Symmetric Electric Field Gradient Research Articles

Strong magnetoelectric coupling at an atomic nonmagnetic electromagnetic probe in bismuth ferrite

Isolated nonmagnetic substitutional defect ions experience huge coupled electric magnetic interaction in the single-phase multiferroic ${\mathrm{BiFeO}}_{3}$. In the ferroelectric state above the magnetic N\'eel temperature ${T}_{N}$, the electric environment generates a single symmetric electric field gradient (EFG) parallel to the electric polarization direction. Below ${T}_{N}$, a distinct magnetic interaction arises, monitored by the probe nuclei via their magnetic moment. Two magnetic environments arise, given by the relative angle of the local magnetic moment within its easy magnetic plane with respect to the EFG orientation. The angle between field gradient orientation and magnetic field direction is the most stable fitting parameter. The magnetic interaction concomitantly increases the EFG dramatically which reflects an outstandingly large local magnetoelectric coupling. In the set of best fits, two different electric environments form concurrently with two distinctly different local magnetic fields. The magnetic ordering in ${\mathrm{BiFeO}}_{3}$ thus completely distorts the electric environment of the nonmagnetic probe nucleus. The implications for the local effect of dopants in ${\mathrm{BiFeO}}_{3}$ are discussed. A third probe environment arising independent of temperature is identified and associated with an iron vacancy.

On spin-lattice relaxation of nuclear quadrupole resonance in polycrystalline solids

The analysis of spin–lattice relaxation in nuclear quadrupole resonance (NQR) of spin-52 reported by Okubo and Igarashi (Z. Naturforsch. A. 56 (2001) 777) is extended to take account of the distribution of the initial non-equilibrium populations created by a resonant radio-frequency pulse in powder. The proposed theory is applicable to axially symmetric electric field gradient tensor and is examined for spin–lattice relaxation of 127I NQR in polycrystalline pyridine iodine monochloride measured at 469 MHz at 77 K.

Mutual Orientation of Electric Intracrystalline and Magnetic Fields in Iron Borate Single Crystals

X-ray structural analysis, Mössbauer spectroscopy, and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ab initio</i> calculations are used to study the structural properties and refine the orientation of intracrystalline fields in FeBO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> crystals in the region of the magnetic phase transition. It is found that in the temperature range of 293–403 K, the trigonal lattice parameters increase monotonically. Analysis of the electron density distribution maps does not show visible local disordering over the entire investigated temperature range. It is found that iron borate has an axially symmetric electric field gradient (EFG) whose main axis is directed along [001]. This orientation is maintained above and below the Néel point. In the magnetically ordered state of the crystal, the main axis of the EFG is orthogonal to the direction of the hyperfine magnetic field at iron nuclei. The results obtained will be used to develop a theoretical model of the formation of hyperfine structure in iron borate, which is important for applications of such crystals in next-generation synchrotron technologies.

Uncovering Halogen Mixing and Octahedral Dynamics in Cs2SnX6 by Multinuclear Magnetic Resonance Spectroscopy

Cs2SnX6 (X = Cl, Br, and I) compounds have emerged as promising lead-free and ambient-stable materials for photovoltaic and optoelectronic applications. To advance these promising materials, it is crucial to determine the correlations between physical properties and their local structure and dynamics. Solid-state NMR spectroscopy of multiple NMR-active nuclei (133Cs, 119Sn, and 35Cl) in these cesium tin(IV) halides has been used to reveal the atomic structure, which plays a key role in the materials’ optical properties. The 119Sn NMR chemical shifts span approximately 4000 ppm, and the 119Sn spin-lattice relaxation times span 3 orders of magnitude when the halogen goes from chlorine to iodine in these diamagnetic compounds. Moreover, ultrawideline 35Cl NMR spectroscopy of Cs2SnCl6 indicates an axially symmetric chlorine electric field gradient tensor with a large quadrupolar coupling constant of ca. 32 MHz, suggesting the presence of a chlorine moiety that is directly attached to Sn(IV) ions. Variable-temperature 119Sn spin-lattice relaxation time measurements support the presence of dynamics of octahedral SnI6 units in Cs2SnI6. We further show that complete mixed-halide solid solutions of Cs2SnClxBr6–x and Cs2SnBrxI6–x (0 ≤ x ≤ 6) form at any halogen compositional ratio. 119Sn and 133Cs NMR spectroscopy resolve the unique local SnClnBr6–n and SnBrnI6–n (n = 0–6) octahedral and CsBrmI12–m (m = 0–12) cuboctahedral environments in the mixed-halide samples. The experimentally observed 119Sn NMR results are consistent with magnetic shielding parameters obtained by density functional theory computations that were obtained to model the random halogen distribution in mixed-halide analogues. Finally, we demonstrate the difference in the local structures and the optical absorption properties of Cs2SnI6 samples prepared by solvent-assisted and solvent-free synthesis routes.

Orientation of the electric field gradient and ellipticity of the magnetic cycloid in multiferroic BiFeO3

The paper deals with the hyperfine interactions observed on the 57Fe nucleus in multiferroic BiFeO3 by means of the 14.41-keV resonant transition in 57Fe and for transmission geometry applied to the random powder sample. Spectra were obtained at 80 K, 190 K and at room temperature. It was found that iron occurs in the high-spin trivalent state. Hyperfine magnetic field follows distribution due to the elliptic-like distortion of the magnetic cycloid. The long axis of the ellipse is oriented along 〈1 1 1〉 direction of the rhombohedral unit cell. The hyperfine magnetic field in this direction is about 1.013 of the field in the perpendicular direction at room temperature. This ratio diminishes to 1.010 at 80 K. Axially symmetric electric field gradient (EFG) on the iron atoms has the principal axis oriented in the same direction and the main component of the EFG is positive. Our results are consistent with the finding that iron magnetic moments are confined to the crystal plane.

14N Quadrupole Resonance line broadening due to the earth magnetic field, occuring only in the case of an axially symmetric electric field gradient tensor

As demonstrated before, the application of a weak static B0 magnetic field (less than 10G) may produce definite effects on the 14N Quadrupole Resonance line when the electric field gradient tensor at the nitrogen nucleus level is of axial symmetry. Here, we address more precisely the problem of the relative orientation of the two magnetic fields (the static field and the radio-frequency field of the pure NQR experiment). For a field of 6G, the evolution of the signal intensity, as a function of this relative orientation, is in very good agreement with the theoretical predictions. There is in particular an intensity loss by a factor of three when going from the parallel configuration to the perpendicular configuration. By contrast, when dealing with a very weak magnetic field (as the earth field, around 0.5G), this effect drops to ca. 1.5 in the case Hexamethylenetetramine (HMT).This is explained by the fact that the Zeeman shift (due to the very weak magnetic field) becomes comparable to the natural line-width. The latter can therefore be determined by accounting for this competition. Still in the case of HMT, the estimated natural line-width is half the observed line-width. The extra broadening is thus attributed to earth magnetic field. The latter constitutes therefore the main cause of the difference between the natural transverse relaxation time (T2) and the transverse relaxation time derived from the observed line-width (T2⁎).

Magnetism of BaFe2Se3 studied by Mössbauer spectroscopy

The compound BaFe2Se3 (Pnma) has been synthesized in the form of single crystals with the average composition Ba0.992Fe1.998Se3. The Mössbauer spectroscopy used for investigation of the valence states of Fe in this compound at temperature ranging from 4.2K till room temperature revealed the occurrence of mixed-valence state for iron. The spectrum is characterized by sharply defined electric quadrupole doublet above magnetic ordering at about 250K. For the magnetically ordered state one sees four iron sites at least and each of them is described by separate axially symmetric electric field gradient tensor with the principal component making some angle with the hyperfine magnetic field. They form two groups occurring in equal abundances. It is likely that each group belongs to separate spin ladder with various tilts of the FeSe4 tetrahedral units along the ladder. Two impurity phases are found, i.e., superconducting FeSe and some other unidentified iron-bearing phase being magnetically disordered above 80K. Powder form of BaFe2Se3 is unstable in contact with the air and decomposes slowly to this unidentified phase exhibiting almost the same quadrupole doublet as BaFe2Se3 above magnetic transition temperature.

β-detected nuclear quadrupole resonance and relaxation of 8Li+ in sapphire

We report detailed behaviour of low energy 8Li implanted near the surface of α- Al2O3 single crystal, as revealed by beta-detected NQR of 8Li. We find that the implanted 8Li occupies at least two sites with non-cubic symmetry in the Al2O3 lattice. In both sites the 8Li experiences axially symmetric electric field gradient, with the main principal axis along the c-crystallographic direction. The temperature and field dependence of the spin lattice relaxation of 8Li in α-Al2O3, indicate that the 8Li diffusion is negligible on the scale of its lifetime, 1.21 s.

Effect of a weak static magnetic field on nitrogen-14 quadrupole resonance in the case of an axially symmetric electric field gradient tensor

The application of a weak static B0 magnetic field (less than 1mT) may produce a well-defined splitting of the 14N Quadrupole Resonance line when the electric field gradient tensor at the nitrogen nucleus level is of axial symmetry. It is theoretically shown and experimentally confirmed that the actual splitting (when it exists) as well as the line-shape and the signal intensity depends on three factors: (i) the amplitude of B0, (ii) the amplitude and pulse duration of the radio-frequency field, B1, used for detecting the NQR signal, and (iii) the relative orientation of B0 and B1. For instance, when B0 is parallel to B1 and regardless of the B0 value, the signal intensity is three times larger than when B0 is perpendicular to B1. This point is of some importance in practice since NQR measurements are almost always performed in the earth field. Moreover, in the course of this study, it has been recognized that important pieces of information regarding line-shape are contained in data points at the beginning of the free induction decay (fid) which, in practice, are eliminated for avoiding spurious signals due to probe ringing. It has been found that these data points can generally be retrieved by linear prediction (LP) procedures. As a further LP benefit, the signal intensity loss (by about a factor of three) is regained.

A 57Fe Mössbauer spectroscopic study of sogdianite: an example of a symmetric electric field gradient around Fe3+

Sogdianite, a double-ring silicate of composition $$ ( {\text{Zr}}_{0. 7 6} {\text{Ti}}_{0. 3 8}^{4 + } {\text{Fe}}_{0. 7 3}^{3 + } {\text{Al}}_{0.13} )_{\Upsigma = 2} \left( {\square_{ 1. 1 5} {\text{Na}}_{0. 8 5} } \right)_{\Upsigma = 2} {\text{K}}[{\text{Li}}_{ 3} {\text{Si}}_{ 1 2} {\text{O}}_{ 30} ] $$ from Dara-i-Pioz, Tadjikistan, was studied by the combined application of 57Fe Mossbauer spectroscopy and electronic structure calculations. The Mossbauer spectrum confirms published microprobe and X-ray single-crystal diffraction results that indicate that Fe3+ is located at the octahedral A-site and that no Fe2+ is present. Both the measured and calculated quadrupole splitting, ΔE Q, for Fe3+ are virtually 0 mm s−1. Such a value is unusually small for a silicate and it is the same as the ΔE Q value for Fe3+ in structurally related sugilite. This result is traced back to the nearly regular octahedral coordination geometry corresponding to a very symmetric electric field gradient around Fe3+. A crystal chemical interpretation for the regular octahedral geometry and the resulting low ΔE Q value for Fe3+ in the Mossbauer spectrum of sogdianite is that structural strain is largely “taken up” by weak Li–O bonds permitting highly distorted LiO4 tetrahedra. Weak Li–O bonding allows the edge-shared more strongly bonded Fe3+O6 octahedra to remain regular in geometry. This may be a typical property for all double-ring silicates with tetrahedrally coordinated Li.

Definitive solid-state 185/187Re NMR spectral evidence for and analysis of the origin of high-order quadrupole-induced effects for I = 5/2

Rhenium-185/187 solid-state nuclear magnetic resonance (SSNMR) experiments using NaReO(4) and NH(4)ReO(4) powders provide unambiguous evidence for the existence of high-order quadrupole-induced effects (HOQIE) in SSNMR spectra. Fine structure, not predicted by second-order perturbation theory, has been observed in the (185/187)Re SSNMR spectrum of NaReO(4) at 11.75 T, where the ratio of the Larmor frequency (ν(0)) to the quadrupole frequency (ν(Q)) is ∼2.6. This is the first experimental observation that under static conditions, HOQIE can directly manifest in SSNMR powder patterns as additional fine structure. Using NMR simulation software which includes the quadrupole interaction (QI) exactly, extremely large (185/187)Re nuclear quadrupole coupling constants (C(Q)) are accurately determined. QI parameters are confirmed independently using solid-state (185/187)Re nuclear quadrupole resonance (NQR). We explain the spectral origin of the HOQIE and provide general guidelines that may be used to assess when HOQIE may impact the interpretation of the SSNMR powder pattern of any spin-5/2 nucleus in a large, axially symmetric electric field gradient (EFG). We also quantify the errors incurred when modeling SSNMR spectra for any spin-5/2 nucleus within an axial EFG using second-order perturbation theory. Lastly, we measure rhenium chemical shifts in the solid state for the first time.

A 57Fe MOSSBAUER SPECTROSCOPIC STUDY OF SUGILITE, KNa2(Fe3+,Mn3+,Al)2Li3Si12O30

Sugilite, ideally KNa(2)(Fe(3+),Mn(3+),Al)(2)Li(3)Si(12)O(30), from the Wessels mine, Kalahari, South Africa, was studied using (57)Fe Mossbauer spectroscopy. The spectra confirm published electron-microprobe data and X-ray single-crystal results, which indicate that Fe(3+) is ordered at the A octahedral site. The magnitude of the quadrupole splitting, DEQ for Fe(3+) at both 84 K and room temperature is 0.00 mm/s. This value is very low for a silicate; reported DEQ values for octahedrally coordinated Fe(3+) are generally greater than 0.20 mm/s. Octahedron distortion, calculated from published X-ray-diffraction data, gives an octahedron-angle variance of 7 and a mean elongation of the octahedron of 1.002. This indicates nearly regular octahedral geometry, and hence a symmetric electric-field gradient around Fe(3+). A crystal-chemical interpretation for the regular octahedral geometry and the resulting low DEQ value for Fe(3+) in the Mossbauer spectrum of sugilite is that structural strain is largely taken up by weak Li-O bonds. They permit highly distorted LiO(4) tetrahedra, whose variance in the O-Li-O angle, 502, and mean elongation of the tetrahedron, 1.148, are among the largest observed values for inorganic crystal structures. Weak Li-O bonds allow the edge-shared, more strongly bonded Fe(3+)O(6) octahedra to remain regular in geometry.

PAC investigations of radiation damage annealing in 111In implanted ZnO

The structural and electronic environment about implanted radioactive 111In(→ 111Cd) probe atoms as a function of annealing temperature in a single crystal of ZnO(0 0 0 1) has been monitored on an atomic scale using perturbed angular correlation technique, a nuclear hyperfine method. This technique is based upon the hyperfine interaction of the nuclear electric quadrupole moment or magnetic moment of the probes, respectively, with the electric field gradient or magnetic hyperfine field arising from the extra-nuclear electronic charges and spin distributions. The probe atoms 111In were recoil-implanted at room temperature following heavy-ion nuclear reactions. The electric quadrupole interaction was measured at room temperature for as-implanted and annealed samples. The thermal annealing in ambient nitrogen up to 1000 °C showed a progressive reduction of disorder around the probe atom as evidenced via continual decrease in width of the distribution of quadrupole interaction frequencies. Present measurements suggested that annealing at 800 °C for 30 min in flowing nitrogen is enough to produce an optimum recovery of crystallinity. After annealing of radiation damage at 1000 °C we observed an axially symmetric electric field gradient which is characterized by the unique quadrupole interaction frequency of 30.6(3) MHz and a frequency distribution of width nearly zero. The observed electric field gradient was attributed to substitutional incorporation of probe atoms at cation-sites of ZnO. In contrast to annealing in ambient nitrogen at 1000 °C, air annealing of 111In implanted ZnO samples revealed change in local stoichiometry about probe atoms which is attributed to the internal oxidation of the indium probes. The measured electric field gradient and asymmetry parameter at cation-sites of ZnO have been compared with theoretical calculations using a simple point charge model.

Nuclear quadrupole interaction atS44cin the anatase and rutile modifications ofTiO2: Time-differential perturbed-angular-correlation measurements andab initiocalculations

The nuclear quadrupole interaction of the first excited $I=1$ state of $^{44}\text{S}\text{c}$ in the anatase and rutile modifications of bulk ${\text{TiO}}_{2}$ was determined by time-differential perturbed-angular correlation of $\ensuremath{\gamma}$ rays. New ${\text{LaBr}}_{3}(\text{Ce})$ scintillators with excellent energy resolution allowed us to separate the 68 and 78 keV lines of the $\ensuremath{\gamma}\text{\ensuremath{-}}\ensuremath{\gamma}$ cascade. For anatase, an almost axially symmetric electric field gradient (EFG) with an asymmetry parameter of $\ensuremath{\eta}=0.10(1)$ and a nuclear quadrupole frequency of ${\ensuremath{\omega}}_{Q}=9.29(3)\text{ }\text{Mrad}/\text{s}$ was obtained. For rutile, an almost antiaxial EFG with $\ensuremath{\eta}=0.94(1)$ and ${\ensuremath{\omega}}_{Q}=16.14(6)\text{ }\text{Mrad}/\text{s}$ was obtained, which contradicts literature values. Ab initio calculations of the EFG using the WIEN2K code were performed for anatase and rutile for pure systems as well as for relevant impurities, such as Sc and Cd on Ti sites. The nuclear quadrupole moment of the $I=1$ state in $^{44}\text{S}\text{c}$ is redetermined with a sevenfold improved accuracy to be $Q=\ifmmode\pm\else\textpm\fi{}0.214(3)\text{ }\text{b}$.

Electric field gradient at 12 N implanted into ZnO

The nuclear quadrupole interaction of short-lived β-emitter 12N(I=1, T 1/2=11 ms) implanted into a ZnO single crystal has been studied by means of the β-NMR method. We have observed a quadrupole splitting of 12N in ZnO at room temperature, from which the electric field gradient (EFG) q=+(8.6 ±1.1)×1019 V/m2 was deduced assuming axially symmetric EFG with respect to the crystalline c axis. A first principle calculation does not reproduce the data under assumption of the lattice location of 12N at the oxygen substitutional site.

Temperature dependence of the electric field gradient in GaN measured with the PAC-probe 181Hf

Epitaxial GaN layers were implanted with radioactive 181Hf ions in order to study the temperature dependence of the electric field gradient (EFG) at the site of the probes after rapid thermal annealing at 1273 K. Results are compared to recent measurements with the 111In probe that showed a surprising reversible increase of the fraction of undisturbed substitutional probe atoms at measuring temperatures above room temperature (Lorenz et al., Appl Phys Lett 80:4531, 2002). After implantation and annealing the majority of 181Hf atoms are incorporated into undisturbed substitutional lattice sites and experience an axial symmetric EFG with a quadrupole interaction frequency (QIF) of ∼336 MHz at RT and a low frequency distribution. At measuring temperatures between 20 and 1100 K the QIF increases linearly by ∼4% in good agreement with point charge model calculations taking into account the thermal lattice expansion. In contrast, measurements with the 111In probe showed a strong increase by ∼50% of the QIF above RT. Additionally, unlike for 111In, for measurements with 181Hf the substitutional fraction stays unchanged for elevated measuring temperatures.

NMR observation of quadrupolar order parameter in [formula omitted

We report O 17 NMR measurements in a single crystal of NpO 2 . We have observed oscillatory spin–echo decay for certain O sites below T 0 = 26 K . These spin–echo oscillations are well understood in terms of an axially symmetric electric field gradient created by a longitudinal triple- q antiferro-quadrupolar ordering. In the present work, we show that direct observation of the quadrupolar order parameters is possible by means of NMR.

14N pulsed nuclear quadrupole resonance. 1. Nutation experiments in the case of an axially symmetric electric field gradient tensor

An exact theory based on density matrix calculations is provided for assessing the nuclear quadrupole resonance (NQR) behaviour of a spin 1 (14N) subjected to a single radio-frequency pulse. It concerns a powder sample in zero magnetic field with the assumption of an axially symmetric electric field gradient tensor. Theoretical results, in terms of signal evolution as a function of the pulse length (nutation experiments), are checked against values of the radio-frequency field amplitude provided by NMR measurements performed with the same equipment. Good agreement between theory and experiment is obtained.

The TiPd2 compound studied by PAC with [formula omitted] and [formula omitted] probes

The intermetallic compound TiPd2 has been investigated with the perturbed angular correlation technique using radioactive 181Hf/181Ta and 111In/111Cd probes. The measurements confirmed an orthorhombic distortion of the C11b structure in the temperature range from 24 to 1023K. However, the temperature dependence of the 111Cd quadrupole parameters demonstrated that above 650K the indium ions reach the lattice site of high symmetry characterized by an axially symmetric electric field gradient (EFG). The situation for the 181Hf/181Ta probes is more complex: we observed two electric field gradients, whose fractions interchange near 700K, possibly due to 181Hf probes switching their positions but still occupying a low-symmetry site.

Spin-echoes in nitrogen-14 quadrupolar spin-system with axially symmetric electric field gradient tensor

The behaviour of the magnetisation in the spin-1 system with the axial symmetry of the electric field gradient (EFG) tensor was analysed theoretically. The behaviour of the NQR signals in hexamethylenetetramine (C 6H 12N 4) was also studied experimentally using the pulse NQR technique and sensitive equipment. It was shown that the axial symmetry of the EFG in a sample could not be the reason why spin-echo signals were not observed in conventional pulse experiments for the same type of sample. A very short spin–spin relaxation time T 2 seems to be the reason of that. The signal-to-noise ratio was sufficient for measuring T 2 in C 6H 12N 4, which had not been reported earlier. Experimental results of applying certain pulse sequences to the 14N NQR in a sample are also presented.