Electron spin relaxation rates over the temperatue range 1.41-15.6 K are presented for the copper-containing protein plastocyanin. Measurements are described for two samples, each derived from a different preparation of equivalent purity, for which the ionic, redox, and protein compositions varied slightly. X-band data are analyzed in terms of a phonon-limited direct process and a Raman relaxation process, where the index of the Raman transport integral is treated as a fitting parameter. Both samples yield rate data at the highest temperatures that are characterized by small deviations from a simple T(n) power law dependence, with n in the range 4.8-5.2. These deviations are most easily quantified when the T(n) power law fits are compared with similar functions that allow for a finite cutoff in the phonon density of states corresponding to Debye temperatures between 90 and 100 K with n in the range 5.0-5.5.

Electron spin relaxation rates over the temperatue range 1.41-15.6 K are presented for the copper-containing protein plastocyanin. Measurements are described for two samples, each derived from a different preparation of equivalent purity, for which the ionic, redox, and protein compositions varied slightly. X-band data are analyzed in terms of a phonon-limited direct process and a Raman relaxation process, where the index of the Raman transport integral is treated as a fitting parameter. Both samples yield rate data at the highest temperatures that are characterized by small deviations from a simple T(n) power law dependence, with n in the range 4.8-5.2. These deviations are most easily quantified when the T(n) power law fits are compared with similar functions that allow for a finite cutoff in the phonon density of states corresponding to Debye temperatures between 90 and 100 K with n in the range 5.0-5.5.

Relaxation rates of ${\\mathrm{Yb}}^{3+}$ ions incorporated in low concentrations into a host silicate glass have been measured using a pulse saturation and recovery technique at 9.5 GHz over the temperature range 1.5--7.0 K. Compared with similar measurements made on crystalline material, the temperature dependence of the recovery rates for the two-phonon Raman process is anomalously weak (${\\mathit{T}}^{6}$ instead of ${\\mathit{T}}^{9}$). This anomaly suggests the need to modify the Debye density of states. Fractal models have been suggested for the thermal properties of glasses and for similarly anomalous spin-relaxation behavior in proteins. This model is discussed as well as other models of phonon localization in glasses. An estimate for the localization frequency or crossover frequency between extended and localized phonon regimes can be extracted from fits of the data from the sample with the lowest Yb concentration.

Dangling-bond electron-paramagnetic-resonance spectra and relaxation rates have been measured in the (0.3--4)-K temperature range on samples of amorphous silicon produced by sputtering, vacuum evaporation, and ion implantation of silicon, argon, neon, oxygen, and nitrogen into crystalline silicon. Intensity measurements of the dangling-bond resonance associated with silicon made amorphous by Si implantation suggest that the Curie temperature is essentially zero (0\ensuremath{\le}\ensuremath{\Theta}\ensuremath{\le}0.03 K) for temperatures down to 0.4 K. The relaxation rates follow unusual temperature dependencies that cannot be explained on the basis of conventional spin-phonon interactions. Instead, the relaxation rates obey a simple ${T}^{n}$ power law in temperature where n falls within two ranges: 2.09--2.36 and 3.26--3.47. A comparison of rates at microwave frequencies of 9.3 and 16.5 GHz indicates no magnetic field dependence. A relaxation model involving spin coupling to a distribution of two-level states is consistent with the observed ${T}^{n}$ dependence.

Temporal profiles of the recovery signal from paramagnetic Ybsup3+ ions, incorporated in a 50 wt. % PbO--50 wt. % ${\mathrm{P}}_{2}$${\mathrm{O}}_{5}$ glass, have been determined using the pulse saturation-recovery technique in the temperature range from 1.2 to 2.0 K. The recoveries vary exponentially with the square root of time over the last 25% (2.5 decades) of signal strength. No deviation from this dependence is observed in the tail of the recovery. The coefficient of \ensuremath{\surd}t in the exponent varies linearly with temperature and as the square root of the spin concentration.

Two methods of computing the fractal dimension of biopolymer chains are compared for 50 proteins. The chain fractal dimension d̄c is the scaling exponent of the contour length with respect to the end-to-end length, while the reentrant fractal dimension d̄r scales the total mass with respect to distance. Electron spin relaxation data, which yield the spectral dimension d̃, reveal a strong correlation between d̄c and d̃. A study of the apparent value of d̃ for myoglobin azide under 11 solvent conditions is presented and explained in terms of a variation in the protein-solvent coupling. A sharp transition in the effective spectral dimension at T=6 K is interpreted as reflecting a crossover from vibrational modes of the solvent to those of the protein.

Electron spin relaxation rates of ferrous myoglobin complexed with nitric oxide were measured in a frozen solution in the temperature range between 4.2 and 20 K using pulse saturation and recovery techniques. These measurements were made to determine if the relaxation rate of such a paramagnetic complex could probe the fractal dimension of the protein, as with low spin ferric myoglobin complexes. The relaxation rate varied linearly with temperature as 1/T1=376 T over the entire range, indicating a direct relaxation mechanism, unusable as a structural probe of myoglobin.

Published relaxation data from ten samples of paramagnetic proteins are compared to illustrate the uncertainty which existed in identifying the anomalous low temperature relaxation mechanism in frozen solutions of proteins. Relaxation involving localized two level tunneling states or a phonon-limited direct process can explain the T2 temperature dependence of the relaxation rate that is observed in some proteins at temperatures above 1 K. Relaxation data on myoglobin at a microwave frequency of 16.545 GHz and in the temperature range between 0.4 and 1.2 K are presented. These data exhibit a coth2(ℏω/2kBT) dependence upon temperature and identify the relaxation process as phonon limited.

Amorphous silicon, generated within crystalline Si by 28Si+ ion implantation, exhibits an electron spin relaxation rate which varies with temperature as T2.37 between 0.3 and 4.2 K. These results exclude the current model of a phonon-limited, direct relaxation mechanism in a-Si. A relaxation process, consistent with the known temperature variation, is outlined. EPR signal strengths, relative to a known paramagnet at temperatures near 1.2 and 0.4 K, put limits on an antiferromagnetic Curie-Weiss temperature of 0⩽θ⩽0.06 K.

From the temperature dependence of the Orbach relaxation rate of the paramagnetic center in horseradish peroxidase (HRP), we deduce an excited-state energy of 40.9 +/- 1.1 K. Similar studies on the broad EPR signal of HRP compound I indicate a much weaker Orbach relaxation process involving an excited state at 36.8 +/- 2.5 K. The strength of the Orbach process in HRP-I is weaker than one would normally estimate by 2-4 orders of magnitude. This fact lends support to the model of HRP-I involving a spin 1/2 free radical coupled to a spin 1 Fe4+ heme iron via a weak exchange interaction. Such a system should exhibit an Orbach relaxation process involving delta E, the excited state of the Fe4+ ion, but reduced in strength by (Jyy/delta E)2, where Jyy is related to the strength of the exchange interaction between the two spin systems.

Low-temperature spin-lattice relaxation rates of the ${[{F}_{\mathrm{Li}}]}^{0}$ center in single crystals of CaO:Li at $X$- and $\mathrm{Ku}$-band microwave frequencies exhibit an anisotropy in the functional form of the temperature dependence: from $T$ in the [100] direction to csch ($\frac{25}{T}$) in the [111] direction. A model involving longitudinal and transverse tunneling of a Li ion adjacent to the trapped electron can qualitatively explain this and most of the other characteristics of the relaxation data, with the exception of the hyperfine dependence.

Electron spin relaxation data from five ferric proteins are analyzed in terms of the fractal model of protein structures. Details of this model are presented. The results lead to a characterization of protein structures by a single parameter, the fractal dimension, d. This structural parameter is shown to determine the temperature dependence of the Raman electron spin relaxation rate, which varies as T3 + 2d. Computations of d are made using x-ray data for 17 proteins. The results range from d = 1.76 for lysozyme to d = 1.34 for ferredoxin. These values are compared with values of d obtained from the present electron spin relaxation data on five ferric proteins. Typical results are d = 1.34 +/- 0.06 from relaxation data and 1.34 +/- 0.05 from x-ray data for ferredoxin; d = 1.67 +/- 0.03 from relaxation data and 1.66 +/- 0.05 from x-ray data for ferricytochrome c. The data thus support the theoretical model. Applications of this spin resonance technique to the study of changes in protein conformation are discussed.