Nuclear Dipole Fields Research Articles

Anisotropic internal fields behavior in La[formula omitted]Sr[formula omitted]CuO4 ([formula omitted]): Precursor to the spin glass state revealed by muon spin relaxation

In this study, we conducted a zero-field muon spin experiment on slightly doped La2−xSrxCuO4 from 200 K down to near the spin glass temperature (TSG). Utilizing pulsed muon beams with longer time spectra, we investigated the interplay between dynamic and static fields, which influenced the lineshapes of the nuclear dipole field. Our results reveal the emergence and growth of a Lorentzian field associated with localized moments, coexisting with nuclear Gaussian field anisotropy, as the temperature approaches TSG. This behavior of the internal fields may serve as a precursor to the spin glass state. The findings are consistent with a theoretical model that describes the electric field gradient required to characterize the spin glass state.

Absence of μSR evidence for magnetic order in the pseudogap phase of Bi2+xSr2−xCaCu2O8+δ

We present an extended zero-field muon spin relaxation (ZF-$\mu$SR) study of overdoped Bi$_{2+x}$Sr$_{2-x}$CaCu$_2$O$_{8+\delta}$ (Bi2212) single crystals, intended to elucidate the origin of weak quasistatic magnetism previously detected by $\mu$SR in the superconducting and normal states of optimally-doped and overdoped samples. New results on heavily-overdoped single crystals show a similar monotonically decreasing ZF-$\mu$SR relaxation rate with increasing temperature that persists above the pseudogap (PG) temperature $T^*$ and does not evolve with hole doping ($p$). Additional measurements using an ultra-low background apparatus confirm that this behavior is an intrinsic property of Bi2212, which cannot be due to magnetic order associated with the PG phase. Instead we show that the temperature-dependent relaxation rate is most likely caused by structural changes that modify the contribution of the nuclear dipole fields to the ZF-$\mu$SR signal. Our results for Bi2212 emphasize the importance of not assuming the nuclear-dipole field contribution is independent of temperature in ZF-$\mu$SR studies of high-temperature (high-$T_c$) cuprate superconductors, and do not support a recent $\mu$SR study of YBa$_2$Cu$_3$O$_{6+x}$ that claims to detect magnetic order in the PG phase.

Lithium Diffusion in Lithium-Transition-Metal Oxides Detected by μ+SR

Abstract Diffusion of Li+ ionsin solidsisa basic principle behindthe operationof Li-ion batteries. Suchdiffusive behavior is represented by the diffusion equation (Fick's law), J = − D × δ ϕ/ δ x , where J is the diffusion flux, D is the self diffusion coeffcient, ϕ is the concentration, and x is the position. Although D of Li + ions( D Li)in solids is usually evaluatedby 7 Li-NMR, diffculties arise for materials that contain magnetic ions. This is because the magnetic ions contribute additional spin-lattice relaxation processes thatis considerably larger than the1/ T 1 expected from only Li diffusion [1] , [2] , [3] . This implies that 7Li-NMRprovidesa rough estimateof D Li for the positive electrode materials of Li-ion batteries, which include transition metal ions in order to compensate charge neutrality during a Li + intercala-tion/deintercalation reaction. This is an unsatisfactory situation since D Li is one of the primary parameters that govern the charge/discharge rate of a Li-ion battery. We have, therefore, attempted to measure D Li for lithium-transition-metal-oxides with muon-spin relaxation (μ + SR) since 2005 [4] , [5] , [6] . Muons do not feel fluctuating magnetic moments at high T, but instead sense the change in nuclear dipole field due to Li diffusion. Even if magnetic moments still affect the muon-spin depolarization rate, such aneffectis, in principle, distinguishablefromthatof nucleardipole fields.In particular,aweak longitudinal field can be applied that decouples the magnetic and nuclear dipole interactions [7] , [8] . Here, we wish to summarize our μ + SR study on the lithium-transition-metal-oxides, LixCoO2, LiNiO2, and LiCrO2.

Precise measurements of the dynamics of local fields in the underdoped regime of La2-xSrxCuO4 by μSR

Precise zero-field (ZF) and longitudinal-field (LF) muon spin relaxation (μSR) measurements have been carried out on La2-xSrxCuO4 in the underdoped regime of 0.024 ≤ x ≤ 0.15 to investigate the dynamics of local fields in the normal state. ZF-μSR time spectra show the Gaussian shape, indicating that muon spins depolarize mainly by nuclear dipole fields which are randomly distributed at the muon site. A slight deviation of the shape of the ZF-μSR time spectrum from the Gaussian shape has been observed with decreasing temperature. This deviation is due to a change of the dynamic depolarization rate of the muon-spin polarization. From LF-μSR measurements, it has been found that a small and quasi-static local field exists at the muon site even in the normal state around 100 K. The change of the muon-spin depolarization rate observed in ZF is due to a change of the magnitude of the small and quasi-static local field at the muon site.

μSR in two-dimensional hydrogen bonding system squaric acid

Squaric acid, a famous two-dimensional hydrogen-bonded system was studied by μSR. From the temperature dependence of the muon spin relaxation rate as well as from the crystal axis dependences, different muon sites at low temperature (10 K) and at high temperature (300 K) were found. The nuclear dipole field was calculated for possible muon sites. At low temperature the muon attaches C O … HO acceptor oxygen, while at 300 K the muon occupies the regular hydrogen sites.

Possible 6-qubit NMR quantum computer device material; simulator of the NMR line width

For an NMR quantum computer, splitting of an NMR spectrum must be larger than a line width. In order to find a best device material for a solid-state NMR quantum computer, we have made a simulation program to calculate the NMR line width due to the nuclear dipole field by the 2nd moment method. The program utilizes the lattice information prepared by commercial software to draw a crystal structure. By applying this program, we can estimate the NMR line width due to the nuclear dipole field without measurements and find a candidate material for a 6-qubit solid-state NMR quantum computer device.

Development ofinhomogeneous conduction electron spin polarization in the antiferroquadrupolar phase of UPd3

We have measured the Knight shift and inhomogeneous linebroadening of positive muons implanted in monocrystallineUPd3 from 2 K up to 300 K. We find two components in thetransverse-field (Hext = 0.6 T) precession signal withamplitude ratio 2:1, which is independent of temperature up to300 K. The two signals are associated with two different muonsites with axial symmetry. Both the Knight shifts and therelaxation rates show pronounced anomalies at the criticaltemperatures of T2≃4.4 K, believed to reflect, inter alia, a magnetic transition, T1≃6.8 K and T0≃7.6 K, originating from antiferroquadrupolar ordering.Details depend on sample orientation and signal component. It isargued that the particular temperature dependence of both theKnight shift and the inhomogeneous line broadening of thestronger component below 10 K is associated with the contacthyperfine contribution to the Knight shift and reflects aninhomogeneous conduction electron spin polarization caused bythe antiferroquadrupolar order. Additional zero-field µSRmeasurements yield a very small temperature-independentrelaxation rate consistent with the field inhomogeneity arisingfrom the Pd nuclear dipole fields. In particular, below 4.5 Kthere is no evidence for additional static fields due to amagnetically ordered state.

Investigation of nuclear-spin couplings in the lithium fluorides as possible candidates for crystal nuclear magnetic resonance quantum computing devices

We have performed 7Li and 19F nuclear magnetic resonance (NMR) in two lithium fluorides BaLiF3 and YLiF4 to explore the possibility of a crystal NMR quantum computing device. We find that (1) both the absolute values and the angular dependences of the line widths can primarily be accounted for by the nuclear dipolar fields, and (2) the spin–lattice relaxation times are long enough for quantum computations. These characteristics indicate that these crystals can be possible candidates for quantum computing devices. We also find that, in the perovskite structures like BaLiF3, magic angles are quite effective to diminish the nuclear dipole fields, which enables us to treat some nuclei as ‘isolated’. We propose using this feature to create low-dimensional nuclear-spin networks in the crystals.

Investigation for the possible crystal NMR quantum computing device with BaLiF3

The 7Li and 19F NMR have been performed in the single crystal of the lithium fluoride, BaLiF3 with a cubic structure in order to examine the basic requirements for crystal NMR quantum computing devices. The angular dependences of the NMR line widths were explained by the lattice-sum of nuclear dipole fields. We find that magic angles are quite effective in this crystal structure to diminish the nuclear dipole fields from the nearest neighbor sites, enabling us to treat the nuclei as “isolated”. We propose using this feature to create low dimensional nuclear spin networks in crystals.

Magnetic ordering in La 2Cu 2O 5

Muon spin relaxation (μSR) measurements were carried out on La 2Cu 2O 5, which is a candidate for the spin 1 2 4-leg Heisenberg antiferromagnetic ladder system. At room temperature, the μSR spectrum can be fitted with the static Gaussian Kubo–Toyabe function. This spectrum originates from static nuclear dipole fields of copper. At ∼140 K , a sudden decrease of the initial asymmetry was observed. This suggests that a long-range magnetic ordering of the Cu 2+ spins occurs due to nonnegligible interladder interactions.

μSR study of YMn 12

The Mn ions occupy three different sites (8i, 8j, 8f ) in equal population in YMn 12, which has the tetragonal ThMn 12 structure with space group I4/mmm. They possess a different magnetic moment at the 8f site (0.14 μ B) compared to the 8i and 8j sites (0.42 μ B). The compound orders antiferromagnetically with T N ≈100 K . Above T N the muon-spin relaxation is dominated by the nuclear dipole fields of 55Mn. The influence of the electronic moments on Mn is only weakly felt near T N when critical slowing down occurs. Below T N, no spontaneous spin precession is observed and the zero-field spectra can be described by a Lorentzian Kubo–Toyabe pattern. This shows that the muon must occupy an interstitial site where all contributions to the local field cancel for the antiferromagnetic spin structure. Longitudinal field measurements demonstrate that the spectra are essentially static in nature. It is remarkable that the different Mn sites with their different Mn moments do not show in the μSR spectra. The likely muon stopping sites are discussed.

The effect of the crystal electric field on the Kondo-type fluctuations in

We present a positive-muon spectroscopy study of the cubic Kondo lattice , where the crystal-field splittings of the ion amount to a few tens of K. The transition from the paramagnetic to the antiferromagnetic state is detected at . The zero-field data provide evidence of an unusual temperature dependence of the mean nuclear dipole field at the muon site. The longitudinal relaxation rate as well as the published quasi-elastic neutron linewidth, both recorded far into the paramagnetic region (, are analysed in detail. We show that the classical kf exchange interaction cannot explain the observed thermal variation of the dynamical and neutron widths. We perform a calculation of the 4f excitation spectra using the expansion, applied to the Anderson one-impurity Hamiltonian in the non-crossing approximation (NCA), in the presence of crystal-field splittings, and compare the results with the observed thermal variations of the dynamical widths. Whereas the NCA reasonably explains the neutron measurements, it strongly overestimates the low-temperature width. We discuss different possible reasons for this discrepancy.

Zero-field μSR study of CeRu2Si2 heavy fermion compound

Zero — field muon spin relaxation measurements have been carried out on a high-quality single-crystal sample of the paramagnetic heavy-fermion compound CeRu2Si2 from 5K to 300K. The observed relaxation at each temperature was well fitted by a function described by the product of a Kubo-Toyabe type and an exponential one. The temperature dependence of the Kubo-Toyabe relaxation rate σZF shows an almost constant value (0.03 μs−1) which is comparable to the calculated linewidth due to nuclear dipole fields from99Ru and101Ru atoms assuming the possible μ+ stopping sites for the ThCr2Si2 structure. On the other hand, we observed an increase of the exponential relaxation rate λZF to a value of ∼- 0.02 μs−1 with decreasing temperature below about 100K. This suggests a contribution of Ce 4f moments.

Muon diffusion in the metal hydrides LaNi 5H 6 and β-PdH x

Zero- and transverse field muon ( μ +) spin rotation measurements were performed in LaNi 5H 6 and PdH x (0.59 ⩽ x ⩽ 0.86) between 16 K and room temperature. The μ + depolarization is due to the spread in nuclear dipole fields originating predominantly from the protons. Motional averaging is caused by the combined motion of the protons and the β +. The results show a surprisingly low correlation rate 1 τ c which indicates highly correlated μ +-proton diffusion or μ + trapping within regions of largely immobile hydrogen configurations. μ + trapping or a localized μ + jump mode could be considered in LaNi 5H 6 where a linear decrease in the second moment with temperature between 20 and 120 K was measured in contrast with the unchanged relaxation observed by proton magnetic resonance.

Muon diffusion in the metal hydrides β-PdHx(x=0.70 and 0.75) and LaNi5H6

We report on zero and transverse fieldμSR measurements in LaNi5H6 and inβ-PdHx (x=0.70 and 0.75) between 16 K and room temperature. Theμ+-depolarization is predominantly caused by the spread in nuclear dipole fields from the protons. Motional averaging is caused by the combined motion of protons and theμ+. The results are quite unexpected and point toμ+-trapping within regions of largely immobile hydrogen configurations or to a highly correlatedμ+-proton diffusion. In LaNi5H6 a linear change of the second moment with temperature between 20 K and 120 K is indicated.

Response of the Mössbauer spectrum of paramagneticFe3+inAl2O3to nuclear dipole fields

Experimental $^{57}\mathrm{Fe}$ M\"ossbauer (ME) spectra of ${\mathrm{Al}}_{2}$${\mathrm{O}}_{3}$(${\mathrm{Fe}}^{3+}$) single crystals are presented. Measurements were made down to 60 mK and in applied magnetic fields from 0 to 100 G At 60 mK the ME spectra of the ${S}_{z}=\ifmmode\pm\else\textpm\fi{}\frac{1}{2}$ ionic ground state was isolated, and its response to weak (less than 100 G) applied magnetic fields was examined. A qualitative discussion of the anisotropic response to magnetic fields is given. In zero-applied magnetic field the spectrum is strongly influenced by nuclear dipole fields from surrounding $^{27}\mathrm{Al}$ nuclei. From a theoretical reconstruction of the zero-applied-field spectrum the average magnitude of the $^{27}\mathrm{Al}$ nuclear dipole field is determined to be 4.5 \ifmmode\pm\else\textpm\fi{} 1.5 G. Good agreement is obtained with a theoretical calculation which involves the identical lattice sum which occurs in the Van Vleck formula for the second moment of the nuclear dipole broadening of an NMR line. The connection between the dipole field observed in the ME experiment and the second-moment calculation of the broadening of an NMR line is discussed. Also considered are possible relaxation mechanisms. The spin-lattice relaxation rates are estimated using experimental data for the lattice thermal conductivity and application of the fluctuation-dissipation theorem to the reversible heat flow. It is concluded that at 60 mK relaxation effects are not observed in the ME spectra and also that broadening due to ${\mathrm{Fe}}^{3+}$-${\mathrm{Fe}}^{3+}$ interaction is negligible compared to the nuclear dipole broadening, except for a broad single-line contribution in the center of the spectrum.