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Highly precise pulsar timing is very important for understanding the natureof neutron stars and the implied physics, even being used to detect directlygravitational waves. Unfortunately, the accuracy of the pulsar timing isseriously affected by the spin-down irregularities, such as spin fluctuationswith a manifestation of low frequency structures (the so-called red noiseprocesses), and various activities of magnetospheres. Except from the randomtiming noise, significant periodic or quasi-periodic components could also befound in some timing residuals of pulsars, indicating the presence ofunmodelled deterministic effects. The physical origins of these effects stillremain unexplained. In this paper, we suggest a new mechanism involving the deHaas-van Alphen magnetic oscillation, which could trigger the observed lowfrequency structures. We find that the proposed magnetic oscillation period isabout 1-$10^{2}$ yr, which is about $10^{-4}$ times as long as the classicalcharacteristic time scale of interior magnetic field evolution for a normalneutron star. Due to the magnetic oscillation, we estimate both the brakingindex range between $10^{-5}$ and $10^{5}$ and the residuals range between 4 to906 ms for some specific samples of quasi-periodic pulsars. Those areconsistent with the pulsar timing observations. Nonlinear phenomena of deHaas-van Alphen effect and the Condon domain structure are considered.Avalanche-like magnetized process of domain wall motion (rapidly magneticenergy release) could associated with some special emitting manifestations ofneuron star radiation.

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