A new method for determining the relaxation times,T 1 andT 2, from progressive saturation of inhomogeneously broadened lines

An analytical method to determine the spin-lattice (T ₁), and spin-spin (T ₂), relaxation times for inhomogeneously broadened lines obtained from electron paramagnetic resonance (EPR) experiments is presented in this work. To apply this method, the knowledge of the lineshape of the saturation curve is not necesssary, only the Lorentzian and Gaussian widths are required and these are obtained from a non-saturated line. The relaxation times are calculated by using continuous saturation under slow passage conditions. An explicit algebraic equation for the direct calculation ofT ₁, and the general form of the saturation curve for a single line in an EPR signal are given. The equation given to calculateT ₁ can also be used for substances in which the full saturation can not be obtained experimentally. A comparison of the results obtained for some substances by using the present method with respect to other existent ones, is carried out to show its reliability.     

Electron spin-lattice relaxation in noncommon metals YBa2Cu3Ox and Rb1C60

Using an original modulation technique, the electron spin-lattice relaxation have been investigated in two noncommon metals: YBa₂Cu₃O_x, high-T_c material doped with 1% Gd, and Rb₁C₆₀, linear polymer phase fulleride. In the first case, the Korringa-like temperature dependence of the Gd³⁺ longitudinal relaxation time T₁, is found forx = 6.59 in a wide temperature range 4.2 <T < 200 K, both above and below T_c = 56 K. Atx = 6.95 (T_c = 90 K), the T₁ behavior within 50 <T < 200 K is evidently affected by spin gap opening with the gap value of about 240 K. At 200 K, an unexpected acceleration of the relaxation rate takes place, suggesting some change in the relaxation mechanism. The data are discussed in terms of the Barnes-Plefke theory with allowance made for microscopic separation of the normal and superconducting phases. In Rb₁C₆₀, the evolution of the ESR line and relaxation rates have been studied accurately in the range of the metal-insulator transition (below 50 K). Interpretation is suggested which takes into account breaking down the relaxation bottleneck due to opening of the energy gap near the Fermi surface. The gap value of about 100 cm^?1 is estimated from the analysis of relaxation rates, lineshape and spin susceptibilities.     

Anomalous spin relaxation and quantum criticality in Mn1 − x Fe x Si solid solutions

We report results of the high frequency (60 GHz) electron spin resonance (ESR) study of the quantum critical metallic system Mn_{1 ? x} Fe _x Si. The ESR is observed for the first time in the concentration range 0 < x < 0.24 at temperatures up to 50 K. The application of the original experimental technique allowed carrying out line shape analysis and finding full set of spectroscopic parameters, including oscillating magnetization, line width and g factor. The strongest effect of iron doping consists in influence on the ESR line width and spin relaxation is marked by both violation of the classical Korringa-type relaxation and scaling behavior. Additionally, the non-Fermi-liquid effects in the temperature dependence of the ESR line width, which may be quantitatively described in the theory of Wölfle and Abrahams, are observed at quantum critical points x* ～ 0.11 and x _c ～ 0.24.     

Electron spin relaxation of copper(II) ions in diamagnetic crystals

The electron spin-lattice and spin-spin phase relaxation measurements of Cu²⁺ ions in various crystals are reviewed and discussed. Examples of the Debye temperature determination from a wide temperature range measurements of the spin-lattice relaxation time T₁ are shown. An influence of the Jahn-Teller dynamics on T₁ is presented. The phase relaxation described by the phase memory time T_M is affected by temperature due to the spin packet width modulation by molecular motions. The T_M is anisotropic in crystals and can be different for different hyperfine lines of an EPR spectrum.     

Saturation spectroscopy of coherent raman scattering in molecular gases

We present the theory of two-photon Raman saturation of a two-level Raman transition studied by an independent CARS process. The main goal here is to probe the saturated homogeneous Raman line shape. It is shown that there appears a saturation dip with a width determined by the relaxation timeT ₁. In the case of Doppler-broadened line the coherent Raman saturation spectroscopy may be used to determine both theT ₁ andT ₂ relaxation times.     

Multifrequency EPR of four triarylmethyl radicals

Continuous-wave spectra at W-band of four triarylmethyl (trityl) radicals at 100 K in 1∶1 water-glycerol exhibit rhombic electron paramagnetic resonance spectra. The rigid-lattice line widths at W-band are only 3 to 5 times larger than at X-band or S-band, and fluid-solution line widths are much narrower than those for rigid lattice, which indicates that unresolved anisotropic nuclear hyperfine couplings make significant contributions to the rigid-lattice line widths. Spin-flip lines are observed in glassy-solution spectra at X-band and S-band, but not at W-band or 250 MHz. At 100 KT _m is dominated by spin diffusion of solvent protons and is independent of microwave frequency. Between about 130 and 170 K, 1/T _m for trityl-CH₃ is enhanced by rotation of the methyl groups at a rate comparable to inequivalences in the hyperfine interaction. Motional averaging of anisotropic interactions enhances spin echo dephasing between about 200 and 300 K. The temperature dependence of 1/T ₁ is similar for the four radicals and is consistent with assignment of the Raman process and a local mode as the dominant relaxation processes. The similarity inT ₁ values at W-band and X-band supports this assignment.     

Electron density diagnostic potential of Ar XIV soft X-ray emission lines

Theoretical electron density-sensitive line ratios R₁-R₆ of Ar XIV soft X-ray emission lines are presented. We found that these line ratios are sensitive to the electron density n_e, and the ratio R₁ is insensitive to electron temperature T_e. Recent work has shown that accurate atomic data, such as electron impact excitation rates, is very important for an reliable determination of the electron density of laboratory and astrophysical plasmas. Present work indicates that the maximum discrepancy of line ratios introduced from different atomic data calculated with distorted wave and R-matrix approximations, is up to 18% in the range of . By comparison of these line ratios with experiment results carried out in electron beam ion trap (EBIT-II), electron density of the laboratory plasma is diagnosed, and a consistent result is obtained from R₁, R₂ and R₃. Our result is in agreement with that diagnosed by Chen et al. using triplet of N VI. A relative higher diagnosed electron density from R₂ is due to its weak sensitivity to electron temperature. A better consistency at lower T_e indicates that temperature of the laboratory plasma is lower than logT_e(K)=6.5. Comparison between the measured and theoretical ratios reveals that 32.014 Å  line is weakly blended by lines from other Ar ions, while 30.344 Å  line is strongly contaminated.     

Spin gap, phase separation and d-wave pairing as revealed by electron spin-lattice relaxation in 123 and 124 YBaCuO systems doped with Gd3+

With an original modulation technique, the Gd³⁺ electron spin-lattice relaxation has been investigated in normal and superconducting states of YBa₂Cu₃O_6+x (123) and YBa₂Cu₄O₈ (124) compounds doped with 1% Gd. In the 123 sample withx = 0.9T _c = 90 K), theT ₁ behavior within 50 <T< 200 K reveals the [1 ? tanh²(Δ/2kT)]/T dependence typical of a spin gap opening with Δ ≈ 240 K. Below 50 K, the exponential slowing down ofT ₁ is limited by the Korringa-like behaviorT ₁ T = const); the same Korringa-like law is found in the 123 sample withx = 0.59 (T _c = 56 K) within the total 4.2–200 K temperature range. This is interpreted in terms of microscopic separation of the normal and superconducting phases allowing for the electron spin cross-relaxation between them. In the 124 sample (T _c = 82 K), the Gd³⁺ relaxation rate below 60 K is found to obey a power lawT _n with an exponentn ≈ 3. Such a behavior (previously reported for nuclear spin relaxation) is indicative of the d-wave superconducting pairing. Additional paramagnetic centers characterized by relatively slow spin-lattice relaxation are found in both 123 and 124 systems. A well-pronounced change in theT ₁ temperature dependence atTT* ≈ 180–200 K is observed for these slowly relaxing centers as well as for the conventional, fast-relaxing Gd³⁺ ions, suggesting microscopic phase separation and a change in the relaxation mechanism due to electronic crossover related with the opening of the spin gap. This hypothesis is supported by some “180 K anomalies” previously reported by other authors.     

A study on new phase transitions in Cs2CaCl4·2H2O single crystals by observation of Cs NMR

The ¹³³Cs 1/2→−1/2 spin-lattice relaxation rate, , and the spin-spin relaxation rate, , for a Cs₂CaCl₄·2H₂O single crystal have been measured in function of temperature. The dominant relaxation mechanism of this crystal over the whole temperature range investigated here proceeds via quadrupole interaction. The changes in the ¹³³Cs spin-lattice relaxation rate near 325 K (=T_c1) and 360 K (=T_c2) correspond to phase transitions in the crystal. The change in the spin-lattice relaxation rate at T_c1 is small because the crystal lattice does not change very much during this phase transition. The change in near T_c2 is due to the critical slowing down of the soft mode that typically occurs in structural phase transitions. The temperature dependence of the spin-lattice relaxation rate for this crystal has maximum values at about 240 K, which is attributable to the effect of molecular motion as described by Bloembergen-Purcell-Pound theory. The phase transition temperatures T_c1 and T_c2 obtained from the temperature dependence of the relaxation rate is also clear from data obtained using differential scanning calorimetry. Therefore, we know that previously unreported phase transitions occur at 325 and 360 K.     

Fine structure in the proton magnetic resonance spectrum of solid benzene and solid benzene-cyclohexane mixtures

The PMR spectrum of solid benzene in the vicinity of the melting point consists of broad and narrow lines. New narrow lines in the spectrum of benzene containing some impurity appear at the top of the broad line. Intensities of narrow lines increase with rising of temperature. The temperature dependence of line width and relaxation timesT ₁ andT ₂ have been measured in pure solid benzene an benzene-cyclohexane mixtures. It is assumed that narrow lines in spectra of pure benzene and its mixtures are caused by appearance of a phase with mobile molecules located in the crystallite joint or on its surface. The spectrum of imperfect monocrystalline benzene have been studied also. The narrow line of this sample is split into several narrow components. This is explained by demagnetization fields the distribution of which has a discrete character,     

Two-dimensional critical behaviour in antiferrodistortive Al ur6(CIO4)3 and Ga ur6(ClO4)3

Critical behaviour with dimensionality d = 2 has been observed for the 300 K antiferrodistortive phase transition in Al ur₆(ClO₄)₃ and Ga ur₆(ClO₄)₃ by means of the temperature dependence of the ESR parameter D. The systems exhibited d = 2 behaviour in the static critical behaviour for T<T_c?40 K for T>T_c + 40 K. From the ESR data including line width measurements the local order parameter relaxation rate ω₁ has been obtained for various temperatures above T_c, with a lowest value of ω₁ = 150 MHz at T_c + 15 K     

7Li NMR study on Li+ ionic diffusion and phase transition in LixCoO2

The temperature dependence of the spin-lattice relaxation time, T₁ and the line width of the ⁷Li nucleus were measured in delithiated Li_xCoO₂ (x = 0.6, 0.8, 1.0). Two different relaxation behaviors were observed in the temperature dependence of T₁^− 1 in a x = 0.8 sample. These would have arisen from inequivalent Li sites in two coexisting phases; an original hexagonal (HEX-I) and a modified hexagonal (HEX-II) phase in the x = 0.8 sample. We analyzed using a phenomenological non Debye-type relaxation model. Motional narrowing in the line width was observed in each sample, the result revealing that Li⁺ ions begin to move at low temperature in samples with less Li content. It was found that the activation energy associating with Li⁺ ion hopping in the HEX-II phase is smaller than that in the HEX-I phase. These results show that the HEX-II phase produced in the Li deintercalation process would be suitable for Li⁺ ionic diffusion in multi-phase Li_xCoO₂, and it is expected that this would enable fast ionic diffusion. Li⁺ ionic diffusion related to phase transition is discussed from ⁷Li NMR results.     

Collision induced transitions of ammonia calculation of relaxation timesT 1 andT 2, line widths,line shifts,and the double resonance effect

The longitudinal relaxation timeT ₁ and the transverse relaxation timeT ₃ for the inversion levels of the NH₃ molecule have been calculated for NH₃ — NH₃, NH₃ — N₂ and NH₃ — H₂ collisions. The ratioT ₂/T ₁ lies between 1 and 2 which agrees well with the experiment. The phase shift effect onT ₂ and on the collisioninduced line shift δω under the framework of the Mehrotra-Boggs theory have also been evaluated. The change in the line intensity ΔI/I, in four-level double resonance experiments was also calculated, and the significance of higher order interaction terms has been pointed out.     

Electron spin resonance and longitudinal relaxation around phase transition in La0.9Ca0.1 MnO3

With original modulation technique, the longitudinal electron spin-relaxation timeT ₁ has been measured in the La_1-xCa_xMnO₃ manganite (x = 0.1) both in the paramagnetic state and around the temperature (T _c) of the ferromagnetic ordering. The data are compared with the evolution of the transverse relaxation time T₂ as determined from the electron spin resonance (ESR) linewidth. Well above T_c, theT ₁ =T ₂ equality was confirmed, whereas a steep slowing down ofT ₂ was observed asT _c was approached (theT ₁/T₂ ratio increased by two orders of magnitude). The temperature dependence ofT ₁ within the whole temperature range was found to be consistent with that ofT · χ(T), where χ(T) is the electron-spin susceptibility obtained from the ESR absorption area. The interpretation suggests that both the longitudinal and transverse electron-spin relaxation rates are governed by strong exchange interaction between the Mn ions, the ESR linewidth being inhomogeneously broadened in the vicinity of the phase transition.     

Infrared spectroscopy of the intermediate-valence semiconductor YbB12

The dynamic conductivity and permittivity spectra of the intermediate-valence compound YbB₁₂ are measured in the frequency range (6–10⁴) cm^?1 (quantum energy 0.75 meV-1.24 eV) at temperatures of 5–300 K. Analysis of the spectral singularities associated with the response of free charge carriers has made it possible for the first time to determine the temperature dependences of their microscopic parameters, viz., concentration, effective mass, relaxation frequency and time, mobility, and plasma frequency. It is shown that the relaxation frequency decreases upon cooling from 300 K to the coherence temperature T ^* = 70 K for YbB₁₂, which is mainly associated with the phonon mechanism of scattering of charge carriers. For cooling below the coherence temperature T ^* = 70 K, the temperature dependence of the relaxation frequency for charge carriers of the Fermi-liquid type is found to be γ ～ γ₀ + T ², while their effective mass and relaxation time increase, respectively, to m ^*(20 K) = 34m ₀ (m ₀ is the free electron mass) and τ(20 K) = 4 × 10^?13 s, indicating the establishment of coherent scattering of carriers from localized magnetic moments of the f centers. At a temperature of T = 5 K, the conductivity spectrum contains an absorption line at a frequency of 22 cm^?1 (2.7 meV); the origin of this line can be associated with the exciton-polaron bound state. Since such a state was observed earlier in other intermediate-valence semiconductors (such as SmB₆, TmSe_1?x Te, and (Sm, Y)S), it is probably typical of this class of compounds.     

Spin relaxation of conduction electrons in GaAs

We have used optical spin orientation techniques to measure T₁ of conduction electrons in GaAs (NinA ≈ 10¹⁷ cm^-3) for 4.7 K ? T ? 200 K. From Hall effect measurements we estimated the electron momentum relaxation time τ_p. For 50 K ? T ? 200 K, the product T₁τ_p agrees with our earlier order of magnitude estimate of the D'yakonov-Perel' mechanism, in which band structure induced precession is strongly narrowed by momentum relaxation. The Elliott mechanism is one to two orders of magnitude weaker.     

Energy relaxation of electrons in the (100) n-channel of a Si-MOSFET: II. Surface phonon treatment

The electron energy relaxation is investigated as a function of the “electron temperature” T_e in the n-channel of a (100) surface silicon MOSFET device by inspecting the phenomenological energy relaxation time τ_ε(T_e). τ_ε is determined theoretically and compared to experimental results in order to identify the energy relaxation mechanism(s) present at the interface. Two dimensional electron transport is assumed. Single activation temperature (θ) Rayleigh wave scattering and acoustic Rayleigh wave scattering are studied as possible energy loss processes. The effects of electric subbanding near the surface are included. τ_ε is calculated for T_e ? 15 K in the electric quantum limit. We find that a single θ = 12.0 K Rayleigh phonon fits theory to experiment for a single electron inversion density (N_inv) case, but can not provide a fit simultaneously for more than one N_inv value. Theory and experiment disagree when Rayleigh wave acoustic scattering is assumed.     

On the pumping of plasma lasers by a high-frequency-modulated electron beam

The possibility of effective pumping of plasma lasers by a high-frequency-modulated electron beam, i.e. an electron beam in the form of a periodic train of electron bunches, is discussed. It is shown that if such parameters of the medium as the relaxation times of the electron temperature ρ_Te and the electron density ρ_Ne are in agreement with the pulse width ρ_p and the interval between pulses, 1/?_m, this will facilitate effective laser pumping and amplitude modulation of the laser radiation. Existing microwave tubes, such as a traveling-wave tube and a klystron, provide the required parameters of a periodic train of current pulses (electron bunches) over a wide range of pulse widths ρ_p and pumping current amplitudes.     

Measurements of the rotational relaxation times for absorption lines with Voigt profiles

A new method for determining the relaxation parameters T ₁ and T ₂ for the Voigt profile of an absorption line is presented. The method was tested on gaseous OCS with the use of a phase-switching spectrometer. The method is equally applicable for both pure gases and gas mixtures.     

An NMR investigation of naphthalene nanostructures

The molecular mobility of naphthalene molecules in porous silica has been studied over the temperature range 223?K to 363?K using NMR relaxation times T ₂, T ₁ and T _1ρ. The investigations were conducted in silicas with nominal pore diameters of 4?nm, 6?nm, 10?nm, 20?nm and 50?nm. The confined solid behaved in a way that indicated it formed a dual phase system consisting of a solid core in the centre of the pores surrounded by a mobile surface layer. The core naphthalene had the same line width as the bulk. The surface layer exhibited a narrower line of a width that suggested the onset of motional narrowing. This behaviour was characteristic of a plastic crystal phase for naphthalene that does not exist in the bulk. The T ₁ and T _1ρ results were dominated by surface interactions between the confined naphthalene and the pore wall. Magnetization transfer experiments showed that enhanced relaxation occurred throughout the confined material in a time long compared to T ₂ but short compared to T ₁ and T _1ρ. Since the line shape ruled out diffusional motion through the rigid lattice naphthalene core, the magnetization transfer must have occurred via spin diffusion.