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Phase separation in La$_{0.5}$Ca$_{0.5}$MnO$_3$ doped with 1% $^{119}$Sn detected by Mössbauer spectroscopy

1% $^{119}$Sn-doped La$_{0.5}$Ca$_{0.5}$MnO$_3$ was studied by Mössbauer spectroscopy, magnetic moment and resistivity measurements. The Mössbauer spectra below the charge-ordering temperature are explained with ferromagnetic (FM), antiferromagnetic (AF), and ferromagnetic spin cluster (CL) components. The magnetic and thermal hystereses of the relative intensities of the components observed in the Mössbauer spectra, and of the bulk properties such as magnetic moment and electrical resistivity, in the temperature range 125-185 K, are characteristic of phase equilibrium in a first-order transition, i.e. of phase separation in the system below the charge-ordering (CO) transition. The cluster component displays a significant hyperfine field up to $\sim 125$ K. Above this temperature it exhibits superparamagnetism, becoming the dominant component above the charge-ordering transition. These results are discussed in the framework of recent investigations of the manganite system with other techniques which also show phase separation.