Effect of Nuclear Quadrupole Interaction on the Relaxation in Amorphous Solids

Abstract

Recently it has been experimentally demonstrated that certain glasses display an unexpected magnetic field dependence of the dielectric constant. In particular, the echo technique experiments have shown that the echo amplitude depends on the magnetic field. The analysis of these experiments results in the conclusion that the effect seems to be related to the nuclear degrees of freedom of tunneling systems. The interactions of a nuclear quadrupole electrical moment with the crystal field and of a nuclear magnetic moment with magnetic field transform the two-level tunneling systems inherent in amorphous dielectrics into many-level tunneling systems. The fact that these features show up at temperatures T < 100mK , where the properties of amorphous materials are governed by the long-range R −3 interaction between tunneling systems, suggests that this interaction is responsible for the magnetic field dependent relaxation. We have developed a theory of many-body relaxation in an ensemble of interacting many-level tunneling systems and show that the relaxation rate is controlled by the magnetic field. The results obtained correlate with the available experimental data. Our approach strongly supports the idea that the nuclear quadrupole interaction is just the key for understanding the unusual behavior of glasses in a magnetic field.

Acoustic Properties of Amorphous Silica between 1 and 500 mK

“…These include explanations for the quantitative universality of glass [10 -13]. In specific glasses, the unexpected magnetic field dependence of the dielectric susceptibility [14 -16] and polarization echo amplitude [17] was related to nuclear [18,19] and electronic [20] magnetic and quadrupolar moments of two level systems (TLS). Furthermore, it was shown that the nuclear quadrupole interaction could be responsible for the saturation of the dielectric constant observed in several glasses below 5 mK [21].…”

Dielectric susceptibility and heat capacity of ultra-cold glasses in magnetic fields

“…Let us denote by (e 1 , e 2 , e 3 ) the basis in the left well and by (e ′ 1 , e ′ 2 , e ′ 3 ) the corresponding one in the right well. If we suppose that e ′ 3 e 3 ẑ and e ′ 1 , e 1 make an angle θ with each other 25 , we can write the total Hamiltonian in the basis of the operator I 3 = I z in the following form…”

“…For such systems the relaxation or Debye part of the susceptibility shows a large magnetic field dependence [24]. By considering TLSs with small splitting comparable to the nuclear quadrupole energies and using a numerical estimation, a pronounced dependence of the electric permittivity of the applied magnetic field was obtained [25].…”