  A search for the solar neutrino effective magnetic moment has been performed
using data from 1291.5 days exposure during the second phase of the Borexino
experiment. No significant deviations from the expected shape of the electron
recoil spectrum from solar neutrinos have been found, and a new upper limit on
the effective neutrino magnetic moment of $\mu_{\nu}^{eff}$ $<$
2.8$\cdot$10$^{-11}$ $\mu_{B}$ at 90\% c.l. has been set using constraints on
the sum of the solar neutrino fluxes implied by the radiochemical gallium
experiments.Using the limit for the effective neutrino moment, new limits for
the magnetic moments of the neutrino flavor states, and for the elements of the
neutrino magnetic moments matrix for Dirac and Majorana neutrinos, are derived.
