Raman Spin-lattice Relaxation Research Articles

Slow magnetic relaxation of a S = 1/2 copper(II)-substituted Keggin-type silicotungstate.

This is the first report on slow magnetic relaxation in an S = 1/2 system based on a first-row transition metal ion with the polyoxometalate skeleton [(n-C4H9)4N]4H2[SiW11O39Cu] (1). The X-band electron-spin-resonance spectrum of 1 measured at room temperature indicates that the copper ion experiences significantly reduced intermolecular interactions compared to the potassium salt and that it adopts a five-coordinated square-pyramidal coordination geometry. The AC magnetic-susceptibility measurements revealed that 1 undergoes slow magnetic relaxation in an applied static magnetic field (Hdc). The extracted spin-lattice relaxation time (92 ms at 1.8 K and Hdc = 5000 Oe) for 5% magnetically diluted 1, [(n-C4H9)4N]4H2[SiW11O39Cu0.05Zn0.95] (dil.1), is comparable to those of other potential S = 1/2 spin qubits. A relaxation-time analysis indicated that Raman spin-lattice relaxation dominates even at low temperatures in an optimized field. The extracted Raman exponent (n = 2.30) is smaller than those of other S = 1/2 complexes that carry organic ligands, which implies that the decrease in relaxation time at higher temperatures is likely to be moderate.

A Complete Ab Initio View of Orbach and Raman Spin-Lattice Relaxation in a Dysprosium Coordination Compound.

The unique electronic and magnetic properties of lanthanide molecular complexes place them at the forefront of the race toward high-temperature single-molecule magnets and magnetic quantum bits. The design of compounds of this class has so far being almost exclusively driven by static crystal field considerations, with an emphasis on increasing the magnetic anisotropy barrier. Now that this guideline has reached its maximum potential, a deeper understanding of spin-phonon relaxation mechanisms presents itself as key in order to drive synthetic chemistry beyond simple intuition. In this work, we compute relaxation times fully ab initio and unveil the nature of all spin-phonon relaxation mechanisms, namely Orbach and Raman pathways, in a prototypical Dy single-molecule magnet. Computational predictions are in agreement with the experimental determination of spin relaxation time and crystal field anisotropy, and show that Raman relaxation, dominating at low temperature, is triggered by low-energy phonons and little affected by further engineering of crystal field axiality. A comprehensive analysis of spin-phonon coupling mechanism reveals that molecular vibrations beyond the ion’s first coordination shell can also assume a prominent role in spin relaxation through an electrostatic polarization effect. Therefore, this work shows the way forward in the field by delivering a novel and complete set of chemically sound design rules tackling every aspect of spin relaxation at any temperature.

Raman spin–lattice relaxation time and Debye temperature studies of [formula omitted] in ammonium cobalt sulphate hexahydrate single crystal

Electron paramagnetic resonance (EPR) of Cr 3 + doped in ( NH 4 ) 2 Co ( SO 4 ) 2 · 6 H 2 O single crystal has been studied using Q band EPR spectrometer to find spin–lattice relaxation time (SLRT) ( T 1 ) . The observation of resolved chromium spectra at room temperature has been interpreted in terms of random modulation of interaction between trivalent chromium and divalent cobalt ions by SLRT of cobalt ions. The relaxation time of the host is found to be 6.95 × 10 - 12 s using Mitsuma theory and 9.85 × 10 - 15 s using Misra et al. approach at room temperature (300 K). Debye temperature of the host lattice is evaluated using electron spin–lattice relaxation processes. It is found that the Debye temperature of the host is 110 K.

Electron spin echo of Cu2+ in the triglycine sulfate crystal family (TGS, TGSe, TGFB): electron spin–latticerelaxation, Debye temperature and spin–phonon coupling

The electron spin–lattice relaxation ofCu2+ has been studied by the electron spin echo technique in the temperaturerange 4.2–115 K in triglycine sulfate (TGS) family crystals. Assuming thatthe relaxation is due to Raman relaxation processes the Debye temperatureΘD was determined as 190 K for TGS, 168 K for triglycine selenate (TGSe)and 179 K for triglycine fluoroberyllate (TGFB). We also calculated theΘD values from the sound velocities derived from available elastic constants. The elastic Debyetemperatures were found as 348 K for TGS, 288 K for TGSe and 372 K for TGFB.The results shown good agreement with specific heat data for TGS. The elasticΘD are considerably larger than those determined from the Raman spin–lattice relaxation. Thepossible reasons for this discrepancy are discussed. We propose to use a modifiedexpression describing two-phonon Raman relaxation with a single variable only(ΘD) after elimination of the sound velocity. Moreover, we show that the relaxation data can befitted using the elastic Debye temperature value as a constant with an additional relaxationprocess contributing at low temperatures. This mechanism can be related to a local mode of theCu2+ defect in the host lattice. Electron paramagnetic resonanceg-factors and hyperfine splitting were analysed in terms of the molecularorbital theory and the d-orbital energies and covalency factors of theCu(gly)2 complexes were found. Using the structural data and calculated orbital energies thespin–phonon coupling matrix element of the second-order Raman process was calculated as553 cm−1 forTGS, 742 cm−1 forTGSe and 569 cm−1 for TGFB.

Raman spin-lattice relaxation, Debye temperature and disorder effectsstudied with electron spin echo of Cu2+ in Tutton saltcrystals

Spin-lattice relaxation time T1 was determined by the electron spin echo(ESE) method in the temperature range 4-60 K in a series of Tutton saltcrystals MI2MII(SO4)2·6X2O (MI = NH4, K; MII = Zn, Mg; X = H, D) weaklydoped (⩽1018 ions cm-3) with the 63Cu2+isotope. The ESE signal was undetectable at higher temperatures. Therelaxation rate increases over the six decades in the studied temperaturerange with T1 equal to 1 s at 4 K and 0.5 µs at 50 K. Variouspossible relaxation mechanisms are discussed with the conclusion that therelaxation is governed by two-phonon Raman processes without a noticeablecontribution from the reorientations of Cu(H2O)6octahedra between Jahn-Teller distorted configurations. Deuteration of thecrystal has no effect in spin-lattice relaxation. For a few crystals, havingthe largest Cu2+ concentration among the studied crystals, a strongand linear in temperature contribution to the relaxation rate was found below15 K. Possible explanations are discussed with the final conclusion that thiseffect is due to a non-uniform Cu2+ distribution in the hostlattice producing effective relaxation via pairs and triads of the Cu2+ ions. From the T1(T) dependence the Debye temperature ΘDwas determined for the all crystals studied. This varies fromΘD = 166 K for K2Zn(SO4)2·6H2O to ΘD = 238 K for (NH4)2Mg(SO4)2·6H2O. The ΘD values are discussed and usedfor calculation of the sound velocity which was found to be similar in allcrystals and equal to ν = 4150(±150) m s-1.

Multifractality, Levinthal paradox, and energy hypersurface.

Multifractal properties in the potential energy hypersurface of polypeptides and proteins are investigated. Characteristic multifractal behavior for different molecular systems is obtained from the f(alpha) spectra. The analysis shows that the dimension of the phase space of the problem influences the accessibility to different parts of the potential energy hypersurface. Also, we show that it is necessary to take into account the H-bond formation between amino acids in the conformational-folding search. The present findings indicate that the f(alpha) function describes some structural properties of a protein. The behavior of the f(alpha) spectra gives an alternative explanation about the Levinthal paradox. Furthermore, the anomalous temperature dependence of the Raman spin-lattice relaxation rates can be related to the perturbations in the secondary structures.

Raman spin-lattice relaxation and dispersion of damped optical phonon frequencies at phase transition

Abstract The influence of the damped optical phonons on the spin-lattice relaxation rate is considered. In the second order of the perturbation theory the temperature dependence of the transition probability is calculated in the vicinity of the phase transition temperature Tc. It is shown that Raman relaxation rate is the main contribution to the anomalous relaxation processes.

Raman spin-lattice relaxation and dispersion of damped oppical phonon frequencies at phase transition

Abstract The influence of the damped optical phonons on the spin-lattice relaxation rate is considered. In the second order of the perturbation theory the temperature dependence of the transition probability is calculated in the vicinity of the phase transition temperature Tc. It is shown that Raman relaxation rate is the main contribution to the anomalous relaxation processes.

Relaxation and nonradiative decay in disordered systems. III. Statistical character of Raman (two-quanta) spin-lattice relaxation.

Vibrational-mode localization leads to a statistical distribution scrP(W) for the (two-quanta) Raman spin-lattice relaxation rate, W\ensuremath{\equiv}1/${T}_{1}$. The characteristic function of the distribution and the cumulant moments are calculated. The time dependence of the recovery of the magnetization after saturation is obtained. It is shown that the observed Raman spin-lattice relaxation rate should exhibit a ``staircaselike'' structure. The length of the ``steps'' is random and their slope is proportional to the square of the temperature ${T}^{2}$. The steps are centered about the average value of W. A procedure is suggested for analyzing experimental data in a manner which will exhibit these features, if present. Observation of these predictions will serve as proof that localized vibrations contribute to the spin-lattice relaxation process.

A study of the long-wave approximation used in the calculation of Raman spin-lattice relaxation rates

The laws T7I6( theta /T) and T9I8( theta /T) were originally established by using the numerous approximations of the long-wave model. To study their theoretical basis, a rigorous expression is derived for the transition probability without these approximations. From this expression, a term containing the main corrections to the approximations of the long-wave model can be obtained and studied quantitatively, in the case of a paramagnetic centre substituted in a crystal with rocksalt structure. It appears that the different contributions to this term cancel at least in part, so that the residual correction is weak enough to allow the description of the temperature dependence by the laws T7I6 and T9I8 in a large range of temperature. This study emphasises phenomenological character of the parameter theta .

Spin-lattice relaxation in fractal systems.

Stapleton and co-workers have measured the spin-lattice relaxation rates of a number of protein molecules and interpreted the results in terms of the fractal nature of these complex systems. We examine the theoretical foundation of their work by calculating in detail the normal modes, local strain, and the temperature dependence of the Raman spin-lattice relaxation rate 1/${T}_{1}$ of an exactly soluble model system, the elastic Sierpinski gasket. No simple power-law dependence of 1/${T}_{1}$ on temperature is found in the entire temperature range.

Raman spin-lattice relaxation of Pb3+in calcite: hyperfine effects

The unusually large Lorentzian linewidths of Pb3+ EPR spectrum in irradiated calcite and their temperature dependences are analysed in terms of Raman spin-lattice relaxation, corresponding to a Kramers ion with large hyperfine interaction and nuclear spin one-half. The relaxation effects are correlated with the temperature dependence of the hyperfine interaction. A good agreement between theory and experiment is found.

Raman spin-lattice relaxation processes applied to S-electron ions

Raman spin-lattice relaxation processes of Kramers doublets with hyperfine interaction have been studied in detail, especially for S-electron ions. The second-order Raman process is found to be the most important relaxation mechanism, and it has been considered as a direct spin-lattice relaxation mechanism, where the spin system is under non-adiabatic conditions. Such analysis permits us to make a detailed study of this process, including the case of multilevel ground states (S-electron ions with hyperfine interaction), as well as the case of the sharp resonant modes associated with the paramagnetic impurities.

Observation of the H2T7 Raman spin-lattice relaxation process in three cobalt tutton salts

The Raman spin-lattice relaxation times of three cobalt Tutton salts were determined at liquid-hydrogen temperatures in magnetic fields up to 100 kOe by means of a.c. susceptibility measurements. At weak external fields the temperature and field dependence of τ shows that characteristics of the usual T 9 Raman process. Above H= 10 kOe the time constants decrease upon increasing the magnetic field. It is demonstrated that this decrease has to be attributed to the field-dependent H 2 T 7 Raman process. Numerically the relaxation time constants above 2 kOe can be given as τ −1 = BT 9 J 8 ( θ D/ T) + CH 2 T 7 J 6( θ D/ T) with B=1.7×10 −9K −9s −1, C=6.3×10 −15kOe −2K −7 s −1 and θ D=145 K for Co(NH 4) 2(SO 4) 2.6H 2O; B=2.3×10 t-9 K −9s −1, C=6.5×10 −15kOe −2K −7s −1 and θ D=120 K for CoK 2(SO 4) 2.6H 2O and B=6.2×10 −9K −9s −1, C=2.2×10 −14kOe −2K −7s −1 and θ D=95 K for CoCs 2(SO 4) 2.6H 2O

The direct and Raman spin-lattice relaxation process in YbCl 3·6H 2O

Spin-lattice relaxation times are reported for ytterbium chloride hexahydrate. Measurements at strong external magnetic fields showed for a powdered sample a direct process, in numerical agreement with the electron spin-lattice relaxation times calculated from proton spin-lattice relaxation measurements. Studies on a single crystal demonstrated the anisotropic character of the direct process in this salt, although our results were strongly influenced by phonon-bottleneck effects. The temperature dependence of the relaxation process at weak magnetic fields was investigated between 2 and 21 K. These results are described by the T 9 Raman process and not by an Orbach mechanism via the next exited doublet at 197 K as suggested earlier. Summarizing, the paramagnetic spin-lattice relaxation time for powdered YbCl 3·6H 2O can be given by ( H in kOe, T in K): τ −1 = (1.0 ± 0.1) × 10 −2 H 4 T + 0.47 × 10 −8 T 9 J 8 ( θ = 180 K) s −1.

Paramagnetic Resonance and Spin-Lattice Relaxation for Ytterbium in Yttrium Ethyl Sulfate; Large Anisotropies and Evidence for Electric Dipole Transitions

Paramagnetic resonance is detected for $^{172}\mathrm{Yb}^{3+}$ ions diluted in crystals of Y${({\mathrm{C}}_{2}{\mathrm{H}}_{5}\mathrm{S}{\mathrm{O}}_{4})}_{3}$ \ifmmode\cdot\else\textperiodcentered\fi{} 9${\mathrm{H}}_{2}$O at temperatures $1.2\ensuremath{\leqq}T\ensuremath{\leqq}4.2$ \ifmmode^\circ\else\textdegree\fi{}K, and $\ensuremath{\nu}=23$ GHz, for $0\ensuremath{\leqq}\ensuremath{\theta}\ensuremath{\leqq}70\ifmmode^\circ\else\textdegree\fi{}$, where $\ensuremath{\theta}$ is the angle between the crystal $c$ axis and $\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}$. We find ${g}_{\ensuremath{\parallel}}=3.328\ifmmode\pm\else\textpm\fi{}0.005$; ${g}_{\ensuremath{\perp}}$ is not directly measured, but estimated to be ${g}_{\ensuremath{\perp}}\ensuremath{\approx}0.01$ from the resonance intensity at $\ensuremath{\theta}=0\ifmmode^\circ\else\textdegree\fi{}$. An observed angular variation of ${10}^{2}$ in linewidth can be explained by a $c$-axis wander throughout the crystal, of order ${(\ensuremath{\delta}\ensuremath{\theta})}_{\mathrm{rms}}\ensuremath{\approx}0.05\ifmmode^\circ\else\textdegree\fi{}$. A striking angular variation in line intensity, of the form $\frac{({tan}^{2}\ensuremath{\theta})}{cos\ensuremath{\theta}}$ over five orders of magnitude, is used to deduce that the observed line is an electric dipole transition rather than the usual magnetic dipole transition, observed only at $\ensuremath{\theta}=0\ifmmode^\circ\else\textdegree\fi{}$. This is further confirmed by placement of the crystal in the cavity in regions of maximum electric or magnetic field. The electric dipole transition comes about by the combined action of the Zeeman perturbation and admixtures of even-parity states into the odd-parity $4{f}^{13}$ configuration by odd terms in the ${C}_{3h}$ crystal field. The direct spin-lattice relaxation rate is measured by a microwave pulse-recovery method and found to be ${T}_{1d}^{\ensuremath{-}1}=134T{tan}^{2}\ensuremath{\theta}$ ${\mathrm{sec}}^{\ensuremath{-}1}$ ($T$ in \ifmmode^\circ\else\textdegree\fi{}K) at constant frequency $\ensuremath{\nu}=23.11$ GHz, which corresponds to ${T}_{1d}^{\ensuremath{-}1}=2.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}{H}^{5}{cos}^{3}\ensuremath{\theta}{sin}^{2}\ensuremath{\theta}coth(\frac{h\ensuremath{\nu}}{2kT})$ ${\mathrm{sec}}^{\ensuremath{-}1}$ ($H$ in oersteds), the theoretically expected form. At large angles the data indicate a phonon bottle-neck. It was found that the EPR signal could be reduced by optical pumping in the $1\ensuremath{-} \mathrm{to} 3\ensuremath{-}\ensuremath{\mu}$ region. An optical pulse-recovery method was used to measure the Raman spin-lattice relaxation rate, ${T}_{1R}^{\ensuremath{-}1}=0.0135{T}^{9}$ ${\mathrm{sec}}^{\ensuremath{-}1}$. These data are of central importance in the analysis of nuclear spin refrigerators utilizing this unusually anisotropic crystal.

Raman Spin-Lattice Relaxation of Shallow Donors in Silicon

This work reports both experimental measurements and calculations of two-phonon Raman spin-lattice relaxation times for shallow donors in silicon. Saturation, line broadening, and adiabatic fast passage techniques were used to measure ${T}_{s} (\ensuremath{\Delta}{M}_{s}=\ifmmode\pm\else\textpm\fi{}1,\ensuremath{\Delta}{M}_{I}=0)$ between 2 and 30\ifmmode^\circ\else\textdegree\fi{}K for P, As, Sb, and Bi at 3300 G. ${T}_{x} (\ensuremath{\Delta}{M}_{s}=\ifmmode\pm\else\textpm\fi{}1,\ensuremath{\Delta}{M}_{I}=\ensuremath{\mp}1)$ was measured in the liquid He range for As, Sb, and Bi at 3300 G. The calculations of the spin-lattice relaxation rates $\frac{1}{{T}_{s}}$ and $\frac{1}{{T}_{x}}$ for Raman processes were made using only the $1S$ doublet and triplet valley-orbit excited states. The calculations were made for both the power-law temperature-dependent region and the exponential temperature-dependent region.