Low-energy Effective Theory for Spin Dynamics of Fluctuating Stripes

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We derive an effective Hamiltonian for spin dynamics of fluctuating smectic stripes from the t-J model in the weak coupling limit t >> J. Besides the modulation of spin magnitude, the high energy hopping term would induce a low-energy anti-ferromagnetic interaction between two neighboring ``blocks of spins". Based on the effective Hamiltonian, we applied the linear spin-wave theory and found that the spin-wave velocity is almost isotropic for La₂₋ₓSrₓ CuO₄ unless the structural effect is considered. The intensity of the second harmonic mode is found to be about 10% to that of the fundamental mode.