Investigations on the spin-glass state in $Dy_{0.5}Sr_{0.5}MnO_$3 single crystals through structural, magnetic and thermal properties

Single crystals of $Dy_{0.5}Sr_{0.5}MnO_3$ are grown using the optical floating zone technique, and their structural, magnetic, transport and thermal properties have been investigated. Magnetization measurements under field-cooled and zero-field-cooled conditions display irreversibility below 35 K. The magnetization does not saturate up to fields of 5 T in the temperature range 5–350 K. AC susceptibility shows a cusp around 32 K that shifts to higher temperature with increasing frequency. This frequency dependence of the peak temperature follows a critical slowing down with exponent $zv$ = 3.6. Electrical resistivity shows insulating behavior, and the application of magnetic fields up to 10 T does not change this qualitative behavior. However, a marked negative magnetoresistance is observed in the paramagnetic phase reaching 80% at 70 K and 10 T. The observed resistivity behavior does not obey an activated type of conduction. These features are characteristic of spin-glass behavior in this half-doped insulating manganite. It is argued that the spin-glass-like state originates from the A-site disorder, which in turn results from the random distribution of cations with different ionic radii. Specific-heat measurements reveal a sizable linear contribution at low temperature that may be associated with the glassy magnetic ordering and a Schottky-like anomaly in a wide temperature range between 8 and 40 K. The istribution of Schottky levels is explained by the inhomogeneity of the molecular field in the spin-glass state that leads to variable splitting of the Kramers ground-state doublets in $Dy^{3+}$.