The radio polarization characteristics of millisecond pulsars (MSPs) differ significantly from those of non-recycled pulsars. In particular, the position angle (PA) swings of many MSPs deviate from the S-shape predicted by the rotating vector model,
even after relativistic aberration is accounted for, indicating that they have non-dipolar magnetic geometries, likely due to a history of accretion. Stokes tomography uses phase portraits of the Stokes parameters as a diagnostic tool to infer a pulsars magnetic geometry and orientation. This paper applies Stokes tomography to MSPs, generalizing the technique to handle interpulse emission. We present an atlas of look-up tables for the Stokes phase portraits and PA swings of MSPs with current-modified dipole fields, filled core and hollow cone beams, and two empirical linear polarization models. We compare our look-up tables to data from 15 MSPs and find that the Stokes phase portraits for a current-modified dipole approximately match several MSPs whose PA swings are flat or irregular and cannot be reconciled with the standard axisymmetric rotating vector model. PSR J1939+2134 and PSR J0437$-$4715 are modelled in detail. The data from PSR J1939+2134 at 0.61,GHz can be fitted well with a current-modified dipole at $(alpha, i) = (22 pm 2^circ, 80 pm 1^circ)$ and emission altitude 0.4 $r_text{LC}$. The fit is less accurate for PSR J1939+2134 at 1.414,GHz, and for PSR J0437$-$4715 at 1.44,GHz, indicating that these objects may have a more complicated magnetic field geometry, such as a localized surface anomaly or a polar magnetic mountain.
Precession in an accretion-powered pulsar is expected to produce characteristic variations in the pulse properties. Assuming surface intensity maps with one and two hotspots, we compute theoretically the periodic modulation of the mean flux, pulse-ph
ase residuals and fractional amplitudes of the first and second harmonic of the pulse profiles. These quantities are characterised in terms of their relative precession phase offsets. We then search for these signatures in 37 days of X-ray timing data from the accreting millisecond pulsar XTE J1814-338. We analyse a 12.2-d modulation observed previously and show that it is consistent with a freely precessing neutron star only if the inclination angle is < 0.1 degrees, an a priori unlikely orientation. We conclude that if the observed flux variations are due to precession, our model incompletely describes the relative precession phase offsets (e.g. the surface intensity map is over-simplified). We are still able to place an upper limit on epsilon of 3.0 x 10^{-9} independently of our model, and estimate the phase-independent tilt angle theta; to lie roughly between 5 and 10 degrees. On the other hand, if the observed flux variations are not due to precession, the detected signal serves as a firm upper limit for any underlying precession signal. We then place an upper limit on the product epsilon cos(theta) of leq 9.9 x 10^{-10}. The first scenario translates into a maximum gravitational wave strain of 10^{-27} from XTE J1814-338 (assuming a distance of 8 kpc), and a corresponding signal-to-noise ratio of leq 10^{-3} (for a 120 day integration time) for the advanced LIGO ground-based gravitational wave detector.
