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Linear Spin Wave Analysis for General Magnetic Orders in the Kondo Lattice Model

We extend the formulation of the spin wave theory for the Kondo lattice model, which was mainly used for the ferromagnetic metallic state, to general magnetic orders including complex noncollinear and noncoplanar orders. The 1/S expansion is reformulated in the matrix form depending on the size of the magnetic unit cell. The noncollinearity and noncoplanarity of the localized moments are properly taken into account by the matrix elements of the para-unitary matrix used in the diagonalization of the Bogoliubov-de Gennes type Hamiltonian for magnons. We apply the formulation within the linear spin wave approximation to a typical noncollinear case, the $120^{\circ}$ N{é}el order on a triangular lattice at half filling. We calculate the magnon excitation spectrum and the quantum correction to the magnitude of ordered moments as functions of the strength of the Hund's-rule coupling, $J_{\rm H}/t$. We find that the magnon excitation shows softening at $J_{\rm H}/t \simeq 2.9$, which indicates that the $120^{\circ}$ order is destabilized for smaller $J_{\rm H}/t$. On the other hand, we show that the $120^{\circ}$ order is stable in the entire range of $J_{\rm H}/t \gtrsim 2.9$, and, in the limit of $J_{\rm H}/t \to \infty$, the form of the spin wave spectrum approaches that for the antiferromagnetic Heisenberg model, while the bandwidth is proportional to $t^2/J_{\rm H}$. The reduction of the ordered moment is smaller than that for the spin-only model, except in the vicinity of the softening.