  Iridates abound with interesting magnetic behaviours because of their strong
spin-orbit coupling. Sr$_3$NiIrO$_6$ brings together the spin-orbital
entanglement of the Ir$^{4+}$ ion with a 3$d$ Ni cation and a one-dimensional
crystal structure. It has a ferrimagnetic ground state with a 55 T coercive
field. We perform a theoretical study of the magnetic interactions in this
compound, and elucidate the role of anisotropic symmetric exchange as the
source of its strong magnetic anisotropy. Our first-principles calculations
reproduce the magnon spectra of this compound and predict a signature in the
cross sections that can differentiate the anisotropic exchange from single-ion
anisotopy.
