  We study here the r-modes in the Cowling approximation of a slowly rotating
and magnetized neutron star with a poloidal magnetic field, where we neglect
any deformations of the spherical symmetry of the star. We were able to
quantify the influence of the magnetic field in both the oscillation frequency
$\sigma_r$ of the r-modes and the growth time $t_{gw}$ of the gravitational
radiation emission. We conclude that magnetic fields of the order $10^{15}$ G
at the center of the star are necessary to produce any changes. Our results for
$\sigma_r$ show a decrease of up to $\sim$ $5\%$ in the frequency with
increasing magnetic field, with a $B^2$ dependence for rotation rates
$\Omega/\Omega_K \gtrsim 0.07$ and $B^4$ for $\Omega/\Omega_K \lesssim 0.07$.
(These results should be trusted only within slow rotation approximation and we
kept $\Omega/\Omega_{K}< 0.3$.) For $t_{gw}$, we find that it is approximately
$30\%$ smaller than previous Newtonian results for non-magnetized stars, which
would mean a faster growth of the emission of gravitational radiation. The
effect of the magnetic field in $t_{gw}$ causes a non-monotonic effect, that
first slightly increases $t_{gw}$ and then decreases it further by another
$\sim$ $5\%$. (The value of magnetic field for which $t_{gw}$ starts to
decrease depends on the rotational frequency, but it is generally around
$10^{15}$G.) Future work should be dedicated to the study of the effect of
viscosity in the presence of magnetic fields, in order to establish the
magnetic correction to the instability window.
