Magnetic-oscillation mechanism for understanding periodic or quasi-periodic modulation of the timing residuals from pulsars

Highly precise pulsar timing is very important for understanding the nature of neutron stars and the implied physics, even being used to detect directly gravitational waves. Unfortunately, the accuracy of the pulsar timing is seriously affected by the spin-down irregularities, such as spin fluctuations with a manifestation of low frequency structures (the so-called red noise processes), and various activities of magnetospheres. Except from the random timing noise, significant periodic or quasi-periodic components could also be found in some timing residuals of pulsars, indicating the presence of unmodelled deterministic effects. The physical origins of these effects still remain unexplained. In this paper, we suggest a new mechanism involving the de Haas-van Alphen magnetic oscillation, which could trigger the observed low frequency structures. We find that the proposed magnetic oscillation period is about 1-$10^{2}$ yr, which is about $10^{-4}$ times as long as the classical characteristic time scale of interior magnetic field evolution for a normal neutron star. Due to the magnetic oscillation, we estimate both the braking index range between $10^{-5}$ and $10^{5}$ and the residuals range between 4 to 906 ms for some specific samples of quasi-periodic pulsars. Those are consistent with the pulsar timing observations. Nonlinear phenomena of de Haas-van Alphen effect and the Condon domain structure are considered. Avalanche-like magnetized process of domain wall motion (rapidly magnetic energy release) could associated with some special emitting manifestations of neuron star radiation.