  We have established a quantum antiferromagnetic Heisenberg-Ising model on a
spin-1/2 pyrochlore edge-shared ladder with Heisenberg intra-rung and Ising
inter-rung interactions as a perspicuous candidate to exhibit magnetization mid
and zero plateaus, characteristic peaks of magnetic susceptibility, and thermal
entanglement mid plateau. The model is exactly solvable and thus, all the
essential properties such as the thermal entanglement and the magnetic
properties of the system can be exactly calculated. The calculations are done
both through the transfer matrix technique and through the reduced density
matrix. The magnetization plateaus are observed at zero and half the saturation
value and the magnetic susceptibility exhibits a clear demonstration of the
associated characteristic peaks. The model also displays the mid plateau of the
thermal entanglement as a function of the external magnetic field at low
temperatures.
