Temperature-dependent Frequency Shift Research Articles

The origin of optical dephasing times and line shape functions for electronic transitions to localized and delocalized states in solids

A theory for optical dephasing times and the homogeneous component of the absorption line shape function to localized states and to the k=o levels of Frenkel exciton states is presented. The theory is based upon exchange between two or more optical transitions which are separated by a small frequency difference. Exchange averaging of the optical transition is brought about via phonon–exciton scattering which couples the optical transitions. This process causes both a temperature dependent line broadening and a temperature dependent frequency shift in the optical spectrum when quadratic phonon–exciton coupling terms are present. The optical dephasing time in such cases result from energy differences of the phonon branch in the ground and excited states and consequently it need not necessarily reflect the complete loss of coherence of the exciton wavepacket at k=o. A simple criterion is derived that allows one to determine whether the phonon–exciton interaction causes an optical transition line shape function to reflect random frequency modulation by the exchange of low frequency phonon or vibrational quanta. The theory allows the phonon–exciton scattering times for individual modes to be determined from an analysis of the frequency shift and line broadening relationships in favorable cases. This information coupled with knowledge of the exciton dispersion allows one to semiquantitatively determine the effect individual phonon and vibrational modes have on the exciton coherence time at a particular temperature.

Nichtlineare Phonon-Phonon-Wechselwirkung in elastischen Nichtleitern

For a simplified model we investigate the influence of anharmonicity of the lattice potential on the propagation of sound. In the low temperature region it is possible to describe the lattice dynamics by means of the theory of nonlinear elastic media. It is shown that three-phonon processes are possible even if the colliding phonons have the same polarization. At low temperature the lifetime of a single lattice oscillation is decisively influenced by the processL+L⇄L, whereL stands for longitudinal polarization. By means of temperature dependent doubletime Green functions we investigate energy shift and damping rate of impressed phonons. The temperature dependent frequency shift is interpreted as a temperature dependence of the elasticity modulus. Comparison yields satisfactory agreement between theory and experiment.

Line Shapes, Saturation Behavior, and Temperature Studies in the Nuclear Resonance of Nickel

The nuclear magnetic resonance of ${\mathrm{Ni}}^{61}$ has been studied in pure nickel powders. Both natural nickel (1.25% abundant in ${\mathrm{Ni}}^{61}$) and enriched nickel (99.9% abundant in ${\mathrm{Ni}}^{61}$) were used. The signal observed with a circuit sensitive to the absorption of power is a combination of absorption and dispersion modes. The amount of mode mixing is found to depend on the applied rf field, ambient temperature, annealing temperature, and external magnetic-field intensity. The mode mixing of the resonance is related to electronic losses in the sample. The saturation behavior of the individual absorption and dispersion modes is that of an inhomogeneously broadened line. From the saturation behavior an estimate of the enhancement of the applied rf level for nuclei in domain walls of about 7\ifmmode\times\else\texttimes\fi{}${10}^{3}$ is made. An additional broadening mechanism is observed in the enriched nickel, particularly at 77\ifmmode^\circ\else\textdegree\fi{}K. Application of Redfield's theory of saturation at high rf levels leads to the conclusion that the additional broadening can be attributed to strong indirect exchange between nuclei. Frequency measurements from room temperature to 4.2\ifmmode^\circ\else\textdegree\fi{}K made with a marginal oscillator in both the enriched and unenriched nickel are presented. A temperature-dependent frequency shift is found between the enriched and unenriched nickel which appears to be a maximum at about 200\ifmmode^\circ\else\textdegree\fi{}K where the enriched nickel frequency is about 30 kc/sec higher. From room temperature to 536\ifmmode^\circ\else\textdegree\fi{}K, frequency measurements made with super-regenerative circuits are reported. A comparison of the temperature dependence of the resonance frequency with the saturation magnetization is made.