  Combining density-functional theory calculations with a classical Monte Carlo
method, we show that for B2-type FeCo compounds tetragonal distortion gives
rise to a strong reduction of the Curie temperature $T_{\mathrm{C}}$. The
$T_{\mathrm{C}}$ monotonically decreases from 1575 K (for $c/a=1$) to 940 K
(for $c/a=\sqrtwo$). We find that the nearest neighbor Fe-Co exchange
interaction is sufficient to explain the $c/a$ behavior of the
$T_{\mathrm{C}}$. Combination of high magnetocrystalline anisotropy energy with
a moderate $T_{\mathrm{C}}$ value suggests tetragonal FeCo grown on the Rh
substrate with $c/a=1.24$ to be a promising material for heat-assisted magnetic
recording applications.
