Interplay of Spin, Lattice, Vibration, and Charge Degrees of Freedom in Ca$_3$Mn$_2$O$_7$

Polycrystalline Ruddlesden-Popper structure Ca3Mn2O7 synthesized using solid state technique has been structurally characterized with Synchrotron powder X-ray diffraction. Thermal evolution of octahedral distortions, responsible for transition to orthorhombic state from the parent tetragonal structure, has been explored down to 37K. Change in Mn-O-Mn bond angle connecting MnO6 octahedra have been established as responsible for the magnetic ordering in the system. This has been further confirmed with Raman spectroscopy, which demonstrates spin-lattice coupling. Dipole-relaxation characteristics revealed from dielectric spectroscopy underlie the inter-related spin, lattice, phonon, and charge degrees of freedom consistently in terms of genuine and intrinsic magneto-electricity of the system.