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We report on investigations of the complex magnetostructural and spin-state transitions in the breathing pyrochlore LiFeCr$_{4}$O$_{8}$ by means of magnetization, M\"ossbauer spectroscopy, and density functional theory (DFT) calculations. Three transitions corresponding to the ferrimagnetic transition at $T_N\sim94$ K, the spin-gap transition at $T_{SG}\sim50$ K, and the magnetostructural 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 site from our M\"ossbauer measurements, suggesting that the spin-gap transition is absent at the Fe site. This indicates that the spin-gap transition is an effect of the breathing Cr$_4$ lattice, in agreement with our DFT calculations from which we see nearly decoupled electronic states for the FeO$_4$ and CrO$_6$ units. From the temperature dependence of the hyperfine magnetic field we also observed a spin-state transition for the Fe spins at $T_{MS}$ consistent with earlier neutron diffraction measurements. These local characteristics are believed to be important for a complete understanding of the complex magnetostructural coupling effects observed in similar systems., Comment: 9 pages, 8 figures

In this work, we present detailed $^{57}$Fe M\"ossbauer spectroscopy investigations of (Co$_{0.97}$$^{57}$Fe$_{0.03}$)$_{4}$Nb$_{2}$O$_{9}$ compound to study its possible magnetic structures. We have shown that the previously reported magnetic structures can not satisfactorily describe our low temperature M\"ossbauer spectra. Therefore, in combination with theoretical calculations, we have proposed a modulated helicoidal magnetic structure that can be used to simulate the whole series of our low temperature M\"ossbauer spectra. Our results suggest that the combination of previously reported different magnetic structures are only approximations of the average magnetic structure from our modulated helicoidal model. We anticipate that the proposed modulated non-collinear magnetic structure might shed light on the understanding of the complex magnetoelectric effects observed in this system., Comment: To be published in Journal of Magnetism and Magnetic Materials; online version: https://www.sciencedirect.com/science/article/pii/S0304885323003876 Or DOI link: https://doi.org/10.1016/j.jmmm.2023.170738