Quantum theory of the magneto-optical effect and magnetization of Nd-substituted yttrium iron garnet

The magneto-optical and magnetic properties of Nd ³⁺ ions in Y ₃Fe ₅O ₁₂ garnet are analyzed by using quantum theory. In the spontaneous state, the magneto-optical effects originate mainly from the intra-ionic electric dipole transitions between the 4 f ³ and 4 f ²5d states split by the spin-orbit, crystal field, and superexchange interactions. For the excited configuration, the coupling scheme of Yanase is extended to the Nd ³⁺ ion. The magneto-optical resonance frequencies are mainly determined by the splitting of the 5d states induced by the crystal field. The theoretical results of both Nd magnetization and Faraday rotation are in good agreement with experiments. The observed Faraday rotation is proved to be of the paramagnetic type. Although the value of the magneto-optical resonance frequency derived from a macroscopic analysis is approximately confirmed by our theoretical study, a new assignment about the transitions associated with this resonance is unambiguously determined. The spin-orbit coupling of the ground configuration has a great influence on both the Faraday rotation and magnetization, but, unlike the theoretical results obtained in some metals and alloys, the relation between the Faraday rotation and the spin-orbit coupling strength is more complex than a linear one. The magnitude of the magneto-optical coefficient increases as the spin-orbit interaction strength of the ground configuration decreases when the strength is not very weak. Finally, the temperature dependence of the magneto-optical coefficient and the effect of the mixing of different ground-term multiplets induced by the crystal field are analyzed. Received 8 November 2000     

Faraday rotation in single crystal erbium iron garnet

Measurements of the Faraday rotation of ErIG, Er₃Fe₅O₁₂, have been performed in the 4.2–300 K temperature range in magnetic field up to 20 kOe applied along the [111] direction and at 1.15 μm wavelength. The results are analysed under the assumption that the contribution of the Fe³⁺ ions to the total Faraday rotation is the same as that of YIG, Y₃Fe₅O₁₂. The temperature and field dependences of the contribution of the Er³⁺ ions are deduced. Both magnetic and electric dipole contributions of the Er³⁺ ions are calculated; the electric dipole coefficient C_e is found to present a linear temperature dependence between 30–300 K. The temperature dependence of the Faraday rotation susceptibility differs strongly from that of the magnetic susceptibility.     

Magneto-optical study of the 5ƒ2 → 5ƒ16d1 transition in UO2

High field Faraday rotation and magnetic circular dichroism measurements in the energy range between 1.4 and 5.4eV are reported for UO₂. The measurements are compared with two modified atomic models for the 5?² → 5?¹6d¹ transition using LS- and jj-coupling, respectively. Excellent agreement between theory and experiment is found only for a jj-coupling treatment of the final state.The Faraday rotation for magnetic saturation is estimated to be 3 × 10⁶ deg cm^?1 at 4.5 eV.     

Reciprocal and nonreciprocal magnetic linear birefringence in the γ-Dy<Subscript>2</Subscript>S<Subscript>3</Subscript> sesquisulfide

A study has been made of the spectral dependence of the Cotton-Mouton effect (CME) quadratic in magnetic field, nonreciprocal birefringence (NB) linear in magnetic field, and the Faraday effect (FE) in the cubic magnetic semiconductor γ-Dy₂S₃. Unlike the FE, the CME and the NB in this crystal are anisotropic, with the pattern of the anisotropy being dependent on the photon energy. The dependence of the CME and NB dispersion on the direction of the magnetic field B indicates contribution from a variety of electronic transitions and mechanisms to these phenomena. It is shown that the resonant contributions to the CME and NB in the transparency region originate from electronic transitions near E?3.4 eV (beyond the band edge E _g=2.8 eV), which are likely transitions from the localized ground state of the Dy³⁺ ion to states derived from mixing of the band and 4f ^N?1 5d states of the dysprosium ion. The character of the CME anisotropy in the transparency region and near the local electronic transition ⁶ H _15/2 → ⁶ F _3/2 connecting states of the unfilled 4f shell of the Dy³⁺ ion suggests the presence of a strong axial component of the crystal field acting on the rare earth ion.     

Faraday effect on the Rb <Emphasis Type="Italic">D</Emphasis> <Subscript>1</Subscript> line in a cell with a thickness of half the wavelength of light

The rotation of the radiation polarization plane in a longitudinal magnetic field (Faraday effect) on the D₁ line in atomic Rb vapor has been studied with the use of a nanocell with the thickness L varying in the range of 100–900 nm. It has been shown that an important parameter is the ratio L/λ, where λ = 795 nm is the wavelength of laser radiation resonant with the D₁ line. The best parameters of the signal of rotation of the radiation polarization plane have been obtained at the thickness L = λ/2 = 397.5 nm. The fabricated nanocell had a large region with such a thickness. The spectral width of the signal reached at the thickness L = 397.5 nm is approximately 30 MHz, which is much smaller than the spectral width (≈ 500 MHz) reached with ordinary cells with a thickness in the range of 1–100 mm. The parameters of the Faraday rotation signal have been studied as functions of the temperature of the nanocell, the laser power, and the magnetic field strength. The signal has been reliably detected at the laser power P_L ≥ 1 μW, magnetic field strength B ≥ 0.5 G, and the temperature of the nanocell T ≥ 100°C. It has been shown that the maximum rotation angle of the polarization plane in the longitudinal magnetic field is reached on the F_g = 3 → F_e = 2 transition of the ⁸⁵Rb atom. The spectral profile of the Faraday rotation signal has a specific shape with a sharp peak, which promotes its applications. In particular, Rb atomic transitions in high magnetic fields about 1000 G are split into a large number of components, which are completely spectrally resolved and allow the study of the behavior of an individual transition.     

Magneto-optical effects of the antiferromagnetic semiconductor EuTe

The Faraday rotation and the absorption of EuTe have been measured on thin films in the fundamental absorption region from 2·0 to 4·3 eV. Above the Néel temperature,T _N =9·6 °K, we observe in the energy range of the 4f ⁷–4f ⁶ 5dt _2g transition, one minimum and two main maxima of rotation. The temperature dependence of the maxima is found to be different: for one extremum the rotation resembles the magnetization curve of an antiferromagnet with a maximum at the Néel temperature; for the second, however, the rotation shows a ferromagnetic dependence on temperature with a point of inflexion at the Néel temperature and saturation for lower temperatures.This ferromagnetic behaviour within the antiferromagnetic structure of EuTe can be explained by assuming a ferromagnetic superlattice which gives rise to a magnetic Brillouin zone. Thus the ferromagnetic peak is attributed to transitions from the localized 4f ground state to the new zone boundaries.We wish to thank Mr. H. P. Staub for technical assistance, Dr. E. Kaldis for supplying the substances and Dr. J. Muheim for the mass spectroscopic analysis. Financial support by the Schweizerische Nationalfonds zur Förderung der wissenschaftlichen Forschung is gratefully acknowledged.     

Faraday effect in Tb3Ga5O12 in a rapidly increasing ultrastrong magnetic field

The Faraday effect is measured in paramagnetic terbium gallate garnet Tb₃Ga₅O₁₂ at a wavelength λ=0.63 μm at 6 K in pulsed magnetic fields up to 75 T increasing at a rate of 10⁷ T/s for field orientation along the crystallographic direction 〈110〉. The experimental data are compared with the results of theoretical calculations taking into account the crystal fields acting on the Tb³⁺ ion and various contributions to the Faraday rotation. Since the measurements in pulsed fields are carried out in the adiabatic regime, the dependence of the sample temperature on the magnetic field acting during a current pulse is obtained from the comparison of the experimental dependence of Faraday rotation with the theoretically calculated dependences of the Faraday effect under isothermal conditions at various temperatures. __________ Translated from Fizika Tverdogo Tela, Vol. 44, No. 11, 2002, pp. 2013–2017. Original Russian Text Copyright ? 2002 by Levitin, Zvezdin, Ortenberg, Platonov, Plis, Popov, Puhlmann, Tatsenko.     

Magnetic Faraday modulation spectroscopy of the 1–0 band of 14NO and 15NO

Magnetic rotation spectroscopy signals of the nitric oxide (NO) fundamental band near 5 μm have been observed and compared with calculated signals. This spectroscopic approach exploits magnetic field modulation in the Faraday configuration for very sensitive detection of NO. Line shapes and strengths of the Faraday signals depend on molecular parameters, like J and Ω quantum numbers of the transitions involved, and on experimental parameters, like pressure of the gas sample and applied external magnetic field strength. In this study we implemented a software model which provides a simulation of the complete v=1–0 Faraday spectrum of NO. The algorithm considers the magnetic field modulation, the collisional and Doppler broadening of the line shapes, and the line intensities of ¹⁴NO and ¹⁵NO fundamental band lines. Optimum values for pressure and magnetic field modulation for maximum sensitivity are given. Suitable spectral windows for simultaneous detection of ¹⁴NO and ¹⁵NO are discussed. Experimental data were obtained in the wavenumber region from 1840 to 1900 cm^?1 by means of a CO sideband laser and a quantum cascade laser. Comparison between calculated and observed signals shows excellent agreement.     

Cascade-fluorescence spectroscopy on impact-excited He-atoms using level-crossing techniques

He atoms have been excited by 35 keV-Ne⁺ ions, and magnetic depolarization signals of the induced fluorescent light at 667.8nm (1s3d ¹ D-1s 2p ¹ P) have been investigated. By applying suitable electric fields in addition to the variable magnetic field, the complicated superposition structure of the depolarization signal resulting from cascade processes could be analyzed. Beside direct excitation of 1s 3d ¹ D (53%), cascade excitation through 1s4f (26%), 1s 5g (12%), and 1s5f-levels (6%) contributes significantly to the magnetic depolarization signal. From the signal widths the radiative lifetimes of the 1s4f-levels and 1s5g-levels have been deduced: τ(1s4f)=(74±3)ns, τ(1s5g)=(230±20)ns.     

High pressure-high field Mössbauer spectroscopy on pure and magnetically diluted europium-monochalcogenides

By simultaneously applying pressures up to 19.6 kbar and magnetic fields up to 13 T, the magnetic hyperfine (hf) fields of the Eu-monochalcogenides Eu X (X = S, Se, Te) and of the magnetic dilution system Eu_xSr_1-xS were studied using the ¹⁵¹Eu Mössbauer effect. Expected relations between the magnetic exchange interactions and the transferred hyperfine (thf) fields have been confirmed. The pressure dependence of the total hf field in the ferromagnetically saturated state of EuS, EuSe and EuTe has been shown to be due mainly to the pressure response of the thf field of the nearest Eu-neighbours. Except with EuO the thf fields of the next nearest Eu-neighbours and the Eu-core polarization field are nearly insensitive to pressure. The results are discussed in terms of the exchange model proposed by T. Kasuya.     

Quantum theory of the magneto-optical effect induced by Ni ions in barium ferrites

To reveal the physical origin of the giant magneto-optical enhancement of Ni²⁺ ions in barium ferrite, quantitative calculations of the contributions of both the intra-ionic electric dipole transition between the 3d⁸ and 3d^{7 4p} configurations of the Ni²⁺ ions and the intra-ionic electric dipole transition induced by odd-parity crystal field terms are presented. It is deduced that the transition is important in the origin of the considered magneto-optical enhancement. The most important factor is the Ni-Fe superexchange interaction; since it is strong enough, the Faraday rotation produced by the Ni²⁺ ions is large though the energy difference between the 3d⁸ and 3 d7 4 p configurations is large. It is demonstrated that though the intra-ionic electric dipole transition does produce Faraday rotation peaks in the visible range, their magnitude is too small to explain the observed Faraday rotation. The effect of the spin-orbit interaction on the Faraday rotation is analysed. The spin-orbit interaction of the ground configuration plays a very important role in the occurrence of Faraday effects, but the Faraday rotation does not increase linearly with the strength of the spin-orbit coupling. On the contrary, the spin-orbit interaction of the excited configuration has almost no effect on the Faraday rotation. It is shown that the mixing of the different multiplets of the ground term induced by the crystal field has a great influence on the magneto-optical properties. Received 7 January 1998     

Giant exciton Faraday rotation in Cd1−xMnxTe mixed crystals

New semiconductor compound Cd_1?xMn_xTe exhibits strong Faraday rotation in the interband region. It is shown by measurements of magneto-optical Kerr effect and reflection in magnetic field that unusually large exciton Zeeman splitting plays an essential role in the observed Faraday rotation. A possible explanation of the observed splitting (corresponding to a “g factor” value up to 100) by exchange interaction of excitons with manganese d states is suggested.     

A characteristic class of quantities in nonequilibrium thermodynamics and a statistical justification of the local equilibrium approximation

A theory of bandwidth anisotropy in metallic ferromagnets developed previously is specialised to the case of 5d electrons in a hexagonal close-packed lattice. This theory is combined with a model for 5d electrons in the heavy rare earth metals to give a new theory for the low temperature values of the magnetic anisotropy coefficientsκ ₂ ⁰ andκ ₄ ⁰ in Tb, Dy, Ho, Er and Tm. In this theory the magnetic anisotropy is due to a combination of (i) crystal fields acting on 5d and 4f electrons and (ii) bandwidth anisotropy associated with a dependence of 5d bandwidths on magnetization direction. After use is made of empirical upper limits on the eighth order magnetic anisotropy in Gd, there remain four partially adjustable parameters of importance in the theory. These can be chosen to give a good fit to the six observed values forκ ₂ ⁰ andκ ₄ ⁰ in Tb, Dy and Ho. Crystal fields corresponding to negative point charges are seen by 5d electrons, but because of 4f – 5d interactions effective fields of larger magnitude and opposite sign act on 4f shells. Bandwidth anisotropy gives a significant contribution toκ ₄ ⁰ of opposite sign to that due to crystal fields, and dominates the latter in Tb and Er.     

Fluoreszenz der magnetisch ordnenden Halbleiter EuS,EuSe und EuTe

The photoluminescence properties of the europium-chalcogenides EuS, EuSe and EuTe are described. Below approximately 150°K these compounds show a characteristic near-infrared fluorescence band with a half-width of about 0.25 eV. This radiative recombination is ascribed to an intrinsic transition 4f ⁶ 5d→4f ⁷ of the Eu-ions. Its important frequency shift with respect to the corresponding optical absorption in the vicinity of the absorption edge is due to a Franck-Condon-type relaxation process. The spectral band position and the quantum efficiency of the emission are found to be very sensitive to magnetic ordering. Within the series of substances the different kind of magnetic order is clearly illustrated by the dissimilar spontaneous fluorescence behaviour: On cooling, the ferromagnet EuS displays a red shift and a quenching of the emission nearT _c, whereas the antiferromagnet EuTe shows a blue shift of the band and an increase of its intensity nearT _N. With respect to this behaviour in zero field an applied magnetic field causes the fluorescence to be quenched and shifted towards longer wavelengths. The largest response to the field is observed in the vicinity of the ordering temperatures and in the metamagnetic temperature range of EuSe. The results are discussed in connection with measurements of the magnetization, the optical absorption and the photoconductivity and compared with fluorescence measurements on Eu(II)-silicates. The behaviour of the excitation spectra is closely related to the absorption edge shift. On the other hand the shift of the emission is not similarly discribed by the mean ion spin correlation. We propose to ascribe this to a magnetic relaxation in the vicinity of the excited state. The unusual intensity behaviour is also discussed.      

THE INFLUENCE OF THE ADMIXING OF DIFFERENT MULTIPLETS ON THE SPIN MAGNETIC MOMENT AND FARADAY EFFECT OF HARE EARTH IONS IN GARNETS

The influence of the admixing of the excited multiplets of the ground configuration with the ground multiplet on the spin magnetic moment of the crystal- field-and exchange-interaction-split ground state, the Faraday rotation and the magneto-optic coefficient induced by the rare earth ions in rare-earth-substituted garnets Y_3-xR_xFe₅O₁₂ (R=Ce and Pr) has been calculated in this paper. It is found that, in the case of Ce³⁺ ions, the admixing of the 4f^{1 2}F_7/2 multiplet with the ²F_5/2 multiplet makes the spin magnetic moment of the crystal-field- and exchange-interaction-split ground state increase by 140% and the Faraday rotation increase by 180% at 633nm wavelength, and 150% at 1150nm at 294 K. In the case of Pr³⁺ ions, the admixing of the 4f^{2 3}H₅ multiplet with the ³H₄ multiplet makes the spin magnetic moment of the crystal-field- and exchange-interaction-split ground state increase by 34% and the Faraday rotation increase by 59% at 294K. The admixing of different multiplets of the Ce³⁺ ions makes the ratio between the magneto-optic coefficients at 50 and 294K increase by 7% at 633nm wavelength and 15% at 1150nm.     

Features of faraday rotation in cs atomic vapor in a cell thinner than the wavelength of light

Features of the effect of Faraday rotation (the rotation of the radiation polarization plane) in a magnetic field of the D ₁ line in Cs atomic vapor in a nanocell with the thickness L varying in the range of 80–900 nm have been analyzed. The key parameter is the ratio L/λ, where λ = 895 nm is the wavelength of laser radiation resonant with the D ₁ line. The comparison of the parameters for two selected thicknesses L = λ and λ/2 has revealed an unusual behavior of the Faraday rotation signal: the spectrum of the Faraday rotation signal at L = λ/2 = 448 nm is several times narrower than the spectrum of the signal at L = λ, whereas its amplitude is larger by a factor of about 3. These differences become more dramatic with an increase in the power of the laser: the amplitude of the Faraday rotation signal at L = λ/2 increases, whereas the amplitude of the signal at L = λ almost vanishes. Such dependences on L are absent in centimeter-length cells. They are inherent only in nanocells. In spite of a small thickness, L = 448 nm, the Faraday rotation signal is certainly detected at magnetic fields ≥0.4 G, which ensures its application. At thicknesses L < 150 nm, the Faraday rotation signal exhibits “redshift,” which is manifestation of the van der Waals effect. The developed theoretical model describes the experiment well.     

Influence of transverse magnetic fields and depletion of working levels on the nonlinear resonance Faraday effect

The nonlinear resonance Faraday effect is studied under the condition of coherent population trapping in ⁸⁷Rb vapor at the D₁-line F=2→F′=1 transition. The influence of transverse magnetic fields on the nonlinear optical Faraday rotation is studied. For the transverse fields perpendicular to the electromagnetic-wave polarization, a simple theoretical model is proposed, which is in good agreement with experimental data. The optimal intensity providing the maximum sensitivity is found based on the results obtained. The influence of working-level depletion on the parameters of Faraday rotation in open systems is studied experimentally and theoretically. The system was closed in the experiment by using an additional laser to increase the sensitivity and extend the dynamic range of measured fields. The importance of compensating for the depletion in the presence of spurious magnetic fields is shown; in particular, the sensitivity was enhanced by a factor of 50 in experiments with a buffer gas.     

Weak magnetic field behavior of photon echo in a LuLiF4:Er3+ crystal

We report the first observation and study of the photon echo in Er³⁺:LuLiF₄. The energy transition is ⁴ I _15/2 → ⁴ F _9/2 (λ = 6536 Å). The density of ErF₃ is 0.025 wt %. The operation temperature is 1.9 K. Measurements were made at low (up to 1200 Oe) and even zero external magnetic fields. We studied the behavior of the photon echo intensity vs. the magnetic field magnitude and direction about the crystal axis C and vs. the laser pulse separation t ₁₂ and observed an exponential growth and then, after a certain plateau, an exponential decrease in the photon echo intensity as a function of magnetic field upon increasing the magnetic field from zero. The parameters describing the exponential growth and decrease are independent of the direction of magnetic field. The value of the magnetic field (～20–200 Oe) at which the echo intensity is maximal and the value of the maximum itself decrease with increasing pulse separation t ₁₂ and the angle Θ between the magnetic field and crystal axis. The echo intensity decreases exponentially with increasing Θ. The parameter describing the exponential decrease is independent of the magnitude of the field. The echo intensity as a function of pulse separation shows exponential decay. The phase relaxation time depends on the magnitude and direction of the magnetic field. T ₂ is equal to 202 ± 16 ns at zero magnetic field. A phenomenological formula is suggested, which qualitatively presents the mentioned dependences, and the polarization properties of the backward photon echo in this crystal are studied. Because the ion of trivalent erbium is an optimum data carrier, the above results show that fine control of the multichannel transfer of processed optical information may be achieved by weak magnetic fields.     

On the optimum method of analysis of Faraday rotation and ellipticity measurements in a metal-oxide-semiconductor system

We have previously calculated the Faraday rotation θ and ellipticity δ due to the two-dimensional electron gas at the oxide-semiconductor interface of a metal-oxide-semiconductor system. The results depend on such parameters of the system as the effective mass m¹, the relaxation time τ, and the electron surface concentration N, and in fact the motivation is to enable one to determine such parameters from measurements of θ and δ. Here we discuss the optimum method for the determination of these parameters from the data. In particular, we argue that it is more desirable to carry out measurements at fixed magnetic field B and variable photon frequency ω, rather than at fixed ω and variable B. We also demonstrate how our analysis can be used to determine the predicted dependence of τ on magnetic field, without explicit knowledge of m¹ or N.