Zeeman Perturbation Research Articles

Nature of visons in the perturbed ferromagnetic and antiferromagnetic Kitaev honeycomb models

The Kitaev honeycomb model hosts a fascinating fractionalized state of matter featuring emergent Majorana fermions and a vison particle that carries the flux of an emergent gauge field. In the exactly solvable model these visons are static but certain perturbations can induce their motion. We show that the nature of the vison motion induced by a Zeeman field is sharply distinct in the ferromagnetic vs the antiferromagnetic Kitaev models. Namely, in the ferromagnetic model the vison has a trivial non-projective translational symmetry, whereas in the antiferromagnetic Kitaev model it has a projective translational symmetry with $\pi$-flux per unit cell. The vison band of the ferromagnetic case has zero Berry curvature, and no associated intrinsic contribution to the thermal Hall effect. In contrast, in the antiferromagnetic case there are two gapped vison bands with opposite Chern numbers and an associated intrinsic vison contribution to the thermal Hall effect. We discuss these findings in the light of the physics of the spin liquid candidate $\alpha$-RuCl$_3$.

Luminescent and magnetic bifunctional coordination complex based on a chiral tartaric acid derivative and europium.

A new mononuclear europium complex incorporating the (+)-di-p-toluoyl-D-tartaric acid (D-H2DTTA) ligand, namely, catena-poly[tris{μ2-3-carboxy-2,3-bis[(4-methylphenyl)carbonyloxy]propanoato}tris(methanol)europium(III)], [Eu(C20H17O8)3(CH3OH)3]n, (I), has been synthesized and characterized by IR spectroscopy, elemental analysis, powder X-ray diffraction and single-crystal X-ray diffraction analysis. The structure analysis indicates that complex (I) crystallizes in the trigonal space group R3 and exhibits an infinite one-dimensional chain structure, in which the Eu3+ ion is surrounded by six O atoms from six D-HDTTA- ligands and three O atoms from three coordinated methanol molecules, thus forming a tricapped trigonal prism geometry. The D-H2DTTA ligand is partially deprotonated and adopts a μ1,6-coordination mode via two carboxylate groups to link adjacent Eu3+ ions, affording an infinite one-dimensional propeller-shaped coordination polymer chain along the c axis, with an Eu...Eu distance of 7.622 (1) Å. Moreover, C-H...π interactions lead to the formation of helical chains running along the c axis and the whole structure displays a snowflake pattern in the ab plane. The circular dichroism spectrum confirms the chirality of complex (I). The solid-state photoluminescence properties were also investigated at room temperature and (I) exhibits characteristic red emission bands derived from the Eu3+ ion (CIE 0.63, 0.32), with a reasonably long lifetime of 0.394 ms, indicating effective energy transfer from the ligand to the metal centre. In addition, a magnetic investigation reveals single-ion magnetic behaviour. The spin-orbit coupling parameter (λ) between the ground and excited states is fitted to be 360 (2) cm-1 through Zeeman perturbation. Therefore, complex (I) may be regarded as a chiral optical-magneto bifunctional material.

Semiclassical Szegö Limit of Eigenvalue Clusters for the Hydrogen Atom Zeeman Hamiltonian

We prove a limiting eigenvalue distribution theorem (LEDT) for suitably scaled eigenvalue clusters around the discrete negative eigenvalues of the hydrogen atom Hamiltonian formed by the perturbation by a weak constant magnetic field. We study the hydrogen atom Zeeman Hamiltonian $H_V(h,B) = (1/2)( - i h {\mathbf \nabla} - {\mathbf A}(h))^2 - |x|^{-1}$, defined on $L^2 (R^3)$, in a constant magnetic field ${\mathbf B}(h) = {\mathbf \nabla} \times {\mathbf A}(h)=(0,0,\epsilon(h)B)$ in the weak field limit $\epsilon(h) \rightarrow 0$ as $h\rightarrow{0}$. We consider the Planck's parameter $h$ taking values along the sequence $h=1/(N+1)$, with $N=0,1,2,\ldots$, and $N\rightarrow\infty$. We prove a semiclassical $N \rightarrow \infty$ LEDT of the Szeg\"o-type for the scaled eigenvalue shifts and obtain both ({\bf i}) an expression involving the regularized classical Kepler orbits with energy $E=-1/2$ and ({\bf ii}) a weak limit measure that involves the component $\ell_3$ of the angular momentum vector in the direction of the magnetic field. This LEDT extends results of Szeg\"o-type for eigenvalue clusters for bounded perturbations of the hydrogen atom to the Zeeman effect. The new aspect of this work is that the perturbation involves the unbounded, first-order, partial differential operator $w(h, B) = \frac{(\epsilon(h)B)^2}{8} (x_1^2 + x_2^2) - \frac{ \epsilon(h)B}{2} hL_3 ,$ where the operator $hL_3$ is the third component of the usual angular momentum operator and is the quantization of $\ell_3$. The unbounded Zeeman perturbation is controlled using localization properties of both the hydrogen atom coherent states $\Psi_{\alpha,N}$, and their derivatives $L_3(h)\Psi_{\alpha,N}$, in the large quantum number regime $N\rightarrow\infty$.

Analyses of sizable ZFS and magnetic tensors of high spin metallocomplexes.

The fictitious spin-1/2 Hamiltonian approach is the putative method to analyze the fine-structure/hyperfine ESR spectra of high spin metallocomplexes having sizable zerofield splitting (ZFS), thus giving salient principal g-values far from around g = 2 without explicitly providing their ZFS parameters in most cases. Indeed, the significant departure of the g-values from g = 2 is indicative of the occurrence of their high spin states, but naturally they never agree with true g-values acquired by quantum chemical calculations such as sophisticated DFT or ab initio MO calculations. In this work, we propose facile approaches to determine the magnetic tensors of high spin metallocomplexes having sizable ZFS, instead of performing advanced high-field/high-frequency ESR spectroscopy. We have revisited analytical expressions for the relationship between effective g-values and true principal g-values for high spins. The useful analytical formulas for the geff-gtrue relationships are given for S's up to 7/2. The genuine Zeeman perturbation formalism gives the exact solutions for S = 3/2, and for higher S's it is much more accurate than the pseudo-Zeeman perturbation approach documented so far (A. Abragam and B. Bleaney, Electron Paramagnetic Resonance of Transition Metal Ions, 1970; J. R. Pilbrow, J. Magn. Reson., 1978, 31, 479; F. Trandafir et al., Appl. Magn. Reson., 2007, 31, 553; M. Fittipaldi et al., J. Phys. Chem. B, 2008, 112, 3859), in which the E(Sx2 - Sy2) term is putatively treated to the second order. To show the usefulness of the present approach, we exploit FeIII(Cl)OEP (S = 5/2) (OEP: 2,3,7,8,12,13,17,18-octaethylporphyrin) and CoIIOEP (S = 3/2) well magnetically diluted in the diamagnetic host crystal lattice of NiIIOEP. The advantage of single-crystal ESR spectroscopy lies in the fact that the molecular information on the principal axes of the magnetic tensors is crucial in comparing with reliable theoretical results. In high spin states of metallocomplexes with sizable ZFS in pseudo-octahedral symmetry, their fine-structure ESR transitions for the principal z-axis orientation appear in the lower field far from g = 2 at the X-band, disagreeing with the putative intuitive picture obtained using relevant ESR spectroscopy. A ReIII,IV dinuclear complex in a mixed valence state exemplifies the cases, whose fine-structure/hyperfine ESR spectra of the neat crystals have been analyzed in their principal-axis system. The DFT-based/ab initio MO calculations of the magnetic tensors for all the high spin entities in this work were carried out.

Theory of Monte Carlo simulations of the magnetic circular dichroism spectra of alkali metal/rare gas systems

AbstractThe history of magnetic circular dichroism (MCD) spectroscopy in the study of alkali metal/rare gas (M/Rg) cryogenic systems is reviewed in the context of developing a better understanding of alkali metal/hydrogen systems of current interest to the U.S. Air Force as enhanced‐performance cryogenic rocket propellants. A new theory for simulating the MCD spectra of M/Rg systems is presented together with a careful discussion of the theory's implicit and explicit approximations and their implications. This theory uses a classical Monte Carlo (MC) simulation scheme to model the perturbing effects of the Rg environment on the 2S → 2P MCD‐active transition of the M atom. The theory sets up the MC–MCD simulation as a 6 × 6 matrix eigenvalue/eigenvector problem in the 2P manifold in which are included the effects of M–Rg interactions, metal atom spin‐orbit coupling in the 2P manifold, magnetic Zeeman perturbations of the 2S and 2P manifolds, Boltzmann temperature factors, and electric dipole transition moment integrals for left circularly polarized (LCP) and right circularly polarized (RCP) light. The theory may be applied to any type of trapping site of the host M in the guest Rg matrix; a single atom substitutional metal atom trapping site (one host Rg atom is replaced by one guest M atom) is modeled in this study for M = Na and Rg = Ar. Two temperature factors are used in these simulations; a lattice temperature to model the mobility of the Rg lattice and a magnetic temperature to model Boltzmann factors in the 2S ground manifold. The 6 × 6 eigenvalue/eigenvector problem is solved for a number of randomly generated and suitably averaged Rg configurations to yield the simulated MC‐MCD spectrum for the single substitutional Na/Ar system. The MC–MCD simulations of Na/Ar give the characteristic triplet MCD spectrum with the correct Boltzmann temperature dependence. The simulated MC–MCD spectrum correctly inverts when the direction of the applied magnetic field is reversed. Addition of the LCP and RCP absorbances gives rise to a characteristic 2S → 2P triplet absorption feature. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005

A series of novel metal-ferrocenedicarboxylate coordination polymers: crystal structures, magnetic and luminescence properties

Novel two-dimensional layered lanthanide(III)-ferrocenedicarboxylate coordination polymers {[M(η 2-O 2CFcCO 2-η 2)(μ 2-η 2-O 2CFcCO 2-η 2-μ 2) 0.5(H 2O) 2]· mH 2O} n (Fc=(η 5-C 5H 4)Fe(η 5-C 5H 4), M=Tb 3+, m=2, 1; M=Eu 3+, m=2, 2; M=Y 3+, m=1, 3) with trapezium-shaped units and one-dimensional wave-shaped Cd(II)-ferrocenedicarboxylate polymer {[Cd(η 2-O 2CFcCO 2-η 2)(H 2O) 3]·4H 2O} n ( 4) have been prepared and structurally characterized by single crystal diffraction. In polymers 1– 3, each central metal ion (Tb(III), or Eu(III) or Y(III)) is located in a pseudo-capped-tetragonal prism coordination geometry, and ferrocenedicarboxylate anion ligands have two coordination modes (bidentate-chelating mode and tridentate-bridging mode). The magnetic behaviors for 1 and 2 are studied in the temperature range of 5.0–300 K. The results show that the paramagnetic behavior of 2 is mainly due to the effective spin–orbital coupling between the ground and excited states through the Zeeman perturbation, and the weak magnetic interaction between Eu 3+ centers can be observed. In addition, compared with sodium ferrocenedicarboxylate, the fluorescent intensities of the polymers 1– 4 are enhanced in the solid state.

The Structure and Physical Properties of a Novel Three-Dimensional Zeolite-Like Nanoporous Architecture Formed by Two Different Polymeric Layers: [Eu2(btc)(H2btc)(H2O)]·4H2O

The open framework of [Eu2(btc)(H2btc)(H2O)]·4H2O (1), prepared by hydrothermal reaction of EuCl3 with 1,2,4,5-benzenetetracarboxylic anhydride in acidified aqueous solution, is built up from two types of polymeric layers with [EuO6(H2O)]n units as tethers, resulting in nanoporous channels that host water molecules through complex hydrogen bonding. Crystallographic data for 1: monoclinic, P21/n, with a = 10.7562(2) Å, b = 7.2075(2) Å, c = 17.2180(5) Å, β = 97.072(2)° and Z = 2. A study of the temperature dependence of the magnetic susceptibility data reveals that the paramagnetic behavior of 1 is mainly due to the effective spin-orbital coupling between the ground and exited states through the Zeeman perturbation; the magnetic interaction between europium(III) centers is very weak. A study of the electronic properties demonstrates that compound 1 is a semiconductor. A TGA analysis between 30 and 600 °C for 1 suggests that when the lattice water molecules are removed from the network, the skeleton of the network still remains stable up to 150 °C; this is also confirmed by XRPD. (© Wiley-VCH Verlag GmbH, 69451 Weinheim, Germany, 2002)

Magnetic properties of dinuclear cobalt complexes

We report the magnetic investigation of dinuclear Co(II) compounds on the base of hamiltonian which takes into account exchange interaction, zero-field splitting and Zeeman perturbation. The treatment of this hamiltonian is performed with the use of the irreducible tensor operator technique and symmetry of the system. A good agreement of the experimentally observed magnetic susceptibility and the results of calculation is obtained.

EPR polarization studies on Mn catalase from Lactobacillus plantarum.

The binuclear manganese active site of Mn catalase catalyzes redox disproportionation of hydrogen peroxide, forming dioxygen and water. We report here multifrequency EPR and microwave polarization studies of the catalytically active homovalent Mn2+ complex of Lactobacillus plantarum Mn catalase, resolving spectra from each of the thermally accessible multiplet states of the coupled complex by multivariate methods. The experimental spectra have been simulated using computational approaches for the binuclear cluster to predict both intensity and polarization for arbitrary values of the ground state parameters. These two spectroscopic properties define the nature of the ground state wavefunctions and so serve as a sensitive and quantitative measure of the inter-ion interactions in the reduced complex. Interpretation of the spectra in terms of a pair Hamiltonian that includes Heisenberg exchange, dipolar, single site zero field splitting, and Zeeman perturbations leads to the most complete ground state description of the active site metal centers. The results of this spectroscopic analysis support a picture of two high spin ions weakly coupled by exchange interactions (J = 40 cm-1) with relatively small dipole-dipole coupling and single site zero field splittings for the ligand-free reduced enzyme. The coupling between fluoride binding and protonation of the complex has been demonstrated by proton uptake studies. The binding of two fluoride ions in the active site dramatically changes the pair spectra, reflecting a substantially reduced J-coupling (J = 10.5 cm-1) that must be a consequence of perturbation of the bridging ligands. Anion binding to the binuclear Mn complex appears to result in poisoning of the active site by protons, possibly associated with insertion of fluoride into bridging positions of the dimanganese core.

Optical Zeeman and low-field ODMR studies of thenπ* phosphorescence ofp-chlorobenzaldehyde

The emissive triplet states of p-chlorobenzaldehyde and p-chlorobenzaldehyde-d1 as guests in p-dimethoxybenzene host crystals are investigated by optical Zeeman and low field optically detected magnetic resonance (ODMR) studies of their phosphorescence at ⩽4·2 K. The active spin level, the sign of the principal fine structure splitting constant, its magnitude and the approximate location of the fine structure axes are deduced from high-field Zeeman perturbations of the phosphorescence origins of the guests. ODMR measurements confirm the conclusions and yield better values for the constants and locations of the principal axes of the fine structure tensor. The results for the perprotonated guest show that D ≡ -3Z/2 = -0·58290 and E ≡ (Y - X)/2 = -0·00714 cm-1; the fine structure axes are oriented relative to the host with the y axis nearly normal to the molecular plane and the z axis rotated 40° from the long molecular axis; and the phosphorescence arises predominantly from Tz . The d1-isotope of the guest ...

A simple theoretical treatment of quadrupolar effects on magic-angle-spinning solid-state NMR spectra of [formula omitted] nuclei in the limit of large quadrupole coupling constants

A simple approach is discussed for studying the effect of quadrupolar nuclei on the magic-angle-spinning solid-state NMR lines of spin- 1 2 nuclei in the limit of large quadrupole coupling constants. Equations are derived both for the isotropic shifts and the Pake-like powder patterns for any quadrupolar spin and for arbitrary orientations of the internuclear vector with respect to the unique axis of an axially symmetric quadrupole tensor. First-order effects due to a small Zeeman perturbation on these lines are explored, as well as deviations from axial symmetry in the electric field gradient when S = 3 2 quadrupolar nuclei are involved. Spectral parameters likely to be observed in the case of coupling between 31P and 201Hg are also discussed.

N f Rydberg complexes of NO in a magnetic field, probed by double resonance multiphoton ionization

n f (v=1) Rydberg states of NO have been probed by double resonance multiphoton ionization in a 1 T external magnetic field. Due to the nonpenetrating character of the f orbitals, these Rydberg states are very sensitive probes of any external perturbation. As n increases, a decoupling of the angular momentum l of the Rydberg electron from the molecular frame occurs gradually, as the magnetic interaction becomes more and more important with respect to intramolecular forces. Up to n≂15, only the linear Zeeman perturbation has been taken into account. The rotational–electronic structure of the 7f and 15f states has been interpreted theoretically by considering the linear Zeeman perturbation in addition to the Coulombic interaction and the long range interaction due to the quadrupole moment and the polarizability of the ion core. The intensities and line positions of the transitions from the intermediate A 2Σ+,v=1 level to the 7f and 15f levels have been calculated. The alignment of the N, MS, MN Zeeman sublevels of the A state by the two-photon pump excitation from the ground state as well as the polarization of both lasers have been taken into account in the calculations. A good agreement between the observed and the calculated transitions has been obtained. For the 7f levels, the electronic–rotational structure is well described in a coupled case (d) representation. For the 15f levels, the strong coupling of l to the field axis led to the first observation of the Paschen–Back effect in a molecule, within each rotational N+ series, with an accompanying drastic simplification of the spectra. This level is better described in a decoupled case (d) representation corresponding to a moderately strong field regime.

A genuine neutral double acceptor in a II-VI semiconductor-SiTe(?) in ZnTe

The authors report the first clearly identified neutral double acceptor in any II-VI semiconductor, observed in Zn-annealed ZnTe. Optical properties of the associated bound exciton (BE) clearly identify the number of holes present in the exciton and the acceptor ground state and establish Td site symmetry. Zeeman and uniaxial stress perturbation spectroscopies were both required to establish the character of the double acceptor ground state in which the crystal-field ( Gamma 3- Gamma 5) splitting of the J=2 hole-hole state ( approximately 4.8 meV) is unexpectedly large compared to the J=0-J=2 splitting, ( approximately 0.9 meV), so that the Gamma 3(J=2) state of the neutral double acceptor lies lowest and is approximately 2 meV below the Gamma 1(J=0) state. A fourfold splitting is seen in the (2s1,1s1) excited state of the double acceptor when this is observed in the satellites of the main BE line. This is attributed to the presence of states with J=0, 1, 2 and 3 due to the coupling of the spins of the two holes, although residual crystal-field splittings may also be significant.

Vibronic coupling and a magnetic-field-induced avoided crossing in theS1←S0absorption spectrum of palladiumporphin

An avoided crossing of the 786 and 815 cm-1 vibronic bands in the absorption spectra of palladiumporphin (PdP) in n-alkane hosts in the presence of an external magnetic field is reported. A description of this effect is presented in terms of the Zeeman perturbation and intramolecular vibronic coupling. It appears to be closely connected with the orbital degeneracy of the first excited singlet state of the free PdP molecule. It is concluded that the anticrossing is due to a bilinear term in the nuclear potential energy, which gives rise to a vibronic matrix element of 4·8 cm-1.

The charge transfer in some alkaline salts of tetracyanoquinodimethane (TCNQ): A Zeeman perturbation study of the 14N nuclear quadrupole resonance spectrum of polycrystalline Rb–TCNQ

Two 14N nuclear quadrupole resonance absorption lines (2904.4 and 2967.7 kHz) detected in Rb–tetracyanoquinodimethane (TCNQ) at room temperature were studied by the Zeeman perturbation effect and the results interpreted in terms of the theory of Pissanetzky [J. Chem. Phys. 59, 4197 (1973)]. The two lines were identified as ν+ with η of 0.40±0.04 and 0.57±0.05 and coupling constants of 3490 and 3254 kHz, respectively. The observed spectrum is compatible with a crystal structure with two inequivalent nitrogen sites such as the monoclinic phase of Rb–TCNQ II. Using the Townes and Dailey theory and an estimation of the effects of the crystal field, and by comparison of the NQR data of K, Rb, and neutral TCNQ, we found an increase of about 10% to 14% in the πx population and a decrease of about 5% in the σ population at the nitrogen. A two-way charge transfer within the CN group seems to take place upon the molecular charge transfer as predicted by Clementi and Klint [J. Chem. Phys. 50, 4899 (1969)].

I=5/2 NMR in the quadrupole regime: Chemical shift in 121Sb2O3

We report the NMR observation of the transition between the lowest levels of an I=5/2 nucleus (121Sb in Sb2O3 powder) subject to a strong quadrupole interaction of zero asymmetry and a weaker Zeeman interaction. We simulate the powder pattern in first order Zeeman perturbation, with emphasis on the dipole broadening of the edge discontinuity near ν=3ν0. Using numerical evaluation of the exact theory, we determine the transverse chemical shift component σ⊥ and the strength νQ of the quadrupole interaction from the field dependence of the resonance frequency.

EPR studies on the high spin Fe III tetraphenylporphine with rhombic character, determination of zero-field splitting parameters from the middle kramers transition

Electron paramagnetic resonance transitions (EPR) in the middle Kramers doublet is observed for the first time in the 6A 1 ground state of Fe (III) complex of tetraphenylporphine (TPP) diluted in the polycrystalline free base tetraphenylporphine (THHP 2). The system shows the EPR spectra and resulting from several distinct species of high spin (Fe (III) TPP with various degress of rhombicity. The middle Kramers as absorptions are in general of much weaker intensity than the corresponding lowest Kramers absorptions, and their g values show marked systematic deviations from the calculated first order prediction. The deviation can be explained by carrying the Zeeman perturbation to the third order. The analysis also rendered it possible to determine the zero-field parameters D and E separately. The results indicate the similarity in the crystal field of the present system with that of cyctochrome P450.

Phosphorescence Microwave Double Resonance Spectroscopy in Ionic Solids and Its Application to Coherent Jahn-Teller States inFCenters of CaO

We demonstrate the use of phosphorescence microwave double resonance (PMDR) in ionic solids applied to the dynamic Jahn-Teller effect in $F$ centers of CaO. A tunnel splitting ($\ensuremath{\Delta}=2.1$ ${\mathrm{cm}}^{\ensuremath{-}1}$) is obtained and Jahn-Teller states are coherent in zero field at least ${10}^{3}$ times longer than the stochastic limit, and possibly as long as the lifetime of the centers. This is demonstrated by showing the loss of coherence by small Zeeman perturbations on the PMDR spectrum.

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.

Zeeman perturbations on shallow acceptor states in germanium : P. J. Lin-Chung and R. F. Wallis, J. Phys. Chem. Solids30 (1969), p. 1453

Zeeman perturbations on shallow acceptor states in germanium : P. J. Lin-Chung and R. F. Wallis, J. Phys. Chem. Solids30 (1969), p. 1453