Stability Theory of the Magnetic Phases for a Simple Model of the Transition Metals

A semiquantitative explanation of the observed distribution of magnetism in the transition metals and alloys is made based on a highly simplified quasiparticle band model. It depends on only two parameters, the valence (number of $d$ electrons) of the metal and the ratio of quasiparticle interaction strength to band-width, $\frac{C_0}{E^{\prime \prime }}$. The quantity $\frac{C_0}{E^{\prime \prime }}$ increases with valence and also increases as one goes from the $5d$ transition metals to the $3d$ transition metals. Ferromagnetism is found to be most likely for those metals with large $\frac{C_0}{E^{\prime \prime }}$ and a valence well away from five. Antiferromagnetism is found to occur for a valence of around five, as do the more complex states such as the ferrimagnetic and spiral-spin-density-wave states, which are explicitly described. It is suggested that the peak in the specific heat of the transition-metal alloys that occurs as one alloys across the $3d$ transition series is closely related to changes in the band structure caused by ordering, at least for the Cr-Mn system.