Muon spin-lattice relaxation and muonium diffusion in ice

Longitudinal muon spin relaxation is measured in ice, using samples with and without enrichment in H₂ ¹⁷O, with a view to studying the mobility of the muonium fraction. A conventional analysis of the data, on the assumption that relaxation of the diamagnetic fraction is negligible, suggests that more than one mechanism of muonium relaxation is at work. A Bayesian analysis warns that separation of the diamagnetic and paramagnetic signals may not be so straightforward.     

MuSR/μ+SR studies in KDP and DKDP

The temperature dependence of muon interactions has been studied in ferroelectric KDP ( H₂KPO₄) and DKDP ( D₂KPO₄) using conventional μSR and muon spin resonance spectroscopy. In longitudinal field measurements, a fast relaxing component and a slow relaxing component were observed. The slow relaxing component is attributed to diamagnetic muons. The muon spin resonance measurements indicate that the fast relaxing component results from some muonium like species: either normal or anomalous. In zero field and weak longitudinal field μSR (0–100 G), a remarkable peak in the fast relaxing component is observed around 220 K in both KDP and DKDP. An additional feature is also seen around 300 K. The amplitude of the resonance measurement has a broad minimum around 200 K which corresponds to the maximum in the relaxation rate in longitudinal field (100 G). The temperature dependence of the muonium relaxation rate in KDP is almost identical to that of DKDP. The diamagnetic fraction also shows almost no difference in relaxation rate or asymmetry for DKDP and KDP. This revised version was published online in August 2006 with corrections to the Cover Date.     

Nuclear quadrupole interaction in the low dimensional hf-trichalcogenides

We report on Time Differential Perturbed Angular Correlation measurements of the nuclear quadrupole interaction of¹⁸¹Hf(β⁻)¹⁸¹ and its temperature dependence in the low dimensional Hf- trichalcogenides HfS₃, HfSe₃ and HfTe₃. In HfS₃ the temperature dependence of the precession frequency is a slowly decreasing function with a negative curvature, the deviation from axial symmetry of the electric field gradient is practically temperature independent. In HfSe₃ the NQI shows a peculiar behaviour; between 10K and 300K the quadrupole frequency and the asymmetry parameter increase, between 300K and 400K the frequency decreases while the deviation from axial symmetry increases, indicating a structural phase transition near room temperature. In HfTe₃ the quadrupole frequency is practically temperature independent below 600K and increases linearely at higher temperatures, the asymmetry parameter increases steadily in the temperature range from 10K to 600K and then decreases. There is a strong correlation between the strength and the asymmetry of the electric field gradient so that the system depends on one control parameter only.     

Temperature dependence of the electric field gradient in HfF4.HF.2H2O

The hyperfine quadrupole interaction in HfF₄.HF.2H₂O was studied using the time differential perturbed angular correlation (TDPAC) technique. The electric field gradient (EFG) and the corresponding asymmetry parameter were measured in the temperature range from 9 to 350 K. The EFG is characterized by a rather strong increase with temperature, whereas the asymmetry parameter reaches its maximum value (η≈1) at aboutT=160 K. At 420 K, the complex is dehydrated and looses HF: The quadrupole parameters determined from subsequent TDPAC measurements are charateristic for HfF₄.     

Orientation of the oxygen-induced non-axially symmetric electric field gradient at181Ta in Ta

The interaction of dilute¹⁸¹Ta in Ta with interstitial oxygen has been investigated via the γ-γ TDPAC-technique applied to the 482 keV state in¹⁸¹Ta. The trapping of Oxygen leading to a quadrupole interaction frequency ν_Q=580(5) MHz with an asymmetry parameter of η-0.37 (1) has been observed after melting the radioactive parent isotope¹⁸¹Hf with Ta. The temperature dependence of the quadrupole interaction frequency between 17 K and 293 K was found to be very weak whereas η varied by about 10%. In a single crystal experiment the orientation of the three principal axes of the electric field gradient leading to ν_Q was determined. The V_zz-axis points in <110>, the V_yy-axis in <100> and the V_xx-axis in <110> direction. These results can be understood in the charge cloud model, suggested by Wrede et al. /1/ for a similar situation found in the HfNb system.     

Electric field gradients at the 111In site in the ferroelectric and paraelectric phases of LiTaO3

The temperature dependence of the electric-field gradient of ¹¹¹Cd in single crystalline LiTaO₃ was studied from room temperature to 1040 K in the ferroelectric and paraelectric phases. The data taken at room temperature show unambiguously the presence of two quadrupole interaction frequencies, ν_Q1=230 MHz and ν_Q2=242 MHz, with nonzero asymmetry parameters, while above the Curie temperature (T_C=878 K) the data are well described by a unique frequency. The electric field gradient shows a usual temperature dependence, increasing aproximately in a linear fashion until T_C and then decreasing faster. The initial increase is explained mostly by the lattice expansion, while above T_C it is necessary to consider Li and O displacements. This revised version was published online in August 2006 with corrections to the Cover Date.     

<Superscript>17</Superscript>O and<Superscript>23</Superscript>Na nuclear quadrupole double resonance of sodium formate and sodium acetate

The¹⁷O and²³Na nuclear quadrupole resonance spectra of powdered sodium formate and sodium acetate have been determined at room temperature by proton-¹⁷O and proton-²³Na double resonance. All¹⁷O sites have been found to be chemically equivalent. The nonzero value of the asymmetry parameter of the electric field gradient tensor at the¹⁷O site shows that the electron density distribution is not cylindrically symmetric around the C−O bond axis.     

Calorimetric study of a phase transition in D2O ice Ih doped with KOD: Ice XI

D₂O ice Ih doped with KOD was found by calorimetry to undergo a phase transition at 76 K. The enthalpy and entropy of the phase transition depended in their magnitude on the annealing of the sample. The largest values obtained were ΔH = 155 J mol⁻¹ and δS = 2.06 J K⁻¹ mol⁻¹. The phase transition removed 64% of the residual entropy. Mechanisms of the isotope effect were discussed to explain the difference in the transition temperatures of the D₂O and H₂O ices and compared with the experiment. The pressure coefficient of the transition temperature was calculated by the use of the Clapeyron-Clausius equation and recent data on the molar volume of the new phase. The name ice XI is proposed to designate the ordered phase of ice Ih.     

Diamagnetic muonium states in InP

Transverse and zero‐field muon spin relaxation reveal several diamagnetic muonium states in InP characterized by their static linewidths and diffusion properties. We tentatively associate low‐temperature diamagnetic states with Mu⁺ in the BC and T_P interstitial sites and a missing fraction with Mu⁰ rapidly diffusing through T_In interstices. Trapping peaks above 250 K imply static centers which depend on doping type, consistent with Mu^- at T_In for n‐type samples and Mu coupled with a dopant or other defect for p‐type. This revised version was published online in August 2006 with corrections to the Cover Date.     

Ab initio calculations of quadrupole interactions and their isotope effects

Calculations are presented of nuclear quadrupole coupling constants in simple closed-shell molecules containing hydrogen, together with their muoniumsubstituted counterparts. Results are given for HCl and MuCl, N₂H⁺ and N₂Mu⁺, and NH ₄ ⁺ and NH₃MU⁺. The quadrupole isotope effect proves to be small, even for the ammonium ion, where isotopic substitution breaks the tetrahedral symmetry. The calculated quadrupole interactions serve to test the quality of the calculations, and also as a signature for these diamagnetic or closed-shell species: they may be compared with values measured by muon level crossing resonance, where known, or used to predict the fields for resonance, where not.     

Mixed hyperfine interactions and defect structure in magnesiowüstite Fe−Mg−O

An analysis of the 4.2 K spectra of Fe_xO (x∼0.91) and (Fe_0.4Mg_0.6)_xO is presented in which it is considered that because of the large electric field gradient at Fe²⁺ defect sites, the spectra cannot be described by Lorentzian sextets. It is assumed that the magnetic hyperfine field vector is oriented at random in the coordinate system defined by the EFG main axis, and that the EFG coordinate system is also distributed randomly. The simplifying assumption of the asymmetry parameter η=0 allows an analytical formula to be used to describe the complex spectra. Distributions of both magnetic hyperfine field and quadrupole interaction were progressively refined resulting in reasonable fits to the spectra with the main features being well reproduced. The magnetic hyperfine field distribution is rather broad with several features present while distinct values were obtained in the distribution of quadrupole interactions. These latter values are considered to correspond to the defect configurations around the Fe²⁺ sites. The distribution of hyperfine fields is considered to reflect the varying strengths of superexchange due to the high defect concentration as well as the effects of magnetic relaxation.     

Muon diffusion and level crossing in copper

We have studied the quantum diffusion of positive muons in pure copper over the temperature range 12 mK≤T≤150 K using weak longitudinal field μSR. Below 150 K, this technique has proved to be the most sensitive to the muon hop rate. Our final results for the behaviour of the muon hop rate are well explained within the framework of theories for the quantum diffusion of light interstitials in metals of Kondo, Yamada and others. In addition, the use of level-crossing resonance has allowed us to measure the electric quadrupole interaction strength (and sign) of the copper nuclei, ω_Q= −3.314(7) μS⁻¹. These results have enabled us to show that the muon occupies the same octahedral site at all the temperatures studied, ruling out the possibility of metastable muon sites contributing to any significant portion of the muon polarization.     

Dynamics of muons in the ferroelectric material KDP

Muon spin relaxation in zero field and longitudinal field was measured in single crystal samples of KH₂PO₄ (KDP) and KD₂PO₄ (DKDP) over a temperature range of 5 K to 300 K. At low temperatures, diamagnetic muons and muon substituted radicals with nuclear hyperfine coupling can be observed. For both KDP and DKDP, a minor change was observed in the dynamics of the muon below 140 K. Above 140 K, the mobility of the muon appears to increase and the diffusion rate becomes faster with increasing temperature. Only a small increase in the relaxation rate is observed in KDP due to the presence of theH ⁺, suggesting that the relaxation effects probably originate from the³¹P.     

Observation of muon level-crossing resonance in antiferromagnetic MnF2

We report the observation of μ⁺ Level-Crossing Resonances (LCR's) in the ordered phase of an antiferromagnetic material. Two LCR's were observed in MnF₂ as a function of longitudinal magnetic field in the temperature range between 10K and 65K. Both are attributed to a muon in an interstitial octahedral-like site. The low field resonance is attributed to a muon-nuclear spin flip-flop transition involving the two nearest neighbour¹⁹F nuclei. The high field resonance occurs when the applied field cancels the local hyperfine field on the muon. The positions and widths of the LCR's were seen to scale with the sublattice magnetization.     

Investigation of Hyperfine Interactions in GdNiIn Compound

Perturbed gamma–gamma angular correlation technique was used to measure the hyperfine interactions in the compound GdNiIn using the ¹¹¹InCd → and ¹⁴⁰La¹⁴⁰Ce probe nuclei at the In and Gd sites, respectively. A unique quadrupole frequency with asymmetry parameter η = 0.78 was observed for ¹¹¹Cd probe at In sites for the measurements above Curie temperature. Below T _C , the spectra for ¹¹¹Cd show combined magnetic dipole and electric quadrupole interaction. Below 85 K, a unique magnetic interaction is observed at ¹⁴⁰Ce. A linear relationship between the saturated magnetic hyperfine field and the magnetic transition temperature was observed for both probes, indicating that the main contribution to the mhf comes from the conduction electron polarization.     

Temperature dependence of the muon and proton hyperfine constants of an \alpha‐muonium‐substituted methyl radical

Muon hyperfine constants A_μ have been measured by transverse field μSR for (CH₃)₃Si\mbox\.CHMu in hexane from 167 K to 332 K. In addition, avoided level‐crossing resonance was used to determine \alpha‐proton coupling constants A_p over a similar range of temperatures. The two hyperfine constants can be described by a common temperature dependence, d|A_i|/ dT=1.4\times 10^-3 MHz\,K^-1, where A_i represents A_p or the reduced muon constant A^\prime_μ=0.3141A_μ. There is a small isotope effect (A^\prime_μ is 2.2 % larger than A_p) consistent with zero‐point motion in the anharmonic C–H bond stretch. The common temperature dependence is tentatively attributed to a coupled deviation of the C–H and C–Mu bonds out of the nodal plane of the p orbital containing the unpaired electron. This revised version was published online in August 2006 with corrections to the Cover Date.     

Analysis of the μSR of carbontetrachloride: As a liquid in various transverse magnetic fields with added scavengers,and as crystalline solids

Carbontetrachloride has been widely used in liquid phase μ SR as a calibrant of the asymmetry in view of its supposed 100% diamagnetic muon yield. However, in the present letter, evidences are presented to show that this conventional use of CCl₄ might be wrong and that there exists thermalized muonium in it that partially leads to a lost polarization.     

Sensitivity of nuclear-quadrupole double-resonance detection of half-integer spin nuclei

The sensitivity of the Slusher and Hahn’s nuclear quadrupole double resonance technique is calculated in general for an arbitrary nuclear spin S of the quadrupole nuclei and for an arbitrary asymmetry parameter η of the electric field gradient tensor. The nuclear spin S = 5/2 (¹⁷O, ²⁵Mg, …) is treated in details. The influence of the cross-relaxation rate between the quadrupole nuclei and the abundant spin system on the sensitivity of double resonance is discussed. The results of the theoretical analysis are applied in the analysis of the ¹H–¹⁷O nuclear quadrupole double resonance spectra in p-toluenesulfonamide and 2-nitrobenzoic acid. The 17O nuclear quadrupole resonance frequencies from a sulfonamide group are determined for the first time. The proton–oxygen cross-relaxation rates and the proton local frequency in zero external magnetic field are experimentally determined from the nuclear quadrupole double resonance spectra.     

Nuclear quadrupole interactions at 187W(β-) 187Re in ZrW2O8

In ZrW₂O₈, a material with negative thermal expansion, two nuclear quadrupole interactions at ¹⁸⁷W(β^-) ¹⁸⁷Re with equal populations were determined by time differential perturbed angular correlation to be (at 295 K): ν_{\mathrm{Q} 1} = 336(1) MHz, η₁ = 0 and ν_Q2 = 1391(2) MHz, η₂ = 0.053(4). The nuclear quadrupole interactions are assigned to two crystallographically distinct tungsten sites. These results are the bases for further TDPAC studies of the negative thermal expansion on a microscopic scale. This revised version was published online in August 2006 with corrections to the Cover Date.     

51V nuclear magnetic resonance in polycrystalline ferroelastic BiVO4

Nuclear magnetic resonance studies on polycrystalline ferroelastic BiVO₄ indicate that the ⁵¹V electric field gradient asymmetry parameter is an order parameter in the ferroelastic transition. Using ∩ = A(T?T_c)^B, B is found to be 0.48(5), in good agreement with earlier studies of this material. Near the phase transition above and below, the vanadium nuclear quadrupole coupling is constant with a value of 4.8(1) MHz.