First-principles calculation of exchange interaction and exchange force between magnetic Fe films

First-principles calculations have been performed for the exchange interaction and exchange force between two magnetic Fe(100) thin films. It is shown that the magnitude of the calculated exchange force is of the order of $10^{-9} $N at $d/a < 1$ and of the order of $10^{-10} $N at $1 < d/a < 1.5$, where $d$ denotes the distance between surfaces of the two thin films and $a$ the lattice constant of bulk Fe. The obtained forces are sufficiently larger than the sensitivity of the current atomic force microscopy of $10^{-12} - 10^{-13}$N, which suggests the feasibility of the exchange force microscopy.