121Sb and 123Sb NQR and the heterophase structure in the SbSI ferroelectric

The temperature dependences of NQR line frequencies and widths of ¹²¹Sb (for the ±1/2→±3/2 transition) and of ¹²³Sb (for the ±1/2→±3/2 and ±3/2→±5/2 transitions), as well as of the principal components and the asymmetry parameter of the electric-field-gradient tensor at the ¹²³Sb nucleus have been studied in a SbSI crystal in the 115–325 K range. The dynamic and static factors governing the character of these relations are discussed. The ±1/2→±3/2 line in the ¹²¹Sb NQR spectrum splits into a doublet within a narrow (0.5 K) temperature interval near the ferroelectric phase transition (T _c=293 K), which is associated with the formation of a macroscopic heterophase structure in the crystal. Fiz. Tverd. Tela (St. Petersburg) 41, 1286–1292 (July 1999)     

Local ordered magnetic fields in bismuth dielectrics. 209Bi NQR in Bi4Ge3O12 single crystal

The results of the ²⁰⁹Bi NQR experiments carried out on α-Bi₂O₃, Bi₃O₄Br, Bi₂M₄O₉ (M=Al, Ga), Bi₂Ge₃O₉, and Bi₄Ge₃O₁₂ showed that these compounds are not diamagnets in the conventional sense. The Zeeman perturbed zero-field ²⁰⁹Bi NQR spectra gave an indication that local ordered magnetic fields of the order of 30–200 G exist in these substances comprising neither transition nor rare earth elements. Further aspects of this principally new phenomenon of yet unknown nature were studied by the ²⁰⁹Bi NQR experiments on the Bi₄Ge₃O₁₂ single crystal in external magnetic fields below 500 Oe, applied at various orientations with respect to the crystal axes. The spectral patterns of dramatically increased intensity and multiplicity, caused by the unknown magnetism of the compound, were observed in applied fields and modeled. Based on the results of the modeling, the conclusions were made that at least four magnetically non-equivalent Bi sites characterized by antiferromagnetically ordered local fields of the order of 30 G are present in the Bi₄Ge₃O₁₂ crystal; the intensity increase was interpreted to arise from the change in orientation of the electric field gradient axes at the Bi site upon applying an external magnetic field.     

Nuclear Spin–Lattice Relaxation of Single Crystal Sr14Cu24O41

Nuclear spin–lattice relaxation rate T ₁ ⁻¹ has been measured for the ladder sites of two single crystals Sr₁₄Cu₂₄O₄₁ (Sr14-A,B) by ⁶³Cu NMR/NQR. The hole localization around 100 K appears as a peak in the T variation of T ₁ ⁻¹(NQR). On the other hand, it is suppressed in the T ₁ ⁻¹ (NMR) data under the magnetic field H ∼ 11 T, and a new peak appears around 20 K. T ₁ ⁻¹(NMR) around the peak is more enlarged for Sr14-B than for Sr14-A. Hence, holes on the ladders of Sr14-B tend to be more localized. This is considered to be an origin for the occurrence of the magnetic order in Sr14-B under H ∼ 11 T.     

Optical magnetometer with submicron spatial resolution based on Rb vapors

It is shown experimentally that use of fluorescence and transmission spectra obtained from nanocells with the thickness of column of rubidium atomic vapor L = λ/2 and L = λ, respectively (λ = 794 nm is the wavelength of laser radiation close to resonance with D ₁-line transition of Rb atoms), by means of a narrowband diode laser allows spectral separation and study of variations of probabilities of atomic transitions between ground and excited states of hfs of D ₁ lines of ⁸⁵Rb and ⁸⁷Rb atoms in the range of magnetic fields from 10 to 5000 G. Small thickness of atomic vapor column (∼390 nm and ∼794 nm) allows applying permanent magnets simplifying essentially creation of strong magnetic fields. Advantages of this technique are discussed as compared with the technique of saturated absorption. The obtained results show that a nanocell with submicrom thickness of vapor column may serve as a basis for designing a magnetometer with submicron local spatial resolution which is important in case of measuring strongly inhomogeneous magnetic fields. Experimental data are in good agreement with the theoretical results.     

Magnetoresistance and magnetic ordering in praseodymium and neodymium hexaborides

The magnetoresistance Δρ/ρ of single-crystal samples of praseodymium and neodymium hexaborides (PrB₆ and NdB₆) has been measured at temperatures ranging from 2 to 20 K in a magnetic field of up to 80 kOe. The results obtained have revealed a crossover of the regime from a small negative magnetoresistance in the paramagnetic state to a large positive magnetoresistive effect in magnetically ordered phases of the PrB₆ and NdB₆ compounds. An analysis of the dependences Δρ(H)/ρ has made it possible to separate three contributions to the magnetoresistance for the compounds under investigation. In addition to the main negative contribution, which is quadratic in the magnetic field (−Δρ/ρ ∝ H ²), a linear positive contribution (Δρ/ρ ∝ H) and a nonlinear ferromagnetic contribution have been found. Upon transition to a magnetically ordered state, the linear positive component in the magnetoresistance of the PrB₆ and NdB₆ compounds becomes dominant, whereas the quadratic contribution to the negative magnetoresistance is completely suppressed in the commensurate magnetic phase of these compounds. The presence of several components in the magnetoresistance has been explained by assuming that, in the antiferromagnetic phases of PrB₆ and NdB₆, ferromagnetic nanoregions (ferrons) are formed in the 5d band in the vicinity of the rareearth ions. The origin of the quadratic contribution to the negative magnetoresistance is interpreted in terms of the Yosida model, which takes into account scattering of conduction electrons by localized magnetic moments of rare-earth ions. Within the approach used, the local magnetic susceptibility χ_loc has been estimated. It has been demonstrated that, in the temperature range T _N < T < 20 K, the behavior of the local magnetic susceptibility χ_loc for the compounds under investigation can be described with good accuracy by the Curie-Weiss dependence χ_loc ∝ (T − Θ _p )⁻¹.     

Spontaneous magnetization of the vacuum and the strength of the magnetic field in the hot Universe

Intergalactic magnetic fields are assumed to have been spontaneously generated at the reheating stage of the early Universe, due to vacuum polarization of non-Abelian gauge fields at high temperature. The fact that the screening mass of this type of fields has zero value was discovered recently. A procedure to estimate their field strengths, B(T), at different temperatures is here developed, and the value B(T _ew)∼10¹⁴ G at the electroweak phase transition temperature is derived by taking into consideration the present value of the intergalactic magnetic field strength, B ₀∼10⁻¹⁵ G, coherent on the ∼1 Mpc scale. As a particular case, the standard model is considered and the field scale at high temperature is estimated in this case. Model-dependent properties of the phenomena under investigation are briefly discussed, too.     

NQR indications of unconventional magnetism in some bismuth-based diamagnets

An evidence that local ordered magnetic fields from 30 to 200 G exist in diamagnets α-Bi₂O₃, Bi₃O₄Br, Bi₄Ge₃O₁₂, Bi₂Al₄O₉ which comprise neither d- nor f-elements was earlier given by the zerofield and Zeeman-perturbed²⁰⁹Bi nuclear quadrupole resonance (NQR) spectra. With a view to find similar spectroscopic effects in other compounds, we examined the²⁰⁹Bi NQR Zeeman-perturbed spectra of the Bi₃B₅O₁₂ oriented single crystal as well as the zero-field spin echo envelopes in Bi₃B₅O₁₂ and Bi₂Ge₃O₉. Distinctive modulations were displayed by the zero-field²⁰⁹Bi spin echo envelopes in Bi₂Ge₃O₉ powder. The modeling of the spin echo envelopes within the density matrix formalism explained the observed effect by the presence of local ordered magnetic field of the order of 65 G at the Bi atoms. The zero-field modulations of the²⁰⁹Bi spin echo envelopes were also observed in Bi₃B₅O₁₂ indicating the presence of the internal source of line splitting. This finding and considerable deviation of the resonance intensity ratios from that in a pure NQR, found in the zero-field²⁰⁹Bi spectrum of the single crystal, were understood as indirect evidences that a local ordered magnetic field exists also in Bi₃B₅O₁₂. The zero-field²⁰⁹Bi spin echo envelopes assigned to the lines split by the local magnetic fields in α-Bi₂O₃ and Bi₄Ge₃O₁₂ were observed to display modulations on the appropriate curves.     

Studies of the positive muon behavior in solid H2 and D2

Using a pulsed muon beam, we have investigated the microscopic μ⁺ behavior in solid H₂ and D₂ down to 0.6 K by the μ⁺SR method. From the studies of μ⁺ spin relaxation phenomena in solid para‐ H₂ and ortho‐ D₂, we have found that μ⁺ forms three distinct microscopic states; H₂μ⁺( D₂μ⁺)(20\sim25\%), muonium (15\sim20\%) and μ⁺(\sim60\%). In H₂μ⁺, the μ⁺ spin is depolarized in solid para‐ H₂ and a local magnetic field B_loc=1\sim2 G is deduced from LF‐μ⁺SR measurements. The magnitude of B_loc is inconsistent with the magnetic dipolar field (\sim25 G) expected from the magnetic moments of two protons in the H₂μ⁺ molecule and suggests that the H₂μ⁺ molecule might be in the rotationally excited state. From LF‐μ⁺SR measurements, muonium and μ⁺ have been found to diffuse in solid o‐ D_2. The diffusion rate of muonium is two order of magnitude larger than that of μ⁺. This revised version was published online in August 2006 with corrections to the Cover Date.     

Local magnetism of Ce in the Kondo lattice compound CeFeGe3

Local magnetism of Ce in the Kondo lattice compound CeFeGe₃ studied by measuring local susceptibility χ_loc at ¹⁴⁰Ce probe site using TDPAC method is presented. The magnitude and temperature dependence of χ_loc reflect Kondo behaviour with Kondo temperature T_K∼150 K. This revised version was published online in August 2006 with corrections to the Cover Date.     

Quantum oscillations of the resistivity and hall coefficient and the quantum limit in Bi<Subscript>0.93</Subscript>Sb<Subscript>0.07</Subscript> alloys in a magnetic field along the trigonal axis

The dependences of the electrical resistivity ρ and the Hall coefficient R on the magnetic field have been measured for single-crystal samples of the n-Bi_0.93Sb_0.07 semiconductor alloys with electron concentrations in the range 1 × 10¹⁶ cm⁻³ < n < 2 × 10¹⁸ cm⁻³. It has been found that the measured dependences exhibit Shubnikov-de Haas quantum oscillations. The magnetic fields corresponding to the maxima of the quantum oscillations of the electrical resistivity are in good agreement with the calculated values of the magnetic fields in which the Landau quantum level with the number N intersects the Fermi level. The quantum oscillations of the Hall coefficient with small numbers are characterized by a significant spin splitting. In a magnetic field directed along the trigonal axis, the quantum oscillations of the resistivity ρ and the Hall coefficient R are associated with electrons of the three-valley semiconductor and are in phase with the magnetic field. In the case of a magnetic field directed parallel to the binary axis, the quantum oscillations associated both with electrons of the secondary ellipsoids in weaker magnetic fields and with electrons of the main ellipsoid in strong magnetic fields (after the overflow of electrons from the secondary ellipsoids to the main ellipsoid) are also in phase. In magnetic fields of the quantum limit ħω _c /2 ≥ E _F, the electrical conductivity increases with an increase in the magnetic field: σ₂₂(H) ∼ H ^k . A theoretical evaluation of the exponent in this expression for a nonparabolic semiconductor leads to values of k close to the experimental values in the range 4 ≤ k ≤ 4.6, which were obtained for samples of the semiconductor alloys with different electron concentrations. A further increase in the magnetic field results in a decrease of the exponent k and in the transition to the inequality σ₂₂(H) ≤ σ₂₁(H).     

Investigation of Rb <Emphasis Type="Italic">D</Emphasis><Subscript>1</Subscript> atomic lines in strong magnetic fields by fluorescence from a half-wave-thick cell

It has been experimentally demonstrated that the use of the effect of significant narrowing of the fluorescence spectrum from a nanocell that contains a column of atomic Rb vapor with a thickness of L = 0.5λ (where λ = 794 nm is the wavelength of laser radiation, whose frequency is resonant with the atomic transition of the D ₁ line of Rb) and the application of narrowband diode lasers allow the spectral separation and investigation of changes in probabilities of optical atomic transitions between levels of the hyperfine structure of the D ₁ line of ⁸⁷Rb and ⁸⁵Rb atoms in external magnetic fields of 10–2500 Gs (for example, for one of transitions, the probability increases ∼17 times). Small column thicknesses (∼390 nm) allow the application of permanent magnets, which facilitates significantly the creation of strong magnetic fields. Experimental results are in a good agreement with the theoretical values. The advantages of this method over other existing methods are noted. The results obtained show that a magnetometer with a local spatial resolution of ∼390 nm can be created based on a nanocell with the column thickness L = 0.5λ. This result is important for mapping strongly inhomogeneous magnetic fields.     

Evidence for complex magnetic order in U2Zn17: A μ+ SR studySR study

μ⁺ SR-measurements in transversally applied magnetic fields of 2000 G and 4000 G on heavy-electron single crystal U₂Zn₁₇ are presented. They reveal that at least two types of interstitial sites are occupied by the positive muons. One of these sites (1/3, 2/3, 5/6) could be identified via induced local dipolar fields which aboveT _N=9.7 K can exactly be derived from the magnetic susceptibility. The corresponding component of the μ⁺-signal exhibits a steplike decrease by about 40% atT _N which is caused by the onset of a very broad distribution of static internal magnetic fields (ΔB≈1000 G) with zero average. Such a field distribution is in distinct contrast to dipolar-field calculations performed for the simple antiferromagnetic structure deduced from neutron diffraction. The remaining 60% of the muons contributing to this component belowT _N are subject to a narrow static field distribution (ΔB≈1 G). The induced dipolar fields at the site (1/3, 2/3, 5/6) are temperature-independent belowT _N. A weak dipolar coupling to the U-moments renders similar observations for muons occupying the second type of interstitial impossible.     

Influence of antiferromagnetic ordering on the de Haas-van Alphen effect in a semimetal

The distinctive characteristics of the de Haas-van Alphen effect in semimetals with antiferromagnetic long-range order are investigated theoretically. It is shown that the transition of the subsystem of localized spins from the canted antiferromagnetic phase to the ferromagnetic phase is accompanied by an abrupt change in the “frequency” of the magnetization oscillations of band carriers M _∼. In the below-critical range of magnetic fields, M _∼ is not a function periodic in 1/H. Significantly, the additional contribution to the phase of the oscillatory factors is proportional to H ² and is determined entirely by quantum fluctuations in the antiferromagnetic subsystem. Fiz. Tverd. Tela (St. Petersburg) 39, 204–210 (February 1997)     

Local Magnetic Fields in Some Bismuth-Based Diamagnets

Evidence that local ordered magnetic fields from 30 to 250 G exist in bismuth-based diamagnetic compounds comprising neither d- nor f-elements was given by ²⁰⁹Bi NQR spectroscopy and supported by SQUID measurements of α-Bi₂O₃. The NQR experiments involved a study of the zero-field line shapes, analysis of the Zeeman-perturbed patterns, and examination of the zero-field spin-echo envelopes in single crystals and powders. The results of the experiments followed by computer modeling of the observed spectra were interpreted assuming that ordered magnetic fields are located at the bismuth sites in α-Bi₂O₃, Bi₃O₄Br, Bi₂Al₄O₉, Bi₄Ge₃O₁₂, Bi₂Ge₃O₉ and perhaps in Bi₃B₅O₁₂. A survey of the related ²⁰⁹Bi NQR data is here presented.     

Structure and lithium ionic conduction mechanism in La4/3−yLi3yTi2O6

The solid solutions La_4/3−yLi_3yTi₂O₆ (y=0.09∼0.33) have been studied by complex impedance spectroscopy, X-ray diffraction (XRD) and nuclear magnetic resonance (NMR) methods. The ionic conductivity shows a maximum value at around y=0.21, and keeps high values at high y concentrations. The XRD patterns show a single phase for all concentration. The crystal structure is orthorhombic with space groupPmmm for y=0.09∼0.15 and tetragonal with space groupP4/mmm for y=0.17∼0.33. The⁷Li static NMR spectra show a main central peak with a Lorenzian shape for y=0.09∼0.21. The central peak is divided into two parts for y=0.23∼0.33. The narrow intense peak is a mobile component due to mobile ions, and a small broad central peak is due to less mobile lithium ions which contribute to immobile component. The⁷Li MAS NMR spectra show negative chemical shifts which decrease with increasing y concentration. In this paper, we discuss the conduction mechanism and the structure from the analysis of conductivity, lattice parameters, occupation, atomic positions and the⁷Li static/MAS NMR spectra.     

Positive muon sites and possibility of anyons in the YBa2Cu3O x system

Possible positive muon sites in YBa₂Cu₃O _x were determined from the observedμ ⁺ hyperfine fields in antiferromagnetically ordered YBa₂Cu₃O _x and GdBa₂Cu₃O₇. After determining theμ ⁺ sites, the possibility of anyons or chiral spin ordering in the superconducting YBa₂Cu₃O₇ is discussed. Positive muon implanted in YBa₂Cu₃O₇ feel static magnetic fields of average 1.4G, which are explicable in terms of nuclear magnetic dipolar fields. Non observation of static local magnetic fields of electronic origin (the upper limit is the order of 0.1 G) means that anyons or chiral spin ordering might not exist in superconducting YBa₂Cu₃O₇.     

Single‐crystal Raman spectroscopy of brandholzite Mg[Sb(OH)6]2•6H2O and bottinoite Ni[Sb(OH)6]2• 6H2O and the polycrystalline Raman spectrum of mopungite Na[Sb(OH)6]

The single‐crystal Raman spectra of minerals brandholzite and bottinoite, formula M[Sb(OH)₆]₂•6H₂O, where M is Mg⁺² and Ni⁺², respectively, and the non‐aligned Raman spectrum of mopungite, formula Na[Sb(OH)₆], are presented for the first time. The mixed metal minerals comprise alternating layers of [Sb(OH)₆]⁻¹ octahedra and mixed [M(H₂O)₆]⁺²/[Sb(OH)₆]⁻¹ octahedra. Mopungite comprises hydrogen‐bonded layers of [Sb(OH)₆]⁻¹ octahedra linked within the layer by Na⁺ ions. The spectra of the three minerals were dominated by the Sb O symmetric stretch of the [Sb(OH)₆]⁻¹ octahedron, which occurs at approximately 620 cm⁻¹. The Raman spectrum of mopungite showed many similarities to spectra of the di‐octahedral minerals, supporting the view that the Sb octahedra give rise to most of the Raman bands observed, particularly below 1200 cm⁻¹. Assignments have been proposed on the basis of the spectral comparison between the minerals, prior literature and density functional theory (DFT) calculations of the vibrational spectra of the free [Sb(OH)₆]⁻¹ and [M(H₂O)₆]⁺² octahedra by a model chemistry of B3LYP/6‐31G(d) and lanl2dz for the Sb atom. The single‐crystal spectra showed good mode separation, allowing most of the bands to be assigned to the symmetry species A or E. Copyright © 2010 John Wiley & Sons, Ltd.     

New phase transition in an easy-axis “triangular” antiferromagnet

The NMR of ⁵⁵Mn in the quasi-one-dimensional noncollinear anti-ferromagnet CsMnI₃ is investigated at T=1.3 K in magnetic fields up to ∼80 kOe and angles between the field and C ₆ axis ϕ≈ 0.5° and ϕ=7°. A new reorientational magnetic phase transition is observed in a field H _c1≈39.0 kOe. The magnetic structure for H>H _c1 is determined. The average Mn²⁺ spins of the magnetic sublattices in the new phase are determined from an analysis of the NMR spectrum to be 〈 S _C 〉=1.63 and 〈S _D 〉=1.72. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 12, 988–993 (25 June 1998)     

Pauli Operator and Aharonov–Casher Theorem¶ for Measure Valued Magnetic Fields

We define the two dimensional Pauli operator and identify its core for magnetic fields that are regular Borel measures. The magnetic field is generated by a scalar potential hence we bypass the usual A∈L ² _loc condition on the vector potential, which does not allow to consider such singular fields. We extend the Aharonov–Casher theorem for magnetic fields that are measures with finite total variation and we present a counterexample in case of infinite total variation. One of the key technical tools is a weighted L ² estimate on a singular integral operator. Received: 14 May 2001 / Accepted: 5 September 2001     

Observation of spin-reduction anisotropy in the quasi-one-dimensional antiferromagnet CsMnI3

The NMR of ⁵⁵Mn in the quasi-one-dimensional noncollinear antiferromagnet CsMnI₃ at T=1.3 K is investigated in magnetic fields up to ∼40 kOe. Six NMR branches corresponding to six manganese spins per magnetic unit cell are observed. The NMR spectra correspond satisfactorily to the well-known magnetic structure of CsMnI₃, taking into account the dynamic frequency shift due to the interaction with the low-lying AFMR modes. The average spins 〈S _A〉=1.86 and 〈S _B〉=1.74 of the magnetically nonequivalent Mn²⁺ ions are determined from the measured values of the hyperfine fields. The results obtained agree qualitatively with the calculations of spin reduction in quasi-one-dimensional antiferromagnets [Y. Watabe, T. Suzuki, and Y. Natsume, Phys. Rev. B 52, 3400 (1995)]. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 9, 661–665 (10 May 1998)