Theory of itinerant antiferromagnetism: Zero-temperature properties

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 U/W ratio. The AFM ground state in the phase diagram is restricted between the electron density n₁<1 and n₂=2-n₁. It is also bounded from below by a critical value of U/W. The complete AFM ordering appears only for $n=1$. As n approaches n₁ or n₂ along the phase boundary, the AFM ordering gradually disappears. The AFM ordering is essentially due to virtual electron hopping, and the values of n₁, n₂, and critical 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 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 V₂{O}₃$-type phase diagram follows from the present theory.