Analysis of low temperature specific heat in the ferromagnetic state of the Ca-doped manganites

The reported specific heat C (T) data of the perovskite manganites La$_{1-x }$CaxMnO3, with x = 0.1, 0.2 and 0.33, is theoretically investigated in the temperature domain $4 \le T \le 10$ K. Calculations of C (T) have been made within the two component scheme: one is the Fermionic and the other is Bosonic (phonon or magnon) contribution. Lattice specific heat is well estimated from the Debye model and Debye temperature for Ca doped lanthanum manganites is obtained following an overlap repulsive potential. Fermionic component as the electronic specific heat coefficient is deduced using the band structure calculations for ferromagnetic metallic phase. Later on, for x = 0.1, following double exchange mechanism the role of magnons is assessed towards specific heat and find that at much low temperatures (T < 10 K), specific heat increases and show almost $T^{3/2}$ dependence on the temperature. We note that, the lattice specific heat is smaller for x = 0.1 when compared to that of magnon specific heat below 10 K. For x = 0.2, i.e., in the ferromagnetic metallic phase the magnon contribution is larger with the electron contribution while the reverse is true for x = 0.33. It is further noticed that in the ferromagnetic metallic phase, electronic specific heat is small in comparison to the lattice specific heat in low temperature domain. The present investigations allow us to believe that electron correlations are essential to enhanced density of state over simple Fermi liquid approximation in the metallic phase of La$_{1-x}$CaxMnO3 (x = 0.2, 0.33). The present numerical analysis of specific heat shows similar results as those revealed from experiments