  It is shown that depletion of the magnetic field pressure in a quaking
neutron star undergoing Lorentz-force-driven torsional seismic vibrations about
axis of its dipole magnetic moment is accompanied by the loss of vibration
energy of the star that causes its vibration period to lengthen at a rate
proportional to the rate of magnetic field decay. Highlighted is the
magnetic-field-decay induced conversion of the energy of differentially
rotational Alfv\'en vibrations into the energy of oscillating magneto-dipole
radiation. A set of representative examples of magnetic field decay
illustrating the vibration energy powered emission with elongating periods
produced by quaking neutron star are considered and discussed in the context of
theory of magnetars.
