Spin dynamics and magnetic phase diagram of ${\mathrm{La}}_{1-x}{\mathrm{Ca}}_x{\mathrm{MnO}}_3$ $(0\mathrm{}<~x<~0.15)$

Spin dynamics of ceramic ${\mathrm{La}}_{1-x}{\mathrm{Ca}}_x{\mathrm{MnO}}_3$ with $x=0,$ 0.05, and 0.15 and the relative ${\mathrm{Mn}}^{4+}$ concentration $c=0.18\mathrm{}–0.22$ is investigated by measurements of the ac susceptibility and the relaxation of the thermoremanent magnetization (TRM). The ${\chi }_{\mathrm{ac}}\mathrm{}\left(T\right)\mathrm{}$ function exhibits a transition from the paramagnetic to a mixed spin-glass and ferromagnetic phase. Below that is found a steep decrease and onset of the frequency dependence of ${\chi }_{\mathrm{ac}}\mathrm{}\left(T\right),$ providing evidence for existence of a reentrant spin glass (RSG) phase. The dependence of the spin-glass freezing temperature, $T_f,$ on f satisfies the conventional critical slowing-down law, $\tau /{\tau }_0{=(T}_f{/T}_G-{1)}^{-\mathrm{zv}}$ with $\tau =1/f,$ $zv=12\mathrm{}\pm 2,$ ${\tau }_0\sim {10}^{-12}\mathrm{s}$ and the glass temperature, $T_G,$ decreasing from 93 to 70.5 K when x is increased from 0 to 0.15. The relaxation rate $S\left(t\right)\mathrm{}$ of TRM has a clear maximum near a wait time $t_w\sim \left(2\mathrm{}-4\right)\times {10}^3\mathrm{s}$ and the function $S\left(T\right)\mathrm{}$ shows a sharp maximum near $T_G.$ The plots of $S\left(T\right)\mathrm{}$ exhibit a substantial decrease at $T>\mathrm{}{T}_G$ while for $T<\mathrm{}{T}_G$ they collapse into a single curve, as typical for mixed ${(T}_G<T<\mathrm{}{T}_C)$ and RSG phases, respectively. The observed spin dynamics agrees completely with the magnetic phase diagram (paramagnetic, mixed, and RSG phases with decreasing T) predicted recently for a system containing lattice disorder and competing superexchange and double exchange interactions.