm{CoIr}{\mathrm{O}}₆$ while preserving the symmetry of the lattices ($P{2}₁/n$) and the magnetism $[{\mathrm{\ensuremath{\Gamma}}}₁({A}_g)]$. And more importantly, the magnitude of the symmetric distortion is correlated strongly with the size of the magnetic moment at temperatures below the Curie temperature (\ensuremath{\sim}95 K). This strongly suggests a magnetoelastic coupling of the CBD mode. The order parameters for CBD, e.g., the movement of O1 toward Ir ions at low temperatures, are found to be in a linear-quadratic relationship with the value of the magnetic moment ($\ensuremath{\sim}0.002\phantom{\rule{0.16em}{0ex}}\AA{}/{{\ensuremath{\mu}}_{\mathrm{B}}}²{{M}_{\mathrm{Co}}}²$), manifesting the magnetoelastic CBD in double perovskite.