  While 3$d$-containing materials display strong electron correlations, narrow
band widths, and robust magnetism, 5$d$ systems are recognized for strong
spin-orbit coupling, increased hybridization, and more diffuse orbitals.
Combining these properties leads to novel behavior. Sr$_3$NiIrO$_6$, for
example, displays complex magnetism and ultra-high coercive fields - up to an
incredible 55~T. Here, we combine infrared and optical spectroscopies with
high-field magnetization and first principles calculations to explore the
fundamental excitations of the lattice and related coupling processes including
spin-lattice and electron-phonon mechanisms. Magneto-infrared spectroscopy
reveals spin-lattice coupling of three phonons that modulate the Ir environment
to reduce the energy required to modify the spin arrangement. While these modes
primarily affect exchange within the chains, analysis also uncovers important
inter-chain motion. This provides a mechanism by which inter-chain interactions
can occur in the developing model for ultra-high coercivity. At the same time,
analysis of the on-site Ir$^{4+}$ excitations reveals vibronic coupling and
extremely large crystal field parameters that lead to a t$_{2g}$-derived
low-spin state for Ir. These findings highlight the spin-charge-lattice
entanglement in Sr$_3$NiIrO$_6$ and suggest that similar interactions may take
place in other 3$d$/5$d$ hybrids.
