  The relatively large value of neutrino mixing angle \theta_{13} set by recent
measurements allows us to use solar neutrinos to set a limit on neutrino
magnetic moment involving second and third families, \mu_{\mu\tau}. The
existence of a random magnetic field in solar convective zone can produce a
significant anti-neutrino flux when a non-vanishing neutrino magnetic moment is
assumed. Even if we consider a vanishing neutrino magnetic moment involving the
first family, electron anti-neutrinos are indirectly produced through the
mixing between first and third families and non-vanishing \mu_{\mu\tau}. Using
KamLAND limits on the solar flux of electron anti-neutrino, we set the limit
\mu_{\mu\tau} < 0.5e-11 Bohr magneton for a reasonable assumption on the
behavior of solar magnetic fields. This is the first time a limit on
\mu_{\mu\tau} is established in the literature directly from neutrino
interaction with magnetic fields, and, interestingly enough, is comparable with
the limits on neutrino magnetic moment involving the first family and with the
ones coming from modifications on electroweak cross section.
