Magnetic Properties of Binary Alloys: Model of Uniform Exchange Interactions

Abstract

The paramagnetic spin susceptibility ${\chi }^0\mathrm{}\left(Q\right)\mathrm{}$ of substitutional binary alloys at $T=0\mathrm{}$ is calculated in the framework of the coherent-potential approximation. Vertex corrections to the polarization diagram are found to be important and are included. Numerical values of ${\chi }^0\mathrm{}\left(Q\right)\mathrm{}$ with $Q=0\mathrm{}$ and $Q=\left(\frac{\pi }{a}\right)$ (1, 1, 1) in a simple-cubic crystal having lattice spacing $a$ are explicitly calculated under some approximations, for the density of states. From the electron-number-density dependence of ${\chi }^0$ thus obtained, we deduce the kind of magnetic state arising after a second-order transition from the paramagnetic state. This shows that in the model with uniform exchange interaction between electrons the commensurate antiferromagnetic state occurs for a finite region of electron number density $n$. This is in contrast to the case of the perfect crystal discussed by Penn which shows the commensurate antiferromagnetic state occurs only for $n=1\mathrm{}$.