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The Mott insulator $\alpha$-RuCl$_3$ has generated great interest in thecommunity due to its possible field-induced Kitaev quantum spin liquid state.Despite enormous effort spent trying to obtain the form of the low energyHamiltonian, there is currently no agreed upon set of parameters which is ableto explain all of the data. A key piece of missing information lies in thedetermination of the magnetic form factor of Ru$^{3+}$, particularly for a truequantitative treatment of inelastic neutron scattering data. Here we presentthe experimentally derived magnetic form factor of Ru$^{3+}$ in the low spin4$d^5$ state using polarized neutron diffraction within the paramagnetic regimeon high quality single crystals of $\alpha$-RuCl$_3$. We observe strongevidence of an anisotropic form factor, expected of the spin-orbit coupled$j_{\textrm{eff}} = \frac{1}{2}$ ground state. We model the staticmagnetization density in increasing complexity from simple isotropic cases, toa multipolar expansion, and finally \emph{ab initio} calculations of thegeneralized $j_{\textrm{eff}} = \frac{1}{2}$ ground state. Comparison of bothsingle ion models and inclusion of Cl$^-$ anions support the presence ofhybridization of Ru$^{3+}$ with the surrounding Cl$^{-}$ ligands.

Experimental Evidence for Non-spherical Magnetic Form Factor in Ru$^{3+}$