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 ${n}_{1}<1$ and ${n}_{2}=2\ensuremath{-}{n}_{1}$. It is also bounded from below by a critical value of $\frac{U}{W}$. The complete AFM ordering appears only for $n=1$. 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 $n=1$ is insulating. Depending on the value of $\frac{U}{W}$, the present theory predicts either an AFM insulating \ensuremath{\rightarrow} PM metallic or an AFM insulating \ensuremath{\rightarrow} PM insulating \ensuremath{\rightarrow} PM metallic transition as the temperature is raised. Therefore, the ${\mathrm{V}}_{2}$${\mathrm{O}}_{3}$-type phase diagram follows from the present theory.