Theory of itinerant antiferromagnetism: Zero-temperature properties

Abstract

The method of Gutzwiller is extended to include antiferromagnetism in a $s$-band Hubbard model. A first-order paramagnetic (PM) to antiferromagnetic (AFM) transition is obtained with increasing $\frac{U}{W}$ ratio. The AFM ground state in the phase diagram is restricted between the electron density $n_1<1\mathrm{}$ and $n_2=2-n_1$. It is also bounded from below by a critical value of $\frac{U}{W}$. The complete AFM ordering appears only for $n=1\mathrm{}$. As $n$ approaches $n_1$ or $n_2$ along the phase boundary, the AFM ordering gradually disappears. The AFM ordering is essentially due to virtual electron hopping, and the values of $n_1$, $n_2$, and critical $\frac{U}{W}$ depend on the bare density of states and the coordination number. The probability of having antiparallel-spin nearest-neighbor pair is computed. The result is consistent with the phase diagram. We also found a region in the phase diagram where the PM and the AFM states coexist. The AFM ground state at $n=1\mathrm{}$ is insulating. Depending on the value of $\frac{U}{W}$, the present theory predicts either an AFM insulating → PM metallic or an AFM insulating → PM insulating → PM metallic transition as the temperature is raised. Therefore, the ${\mathrm{V}}_2$ ${\mathrm{O}}_3$-type phase diagram follows from the present theory.