  Unconventional anomalous Hall effect in frustrated pyrochlore oxides is
originated from spin chirality of non-coplanar localized spins, which can also
be induced by the competition between ferromagnetic (FM) double exchange
interaction $J_{H}$ and antiferromagnetic superexchange interaction $J_{AF}$.
Here truncated polynomial expansion method and Monte Carlo simulation are
adopted to investigate the above model on two-dimensional triangular lattice.
We discuss the influence of the range of FM-type spin-spin correlation and
strong electron-spin correlation on the truncation error of spin-spin
correlation near quarter filling. Two peaks of the probability distribution of
spin-spin correlation in non-coplanar spin configuration clearly show that
non-coplanar spin configuration is an intermediate phase between FM and
120-degree spin phase. Near quarter filling, there is a phase transition from
FM into non-coplanar and further into 120-degree spin phase when $J_{AF}$
continually increases. Finally the effect of temperature on magnetic structure
is discussed.
