Spin Density Wave in Chromium and Its Alloys

Antiferromagnetic, helical, and sinusoidal spin density waves (SDW) in chromium and its alloys with Mn and V are studied on the basis of a simplified model of the known band structure of chromium. Octahedral Fermi surfaces of different sizes are assumed for the electron band and hole band, and these bands are considered to play the main role in the formation of a SDW; other bands having free Fermi surfaces are considered to supply electrons to these bands during the formation of a SDW and are called the reservoir. The exchange potential for each electron due to the SDW mixes the electron band and hole band, and produces the SDW itself, so that a self-consistency equation is set up and solved. It is found that the sinusoidal SDW gives the lowest energy. Its wave vector Q at absolute zero (as well as that of a helical SDW) is the distance between the parallel surfaces of the electron and hole octahedra, but the distance changes with the supply of electrons from the reservoir. With the rigid-band model for alloys, it is found that $Q$ jumps at a small concentration of Mn to a higher value not equal to that for the exact antiferromagnetism, in agreement with neutron observations. The observed abrupt transition to the exact antiferromagnetism at a higher concentration is not predicted, however. The Néel temperature for a second-order transition is calculated. The value of $Q$ at the Néel temperature increases rapidly with increasing Mn concentration and attains the value for the exact antiferromagnetism, in agreement with observations. A discussion of the magnetic moment amplitude is given.