Vleck Theory Research Articles

Revisiting the Van Vleck second moment for characterizing molecular motion in organic solids.

Van Vleck's classic theory of the second moment of lineshapes in 1H nuclear magnetic resonance (NMR) is reworked in a form that allows the effect of rapid molecular motion on second moments to be calculated in a semi-analytical fashion. This is much more efficient than existing approaches and also extends previous analyses of (non-dynamic) dipolar networks in terms of site-specific root-sum-square dipolar couplings. The non-local nature of the second moment means that it can discriminate between overall motions that are difficult to discriminate using alternative approaches, such as measurements of NMR relaxation. The value of reviving second moment studies is illustrated on the plastic solids diamantane and triamantane. In the case of triamantane, straightforward measurements of 1H lineshapes on milligram samples show that the molecules in the higher temperature phase undergo multi-axis jumps, information that is not accessible either to diffraction studies or to alternative NMR approaches. The efficiency of the computational methods means that the second moments can be calculated using a readily extensible and open-source Python code.

Van Vleck paramagnetism of europium oxyhydroxide

Europium oxyhydroxide crystals were synthesized by the flux method. The as-grown crystals were transparent and had a plate-like shape with natural flat surfaces. The powder XRD data were refined by assuming a monoclinic structure of the space group P21/m and lattice parameters of a=0.4346 nm, b=0.3744 nm, c=0.6107 nm, and β=108.62°. The magnetic susceptibility of the EuOOH crystals exhibited typical Van Vleck temperature-independent paramagnetism below 120 K. The calculated susceptibility, based on Van Vleck's theory, agreed with the experimental data to some extent, with the coupling constant λ=458±10 K. The experimental results were in close agreement with the results calculated using a modified formula with λ=505±2 K and a constant term C=4.6×10−4 emu/(mol·Oe).

Studies in perturbation theory. XIV. Treatment of constants of motion, degeneracies and symmetry properties by means of multidimensional partitioning

The multidimensional partitioning technique is reviewed, with particular emphasis on its formal properties. The treatment of constants of motion by this method coincides with a treatment given previously, involving a modified resolvent in the ordinary approach. On the other hand the present method, upon expansion, coincides with Van Vleck's perturbation theory for quasidegenerate states. Bounds and estimates of the remainder related to Padee approximants obtained via inner projections are discussed. The construction of effective-hamiltonians is considered, in particular the energy-independent non self-adjoint ones.

Harry George Drickamer (1918–2002): Electronic Phenomena in Condensed Matter at High Pressure

Harry George Drickamer (1918–2002): Electronic Phenomena in Condensed Matter at High Pressure

A local diabatic representation of non-Born–Oppenheimer dynamics

We propose a new canonical procedure for investigating non-Born–Oppenheimer dynamics. This procedure is based on Van Vleck's theory and expressed in the normal coordinates of one of the diabatically coupled electronic surfaces. Up to intermediate energies, the successive unitary transformations convert the smooth, non-resonant part of the energy shifts due to the diabatic coupling into anharmonicities and off-diagonal couplings inside each surface. As a result, in this energy range, the two transformed electronic surfaces remain fairly decoupled. We also show that, because of the reduced coupling range, the size of the matrix needed to calculate the exact energy levels is substantially reduced, which is promising for future practical applications.

A new canonical perturbation procedure for studying nonadiabatic dynamics

We propose a new canonical perturbation procedure, based on Van Vleck's theory, for investigating nonadiabatic (i.e., non Born–Oppenheimer) dynamics. The basic idea is to let the unitary transformations depend on the matrix representations of angular momentum operators. The new procedure is applied to a simple model with two 2-dimensional diabatic electronic surfaces coupled by a λq term, which to some extent mimicks the bending and antisymmetric stretching degrees of freedom of NO 2 in the ground and first excited electronic states. It is shown that the anharmonicities induced in the lowest surface by the coupling to the excited one are very precisely obtained from the proposed procedure.

Low-temperature magnetic properties of SmB 6

We have performed measurements of the magnetic susceptibility of three SmB 6 single crystals with various purities in the temperature range between 300 and 2 K. In the high-temperature region the observed data follow the Curie–Weiss-like dependence indicating a local-moment behavior. Below 10 K, where a temperature-independent behavior due to Van Vleck's theory is expected, all samples exhibit an increase of magnetization which can be accounted for by a small amount of bare Sm 3+ ions, magnetic 4f 55d 1 states or by magnetic rare-earth impurities.

Defects in diamond thin films.

Defects in diamond films, produced by the filament-assisted chemical-vapor deposition of methane and hydrogen as a function of total gas pressure and substrate temperature, were investigated by electron-paramagnetic-resonance measurements. We found an isotropic g value (2.0028\ifmmode\pm\else\textpm\fi{}0.0002) independent of growth conditions. The peak-to-peak linewidth increases with pressure from 3.5 to 5 G and the spin density decreases with increasing pressure and temperature and varies between ${10}^{19}$ and ${10}^{17}$ spins/${\mathrm{cm}}^{3}$. The line shape was found to be the superposition of two components, a narrower Lorentzian and a broader Gaussian, suggesting exchange narrowing and a nonuniform distribution of paramagnetic defects. The line shape was analyzed using Van Vleck's theory of moments and a model regarding the distribution of the dominant paramagnetic center in diamond films was proposed and compared with structural studies on the same films. The temperature dependence of the spin-lattice relaxation rate, evaluated by the saturation method, was also investigated.

Single-ion and pair EPR lineshape in diluted magnetic systems

An application of Van Vleck's theory to single-ion and pair EPR spectra in diluted magnetic systems, resulting in an expression suitable for computer analysis, is presented. The linewidth temperature dependence for single and polycrystalline samples is discussed.

Das ESR-Linienprofil antiferromagnetischer Verbindungen und die Abweichungen von der Lorentz-Form

The ESR-absorption of antiferromagnetic compounds is usually described by a Lorentzian profile given by (1 + z2 )-1 with z = (H - H0)/ΔH. To obtain further improvements an additional term of 4th order is introduced. This modified profile given by (1 + z2 + αz4)-1 with α > 0 changes the properties of several ESR parameters. First of all there is a finite second moment which is given by α-1/4 · ΔH. For small values of α the integrated intensity will be reduced by a1 / 2 while the differentiated line-width ΔHpp increases linearly with x. The application of this modified Lorentzian profile to the ESR spectra of antiferromagnetic Cr2O3 and MnF2 results in an improved fit. In both cases, the parameter α took on values between (20-100) · 10-4. For Cr2O3 there is an increase of α for rising temperature in the range from 320 K to 520 K. The second moment of Cr2O3 at T = 330 K was found to be 2100 G. For MnF2 a value of 1225 G was derived which is in rough accordance with results of Van Vleck's theory of line broadening.

Dipole–Dipole Interaction and Short‐Range Order in Amorphous NiP, NiCuP, and NiPB Alloys

AbstractThe field‐independent 31P NMR linewidth, δHo, is measured in nonmagnetic amorphous Ni‐based alloys. In addition, the second moment contribution M originating from direct nuclear dipole–dipole interaction is calculated using Van Vleck's theory based on a computer generated DRPHS amorphous model cluster. The calculated second moment M and the experimental second moment M obtained from δHo by Gaussian line shape approximation (i.e., M = (δHo)2/4) agree fairly well for a (Ni0.27Cu0.73)82P18 metallic glass. In the case of amorphous NiP and NiPB alloys M exceeds M by a factor of two or three. This excess second moment seems to indicate the presence of some indirect indirect interactions between nuclear spins.

Antiferromagnetism and paramagnetism of some intermetallic compounds of rare-earth metals with silver

An investigation was made of the temperature dependence of the magnetic susceptibility of intermetallic compounds of Gd, Tb, Dy, and Ho with silver having CsC1 structure. It was established that in these compounds there exists an antiferromagnetic ordering with ΘN = 135°K for GdAg and ΘN = 105°K for TbAg. The paramagnetic Curie temperature Θp has a negative value for all compounds. For the compound SmAg, the temperature dependence of the susceptibility is complicated. The results are explained on the basis of the theory of the Ruderman-Kittel-Kasuya-Yosida interaction and Van Vleck's theory of paramagnetism.

The magnetic properties of rare earth dodecaborides

The temperature dependence of the magnetic susceptibility of the dodecaborides YB 12, TbB 12, DyB 12, HoB 12, ErB 12, TmB 12, YbB 12 and LuB 12 over the temperature range 90–1200 K was studied. The experimental data were compared with the theory based on 4f localized electrons and Van Vleck's theory of paramagnetism. An explanation using the RudermanKittel-Kasuya-Yoshida model is also given; this is based on the interaction between the rare earth metal ions in high borides which have a boron framework structure.

Muon location and mobility in high-purity metals

Positive muons are expected to be easily trapped by imperfections including impurities in metals (Seeger 1975). Therefore it is essential to study muon diffusion and localization on well-characterized high-purity materials. The sensitivity to impurities has been confirmed by recent ~SR studies on Nb (Birnbaum et al. 1978, Borghini et al. 1978). In this note we report results of DSR experiments on high-purity monocrystals of beryllium, tantalum, and niobium. Starting from high-purity material, the Be target was vacuum melted and zone-refined i0 times resulting in a residual resistivity ratio F ~ R2g3K/R4.2K = 400, corresponding to a purity of 99.993 wt% (Aldinger 197~).0f the remaining 70 wt.ppm impurities, the principal constituent was iron. The preparation of the Ta (F = 5000, interstitial C+O+N<5 at 9 and Nb (F = 3000, N<2 at.ppm, 0 < 1 at.ppm, Ta ~ 5 at.ppm) targets is described elsewhere (Gladisch et al. 1978). The experimental setup used in our measurements is similar to that of Dorenburg et al. (1978)._The ~SR data were analyzed by computing the mean polarization P for each precession period of the muon spin and assigning it to the time t at the centre of the period. In order to obtain the depolarization rate A e ~ t~l(~(t e) Z P(O)/e),) suitable theoretical functions were adapted to the experimental ~(t in the cases of Be and Ta. In the case of Nb, however, the rapid decrease of polarization allowed t e to be found by mere interpolation. The temperature dependence of A e in Be was measured in 24.6 mT external magnetic field transverse to the muon polarization and at angles of O, 50,and 90 degrees with respect to the c-axis of the hcp lattice structure. No significant orientation dependence of A e was found at any of the investigated temperatures. Therefore, in Fig.1 only averaged values are shown, except for temperatures around lOOK, where the maximum A e values are found. Here the results for individual orientations are given separately. They are also presented in Table I, together with results of calculations using van Vleck's theory under the assumption that muons are located either on tetrahedral or octahedral interstitial sites in an unrelaxed Be lattice 9 For completeness, we also include polycrystalline averages of the theoretical values for these types of interstitial sites. These results are in accordance with the assumption that quadrupole coupling (Hartmann 1977) suppresses the orientation dependence of A e at lOOK in a similar way as in Cu, where comparably weak orientation and field dependences were found up to ~50 mT (Camani et al. 1977). The magnetic field strength B_ above which dipolar coupling (nuclear spln I, gyromagnetlc ratlo YI) starts to determine the orientation dependence of A e is given by

Λ-type doubling in the molecules14NH+,15NH+, and14ND+

Ab initio calculations of the Λ-type doubling in the X 2II states of 14NH+, 15NH+, and 14ND+ are reported for rotational levels with J = ½ to . It is found that to account successfully for the Λ-type doubling in these levels Van Vleck's theory of Λ-type doubling in 2II states has to be extended to include the effect of interactions between the X 2II state and a low-lying 4Ω- state. The interaction between the X 2II state and the a 4Ω- state was treated using an exact matrix diagonalization, and the interactions between the X 2II state and the A 2Ω- and C 2Ω+ states, which are the only interactions considered in Van Vleck's theory, were treated using second-order perturbation theory. Excellent agreement was achieved with existing experimental values. The X 2II-a 4Ω- interaction was found to make an important contribution to the calculated values of the Λ-type doubling. The calculated values of the Λ-type doubling should aid the search for the interstellar radio spectrum of NH+.

Average magnetic susceptibility of rare earth sesquisulfides

Measurements of the average magnetic susceptibility of Nd 2S 3, Gd 2S 3 and Dy 2S 3 are reported over the temperature range 4–300 K. Paramagnetic Gd 2S 3 becomes ferromagnetic below about 30 K. Magnetic ordering in Nd 2S 3 appears to take place near 60 K. Dy 2S 3 appears to remain paramagnetic to the lowest temperatures investigated. Reasonable agreement has been obtained between a calculation using Van Vleck's theory and the data obtained from these Faraday experiments.

Notizen: Low Temperature Magnetic Susceptibility of Sm2(WO4)3

Abstract The magnetic susceptibility of powder samples of Sm2(WO4)3 has been measured in the temperature range 4.2 to 300 K. At low temperatures the measured values disagree with those calculated for Sm3+-ions using Van Vleck's theory. The high values below 100 K are assigned to magnetic exchange and dipol interactions. There might be magnetic ordering below 4.2 K. The effects of the crystal field and impurities have been shown to be unimportant.

Antiferromagnetic Properties of Light Rare Earth Monochalcogenides

Magnetic investigation of monochalcogenides MeX where Me = Ce, Pr, or Nd and X = S, Se, or Te at 4°–1300°K was undertaken. Van Vleck's theory was used for describing experimental χ(T) dependences at T&amp;gt;500°K. It has been observed that monochalcogendies formed by the ions with an odd number of electrons exhibit an antiferromagnetic ordering near ∼10°K in contrast to the monochalcogenides formed by the ions with an even number of 4f electrons (Pr3+, Sm2+) except PrS. An attempt to evaluate the parameters of the exchange interaction using molecular field approximation was made. In order to explain the χ(T) dependences obtained at T &amp;lt; 100°K the approximation which included crystal-field and exchange effects simultaneously is required.

Theory of Exchange-Narrowed Magnetic-Resonance Linewidth at Finite Temperature

General formulas are derived for the width of an exchange-narrowed magnetic-resonance absorption line at a finite temperature where the Zeeman and/or exchange energies can be comparable to the thermal energy $\mathrm{kT}$. The perturbation which gives rise to line broadening also is allowed to be comparable to $\mathrm{kT}$ in our treatment, and this marks a departure from previous theories of exchange narrowing. The relaxation-function approach of Kubo and Tomita is used, and it is assumed, as in the infinite-temperature limit, that the appropriate correlation times are sufficiently short. We show that the correlation function $〈{M}_{x}(t){M}_{x}(0)〉$ of the $x$ component of the magnetization has an apparent relaxation rate which is given by an obvious extension of the Van Vleck moments formula to finite temperature. This relation holds for an arbitrary ratio of perturbation energy to $\mathrm{kT}$. However, it appears that only if the perturbation energy is much less than $\mathrm{kT}$ can this relaxation function be simply related to ${\overline{M}}_{x}(t)$, which describes relaxation of the macroscopic magnetization. If this is the case, then an unambiguous result for the linewidth is obtained which is clearly related to Van Vleck's infinite-temperature theory.

Anisotropy of the NMR in Copper Sheets (II)

AbstractIn NMR measurements on vacuum annealed copper sheets, for various orientations with respect to the magnetic field, it has been shown previously [1] that the anisotropy of the second moment can be interpreted by Van Vleck's theory assuming a (100) [001]‐type cubic recrystallization texture. The present paper extends the investigation to several other orientations. The effect of non‐uniformly oriented crystallites on the spectrum parameters is also studied. It is found that the scatter in crystallite orientation can be determined if the additional broadening is assumed to be isotropic.