We measure higher partial wave Feshbach resonances in an ultracold mixture of fermionic $^6$Li and bosonic $^{133}$Cs by magnetic field dependent atom-loss spectroscopy. For the $p$-wave Feshbach resonances we observe triplet structures corresponding to different projections of the pair rotation angular momentum onto the external magnetic field axis. We attribute the splittings to the spin-spin and spin-rotation couplings by modelling the observation using a full coupled-channel calculation. Comparison with an oversimplified model, estimating the spin-rotation coupling by describing the weakly bound close-channel molecular state with the perturbative multipole expansion, reveals the significant contribution of the molecular wavefunction at short internuclear distances. Our findings highlight the potential of Feshbach resonances in providing precise information on short- and intermediate-range molecular couplings and wavefunctions. The observed $d$-wave Feshbach resonances allow us to refine the LiCs singlet and triplet ground-state molecular potential curves at large internuclear separations.
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