Magnetic long-range order in thet-Jmodel with finite doping

Abstract

The spiral phase of the two-dimensional t-J model and the t-t'-J model is studied in the S\ensuremath{\rightarrow}\ensuremath{\infty} limit and in the low-doping limit. By rewriting the model in a form that is more transparent for analyzing the carrier-spin interaction, we show that a wave vector characterizing spiral long-range order in the t-J model varies linearly with hole density \ensuremath{\delta}. If we dope more holes, the spiral phase changes discontinuously towards a ferromagnetic phase, the Nagaoka state, at a critical hole density ${\mathrm{\ensuremath{\delta}}}_{\mathit{c}}$=3(1+ \ensuremath{\surd}2 )J/8t. The spiral phase, however, does not maintain its stability because of electron-density fluctuations. The next-nearest-neighbor hopping t' stabilizes the Ne\ifmmode\acute\else\textasciiacute\fi{}el phase and allows it to occupy a finite area in the magnetic phase diagram. We also investigate the effect of spiral-spin fluctuations upon the stability of the spiral phase, and find that the stability is not recovered by the spin fluctuations.