Magnetization plateau and supersolid phases in the spin-1/2 antiferromagnetic Heisenberg model on a tetragonally distorted fcc lattice

The Heisenberg model on a face center cubic (fcc) lattice is a typical three-dimensional frustrated spin system expected to have magnetization plateaus and supersolid phases. There are model compounds ${A}_{2}{\mathrm{CoTeO}}_{6}$ ($A=\text{Ca}$, Sr, Pb) for the fcc lattice but with lattice distortions. Motivated by the presence of the compounds, we investigate the ground state of the spin-1/2 antiferromagnetic Heisenberg model on a tetragonally distorted fcc lattice in the magnetic field using a large-size cluster mean-field method for the sake of finding new supersolid phases. We find five supersolid phases in the model, indicating the possibility to observe supersolid phases in these compounds. We also find that one of the supersolid phases is similar to the nonclassical coplanar phase obtained in the $XXZ$ model on the triangular lattice.