Fermi Surface and Antiferromagnetism in Europium Metal

We have calculated the Fermi surface of europium in order to find those features which determine the wave vector of the helical moment arrangement below the Néel point. We find that there are two pieces of Fermi surface: an electron surface at the symmetry point $H$, which has the shape of rounded-off cube, and a hole surface at the point $P$, which is also a rounded-off cube (half the size of the one at $H$) but with ellipsoids tetrahedrally positioned on four of the corners. We propose that the wave vector of the helical moment arrangement is fixed by the separation between opposing faces of the nearly cubical part of the hole surface at $P$, and we also discuss the effects of the electron surface at $H$. Since it is likely that barium and europium have similar Fermi surfaces, we have presented several extremal areas and the corresponding de Haas-van Alphen frequencies in the hope that experimental results may soon become available.