Strong Spin-Phonon Coupling Mediated by Single Ion Anisotropy in the All-In–All-Out Pyrochlore Magnet ${\mathrm{Cd}}_2{\mathrm{Os}}_2{\mathrm{O}}_7$

Spin-phonon coupling mediated by single ion anisotropy was investigated using optical spectroscopy and first-principles calculations in the all-in–all-out pyrochlore magnet ${\mathrm{Cd}}_2{\mathrm{Os}}_2{\mathrm{O}}_7$. Clear anomalies were observed in both the phonon frequencies and linewidths at the magnetic ordering temperature. The renormalization of the phonon modes was exceptionally large, signifying the presence of an unconventional magnetoelastic term from large spin-orbit coupling. In addition, the relative phonon frequency shifts show a strong correlation with the modulation of noncubic crystal field by the corresponding lattice distortion. Our observation establishes a new type of spin-phonon coupling through single ion anisotropy, a second-order spin-orbit coupling term, in ${\mathrm{Cd}}_2{\mathrm{Os}}_2{\mathrm{O}}_7$.

Figure 1

$T$-dependent ${\sigma }_1(\omega )$ below $800{\mathrm{cm}}^{-1}$. Seven phonon modes are highlighted by solid triangles. The black solid line indicates the best fitting results for the 227 K data with Lorentz and Fano oscillators. The asymmetry parameter $q$ for the two asymmetric modes are indicated.

Figure 2

Eigenvectors, $\omega (T)$, $\mathrm{\Gamma }(T)$, and $\mathrm{\Omega }(T)$ of the (a) Cd-O2 bending, (b) Os-Os stretching, (c) Os-O1 polar, (d) Os-O1 bending, and (e) Os-O1 stretching modes. The black solid arrows in the top panels indicate the displacement of the ions by each phonon mode. The red dashed lines indicate $T_N$.

Figure 3

(a) $\mathrm{\Delta }\omega /{\omega }_0$ (solid squares) and $\mathrm{\Delta }\mathrm{\Gamma }/{\omega }_0$ (open circles) of five phonon modes. (b) Normalized trigonal and hexagonal crystal field change with the corresponding lattice distortion. The inset shows a schematic diagram of the orbital states of the Os ions.