Nanoelectronic devices emulating neuro-synaptic functionalities through their intrinsic physics at low operating energies is imperative toward the realization of brain-like neuromorphic computers. In this work, we leverage the non-linear voltage dependent partial polarization switching of a ferroelectric field effect transistor to mimic plasticity characteristics of biological synapses. We provide experimental measurements of the synaptic characteristics for a $28nm$ high-k metal gate technology based device and develop an experimentally calibrated device model for large-scale system performance prediction. Decoupled read-write paths, ultra-low programming energies and the possibility of arranging such devices in a cross-point architecture demonstrate the synaptic efficacy of the device. Our hardware-algorithm co-design analysis reveals that the intrinsic plasticity of the ferroelectric devices has potential to enable unsupervised local learning in edge devices with limited training data.