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We report on investigations of the complex magnetostructural and spin-statetransitions in the breathing pyrochlore LiFeCr$_{4}$O$_{8}$ by means ofmagnetization, M\"ossbauer spectroscopy, and density functional theory (DFT)calculations. Three transitions corresponding to the ferrimagnetic transitionat $T_N\sim94$ K, the spin-gap transition at $T_{SG}\sim50$ K, and themagnetostructural transition at $T_{MS}\sim19$ K were observed from the$\chi$(T) curve, whereas only $T_N$ and $T_{MS}$ were evidenced for the Fe sitefrom our M\"ossbauer measurements, suggesting that the spin-gap transition isabsent at the Fe site. This indicates that the spin-gap transition is an effectof the breathing Cr$_4$ lattice, in agreement with our DFT calculations fromwhich we see nearly decoupled electronic states for the FeO$_4$ and CrO$_6$units. From the temperature dependence of the hyperfine magnetic field we alsoobserved a spin-state transition for the Fe spins at $T_{MS}$ consistent withearlier neutron diffraction measurements. These local characteristics arebelieved to be important for a complete understanding of the complexmagnetostructural coupling effects observed in similar systems.

M\"ossbauer spectroscopy study of the magnetostructural and spin-state transitions in the breathing pyrochlore LiFeCr$_{4}$O$_{8}$