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

Recent experiments demonstrated unexpected, even intriguing properties of certain glassy materials in magnetic fields at low temperatures. We have studied the magnetic field dependence of the static dielectric susceptibility and the heat capacity of glasses at low temperatures. We present a theory in which we consider the coupling of the tunnelling motion to nuclear quadrupoles in order to evaluate the static dielectric susceptibility. In the limit of weak magnetic field we find the resonant part of the susceptibility increasing like B-2 while for large magnetic field it behaves as 1/B. In the same manner we consider the coupling of the tunnelling motion to nuclear quadrupoles and angular momentum of tunnelling particles in order to find the heat capacity. Our results show the Schottky peak for the angular momentum part, and B-2 dependence for the nuclear quadrupole part of the heat capacity, respectively. We discuss whether or not this approach can provide a suitable explanation for such magnetic properties.