Zeeman Parameters Research Articles

Updated Zeeman effect splitting coefficients for molecular oxygen in planetary applications

We comment on a common practice to use pure Hund case (b) Zeeman parameters in planetary atmospheric radiative transfer applications involving molecular oxygen. A detailed theoretical formulation is presented for the Zeeman splitting coefficients of molecular oxygen in its ground vibronic state, taking also the relevant fine-structure interactions into account. The updated Zeeman parameters are compared to the simplified Hund case (b) approach used in earlier works. The biggest differences between the output of these formulations occur for states with low rotational energy, and the differences are greater for 16O18O than for 16O2. To get the order of magnitude error introduced by the simplification of the splitting coefficient computations, we perform a limited case study of forward simulations for a few space-borne and ground-based instruments. Our analysis shows that using simplified Zeeman coefficients introduces errors in the forward modelled radiation varying from insignificant up to 10 K.

Field-induced ferromagnetic phase transition in two-dimensional Fermi systems with magnetic dipole-dipole interaction

Magnetic properties of the two-dimensional spin-polarized Fermi gas with dipole-dipole interaction are studied in the presence of external magnetic field at zero temperature. Within perturbation theory and the second quantization formalism, the total energy is explicitly obtained as a function of three dimensionless parameters, the spin polarization, dipolar coupling and Zeeman parameters. We examine the effects of these agents on the magnetic properties of 2D Fermi gas. The results show that an induced ferromagnetic phase transition is observed only for adequately large values of magnetic field. This paper offers two controllable factors to change the spin polarization of the system.

A Spectroscopic Investigation of Magnetic Exchange Between Highly Anisotropic Spin Centers

Structurally similar, magnetically diverse: The exchange and Zeeman parameters of two dimetallic, six-coordinate cobalt(II) compounds—i.e., with orbitally degenerate metal ions—have been determined by a combination of high-resolution EPR and INS spectroscopies, together with ab intio calculations. It is suggested that the correlation between the local crystal field about the CoII centers and the superexchange pathway controls the magnetic interaction.

Spectroscopic study of the 14NH radical in vibrationally excited levels of the X3Σ− state by far infrared laser magnetic resonance

Rotational transitions of vibrationally excited NH (ν = 1 and 2) in the ground X3Σ− electronic state have been detected by far-infrared laser magnetic resonance. The first four rotational intervals were investigated (N = 1 − 0, 2 − 1, 3 − 2, and 4 − 3) with a total of 17 far-infrared laser lines ranging in wavelength from 81.1 to 373.6 µm. For some rotational intervals, transitions between all components of the Zeeman manifolds were observed. An effective Hamiltonian was used to model the experimental measurements. The magnetic hyperfine parameters have been determined for the first time for the ν = 2 level and have been significantly improved for the ν = 1 level. In addition, the rotational, centrifugal distortion, spin-spin, spin-rotation, and Zeeman parameters have all been experimentally determined for the ν = 1 and 2 levels of NH.

The X2Π and A2Σ+ states of FH+, ClH+ and BrH+: theoretical study of their g -factors and fine/hyperfine structures

Theoretical calculations on the fine, hyperfine and Zeeman (g-factor) parameters are reported for the X2Π and A2Σ+ states of FH+, ClH+ and BrH+. The fine-structure constants [spin–orbit (A), Λ-doubling (p, q) and spin–rotation constants (γ Π, γ Σ)] are evaluated up to second order (via SO/L couplings with several excited states) using a multireference configuration interaction (MRCI) method, a Breit–Pauli Hamiltonian and 6-311++(2d,2pd) basis sets. Hyperfine constants of magnetic and electric type [Frosch–Foley (a, b, c, d) and nuclear quadrupole (eQq 0, eQq 2)] are studied with density functional methods and various basis sets. Magnetic dipole moments (parameterized via g-factors) are calculated in second order like the fine structure constants. The situation is somewhat complex for X2Π since no less than five different g’s have to be evaluated in second order. In general, our results are in good agreement with those reported in the literature, mostly limited to the ground state. Our calculations confirm that, at equilibrium, all second-order properties are dominated by the couplings between the electronic states X and A.

On the energy dependence of the Zeeman and hyperfine parameters in the state of OH and OD

Abstract We report quantum beat studies of the energy dependence of the Zeeman parameters in the A 2 Σ + state of OH and OD, and the nuclear hyperfine parameters of OD( A 2 Σ + ). In contrast to previous work, we find that the sign and magnitude of the anisotropic g-factor gl for υ′=0 is consistent with that expected from Curl’s relationship. However, at higher energies gl changes sign, a result we attribute to interaction with the repulsive 1 4 Π state, which is known to lead to predissociation at higher energies. The magnetic and electric quadrupole hyperfine constants were determined for OD( A 2 Σ + ,υ ′ =0–3) , and the constants for υ′=2,3 are reported here for the first time. The derived values are consistent with previous experimental results and available ab initio calculations.

Low-energy excitations of double quantum dots in the lowest Landau level regime

We study the spectrum and magnetic properties of double quantum dots in the lowest Landau level for different values of the hopping and Zeeman parameters by means of exact diagonalization techniques in systems of N=6 and N=7 electrons and filling factor close to 2. We compare our results with those obtained in double quantum layers and single quantum dots. The Kohn theorem is also discussed.

The accurate determination of magnetic hyperfine and Zeeman parameters for 2II diatomic molecules from experimental data

The parameters γ and AD (for the spin-rotation coupling and the centrifugal correction to the spin-orbit coupling) in the effective Hamiltonian of a diatomic molecule in a 2Λ state, Λ ≠ 0, make indistinguishable contributions to the energy, and one or other of these terms can be removed by a unitary transformation. The present work considers the effects of this and other transformations on the terms of the magnetic hyperfine and Zeeman Hamiltonians. It is found that the hyperfine parameter b is particularly affected by the transformations, and that care must be taken in correcting b before interpreting its value in terms of the electronic structure. An application to 15NO gives consistent values of the corrected b between ÃD and fits. The transformation of the Zeeman Hamiltonian produces higher order Zeeman terms that so far have not been included in fits of data in magnetic fields. Neglect of these contributions is equivalent to a constraint on the fit. A re-fit of LMR data for the FO radical shows that this approach is viable, and leads to the determination of separate values for AD and γ. These values and those obtained for b and gl correspond to the unitary transformation that optimizes the chosen form of the Zeeman Hamiltonian.

Rotational Spectrum of the AsH2 Radical in Its Ground State, Studied by Far-Infrared Laser Magnetic Resonance

The rotational spectrum of AsH2 in its ground X̃2B1 electronic state has been recorded using a far-infrared laser magnetic resonance spectrometer. The AsH2 radical was produced inside the spectrometer cavity by the reaction of arsine (AsH3) with fluorine atoms. Hyperfine splittings from both 75As and 1H nuclei were observed, and analysis of the spectra has yielded accurate values for rotational, hyperfine, and Zeeman parameters.

Rotational Spectrum of the AsH Radical in Itsa1Δ State, Studied by Far-Infrared Laser Magnetic Resonance

The rotational spectrum of AsH in its metastablea1Δ state has been recorded using a far-infrared laser magnetic resonance spectrometer. The AsH radical was produced inside the spectrometer by the reaction of arsine (AsH3) with fluorine atoms. Hyperfine splittings from both75As and1H nuclei were observed, and analysis of the spectra yielded accurate values for rotational, hyperfine, and Zeeman parameters.

10 K electron paramagnetic resonance of a d1 Ti3+ centre in X-irradiated zircon (zirconium silicate)

A d1 Ti3+ centre formed by X-irradiation of a synthetic zircon single crystal at 77 K has been studied by electron paramagnetic resonance (EPR) at 10 K. The Ti3+ ion occupies a substitutional site of point group symmetry 42m (D2d). Absence of both site splitting in general crystal orientations and of superhyperfine structure from a +1 ion indicated that a nearby charge compensator was not involved. Comparison with EPR measurements on Ti3+/ alpha quartz centres, point charge calculations and 29Si hyperfine splittings indicated that the Ti3+ centre results from electron capture by Ti4+ occupying a Zr4+ site in the crystal; the designation (TiO8)/sup /s suggested. Precise spin-Hamiltonian parameters, including 47Ti (I=5/2, 7.4%) and 49Ti (I=7/2, 5.4%) hyperfine, nuclear electric quadrupole and nuclear Zeeman parameter matrices, together with high-spin nuclear terms of dimension I4, I3S, I5S, BI3 and BI5 were determined. The set of terms BI, BI3 and BI5 were found to be crucial in obtaining a good fit to the many 'forbidden' hyperfine lines observed. This resulted in determination of nuclear quadrupole and nuclear Zeeman parameters with precisions not hitherto attained in conventional single-crystal EPR measurements.

Identification and Analysis of the Far-Infrared Laser Magnetic Resonance Spectrum of the HS 2 Radical

The first observation of the far-infrared laser magnetic resonance spectrum of the HS 2 radical in its ground 2 A″ state is reported. The radical was produced in the gas-phase reaction between fluorine atoms and hydrogen sulfide, H 2S. Spectra associated with several different rotational transitions (with values of N up to 30 and K a up to 4) have been identified and analyzed to give an improved set of molecular parameters. In particular, the value for the centrifugal distortion constant Δ K of 24.339(10) MHz is significantly different from the value assumed by S. Yamamoto and S. Saito ( Can. J. Phys. 72, 954 (1994)) in their earlier millimeter-wave study, Zeeman parameters have also been determined.

The laser magnetic resonance spectrum of the ν1 band of the CCN radical in its state

Vibration–rotation transitions in the ν1, band of the CCN free radical in the [Formula: see text] state have been observed by CO laser magnetic resonance (LMR) spectroscopy. The observations have been combined with existing diode laser data to determine the parameters of an N2 effective Hamiltonian modified to include the Renner–Teller effect in the [Formula: see text] state explicitly. The LMR observations are well modelled by estimated Zeeman parameters that take into account non-adiabatic vibronic interactions. The analysis suggests a small systematic error in the diode laser measurements and leads to a revision of the band origin, ν1, to 1923.252 92 (42) cm−1.

Zeeman and zero-field splitting of 3d 4 and 3d 6 ions with orbital singlet ground state at orthorhombic and tetragonal symmetry sites

The spin Hamiltonian (SH) parameters for 3 d 4 and 3 d 6 ions with the spin S = 2 in the first- and second-kind orthorhombic crystal field (CF) are studied within the 5 D approximation. Four possible energy level schemes with a distinct orbital singlet ground state with S = 2 have been established due to our previous CF studies. For each scheme the microscopic spin Hamiltonian (MSH) formulas for the zero-field splitting (ZFS) parameters in the extended Stevens operator notation B q k as well as the electronic Zeeman parameters g i are derived by computer using the ALTRAN algebraic program. The microscopic approach enables one to express the parameters B q k and g i in terms of the spin-orbit (λ) and spin-spin (ρ) coupling parameters, the orthorhombic energy level splittings (Δ i) and mixing coefficients (q,s). The present perturbation calculations extend to higher orders of perturbation theory as well as being more comprehensive than the earlier ones, since two new energy level schemes not considered before are now dealt with. Due to the ascent in symmetry method, the MSH results are also applicable to tetragonal symmetry cases involving the real ZFS terms. Some inconsistencies in the previous MSH derivations carried out by hand are clarified. Conversion relations between the ZFS parameters B 0 2, B 2 2, B 0 4, B 2 4, B 4 4 and those expressed in several other notations used in the EPR literature are provided. Specific applications of the MSH formulas derived here provide guidelines for the millimeter/submillimeter and high magnetic field EPR studies of 3 d 4 and 3 d 6 ions at orthorhombic and tetragonal symmetry sites.

Methyl Nitrate, its Molecular Values, Magnetic Susceptibility Anisotropies, Molecular Electric Quadrupole Moment, Second Moments of the Electronic Charge Distribution, and Electric Field Gradient at the Nitrogen Nucleus

The high field molecular Zeeman effect of low-J rotational transitions has been observed in methyl nitrate. The spectrum is complicated by the presence of the small 14N nuclear quadrupole coupling. Methyl top internal rotating splitting is negligible in the transitions studied here. From line shape analyses the individual satellite frequencies in the Zeeman-hfs-multiplets could be determined with experimental uncertainties typically smaller than ±2 kHz. The molecular Zeeman parameters and the 14N nitrogen coupling constants were fitted simultaneously to the observed splittings. The molecular g-values are gaa = -0.1168(5), gbb= -0.0449(3), and gcc= -0.0235(4). The molecular magnetic susceptibility anisotropies in units of 10-6 erg gauss-2 mol-1 are 2ξaa -ξbb -ξcc = +1.24(54) and 2ξbb - ξcc - ξaa = +13.14(53). The 14N nuclear quadrupole coupling constants are χaa - + 0.308(17) MHz, χbb - χcc -0.262(31) MHz. The molecular electric quadrupole moments calculated from the observed rotational constants and Zeeman parameters in units of 10-26 esu cm2 are Qaa = +3.4(6), Qbb= -4.6(6), and Qcc= +1.2(10). Knowledge of the molecular structure and the molecular g-values also gives the diagonal elements in the paramagnetic susceptibility tensor and the ansiotropies in the second moments of the electronic charge distribution. The results in units of 10-6 era gauss-2 mole-1 are ξp aa = + 118.14(10), ξp bb = +279.73(14), and ξp cc = + 357.40(26), and ⟨a2⟩ - ⟨b2⟩ = + 37.14(14) Å2, ⟨b2⟩ - ⟨c2⟩ = +20.46(22) Å2, and ⟨c2⟩ -⟨a2⟩ = -57.60(21) Å2

The Rotational Zeeman Effect of 1,2,4-Trifluorobenzene

Abstract The rotational Zeeman effect of 1,2,4-trifluorobenzene has been studied for 8 low-J rotational transitions in magnetic fields between 1.9 and 2.4 Tesla. The observed susceptibility anisotropics and molecular g-values are: (2χaa−χbb−χcc) = 37.85(69) • 10−6 erg G−2 mole−1, (2χbb−χcc−χaa) = 56.85(54) • 10−6 erg G−2 mole−1, gaa= −0.0393(3), gbb= −0.0277(3), and gcc = 0.0042(2). The Zeeman parameters have been used to derive the molecular electric quadrupole moments and vibronic ground state expectation values for the electronic second moments. The observed out-of-plane quadrupole moment is discussed with reference to an additivity scheme proposed earlier. The observed out-of-plane component of the molecular magnetic susceptibility tensor is in excellent agreement with the value predicted earlier from the CNDO/2-π-electron density alternation at the ring atoms.

Laser magnetic resonance of NH_2 in Ã^2A_1 and highly excited vibrational states of X˜^2B_1

The CO2/N2O laser magnetic resonance spectra of NH2 of the A2A1 (0, 12, 0)–(0, 11, 0) band and also of transitions between the A2A1 (0, 11, 0) state and highly excited vibrational states (u) of X˜2B1 were observed at sub-Doppler resolution by using an infrared-optical double-resonance technique. The observed lines were analyzed to determine the Zeeman parameters and hyperfine-coupling constants of the states involved and also to make rotational assignments for the u levels. The observed hyperfine structure gave support for identifying the u level to be associated with X˜ state.

Far infrared laser magnetic resonance detection of NH and ND (a 1Δ)

Rotational spectra of the excited a 1Δ state of NH and ND have been observed by far infrared laser magnetic resonance spectroscopy. For ND(a 1Δ) the spectroscopic constants are B0=264 750.263(30) MHz, D0=14.383 83(91) MHz, aN =109.63(22) MHz, aD =11.03(23) MHz, eqQ(N)=−4.0(15) MHz, gr=−0.000 86(10), and gL =1.000 506(17). For NH (a 1Δ), the constants are B0=493 043.182(95) MHz, D0=50.453 MHz (constrained in fit), aN =109.65(85) MHz, aH =70.9(14) MHz, eqQ(N)=−4.0 MHz (constrained in fit), gr =−0.001 58(6), and gL =1.001 03 (constrained in fit). Aspects of the electronic structure of the radical as revealed by the magnetic hyperfine constants are discussed in relation to those of chemically similar systems. The Zeeman parameters are interpreted in terms of mixing of the a 1Δ state with the c 1Π state.

The rotational Zeeman effect in the ArOCS van der Waals complex

The rotational Zeeman effect has been measured in the weakly bound complex ArOCS. The study was carried out on a pulsed Fourier-transform microwave spectrometer employing a supersonic nozzle and a Fabry–Perot cavity. The following spectroscopic constants were obtained: Projection equations are used to relate the magnetic properties of free OCS to those of the complex. An analysis of the force field as obtained from centrifugal distortion is used to determine an average structure for ArOCS and mean square amplitudes of the van der Waals motions. These are used to augment the projection analysis. The molecular quadrupole moment of ArOCS is calculated from the Zeeman parameters. With an estimated bulk magnetic susceptibility, diamagnetic susceptibilities and the second moments of electronic charge distribution are also calculated.

The rotational Zeeman effect in ArHBr: An interpretation of the rotational Zeeman parameters in rare gas hydrogen halide complexes

The rotational Zeeman effect in the ArHBr van der Waals molecule has been studied using the method of pulsed Fourier transform microwave spectroscopy carried out in Fabry–Perot cavity located in the bore of a superconducting magnetic solenoid. The rotational magnetic dipole moment, magnetic susceptibility anisotropy, and bromine bulk shielding constant were determined. The values for ArH79 Br are: g⊥=0.000 20(5), χ∥–χ⊥ =−0.13(9)×10−9 MHz/G2, and σBr=4000(2000) ppm. The equations describing these molecular Zeeman parameters in terms of the properties of the constituent subunits of the complex are derived from the full dynamic molecular Hamiltonian. The rotational g value is a sensitive measure of the degree of Coriolis coupling in the complex. The molecular quadrupole moment of ArHBr is calculated.