Transferred Hyperfine Interaction Research Articles

Hyperfine interactions in europium chalcogenides

The hyperfine interaction in europium chalcogenides is discussed theoretically. The f–s transfer mechanism explains the nearest neighbour transferred hyperfine interaction. Moreover the p-s and p-f transfer mechanisms explain the next nearest neighbour transferred hyperfine interaction. The estimated values and chalcogen dependences of these are in good agreement with the experiments.

Spin-state equilibria in theLCoO3system fromCo59NMR

Spin-state equilibria in the whole set of $L\mathrm{Co}{\mathrm{O}}_{3}$ (where $L$ stands for a rare-earth metal or Y) have been investigated with the use of $^{59}\mathrm{Co}$ NMR as a probe for the polycrystalline samples (except Ce) in the temperature interval 110-550 K and frequency range 3- 11.6 MHz. Besides confirming the coexistence of the high-spin---low-spin state in this temperature range, a quadrupolar interaction of \ensuremath{\sim}0.1 -0.5 MHz has been detected for the first time from $^{59}\mathrm{Co}$ NMR. The NMR line shape is found to depend strongly on the relative magnitude of the magnetic and quadrupolar interactions present. Analysis of the powder pattern reveals two basically different types of transferred hyperfine interaction between the lighter and heavier members of the rare-earth series. The first three members of the lighter rare-earth metals La, Pr (rhombohedral), and Nd (tetragonal), exhibit second-order quadrupolar interaction with a zero-asymmetry parameter at lower temperatures. Above a critical temperature ${T}_{S}$ (dependent on the size of the rare-earth ion), the quadrupolar interaction becomes temperature dependent and eventually gives rise to a first-order interaction thus indicating a possible second-order phase change. Sm and Eu (orthorhombic) exhibit also a second-order quadrupolar interaction with a nonzero asymmetry parameter (($\ensuremath{\eta}\ensuremath{\sim}0.47$)) at 300 K, while the orthorhombic second-half members (Dy,..., Lu and Y) exhibit first-order quadrupolar interaction at all temperatures. Normal paramagnetic behavior, i.e., a linear variation of ${K}_{\mathrm{iso}}$ with ${T}^{\ensuremath{-}1}$, has been observed in the heavier rare-earth cobaltites (Er,..., Lu and Y), whereas an anomalous variation has been observed in (La,..., Nd)Co${\mathrm{O}}_{3}$. Thus, ${K}_{\mathrm{iso}}$ increases with increasing temperature in PrCo${\mathrm{O}}_{3}$ and NdCo${\mathrm{O}}_{3}$. These observations corroborate the model of the spin-state equilibria in $L\mathrm{Co}{\mathrm{O}}_{3}$ originally proposed by Raccah and Goodenough. A high-spin---low-spin ratio, $r=1$, can be stabilized in the perovskite structure by a cooperative displacement of the oxygen atoms from the high-spin towards the low-spin cation. Where this ordering into high- and low-spin sublattices occurs at $r=1$, one can anticipate equivalent displacement of all near-neighbor oxygen atoms towards a low-spin cobalt ion. Thus the heavier $L\mathrm{Co}{\mathrm{O}}_{3}$ exhibits a small temperature-independent first-order quadrupolar interaction. Where $r<1$, the high- and low-spin states are disordered, giving rise to a temperature-dependent second-order quadrupolar interaction with an anomalous ${K}_{\mathrm{iso}}$ for the lighter $L\mathrm{Co}{\mathrm{O}}_{3}$.

Nuclear magnetic resonance of51V (I=7/2) in lanthanide vanadates: I. The paramagnetic shifts

Nuclear magnetic resonance of 51V (I=7/2) has been studied at temperatures down to 1.5K in single crystals of lanthanide vanadates LnVO4 where Ln3+ ranges from Pr3+, 4f2 to Yb3+, 4f13. The crystals are tetragonal, four molecules per unit cell, but all V5+ sites and all Ln3+ sites are magnetically equivalent. Measurements are made with applied fields parallel and perpendicular to the tetragonal axis, and fitted to the spin-Hamiltonian H=- gamma //h(cross)BzIz- gamma perpendicular to h(cross)(BxIx+ByIy)+P(Iz2-1/3I(I+1)). Values for the paramagnetic shifts are used to deduce the local fields at both the V5+ and Ln3+ sites. These fields are compared with the dipolar values, from which the magnitude of the transferred hyperfine interaction at the V5+ sites is deduced, together with estimates of the exchange interaction between the Ln3+ ions. The nuclear electric quadrupole interaction for 51V is discussed in paper II, and measurements in the antiferromagnetic phases of GdVO4 and DyVO4 in paper III.

The peculiarities of the transferred hyperfine interaction in CaF2:Ti2+, V3+and SrF2:Ti2+

The experimental data for the transferred hyperfine interaction (THFI) of Ti2+ ion in CaF2, SrF2 and V3+ ion in CaF2 are analysed in this work. The analytical expressions of THFI parameters for d2 configuration in the cubic crystalline field are obtained by a configurational interaction method. The agreement between calculation and experiment is good.

Direct NMR measurements of theF19-Mn transferred hyperfine interaction in Mn: PbF2

The $^{19}\mathrm{F}$-Mn transferred hyperfine interaction $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{A}$ in Mn: Pb${\mathrm{F}}_{2}$ has been determined by direct observation of the NMR of $^{19}\mathrm{F}$ nuclei nearest neighbor to the ${\mathrm{Mn}}^{2+}$ impurity. The angular dependence of the NMR of three inequivalent sites was studied for applied fields in the (110) plane and was fitted with the values ${A}_{s}=33.82$ MHz and ${A}_{p}=7.82$ MHz. The NMR was unobservable for $Tg2$ K, suggesting rapid electronic spin relaxation. For $Tl1.5$ K, NMR was observed in the eigenstates of the ${\mathrm{Mn}}^{2+}$ with ${S}_{z}=\frac{5}{2} \mathrm{and} \frac{3}{2}$; the linewidth $\ensuremath{\Delta}H$ became temperature independent and probably inhomogeneously broadened, with a pronounced angular variation.

ENDOR determination of covalency in K2NaAlF6:Fe3+, Cr3+

ENDOR measurements have been made on 19F ligand, 23Na and second-neighbour 19F nuclei surrounding the dilute paramagnetic sites in single crystals of K2NaAlF6:Fe3+, Cr3+. On the basis that the main contribution to the isotropic transferred hyperfine interactions with the 23Na and second-neighbour 19F nuclei is through overlap mechanisms with the ligand 2p orbitals, the data have been interpreted by comparison of the relative values of these quantities in the two systems. The result is that the unpaired spin fractions for the ligand 2p orbitals, fsigma and fpi , may be estimated independently and are found to be in general agreement with other methods, particularly in the verification of a significant negative fsigma for the (CeF6)3- complex. Little evidence of ligand polarisation is found in these systems.

General solution of the spin Hamiltonian for complex electron nuclear double resonance spectra

An electron nuclear double resonance investigation of CsCdF3:M (M = Mn2+, Ni2+, Cr3+, and Co2+) has been carried out to measure the transferred hyperfine interaction (thfi) between M and nearest neighbour fluorine ions. A general spin Hamiltonian which takes account of the multiplicity of the interacting nuclei, is solved for a general orientation of the magnetic field. An example is given to show that theory agrees well with experiment. Spin transfer parameters obtained are of similar order of magnitude for the same ions in similar host lattices.

Origin of 19F hyperfine interaction in Mn 2+ ion and ion pair

The theory of transferred hyperfine interaction at the F - site in the mixed σ - and π - bonding Mn 2+F - and Mn 2+F -Mn 2+ systems is developed from first principles. The transfer of electrons from the occupied p and s orbitals of F - ion to the empty d orbits on the Mn 2+ ion is considered and all the integrals of the kinetic energy and the Coulomb interactions are evaluated using the Hartree-Fock wave functions. The spin density for 1s, 2s, 2p σ and 2p π orbits at the F - ion is calculated as a function of interatomic distance and from the hyperfine field is calculated. It is found that there are large cross terms between 1s and 2s functions. The order of magnitude of the hyperfine field at the F - site can be predicted only if the covalency is taken into account. There occurs considerable change in the spin density in going from the single magnetic ion to the magnetic ion pair as a result of a change redistribution effect associated with the electron transfer in the pair.

NMR-analysis of indirect magnetic interactions in intermetallic rare-earth compounds

NMR Spectroscopy has given several pieces of information with regard to the indirect magnetic interactions in intermetallic compounds of gadolinium or europium. These comprise information on the contribution of non-s conduction electrons, on the predominance of short-range interactions, on the anisotropy of the transferred hyperfine interaction and on the range of d electron spin polarization.

EPR and ENDOR of Gd3+at cubic sites in PbF2

The crystal-field parameter b4 and transferred-hyperfine-interaction (THFI) parameters for ligands and second-neighbour 19F nuclei have been measured for Gd3+ at cubic sites in PbF2. So also has b4 for Eu2+ at cubic sites in CdF2. The values of b4 indicate, for Gd3+ that the ligand distance in PbF2 is less than in SrF2, and for Eu2+ that the ligand distance in CaF2 is less than in CdF2 in the opposite order to ligand distances in the undistorted host crystals. The ENDOR measurements of second neighbours show angular as well as radial displacements from the ionic positions in the undistorted host crystal. They also show that erroneous conclusions could be drawn from ENDOR measurements for only one direction of the external field, which may cast doubt on conclusions drawn from some earlier measurements of THFI parameters of second neighbours in fluorite crystals.

Lattice dynamics and ionic charge of VI 2

We present an Extended Shell Model calculation of the phonon dispersion curves in VI 2. The dynamical matrix is derived from interionic potentials including Coulomb monopole and dipole, van der Waals, nearest-neighbor and next-nearest-neighbor Born-Mayer repulsive interactions. The potential parameters are either known in literature or derived from lattice constants and cohesive energy. A suitable choice of only three adjustable parameters (net charge Z, shell charge and shell-core displacement) yields an excellent fit of the five optical frequencies and of the anion static dipole. The resulting ionic charge Z = 0.75 is very well consistent with the recent neutron data on transferred hyperfine interaction.

Theory of transferred hyperfine interaction

The theory of transferred hyperfine interaction at the ${\mathrm{F}}^{\ensuremath{-}}$ site in the $\ensuremath{\pi}$-electron systems ${\mathrm{V}}^{2+}$${\mathrm{F}}^{\ensuremath{-}}$ and ${\mathrm{V}}^{2+}$${\mathrm{F}}^{\ensuremath{-}}$${\mathrm{V}}^{2+}$ in cubic crystals is given. All the Hartree-Fock integrals of the kinetic energy and the Coulomb interactions are evaluated. It is found that the spin density at an ${\mathrm{F}}^{\ensuremath{-}}$ site is somewhat smaller in the pair ${\mathrm{V}}^{2+}$${\mathrm{F}}^{\ensuremath{-}}$${\mathrm{V}}^{2+}$ of magnetic atoms than in the ${\mathrm{V}}^{2+}$${\mathrm{F}}^{\ensuremath{-}}$ case, as a result of a charge redistribution effect associated with electron transfer from the occupied ${\mathrm{F}}^{\ensuremath{-}}({p}_{x})$ orbitals to empty ${d}_{\mathrm{xz}}$ functions on ${\mathrm{V}}^{2+}$ ion. The calculation is performed as a function of the interatomic distance which shows that in the neighborhood of ${\mathrm{V}}^{2+}$${\mathrm{F}}^{\ensuremath{-}}$ separation of \ensuremath{\sim} 2 \AA{}, the spin density at the ${\mathrm{F}}^{\ensuremath{-}}$ site varies approximately as ${R}^{\ensuremath{-}6}$ in the one ${\mathrm{V}}^{2+}$ case and ${R}^{\ensuremath{-}7}$ in the pair case.

ENDOR of trigonal sites of Yb3+in CeO2and ThO2

Trigonal sites of Yb3+ in CeO2 and ThO2, where an F- ion substitutes for an O2- ligand, have been characterised by 19F ENDOR. Transferred hyperfine interaction (THFI) parameters have been measured for the 19F ligand, and also in CeO2 for the 17O ligand on the C3 axis. A model which accounts for the magnitude and anisotropy of these interactions has been constructed based upon a molecular orbital theory: this requires large contributions to the THFI parameters from the electrostatic polarisation of both the ligand and the paramagnetic ion.

V51NMR studies of transferred hyperfine effects in the rare-earth vanadates

$^{51}\mathrm{V}$ ($I=\frac{7}{2}$) NMR investigation in the whole set of rare-earth vanadates ($R\mathrm{V}{\mathrm{O}}_{4}$) in the polycrystalline form at 300 K has revealed transferred hyperfine effects. It has been observed that the $^{51}\mathrm{V}$ NMR line shape strongly depends on the relative strength of the magnetic and quadrupolar parts of the transferred hyperfine interaction. On the basis of the powder pattern the $R\mathrm{V}{\mathrm{O}}_{4}$ system may be divided into two halves. The first-half members always exhibit a quadrupolar split central transition in the frequency range 2-12 MHz, whereas the members of the second half exhibit at higher frequencies an asymmetric line which, however, splits as the frequency is lowered. The hyperfine-interaction parameters, viz., the isotropic shift ${K}_{\mathrm{iso}}$, the anisotropic shift ${K}_{\mathrm{an}}$, and the quadrupolar coupling constant $\frac{{e}^{2}\mathrm{qQ}}{h}$ have been estimated from the central transition. The linear plot of ${K}_{\mathrm{iso}}$ against calculated $〈{S}_{z}〉$ values of rare-earth ions is indicative of the contact nature of ${K}_{\mathrm{iso}}$. Though ${K}_{\mathrm{an}}$ is dominated by the dipolar part, a small amount of anisotropic hyperfine part ${K}_{\mathrm{an}}^{\mathrm{hf}}$ could be separated from the experimental shift. Thus the results of both ${K}_{\mathrm{iso}}$ and ${K}_{\mathrm{an}}^{\mathrm{hf}}$ seem to uphold the presence of a small amount of covalent contribution (${f}_{s}\ensuremath{\sim}0.01%$ and ${f}_{s}\ensuremath{\sim}0.0001%$) in these basically ionic compounds. A comparison of the ligand NMR shifts in $3d$ and $4f$ systems (oxysalts) suggests that the mechanism of spin transfer within the oxyanion is not the same in these two series. Finally, the $\frac{{e}^{2}\mathrm{qQ}}{h}$ values (0.400-0.300 MHz) exhibit a gradual decrease along the isostructural series of $R\mathrm{V}{\mathrm{O}}_{4}$. The value of the coupling constant and its variation across the rare-earth series in different compounds have been qualitatively interpreted by taking into account the bonding effects.

Limited quenching of the holmium moment by the crystal field in the (Gd,Y)Ni2cubic Laves phase compounds

The hyperfine interaction of $^{165}\mathrm{Ho}$ in the cubic Laves phase compounds ${\mathrm{Ho}}_{0.01}{\mathrm{Gd}}_{1\ensuremath{-}x}{\mathrm{Y}}_{x}{\mathrm{Ni}}_{2}$ has been investigated by spin-echo NMR in the composition range $0<x<0.18$. In the end compound ($x=0$) a value of ${9.5}_{\mathrm{\ensuremath{\mu}}\mathit{B}}$ is obtained for the holmium moment which indicates a 5% quenching by the crystalline electric field. Further quenching takes place with substitution of yttrium for gadolinium. The magnetization anisotropy of these compounds is weak. The substitution of 1-at.% Ho for Gd suffices to rotate the easy axis of magnetization in Gd${\mathrm{Ni}}_{2}$ from the $〈110〉$ to the $〈100〉$ direction. This direction remains the easy magnetization direction in all compounds studied. The transferred hyperfine interaction is long range and analysis of data indicates considerable participation of the $d$ electrons in the hyperfine interaction in this series.

Ligand polarisation and transferred hyperfine interactions

Recent ENDOR measurements of transferred hyperfine interactions in the linear structure M3+-F--Cd2+, where M3+=Fe3+ or Cr3+ and the host lattice is CsCdF3, have given anomalous results when interpreted by standard ligand hyperfine structure theory. The data have therefore been reinterpreted allowing for polarisation of the F- ligand by the electric field from its neighbours. This is found to improve agreement between theory and experiment, especially if the fluoride ion is allowed to relax towards the M3+ ion, but some difficulties still remain.

Temperature and field independence of the fluorine and lithium NMR shift tensors in lithium rare-earth tetrafluorides

The fluorine and lithium NMR line shifts have been followed in temperature from 300 to 1.3 K and in fields up to 40 kG for LiTb${\mathrm{F}}_{4}$ and LiHo${\mathrm{F}}_{4}$. The ${\mathrm{Tb}}^{3+}$ and ${\mathrm{Ho}}^{3+}$ ionic moments cause these shifts. The Li shifts are dominated by dipole interactions, whereas the F shifts also have transferred hyperfine contributions of comparable sizes. The transferred hyperfine interactions turn out to be almost isotropic and exhibiting no temperature or field dependence. In LiHo${\mathrm{F}}_{4}$ the line shifts are detectable within the entire temperature range. In LiTb${\mathrm{F}}_{4}$ the fluorine and lithium lines broaden to such an extent that they disappear in a region from 10 to 60 K and from 15 to 40 K, respectively, probably due to a long relaxation time of the Tb ionic moment.

17O ENDOR of CeO2:Yb3+: Evidence for covalency

Transferred hyperfine interaction (THFI) parameters As and (Ap+Ad) have been measured by ENDOR for 17O2- ligands of Yb3+ in CeO2 in which about 10% of the oxygen has been replaced by 17O. A molecular orbital model is used to interpret the experimental parameters, and comparison is made with the analogous system CaF2:Yb3+. It appears that the simple molecular orbital model gives an internally consistent explanation of the THFI, orbital reduction factors and crystal field splittings in both materials, in terms of empirically deduced covalency parameters. These parameters for the two materials are related to one another in the way that theory predicts. But the magnitudes of the covalency parameters required for this interpretation are more than three times larger than those calculated ab initio.

Transferred hyperfine interaction between the rare-earth ions and the fluorine nuclei in rare-earth trifluorides

The isotropic and anisotropic transferred hyperfine interactions between F ions in the two chemically inequivalent sites and the rare-earth ions ($R$) have been derived from $^{19}\mathrm{F}$ NMR measurements in the temperature region 100-300 K on single crystals of Tb${\mathrm{F}}_{3}$ and Dy${\mathrm{F}}_{3}$. The isotropic interactions are found to be negative and constant in this temperature region and with the numerical values decreasing slightly from Tb${\mathrm{F}}_{3}$ to Dy${\mathrm{F}}_{3}$. The anisotropic interactions, when the point dipole contributions are subtracted, are found to be substantially smaller and about equal for the two materials. The crystals contain two symmetry related magnetic sublattices $A$ and $B$, contributing to the macroscopic susceptibility. The sublattice susceptibility has an off-diagonal component ${\ensuremath{\chi}}_{\mathrm{ac}}^{A}$ and ${\ensuremath{\chi}}_{\mathrm{ac}}^{B}=\ensuremath{-}{\ensuremath{\chi}}_{\mathrm{ac}}^{A}$ in the crystalline axes system. The orientations of the principal axes of the two subattice susceptibilities are found to vary only slightly with temperature. They are further assigned to definite $R'\mathrm{s}$ in the unit cell, which cannot be done from macroscopic magnetic measurements.

17O transferred hyperfine interactions in K 2CuCl 4.2H 2O and isomorphous compounds

Nuclear resonance techniques are used to determine the magnetic and electric quadrupolar interactions of the 17O nucleus in six isomorphous 3-dimensional b.c.c. Heisenberg ferromagnets with the K 2CuCl 4.2H 2O structure. From a careful analysis of the results the occurrence of local, magnetostrictive, distortions is evident in both the ferromagnetic and paramagnetic state. From the magnetic hyperfine interaction spin densities in the oxygen 2s and 2p orbitals are calculated. Typical values are f s = 1.5% and f p = 5.3%, with only a weak variation over the series. These spin densities are slightly larger in the deuterated analogons.