Location and associated hyperfine properties of μ+ in La2CuO4

The location of the positive muon used as a probe in highT _c systems is investigated using the unrestricted Hartree-Fock cluster procedure. Our calculations indicate that ⁺ is located in thea–c plane at a distance of 1.08 Å from the apical oxygen at a ⁺-O(a)-Cu angle of 25°. The hyperfine field at this site is also calculated. Our results show the importance of including the local contact and dipolar contributions to the hyperfine field which arise from the unpaired electron spin distribution in the vicinity of the muon.     

Local hyperfine field vector of positive muon in mono-domain single crystal of antiferromagnetic La2CuO4

By using a monodomain single crystal La₂CuO₄ grown by the travelling solvent floating zone method, the strength and direction of the local hyperfine field vector at positive muon sites were determined. Combining with the ⁺ location determined separately, we found the importance of the local hyperfine field contributions with dipolar symmetry as well as the distant dipolar field from surrounding point dipoles of Cu atomic moments.     

Hyperfine field calculations: Search for muon stopping sites in Fe3O4

Muon Spin Rotation (SR) results for magnetite (Fe₃O₄) are analyzed and discussed. At room temperature, a SR signal is observed due to the presence of an internal magnetic field (B_int) at the muon site. External transverse field measurements show that B_int is parallel to the magnetic spin direction, the <111> direction in zero applied field. Calculations of the hyperfine field to pinpoint muon stopping sites in magnetite show that the local field contains supertransfer (covalent) and dipolar field contributions. The implanted muons appear to stop at sites structurally similar to those reported for hematite (-Fe₃O₄), where muon-oxygen bond formation was strongly indicated.Research partially supported by US Department of Energy     

Hyperfine fields and neutron scattering in ferromagnetic metals

The origin of ferromagnetism in the transition metal ferromagnets, iron, cobalt, and nickel is discussed, from an ab initio band structure point of view, with proper attention to the explicit roles of exchange, correlation and hybridization effects. The influence of these effects and all the mechanisms such as direct, exchange core polarization and many-body effects that have been found important for the hyperfine properties of atomic systems are included in attempting to understand the experimentally observed hyperfine fields at the nuclei in these metals. Spin-density distributions using calculated spin polarized band wave-functions are used to make comparisons with experimental neutron scattering data. The impact of the results of analyses of hyperfine fields at the nuclei and spin density distributions on the origin of hyperfine fields at muon sites is discussed. This talk, and the corresponding article for the proceedings of this conference, will deal with the theoretical understanding of the hyperfine fields at the nuclei and neutron scattering form factors in the three ferromagnetic metals, iron, cobalt and nickel and the impact of this understanding on that of the origin of the hyperfine fields at positive muon sites in these metals. With these aims in mind, the plan of my talk will be the following.

1. Discussion of a first-principle principle procedure to obtain the energy bands and electronic wave-functions in these metals and the understanding of the origin of their ferromagnetism from a band point of view.
2. Mechanisms contributing to hyperfine fields in atomic systems and their relevance for ferromagnetic metals.
3. The mechanisms for the origin of hyperfine fields in these metals, corresponding theoretical results and comparison with experiment.
4. Comparison between calculated spin-density distributions and experimental results from neutron scattering data.
5. Remarks on the origin of hyperfine fields at muon sites in these metals.

     

<Superscript>55</Superscript>Mn spin relaxation with the participation of mobile carriers in doped perovskites

Analytical expressions are derived for the rates of longitudinal and transverse nuclear spin relaxation under conditions of fast modulation of the magnitude and direction of a hyperfine field induced by unpaired electrons of an ion. The results obtained are used to explain the data available in the literature on the ⁵⁵Mn spin relaxation in the ferromagnetic metallic phase of doped perovskites, in which the modulation of the hyperfine field is caused by the hopping of e _g electrons between Mn³⁺ and Mn⁴⁺ ions. It is demonstrated that, within this model, the rates of longitudinal and transverse relaxation are characterized by the same temperature dependence and their ratio is independent of temperature, which is in agreement with the experimental data.     

Negative muon hyperfine transition rate in aluminum

The residual polarization of theF ^– hyperfine state of ^–27Al has been investigated as a function of applied transverse magnetic field strength using standard TD- ^–SR techniques. TheF ^– precession frequency is –0.2623(5) [theoretical value: –0.2622] times that of the free muon in the same field. The observed muon decay electron asymmetry in theF ^– state decreases with increasing magnetic field strength, due to initial precession in the opposite direction of theF ⁺ state, which most muon initially populate, followed by a rapid transition to theF ^– state. A fit of the data to this model indicates a transition rateR=41(9)s^–1, in good agreement with theoretical predictions. This method can be used to determineR experimentally in other cases where it is too fast to be observed directly.     

The lattice location and hyperfine field of implanted Yb in Fe as a function of annealing temperature

A combined study has been made of the lattice location and hyperfine field of Yb implanted into Fe single crystals. The location has been determined by ion channeling and back-scattering, the hyperfine field by perturbed angular correlation (PAC) measurements on¹⁶⁹Yb (decaying to excited states in¹⁶⁹Tm). The channeling experiments indicate that initially about 60% of the Yb atoms occupy substitutional sites in the Fe lattice, while the remaining atoms are not in any specific crystallographic site. On annealing, Yb migrates from substitutional to non-substitutional sites. No Yb atoms remain substitutional after a 600°C anneal. By making PAC measurements at two temperatures for two - cascades in¹⁶⁹Tm, it is found that the PAC pattern can be described using a combined static and time-dependent magnetic interaction. The PAC results show that the average hyperfine field and relaxation parameter decrease on annealing, and that the field disappears after a 600°C anneal. The correlation between the location and the hyperfine field is discussed. A comparison of the results with previous Mössbauer results for¹⁵¹Gd implanted in Fe, together with relaxation parameter measurements on a¹⁶⁹Yb₂O₃ source, suggests that the non-substitutional Yb is internally oxidized in the Fe host.Work partly carried out while at the Clarendon Laboratory, Oxford, England and Nuclear Physics Division, AERE, Harwell, England.     

Muon spin resonance by strong pulsed r.f. field with pulsed muons

Muon spin resonance experiments have been performed for the ⁺ in H₂O and for some other cases, and the first observation has been made of the time-differential pattern of muon spin resonance, namely, spin precession around the r.f. field vector under various resonance conditions. In the present experiment, a high-power pulsed r.f. field was effectively applied to the pulsed muon beam in our laboratory of the KEK-Booster Meson Facility (BOOM). Potential uses of muon spin resonance, particularly for research in the border regions of solid state and nuclear physics, are discussed in comparison with the conventional spin rotation method.     

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.     

Hartree-Fock cluster investigation of location and hyperfine properties of normal muonium in silicon-trend with respect to diamond

Using the first-principles Hartree-Fock Cluster procedure employed earlier for normal muonium (Mu) in diamond, the total energy and hyperfine field at the muon site in silicon have been studied as a function of muon position along the <111> direction. The muon was found to be localized in the tetrahedral interstitial region, although the potential was significantly shallower as compared to diamond. The vibrationally averaged hyperfine constant for the muon shows a correct trend compared to diamond but is somewhat larger than experiment, possible reasons for which will be discussed. Results for the superhyperfine constants in silicon will be presented and compared with those for diamond.     

Full vector treatment of the polarization evolution in an arbitrary field distribution

This paper presents a vector representation of the ensemble muon polarizationP(t) for static field distributions which emphasizes the different behavior resulting from correlated and non-correlated field distributions. For example, with most local field distributions, such as random dipolar fields, the net muon polarization in the limit of infinite timeP(t) is parallel to the initial muon spin direction when the using transverse field (TF) or longitudinal field (LF) geometries. In general, however, it need not be; this will be demonstrated using the field distribution of an anisotropic superconductor.     

Spin re-orientation in FeCr2S4

The spinel FeCr₂S₄has been studied intensely for its peculiar magnetic and local structural changes which are sensitively influenced by the Jahn?CTeller properties of Fe^2?+?in tetrahedral sulfur coordination. Recent muon spin rotation data give strong evidence that the commonly assumed collinear magnetic structure of this compound is only found between the Curie temperature T_C = 165 K and 50 K. For lower temperatures a helical structure has been proposed. We present new Mössbauer spectroscopic data taken on the same sample as used for muon spin rotation. Also the hyperfine spectra revealing non-equivalent iron sites support the appearance of a spin re-orientation around 50 K which may be related to the onset of short-range orbital order. Below 20 K severe dynamic broadenings are found which may indicate orbital fluctuations. Orbital order occurs around 11 K accompanied by severe changes in the crystalline electric field ground state as traced from quadrupole interaction.     

Theory of muon spin depolarization in condensed phases of hydrogen isotopes

A theory of muon spin depolarization in the molecular ion ( H₂μ)⁺(( D_2μ)) formed in a crystalline phase of hydrogen isotopes is presented. It is shown that the molecular ion ( H_2μ)⁺ has no time to thermalize during the muon lifetime, but after \tau\ll \tau_μ has time to transit to the lowest energy levels of the vibration‐rotation spectrum. The depolarization of the muon spin is determined by the interaction of the ion’s electric dipole moment with the lattice and by spin‐rotation interactions V_LS in the ion. This mechanism is analogous to that of “muonium”, replacing the hyperfine interaction by V_LS. The results can explain the experimental data and in particular the absence of a strong isotopic effect. This revised version was published online in August 2006 with corrections to the Cover Date.     

Pac studies of spin deviations,pressure induced hyperfine field shifts,and temperature variation of supertransferred hyperfine fields

A PAC study of¹¹¹Cd substiuted antiferromagnetic transition metal salts is reported. Supertransferred hyperfine fields at¹¹¹Cd nuclei were used for the first time to observe three effects: zero-point spin deviations, temperature variation, and pressure shift of the hyperfine field. Comparison of KNiF₃ and RbMnF₃ with their corresponding quadraticlayer fluorides K₂NiF₄ and Rb₂MnF₄ yields an estimate for the magnitude of the zeropoint spin deviation in doped antiferromagnets. The temperature dependences of the Cd hyperfine fields in RbMnF₃/Cd and MnF₂/Cd have been determined. The shift in hyperfine field observed for -MnS/Cd under external pressure further supports our model for the origin of the supertransferred hyperfine fields.This work was supported by the US Energy Research and Development Administration.     

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.     

Location of muonium and hydrogen in C60 fullerene and associated electronic structure and hyperfine properties

The unrestricted Hartree-Fock (UHF) procedure is used to investigate the locations, associated electronic structures and hyperfine interactions for muonium and hydrogen in C₆₀ fullerene. Our results indicate that from total energy considerations, in keeping with earlier investigations, the exohedral model has the lowest energy. However, the energies of the endohedral model involving the muonium (hydrogen) inside the fullerene and bonded to one of the carbon atoms, and of the muon at the center are found to be almost equal, contrary to earlier results. The hyperfine interaction constant for the endohedral site is in good agreement with that required to explain the lower observed muon spin-rotation (SR) frequency in the C₆₀-muonium system. The same appears to be the case for the exohedral model. However, there seems to be some uncertainty about the theoretical result in the latter case due to significant admixtures of higher spin states in the UHF wave-function. Additionally, in solid fullerene, the calculated location of the muonium for the exohedral model is such that it could be bonded to two fullerene molecules and therefore a muonium attached to a simple fullerene may not be representative of the exohedral state. This feature as well as the difficulty for the exohedral model of explaining the observed equality of the correlation times for relaxation effects associated with both SR and¹³C relaxation times in nuclear magnetic resonance (NMR) experiments suggests that the endohedral model for muonium cannot at present be ruled out as a viable model in favor of the exohedral model. Possible avenues for future investigations to resolve some of the problems for both exohedral and endohedral models are discussed. Results obtained for muonium at the center of fullerene are presented and compared to the features of the observed high frequency SR signal, and possible improvements in theory are discussed.     

Negative muon spin precession in ferromagnetic iron and the hyperfine anomaly

The hyperfine field (B _μ ^hf ) at the negative muon μ⁻ in ferromagnetic iron was investigated by means of the zero-field μ⁻ spin precession technique. In the temperature range 320–690 K,B _μ ^hf for μ⁻ Fe departs from the magnetization curve of pure iron in the same way as the hyperfine field seen by a⁵⁵Mn impurity in dilute MnFe measured by NMR. The hyperfine anomaly for μ⁻ Fe relative to dilute (1.5 at.%)⁵⁵Mn in iron is found to be −0.9(3)% and temperature independent over the temperature range investigated.     

Paramagnetic resonance in irradiated Sr(NO3)2 single crystal

Paramagnetic resonance absorption of centres with spin 1/2 centered aboutg=2 is reported in gamma-irradiated single crystals of Sr(NO₃)₂. At room temperature four centres are detected which appear to exhibit axial symmetry about the [111] crystal direction. Two of the observed centres have a resolved hyperfine structure of N¹⁴. This hyperfine structure and axial symmetry of the centres indicate that they could be irradiation products of the nitrate ion. To find the number of trapped electrons, a simplified calculation of the molecular orbitals of planar and pyramidal NO₃ is carried out. Centres with a resolved hyperfine structure are then identified as pyramidal NO ₃ ^? and a NO₂ molecule rotating about the [111] direction. Two centres without hyperfine structure are not identified exactly.     

μ + Knight shift and spin relaxation in indium single crystalKnight shift and spin relaxation in indium single crystal

μ ⁺ SR measurements have been performed in a single crystal indium sample between 12 K and 300 K with a stroboscopic μSR spectrometer. The muonic Knight shiftK _μ and the muonic depolarization rate σ were obtained for various angles θ between the tetragonal crystallinec-axis and the direction of the external field. The isotropic part ofK _μ is only weakly temperature dependent and is consistent with the estimated Pauli spin susceptibility value. At a temperature of 12 K the angular dependence ofM ₂ (the second moment of the field distribution at the muon, obtained from the measured σ(θ) values) allows a clear determination of the muon location — the symmetric tetrahedral site. The observed anisotropicK _μ cannot be explained by the dipoles at the In atoms responsible for the bulk magnetic susceptibility but probably originates from an anisotropic Pauli spin susceptibility.