PHYSICAL REVIEW B VOLUME 36, NUMBER 11' 15 OCTOBER 1987-I Analysis of the off-center eSect of Cu+ in alkali halides using crystal-field theory Stephen A. Payne Lawrence Livermore National Laboratory, University of California, Livermore, California 94550 (Received 27 April 1987) We have found that the relative intensity of the 'A &g~ Eg and A]g~ T2g crystal-field com- ponents of the 3d' ~3d 4s transition of Cu+ in alkali halide hosts provides a measure of the Cu+ ground-state ofF-center displacement along the [111]axis. This is shown by deriving the crystal- field potential that describes the off-center e5'ect of Cu+, and then calculating the transition mo- ments to the 'Eg and 'Tzg final states. By analyzing the spectra of Cu+ in numerous alkali halide hosts, it is found that the degree of off-center displacement increases with the lattice constant of the alkali halide. I. INTRODUCTION The spectra of transition-metal-ion impurities have long been understood on the basis of crystal-field theory. Here, the impurity is assumed to be surrounded by nega- tive point charges, and the splitting of the d orbitals are calculated by considering the electrostatic multipole con- tributions from the environment. Crystal-field theory is known, however, not always to reproduce the spectra quantitatively, although it has been successful at indicat- ing the important physical mechanisms and predicting trends. In this work, we use crystal-field theory to cal- culate the odd-parity multipole contributes to the poten- tial that result from the displacement of the Cu+ ion off the center of the metal site in alkali halide crystals. We then use this information to calculate the relative transi- tion strength of two crystal-field-split bands of Cu+. We find that this relative transition intensity is sensitive to the magnitude of the impurity off-center displacement and therefore can be used to give detailed information about the ground-state position of Cu+ in the alkali halide hosts. The spectral properties of Cu+ -doped alkali halide crystals have been studied for several decades, one result being that the near-uv absorption bands due to the spin- allowed 3d ' ~3d 4s transitions of Cu+ have now been extensively documented. Several absorption bands are typically observed, in part due to the octahedral-crystal- field splitting of the 3d 4s excited state into Eg - and T&g-type components. These assignments have only re- cently become definitive due to the experiments of McClure and co-workers, in which two-photon spectros- copy was used to identify the 'A, (s3 d' )o~'E (3d94s) and the 'A &g(3d' )~'Tz (3d 4s) transitions for several Cu+-doped alkali halides. The above picture is based on the assumption that when the Cu+ impurity substitutionally replaces the host cation, it remains at the center of the octahedron of halide ions. Since the d ~s transition is one-photon par- ity forbidden, the average value of the displacement of Cu+ from the center of the octahedron, be it thermally activated or a static effect, determines whether the tran- sition is allowed. Although ground-state Cu+ is, on the average, on center in LiC1, NaF, NaC1, and KF, the most stable position of Cu+ is known to be located off center along the [111]axis in other crystals such as KC1, RbC1, NaBr, KBr, RbBr, and NaI. ' ' ' As a result of this distortion, Cu+ moves closer to three halides ions and further from the other three, lowering the site sym- metry from O~ to C3, and destroying the inversion sym- metry. Although the off-center displacement is known to mix the ' A &g ~ 'Eg and ' A &g ~ ' T2g transitions with each other and with other transitions, the centrosym- metric model is a useful starting point from which to de- scribe the system. To provide an example of the spectra of typical on- center and off-center systems, the excitation spectra for Cu+-doped NaCl and KC1, respectively, are reproduced in Fig. 1 from the work of Nagasaka er al. " (The exci- tation spectra of Cu+-doped alkali halides, as obtained by monitoring the Eg ~ ' A &g emission, are generally quite similar to the absorption data, although they are not beset by scattering background interferences, and are therefore often easier to examine). The 'A &s-'Es and Tzg transitions have been previously identified for these systems using two-photon excitation spectroscopy; these assignments are indicated in the figure. It is clear that the relative intensity of these two transitions is reversed in the NaC1 and KC1 systems. It is the purpose of this work to show that the reversal of the relative intensity of the A ]g ~ Eg and A ]g ~ T2g transitions is a direct consequence of the stable ground-state position of Cu+ shifting from being on center to off center. Previous workers have successfully related the oscilla- tor strength of the d ~s transition to the ground-state position of Cu+. ' The off-center systems have oscilla- tor strengths on the order of 0. 05, and due to the static nature of the distortion, the f number is nearly indepen- dent of temperature. On the other hand, the on-center Cu+ systems have smaller oscillator strengths of about 0. 001 at low temperature, and tend to increase by a fac- tor of 2 — 5 at higher temperatures. The present work is essentially an extension of this effort to relate the spec- tral properties of the d ~s transition to the ground-state position. We use the standard methods of crystal-field theory to show that the relative intensity of the 36 6125 1987 The American Physical Society