Spin relaxation under conditions of the quantum Hall effect with odd filling

Goldstone mode relaxation in a quantum hall ferromagnet due to hyperfine interaction with nuclei

“…Now, at variance with the cited works [13,14], the expectations entering Eq. (6) should be calculated not only for the integer QHF but for the fractional QHF too.…”

“…For the second type, the GM breakdown was theoretically analyzed in the works of Refs. [13] and [14]. (See also Ref.…”

“…As far as the SO coupling does not perturb the translation symmetry, the GM relaxation needs additional perturbative interactions providing the momentum and energy dissipation. These in fact are the electron-phonon coupling [13] or interaction with the smooth random potential [14].…”

“…[13] and [14], now the considered initial deviation is again of the second type, i.e. starting point is the GM state |i = Ŝ − N |0 , where |0 stands for the QHF ground state, andŜ − = jσ…”

“…For the final calculation I only need the sum A In order to describe the QHF states, I use again the excitonic representation by analogy with previous works [7,[11][12][13][14]. Namely, by defining the spin exciton creation operator [21]:…”