Spin-lattice Coefficients Research Articles

Angle-resolved optically detected magnetic resonance as a tool for strain determination in nanostructures

In this paper, we apply the angle-resolved optically detected magnetic resonance (ODMR) technique to study a series of strained (Cd, Mn)Te/(Cd, Mg)Te quantum wells (QWs) produced by molecular beam epitaxy. By analyzing characteristic features of ODMR angular scans, we determine the strain-induced axial-symmetry spin Hamiltonian parameter $D$ with neV precision. Furthermore, we use low-temperature optical reflectivity measurements and x-ray diffraction scans to evaluate the local strain present in the QW material. In our analysis, we take into account different thermal expansion coefficients of the GaAs substrate and CdTe buffer. The additional deformation due to the thermal expansion effects has the same magnitude as the deformation that originates from the different compositions of the samples. Based on the evaluated deformations and values of the strain-induced axial-symmetry spin Hamiltonian parameter $D$, we find the strain spin-lattice coefficient ${G}_{11}=(72.2\ifmmode\pm\else\textpm\fi{}1.9)$ neV for ${\mathrm{Mn}}^{2+}$ in CdTe and shear deformation potential $b=(\ensuremath{-}0.94\ifmmode\pm\else\textpm\fi{}0.11)$ eV for CdTe.

Spin-lattice interaction for ions in low-symmetry sites: The case of Mn2+:CaCO3.

The spin-lattice interaction for ${\mathrm{Mn}}^{2+}$ ions as substitutional impurities in ${\mathrm{CaCO}}_{3}$ has been studied by electron-paramagnetic-resonance (EPR) experiments in crystals under externally applied uniaxial stresses. The shifts of the EPR lines of ${\mathrm{Mn}}^{2+}$ were measured as a function of the stress applied along the three different directions that accept uniaxial forces in this crystal. The values of six second-order spin-lattice coefficients for the ${\mathrm{Mn}}^{2+}$ site were obtained from the data. We also obtained two conditions relating linear combinations of the other four second-order coefficients. Contributions to the spin-lattice interaction of terms of fourth order in the effective spin have been detected. Our results are used to discuss the effect on the EPR spectrum of the different distortions of the carbonate ions surrounding the ${\mathrm{Mn}}^{2+}$.

The estimation of phonon-induced contributions to the second-order spin-lattice coefficients for Gd 3+ in crystals with fluorite structure

Phonon-induced contributions arising from the one-phonon second-order mechanism to the second-order coupling coefficients K Γ (2) ( Γ = E g, T 2g) for Gd 3+ in crystals with the fluorite structure are estimated. It was found that the contributions resulting from the second-order mechanism do not exceed 10 4 cm −1 and are much smaller than the K Γ (2) coefficients determined experimentally as well as the contributions resulting from the first-order mechanism.

Dynamic Orbit-Lattice Interactions for PbF2:Gd3+Single Crystals

Temperature dependence of the second-order spin-lattice coefficients for PbF2:Gd3+ is reported. It is shown that the thermal expansion of the crystal 1attice contributes only in about 14 % to the observed dependence and the rest should be ascribed to a dynamic coupling between the 4f 7 electrons and lattice vibrations. The results are parametrized in both the Einstein and the Debye models and it is shown that the phenomenological parameters obtained from such parametrization can be made to coincide in both models if a specific value of the Einstein frequency ω is properly chosen. Both models of parametrization show that the Γ39 vibrating mode couples to the 4f 7 electrons much weaker than the Γ55 one.

The theory of phonon-induced contributions to the spin-lattice coefficientsfor [formula omitted] ions due to the orbit-lattice interaction linear in static deformations

A theoretical framework permitting the estimation of phonon-induced contributions to spin-lattice coupling coefficients is presented based on the analysis of the one-phonon second-order mechanism. This mechanism involves orbit-lattice couplings that are linear both in static as well as dynamic deformations. The relativistic character of the electronic wave-functions is taken into account. Analytical expressions for the phonon-induced contributions to the spin-lattice coefficients are also given.

On the microscopic interpretation of tetragonal second‐order Spin‐Lattice coefficients of 4f7 ions in the dynamic relativistic crystal field approach

physica status solidi (b)Volume 135, Issue 1 p. K69-K73 Short Note On the microscopic interpretation of tetragonal second-order Spin-Lattice coefficients of 4f7 ions in the dynamic relativistic crystal field approach W. Pastusiak, W. Pastusiak Institute of Physics, Technical University of Szczecin Search for more papers by this authorJ. Kuriata, J. Kuriata Institute of Physics, Technical University of Szczecin Search for more papers by this author W. Pastusiak, W. Pastusiak Institute of Physics, Technical University of Szczecin Search for more papers by this authorJ. Kuriata, J. Kuriata Institute of Physics, Technical University of Szczecin Search for more papers by this author First published: 1 May 1986 https://doi.org/10.1002/pssb.2221350158Citations: 1 Al. Piast'ow 17, PI 70–310 Szczecin, Poland AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Citing Literature Volume135, Issue11 May 1986Pages K69-K73 RelatedInformation

A microscopic interpretation of the spin‐lattice coupling coefficients for S‐state 4f7 ions

AbstractA previously reported model for spin–lattice coupling for 4f7 electrons, based on the assumption that intraionic interactions are perturbed by relativistic interaction with crystal lattice, is developed. Analytical formula for second‐ and fourth‐order spin‐lattice coefficients are derived. Using these formula and the concept of the relativistic crystal field in the point charge approach the values of the spin‐lattice coefficients for Gd3+ in CaF2 are calculated. These values are in much better agreement with the experimental values than those calculated so far. To the best of our knowledge the fourth‐order spin–lattice coefficients are calculated the first time and their values are about ten times smaller than the experimental ones.

A New Model for the Interpretation of Spin‐Lattice Coefficients for S‐State (4f7) Ions

physica status solidi (b)Volume 111, Issue 2 p. K147-K151 Short Note A New Model for the Interpretation of Spin-Lattice Coefficients for S-State (4f7) Ions W. Pastusiak, W. Pastusiak Solid State Division, Institute of Physics, A. Mickiewicz University, Poznań Ul. Matejki 48/49, 60–769 Poznań, Poland.Search for more papers by this authorJ. Kuriata, J. Kuriata Institute of Physics, Technical University of Szczecin Search for more papers by this author W. Pastusiak, W. Pastusiak Solid State Division, Institute of Physics, A. Mickiewicz University, Poznań Ul. Matejki 48/49, 60–769 Poznań, Poland.Search for more papers by this authorJ. Kuriata, J. Kuriata Institute of Physics, Technical University of Szczecin Search for more papers by this author First published: 1 June 1982 https://doi.org/10.1002/pssb.2221110251Citations: 3 Al. Piastów 17, Szczecin, Poland. On leave from Technical University of Szczecin, Poland. AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Citing Literature Volume111, Issue21 June 1982Pages K147-K151 RelatedInformation

Spin-lattice coefficients of Mn 2+ in II–VI compounds

The spin-lattice coefficients of Mn 2+ in CdTe and ZnTe have been measured. Our data allow us to evaluate the random stress distribution within the samples. Our results are compared with values obtained for Mn 2+ in MgO and CaO.

Uniaxial stress method for determination of spin-lattice coefficient for Fe3+in TiO2

The dynamic spin Hamiltonian form for an Fe3+ ion in TiO2 is given and its spin-lattice coefficients computed. On the basis of the change of resonance field with induced stress in an ESR experiment, the quadrupolar contributions SdS is found to exceed by two orders of magnitude the dipolar contribution beta HhS. A complete set of nine spin-lattice coefficients for SdS in orthorhombic symmetry is determined.

Strong spin-lattice coupling of Kramers doublets

Vibronic interactions can induce strong admixture by the magnetic field of other states into Kramers doublets leading to strong spin-lattice coupling of the Kramers doublets. The spin-lattice coefficients of the ground ${\ensuremath{\Gamma}}_{7}$ level of ${d}^{9}$ ions in tetrahedral symmetry are calculated in the cases of strong and moderate Jahn-Teller coupling of the $^{2}T_{2}$ state to $E$ modes of vibration. The electron paramagnetic resonance (EPR) of ${\mathrm{Cu}}^{2+}$ and ${\mathrm{Ag}}^{2+}$ in ZnS, ZnSe, and ZnTe is unobserved because of the strong spin-lattice coupling: the internal strains of the crystals are the cause of broadening of EPR lines thus too weak to be detected.

Spin‐lattice coefficients of Eu2+ in BaF2

Spin‐lattice coefficients of Eu²⁺ in BaF₂

ESR in iron doped silicon crystals under stress

The spin lattice coefficients C 11 and C 44 characterizing the crystal field under stress are measured for neutral iron at interstitial sites in silicon. The coefficients are one order of magnitude larger than for Fe 3+ in MgO. Both C 11 and C 44 turn out to be negative.

Effect of strain on the EPR parameters of cubic Gd3+ in CaF2 determined by the UMER technique

Abstract The EPR strain parameters of cubic Gd 3+ in CaF2 have been measured using the ultrasonic strain modulation technique (UMER) in which 40 kHz strain modulation replaces the magnetic field modulation in conventional EPR. The results are consistent with, but more extensive than, those obtained by static stress measurements of the shift in the resonant field. An analysis of the results shows that the nearest-neighbor superposition model is unable to account for the low value of the fourth-order shear spin-lattice relaxation coefficient Gs.), but for the dilatation and tetragonal spin-lattice relaxation coefficients, the model works satisfactorily.

The spin-lattice interaction for Eu 2+ in CaF 2 and SrF 2

We have measured the spin-lattice coefficients for Eu 2+ in CaF 2 and SrF 2 crystals by measuring the effect of uniaxial stresses on the EPR spectra of these systems. The experimental results are interpreted in terms of the symmetry of the deformations of a cubic lattice under stress and the values of all the second and fourth-order spin-lattice coefficients are given here. The values obtained for the second-order coefficients and that for the fourth-order hydrostatic coefficient are in agreement with existing data, obtained by uniaxial and hydrostatic stress EPR experiments. Those for the trigonal and tetragonal fourth-order coefficients are the first obtained for Eu 2+ in ionic lattices. The reduction of the experimental errors led us to notice an effect which could be explained as an induced anisotropy of the gyromagnetic factor of Eu 2+.

SpinLattice Coefficients of Eu2+ in SrF2

AbstractEPR spectra of Eu2+ in SrF2 under uniaxial stress are observed. The full set of second‐and fourth‐order spin–lattice coefficients is determined. Line shifts of 15 different hyperfine transitions under uniaxial stress are measured. Five coefficients are evaluated by solving a set of 15 equations, some of them are compared with results of other authors. The differences are explained as being due to the introduction of fourth‐order terms in the spin‐Hamiltonian. The results are found to support Stedman and Newman's model. The correlation with the temperature dependence of b is discussed.

Spin–Lattice Coefficients of Gd3+ in CdF2

AbstractEPB spectra of Gd3+ in CdF2 under uniaxial stress were observed and the spin–lattice coefficients of second and fourth order were measured. The measurements were performed in X band in the temperature range 77 to 300 K. Experimental data show that the fourth order term gives an important contribution to the shift of the fine structure resonance lines. Comparison with the results of other authors at different frequencies does not reveal a frequency dependence. Also a temperature dependence of the spin–lattice coefficients is not found. From the value of the coefficient Clg responsible for the symmetric deformation it is deduced that the temperature changes of B are due to thermal expansion.

Effect of Uniaxial Stress on the Zero-Field Splitting ofCr3+in Alums

The effect of uniaxial stress on the zero-field splitting of ${\mathrm{Cr}}^{3+}$ in five alum crystals is reported. In conjunction with uniaxial stress electron-spin-resonance measurements at room temperature are capable of determining the sign of the zero-field-splitting parameter $2D$ in alum crystals. This method provides a means of determining the sign of $D$ in those alums which undergo crystallographic or phase transitions at low temperature. The positive zero-field splitting in the three investigated $\ensuremath{\alpha}$-alums is reduced by an externally applied uniaxial stress along the trigonal axis, and the negative zero-field splitting in the two $\ensuremath{\beta}$-alums is increased by the same stress. These results are in agreement with McGarvey's model of a ${\mathrm{Cr}}^{3+}$ complex in which the zero-field splitting is positive or negative depending on whether the complex is trigonally extended or compressed. If the association is made that $\ensuremath{\alpha}$-alums have a positive $D$ value, and $\ensuremath{\beta}$-alums have a negative $D$ value, a result which seems to be generally valid, the effect of stress on the chromium spectrum in alums can be used to differentiate between $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ types. Stress-induced changes in the zero-field splitting were used to calculate the ${C}_{33}$ spin-lattice coefficient for the five alums.

Temperature dependence of the spin-lattice interaction for Gd3+ in CaF2 and CdF2

The temperature dependence of the second order spin-lattice coefficients of Gd3+ in CaF2 was measured. These values are compared with those obtained for Gd3+ in ThO2 and CeO2.

A Calculation of the Spin–Lattice Coefficients of Gd3+ in CaO, CaF2, Tho2, and CeO2

AbstractThe contributions of three mechanisms to second‐order spin‐lattice coefficients of Gd3+ in CaO, CaF2, Tho2, and CeO2, are calculated with a point‐charge approach for the orbit‐lattice parameters. It is seen that for Gd3+ the Blume and Orbach mechanism has not the importance as for the 3d5 ions, Mn2+ and Fe3+. With the Blume and Orbach mechanism, a relativistic second‐order and a mechanism of fourth order a sign agreement for both coefficients of Gd3+ in CaO and for the tetragonal coefficient in the other lattices is obtained, but not for the trigonal distortions.