Effect of a magnetic field on the dipole echo in glasses caused by nuclear quadrupole moments

The effect of a magnetic field on the amplitude of the dipole echo in glasses at a temperature of about 10 mK caused by the presence of nonspherical nuclei with electric quadrupole moments in the glass has been considered theoretically. It has been shown that in this case, the two-level systems (TLSs) that determine the properties of glasses at low temperatures are transformed into more complicated multilevel systems. These systems have new properties as compared to usual TLSs and, in particular, exhibit oscillations of the electric dipole echo amplitude in the magnetic field. A general formula that describes the echo amplitude in an arbitrarily split TLS has been derived in perturbation theory. Detailed analytic and numerical analysis of the formula has been performed. The theory agrees qualitatively and quantitatively well with the experimental data.