  The rotational period of isolated pulsars increases over time due to the
extraction of angular momentum by electromagnetic torques. These torques also
change the obliquity angle $\alpha$ between the magnetic and rotational axes.
Although actual pulsar magnetospheres are plasma-filled, the time evolution of
$\alpha$ has mostly been studied for vacuum pulsar magnetospheres. In this
work, we self-consistently account for the plasma effects for the first time by
analysing the results of time-dependent 3D force-free and magnetohydrodynamic
simulations of pulsar magnetospheres. We show that if a neutron star is
spherically symmetric and is embedded with a dipolar magnetic moment, the
pulsar evolves so as to minimise its spin-down luminosity: both vacuum and
plasma-filled pulsars evolve toward the aligned configuration ($\alpha=0$).
However, they approach the alignment in qualitatively different ways. Vacuum
pulsars come into alignment exponentially fast, with $\alpha \propto
\exp(-t/\tau)$ and $\tau \sim$ spindown timescale. In contrast, we find that
plasma-filled pulsars align much more slowly, with $\alpha \propto
(t/\tau)^{-1/2}$. We argue that the slow time evolution of obliquity of
plasma-filled pulsars can potentially resolve several observational puzzles,
including the origin of normal pulsars with periods of $\sim1$ second, the
evidence that oblique pulsars come into alignment over a timescale of $\sim
10^7$ years, and the observed deficit, relative to an isotropic obliquity
distribution, of pulsars showing interpulse emission.
