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We study the instability of magnetic fields in a neutron star core driven bythe parity violating part of the electron-nucleon interaction in the StandardModel. Assuming a seed field of the order $10^{12}\thinspace\text{G}$, that isa common value for pulsars, one obtains its amplification due to such a novelmechanism by about five orders of magnitude, up to $10^{17}\thinspace\text{G}$,at time scales $\sim (10^3 - 10^5)\thinspace\text{yr}$. This effect issuggested to be a possible explanation of the origin of the strongest magneticfields observed in magnetars. The growth of a seed magnetic field energydensity is stipulated by the corresponding growth of the magnetic helicitydensity due to the presence of the anomalous electric current in the Maxwellequation. Such an anomaly is the sum of the two competitive effects: (i) thechiral magnetic effect driven by the difference of chemical potentials for theright and left handed massless electrons and (ii) constant chiral electroweakelectron-nucleon interaction term, which has the polarization origin anddepends on the constant neutron density in a neutron star core. The remarkableissue for the decisive role of the magnetic helicity evolution in the suggestedmechanism is the arbitrariness of an initial magnetic helicity including thecase of non-helical fields from the beginning. The tendency of the magnetichelicity density to the maximal helicity case at large evolution times providesthe growth of a seed magnetic field to the strongest magnetic fields inastrophysics.

Generation of the magnetic helicity in a neutron star driven by the electroweak electron-nucleon interaction