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Recently, noncoplanar spin configurations with
spin scalar chirality have drawn considerable
attention as an origin of the anomalous Hall
effect in geometrically frustrated systems.
In this mechanism, itinerant electrons acquire
an internal magnetic field according to the
solid angle spanning three spins through the
so-called Berry phase, which can result in the
anomalous Hall effect. The idea was first
explored in the ferromagnetic Kondo lattice
model on a kagome lattice [1], and extended
to other lattice systems, such as a
face-centered-cubic lattice [2] and a
triangular lattice [3]. In particular, it was
pointed out that in the triangular lattice
system the perfect nesting of the Fermi surface
at 3/4 electron filling might lead to a
noncoplanar foursublattice ordering and the
anomalous Hall effect [3]. While these studies
have successfully revealed the nontrivial
relation between the Berry phase and anomalous
Hall effect, a crucial question has been left
unclear so far, i.e., when and how such
noncoplanar spin order emerges and what is the
role of coupling between charge and spin
degrees of freedom in energetically stabilizing
such ordering.
To clarify the parameter range and the stabilization mechanism of the noncoplanar ordering, we study a ferromagnetic Kondo lattice model on a triangular lattice, and obtain the groundstate phase diagram in the parameter space of electron density, Hund's-rule coupling and antiferromagnetic superexchange interaction between localized spins [4]. In order to determine the ground state for each parameter set, we evaluate and compare the energies of various spinordered states up to four-sublattice orders. As a result, we find that a noncoplanar four-sublattice spin ordering with finite spin scalar chirality emerges in the region near 1/4 filling, in addition to the 3/4 filling indicated in the previous study [3]. This new phase is stabilized in a wider parameter region, covering both metallic and insulating phases, compared to the 3/4 filling phase. The anomalous Hall effect takes place in these chiral-ordered phases, and in particular, the Hall conductivity is quantized according to the Chern number in the insulating regions. We also reveal significance of kinetic-driven multiple-spin interactions hidden in geometrically-frustrated Kondo lattice models. Carefully examining the perturbation in terms of the spin-charge coupling up to the fourth order, we find that a positive biqaudratic interaction is critically enhanced and plays a crucial role on stabilizing a spin scalar chiral ordering near 1/4 filling in a triangular lattice case. The origin of large positive biquadratic interaction is ascribed to the Fermi surface connection by the ordering wave vectors of four sublattice order, which we call the generalized Kohn anomaly [5]. The mechanism is potentially common to frustrated spin-charge coupled systems, leading to emergence of unusual magnetic orders. We also show the results on other frustrated lattices such as face-centered-cubic, checkerboard, and pyrochlore lattices. [1] K. Ohgushi, S. Murakami, and N. Nagaosa, Phys. Rev. B 62 (2000) R6065. [2] R. Shindou and N. Nagaosa, Phys. Rev. Lett. 87 (2001) 116801. [3] I. Martin and C.D. Batista, Phys. Rev. Lett. 101 (2008) 156402. [4] Y. Akagi and Y. Motome, J. Phys. Soc. Jpn. 79 (2010) 083711. [5] Y. Akagi, M. Udagawa, and Y. Motome, preprint (arXiv:1201.3053), accepted for publication in Phys. Rev. Lett. |
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