Saturation of dephasing time in mesoscopic devices produced by a ferromagnetic state

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We consider an exchange model of itinerant electrons in a Heisenberg ferromagnet and we assume that the ferromagnet is in a fully polarized state. Using the Holstein-Primakoff transformation we are able to obtain a boson-fermion Hamiltonian that is well-known in the interaction between light and matter. This model describes the spontaneous emission in two-level atoms that is the proper decoherence mechanism when the number of modes of the radiation field is taken increasingly large, the vacuum acting as a reservoir. In the same way one can see that the interaction between the bosonic modes of spin waves and an itinerant electron produces decoherence by spin flipping with a rate proportional to the size of the system. In this way we are able to show that the experiments on quantum dots, described in D. K. Ferry et al. [Phys. Rev. Lett. 82, 4687 (1999)], and nanowires, described in D. Natelson et al. [Phys. Rev. Lett. 86, 1821 (2001)], can be understood as the interaction of itinerant electrons and an electron gas in a fully polarized state.