Isotope Effect of Pairs of Coupled Tunneling Systems

Abstract

Using dielectric rotary echo experiments we have studied the coherent tunneling of strongly coupled Li+ ions in KC1 crystals. Since our experiments were performed at resonance frequencies of about 1 GHz, we have investigated tunneling systems with energy splittings E/ke ( 50 mK. Measurements of the Rabi frequency for samples doped with different lithium isotopes give a conclusive proof that the low-energy states arise from pairs of coupled Li+ ions. We discuss the tunnel splitting and the microscopic arrangement of such pairs. PACS numbers: 77.22.d, 61.72.Ji The low temperature dynamical behavior of dielectric solids is determined to a large extent by the presence of defects. At high temperatures the motion of defects is thermally activated, but at low temperatures tunneling is the dominating mechanism. Therefore tunneling systems (TSs) formed by defects are responsible for most elastic, dielectric, and thermal properties of dielectrics. Particularly, alkali halides containing a small concentration of point defects have been studied extensively, and their properties are well understood on a microscopic basis: Tunneling of individual impurities between several equivalent sites or orientations give rise to an excitation spectrum with energies typically of the order of F/ks --1 K. Together with selection rules due to the symmetry of the host crystal their low temperature dielectric behavior can be described quantitatively [1 -4]. With rising concentration, interaction between the defects becomes important. This is clearly demonstrated by many experiments on crystals like KBr:CN containing a higher amount of impurities or on glasses where TSs again are responsible for their unusual properties. In all these cases the consequences of the interaction are hardly understood. At concentrations low enough that most of the TSs can still be considered as isolated the properties interacting with TSs have been described by taking into account the statistical occurrence of coupled pairs [5,6]. The complex many body problem at high concentrations has been treated only very recently using a mode coupling approach [7]. On the experimental side the influence of interactions between substitutional molecules, such as OH in KC1, on their vibrational spectrum has been investigated in detail [8]. Moreover, evidence of a common tunneling motion of defects coupled in pairs has been found in several experiments (e.g., Refs. [9 -11]). However, a microscopic understanding of the energy spectrum and the dynamics of these coupled tunneling systems is lacking. We have studied one of the simplest systems, namely, KC1 doped with lithium. From many previous experiments it is well known that the small lithium ions replacing the cations of the host crystal are located in off-center positions in the (111) directions [1,2]. At low temperatures the Li+ ions tunnel between these sites and form eight-level systems. Because of the high symmetry of the host crystal, the eigenstates are partially degenerate. The resulting four levels are equally spaced with ...

Novel Dielectric Relaxation inLi+doped KCl

“…The resulting dipolar interaction with adjacent defects affects the dynamical behavior significantly, even at concentrations as low as 60 ppm. Two striking manifestations have been reported: a reduction of the dielectric susceptibility with rising concentration [7,8], and the observation of pairs of strongly interacting impurities on next-nearest-neighbor sites in rotary echo experiments [9,10].…”

“…The difference between the tunnel energies 6 D 0 and 7 D 0 provides a thorough test for various physical quantities [2,3]. Recently the resulting isotope effect has proven most helpful when investigating rotary echoes [9,10] and the low-frequency susceptibility [8].…”

Magnetic Field Dependent Tunneling of Atoms and Molecules in Non-Magnetic Disordered Solids

“…The tunnel splitting of such pairs is only of the order of 10 mK. The situation is very similar to that in KCI doped with lithium, because in this system the excitations that produce the echo signal originate also from pairs of next nearest Li neighbors [30]. Figure 7 shows the amplitude of two-pulse echoes generated in KCI containing 60 ppm of Li as a function of magnetic field for different delay times t 12 [22].…”

Collective phenomena in defect crystals

“…Early work on ionic crystals with substitutional impurities, such as lithium or cyanide in various alkali halides (KCl:Li, KBr:CN,...), focused on the thermal properties; 4,5 experimental findings at high concentration indicated the relevance of the dipolar interactions 6 . More recently, sensitive echo measurements gave precise information on pairs of interacting impurities that occur at low doping 7 . At impurity concentrations of a few hundred ppm, the dipolar couplings destroy the coherent motion of the impurities 8 .…”

“…More recently, sensitive echo measurements gave precise information on pairs of interacting impurities that occur at low doping 7 . At impurity concentrations of a few hundred ppm, the dipolar couplings destroy the coherent motion of the impurities 8 .…”