Low density ferromagnetism in Extended Hubbard ( t-t'-U ) Model

We study the existence of ferromagnetism in one dimensional Hubbard Model with on site interaction and nearest and next nearest neighbor hopping. Using the Hubbard I approximation, a self consistent equation for $<n_\sigma>$, the particle density with spin $\sigma$ is obtained. We find that ferromagnetism exists over a wide range of values of the next nearest neighbor hopping element t' when on-site interaction U is large. The phase diagram as a function of t'/t and the electron density $<n>$ has been obtained by numerically solving the self consistent equation. It is found that the maximum density at which ferromagnetism can occur, peaks around $t'/t \approx -0.53$. We show that this phenomenon is a result of the peculiar way in which the t' term modifies the density of states.