“…1, the SXC pulses of magnetars, reflecting the spin of the neutron stars (NSs), are easily detectable, but those in the HXC often remain insignificant when we rely on the conventional epoch-folding plus Z 2 statistics searches. As we have revealed so far, this is because the HXC pulses of magnetars are very often subject to slow phase modulations, at a period T ∼ 10 4 P (Makishima et al 2014(Makishima et al , 2016(Makishima et al , 2014(Makishima et al , 2021a(Makishima et al , 2021b, where P denotes the pulse period. Since this effect is presumably caused by the magnetic deformation of NSs, its study will provide valuable clues to the magnetars' ultra-strong toroidal magnetic field B t , which cannot be easily studied with other means.…”