Coupling of magnetism and transport properties to the lattice degrees of freedom in NdBaCo$_2$O$_{5+δ}$ ($δ\sim 0.65$)

Abstract: We have studied the origin of zero volume expansion below the Curie temperature (Tc), variable range hopping (VRH) behaviour using structural, magnetic, transport and thermal studies on the oxygen deficient double perovskite NdBaCo$2$O${5+{\delta}}$ ($\delta \sim 0.65$). The valence state of Co ions and the possible properties exhibited by such compound were studied using electronic structure calculations for $\delta = 0.75$. Careful investigation of structure shows that the compound stabilizes in tetragonal structure (P4/mmm) having $2a_p \times 2a_p \times 2a_p$ (222) superstructure, where $a_p$ is the cubic perovskite lattice parameter. The compound exhibits a minimum in resistivity, ferromagnetic and ferrimagnetic transitions around 375 K, 120 K ($T_c$) and 60 K, respectively with signature of Griffiths phase above $T_c$. Our detailed structural analysis suggests signature of the onset of the above magnetic transitions at temperatures well above its stabilisation at long range level thereby leading to VRH behaviour. The observed zero thermal expansion in volume below Tc appears to be due to competing magnetic interactions within and between the magnetic sublattices. Our electronic structure calculations show (a) the importance of electron-electron correlation in Nd $4f$ and Co $3d$ states (b) Co ions stabilize in intermediate spin (IS) state, having oxidation state less than +3 (c) half metallicity. Our results show the possibility of coupling between magnetism and ferroelectricity. We believe that our results especially on the valence state of the Co ion, zero thermal expansion in volume, short range magnetic orderings and the connection between different degrees of freedom will be helpful in clearing the ambiguities existing in literature on the nature of magnetism and thereby aiding in designing new functionalities.