Electric Quadrupole-quadrupole Interaction Research Articles

Magnetic Interactions between Rare-Earth Ions in Insulators. III. EPR Measurements ofCe3+Pair-Interaction Constants in LaCl3

In order to investigate the form of interaction between non-$S$-state, Kramers rare-earth ions, the electron paramagnetic resonance spectra from pairs of ${\mathrm{Ce}}^{3+}$ ions in La${\mathrm{Cl}}_{3}$ have been measured at 4.2\ifmmode^\circ\else\textdegree\fi{}K and at 25 and 36 GHz. The spectra have been fitted to a general effective-spin pair-Hamiltonian in order to obtain values for the g tensors and certain terms in the interaction tensors K. By using additional data from bulk-property measurements on Ce${\mathrm{Cl}}_{3}$, values for all the terms in K can be deduced. The contributions to the measured parameters from the various interaction mechanisms thought to be present in rare-earth compounds are discussed in detail. Apart from the usual magnetic dipole interaction, it is generally difficult to identify each contribution unambiguously. In the present case, however, because of the simple nature of the ${\mathrm{Ce}}^{3+}$ wave functions, there is clear evidence for the existence of an electric quadrupole-quadrupole interaction between next-nearest-neighbor ions, and its magnitude has been determined. There is also unambiguous evidence for anisotropic superexchange of the type suggested by Levy and by Elliott and Thorpe, and it is found that this has matrix elements of magnitude compariable with the more usual bilinear exchange interaction, which is also present.

Observation of Pair Interaction between Ortho Molecules in SolidH2

A study of the electric quadrupole-quadrupole (EQQ) interaction between ortho-${\mathrm{H}}_{2}$ molecules in solid ${\mathrm{H}}_{2}$ is presented. This work consists in recording and interpreting the pair spectrum of proton nuclear magnetic resonance for low ortho-${\mathrm{H}}_{2}$ concentrations. In the theoretical part of this paper, a calculation of the absorption spectrum for an isolated pair of ortho molecules is presented, and the temperature dependence of this spectrum is derived as a function of the rotational states of the isolated ortho pair. Furthermore, the results of similar calculations on the absorption spectrum of isolated triangles of ortho-${\mathrm{H}}_{2}$ molecules in solid ${\mathrm{H}}_{2}$ are briefly discussed. This spectrum is expected to be less pronounced than the pair spectrum and to be mostly responsible for a broad absorption background. The experimental work, carried out at temperatures between 0.45 and 14\ifmmode^\circ\else\textdegree\fi{}K on several low ortho-${\mathrm{H}}_{2}$ concentrations shows the maxima expected from theory. From the analysis of the results, and assuming the interactions between molecules to be purely EQQ, the coupling constant $\frac{\ensuremath{\Gamma}}{{k}_{B}}=\frac{6{e}^{2}{Q}^{2}}{25{R}^{5}{k}_{B}}$ is found to be 0.82\ifmmode^\circ\else\textdegree\fi{}K. This value is smaller than that expected for the solid rigid lattice, where $\frac{\ensuremath{\Gamma}}{{k}_{B}}=1.00$\ifmmode^\circ\else\textdegree\fi{}K. One also obtains from the analysis a dipolar coupling constant $d=54.5$ kHz which is smaller than that measured for the free ${\mathrm{H}}_{2}$ molecule, where $d=57.7$ kHz. It is suggested that the departures both in $\ensuremath{\Gamma}$ and in $d$ from expectations are caused by the interactions between lattice vibrations and rotations, since solid ${\mathrm{H}}_{2}$ will behave more like a quantum crystal with large zero-point motion than like a classical rigid crystal.

Energy Transfer in Ruby

The transfer of energy from single chromium ions to closely coupled pairs of chromium ions in ruby has been investigated. Ruby samples whose concentrations ranged from 0.003 to 1.0% ${\mathrm{Cr}}_{2}$${\mathrm{O}}_{3}$ were prepared and in each crystal the intensity of single-ion fluorescence and of pair fluorescence was accurately measured. Radiative-decay measurements were also made in an attempt to unravel the dynamics of the transfer process. The transfer from single ions to pairs is shown to occur nonradiatively, and its efficiency is enhanced by a fast energy transfer between individual single ions. The possibility is explored that an electric quadrupole-quadrupole interaction is responsible for this transfer process.

7B5 - Energy transfer in ruby

The transfer of energy from single chromium ions to closely coupled pairs of chromium ions in ruby has been investigated. Ruby samples whose concentrations ranged from 0.003 to 1.0 percent Cr 2 O 3 were prepared and in each crystal the intensity of single-ion fluorescence and of pair fluorescence was accurately measured. Radiative decay measurements were also made in an attempt to unravel the dynamics of the transfer process. The transfer from single ions to pairs is shown to occur nonradiatively, and its efficiency is enhanced by a fast energy transfer between individual single ions. The possibility is explored that an electric quadrupole-quadrupole interaction is responsible for this transfer process.

Energy transfer in ruby

The transfer of energy from single chromium ions to closely coupled pairs of chromium ions in ruby has been investigated. Ruby samples whose concentrations ranged from 0.003 to 1.0% ${\mathrm{Cr}}_{2}$${\mathrm{O}}_{3}$ were prepared and in each crystal the intensity of single-ion fluorescence and of pair fluorescence was accurately measured. Radiative-decay measurements were also made in an attempt to unravel the dynamics of the transfer process. The transfer from single ions to pairs is shown to occur nonradiatively, and its efficiency is enhanced by a fast energy transfer between individual single ions. The possibility is explored that an electric quadrupole-quadrupole interaction is responsible for this transfer process.

Electric Quadrupole-Quadrupole Interaction in Cerium Ethyl Sulfate

Electron paramagnetic resonance (EPR) of cerium ethyl sulfate (CeES) below 2\ifmmode^\circ\else\textdegree\fi{}K gives evidence of a large nondipolar interaction between nearest-neighbor cerium ions. Writing the spin Hamiltonian for the interaction of two spins ${S}_{i}$ and ${S}_{j}$ as ${\mathcal{H}}_{\mathrm{ij}}=({\ensuremath{\alpha}}_{\mathrm{ij}}+{A}_{\mathrm{ij}}){S}_{\mathrm{iz}}{S}_{\mathrm{jz}}+\frac{1}{2}({\ensuremath{\beta}}_{\mathrm{ij}}+{B}_{\mathrm{ij}})({S}_{i+}{S}_{j\ensuremath{-}}+{S}_{i\ensuremath{-}}{S}_{j+}),$ where ${\ensuremath{\alpha}}_{\mathrm{ij}}$ and ${\ensuremath{\beta}}_{\mathrm{ij}}$ are the known contributions from dipole-dipole interaction, the experiments suggest that ${A}_{\mathrm{ij}}=0.105\ifmmode\pm\else\textpm\fi{}0.003$ ${\mathrm{cm}}^{\ensuremath{-}1}$ and ${B}_{\mathrm{ij}}=0.073\ifmmode\pm\else\textpm\fi{}0.003$ ${\mathrm{cm}}^{\ensuremath{-}1}$. Although there is no proof, there are four pieces of evidence which strongly support the hypothesis that the interaction is due to electric quadrupole-quadrupole (QQ) interaction. Firstly, the order of magnitude of ${A}_{\mathrm{ij}}$ and ${B}_{\mathrm{ij}}$ are reasonable. Secondly, QQ interaction affords an explanation of the differences between the temperature dependence of the EPR spectra of diluted and undiluted CeES. Thirdly, the spectra of rare-earth impurities in CeES, and fourthly, the spectra of pairs of interacting cerium ions in dilute specimens, are consistent with QQ interaction. Finally, it is shown that superexchange and exchange of virtual phonons probably contribute very little to the observed interaction.

Nondipolar Interaction Between Nearest-Neighbor Neodymium Ions in the Ethyl Sulfate

Measurements made on the EPR spectrum of a pair of interacting nearest-neighbor neodymium ions in lanthanum ethyl sulfate show that the interaction is predominantly dipolar, but that there is an additional term ${A}_{\mathrm{ij}}{S}_{\mathrm{iz}}{S}_{\mathrm{jz}}+\frac{1}{2}{B}_{\mathrm{ij}}({S}_{i+}{S}_{j\ensuremath{-}}+{S}_{i\ensuremath{-}}{S}_{j+})$, with ${A}_{\mathrm{ij}}=(+32\ifmmode\pm\else\textpm\fi{}6)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ ${\mathrm{cm}}^{\ensuremath{-}1}$ and ${B}_{\mathrm{ij}}=(\ensuremath{-}3\ifmmode\pm\else\textpm\fi{}3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ ${\mathrm{cm}}^{\ensuremath{-}1}$. A semiquantitative discussion is given of the possible origins of this nondipolar contribution including super-exchange, electric quadrupole-quadrupole, and virtual-phonon exchange interactions.

Thermal and magnetic properties of cerium ethyl sulphate between 0·02 and 1 °K

Adiabatic demagnetization experiments have been carried out on a spherical single crystal of cerium ethyl sulphate. The absolute temperature scale was determined down to 0·02 °K as a function of the entropy. Measurements were also made of the adiabatic susceptibility in the antiferromagnetic state which sets in at 0·05 °K and by extrapolation the magnetization at T = 0 °K could be estimated to a fair accuracy. The co-operative phenomena are discussed in terms of the theory of electric quadrupole-quadrupole interaction by Finkelstein.

Interatomic Electric Quadrupole-Quadrupole Coupling in Salts of Cerium

We have calculated the magnetic properties of a cerium salt in terms of the one-atom (crystalline field) model at temperatures greater than 1°K. Because the cerium ion is not in an S state, its electronic charge distribution has a quadrupole moment; we have determined the influence of interatomic electric quadrupole-quadrupole interactions on the magnetic moment and optical rotation at very low temperatures. In cerium ethylsulfate this coupling is antiferromagnetic with a characteristic temperature of τ=0.01〈r2〉4 degrees, where 〈r2〉½ is the rms radius of the 4f orbit in A. This interaction may be at least partly responsible for a low temperature anomaly found by Becquerel, de Haas, and van den Handel, as well as for the sharp increase in specific heat noticed during adiabatic demagnetization. In other salts τ may be of opposite sign (ferromagnetic case) and possibly much larger (∼1°K).