case, a spin precession between a left-handed neutrino $\nu_L$ and a right-handed (anti)neutrino $\bar{\nu}_R$ with different flavors occurs in strong magnetic field (e.g., [@lm88; @ak88]). This is called resonant spin-flavor (RSF) conversion. The RSF conversions $\nu_e \leftrightarrow \bar{\nu}_{\mu,\tau}$ or $\bar{\nu}_{e} \leftrightarrow \nu_{\mu,\tau}$ have been investigated in two-flavor models for solar (e.g., [@ak88; @ak91; @pu92; @al93]) and SN (e.g., [@ab92; @ap93; @ts96; @nq97]) neutrinos. The RSF conversions of $\nu_e \leftrightarrow \bar{\nu}_e$ were also found [@ab92].

SN neutrinos are most favorable to find evidence for RSF conversion. Proto-neutron stars that have been formed at core collapse should have strong magnetic field. Observations of pulsars indicated that neutron stars have magnetic field of the order of $10^{12}$ G. Some pulsars indicate much stronger magnetic field with $\sim 10^{14} - 10^{15}$ G, so that they are called magnetars (e.g., [@td95]). The magnetic field in the outer region of Fe core of presupernova stars is evaluated to reach $\sim 10^{10}$ G [@hw05]. Owing to such a strong magnetic field and neutrino magnetic moment, spin-flavor conversion of neutrinos is expected to occur. Detailed features of the RSF conversions have been investigated considering three flavors of neutrinos and antineutrinos numerically [@as03a; @as03b; @as03c] and analytically [@af03; @am03]. 