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The Heisenberg model on a face center cubic (fcc) lattice is a typicalthree-dimensional frustrated spin system expected to have magnetizationplateaus and supersolid phases. There are model compounds $A_2$CoTeO$_6$ ($A$ =Ca, Sr, Pb) for the fcc lattice but with lattice distortions. Motivated by thepresence of the compounds, we investigate the ground state of the spin-1/2antiferromagnetic Heisenberg model on a tetragonally distorted fcc lattice inthe magnetic field using a large-size cluster mean-field method for the sake offinding new supersolid phases. We find five supersolid phases in the model,indicating possibility to observe supersolid phases in these compounds. We alsofind that one of the supersolid phases is similar to the nonclassical coplanarphase obtained in the XXZ model on the triangular lattice.

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