  The configuration of the regular magnetic field in M31 is deduced from radio
polarization observations at the wavelengths 6, 11 and 20 cm. By fitting the
observed azimuthal distribution of polarization angles, we find that the
regular magnetic field, averaged over scales 1--3 kpc, is almost perfectly
axisymmetric in the radial range 8 to 14 kpc, and follows a spiral pattern with
pitch angles of $p\simeq -19\degr$ to $p\simeq -8\degr$. In the ring between 6
and 8 kpc a perturbation of the dominant axisymmetric mode may be present,
having the azimuthal wave number m=2. A systematic analysis of the observed
depolarization allows us to identify the main mechanism for wavelength
dependent depolarization -- Faraday rotation measure gradients arising in a
magneto-ionic screen above the synchrotron disk. Modelling of the
depolarization leads to constraints on the relative scale heights of the
thermal and synchrotron emitting layers in M31; the thermal layer is found to
be up to three times thicker than the synchrotron disk. The regular magnetic
field must be coherent over a vertical scale at least similar to the scale
height of the thermal layer, estimated to be $h\therm\simeq 1$ kpc. Faraday
effects offer a powerful method to detect thick magneto-ionic disks or halos
around spiral galaxies.
