Thermal conductivity and specific heat of SrCu2(BO3)2: A quasi-two-dimensional metal oxide compound with a spin gap

The thermal conductivity and specific heat of SrCu₂(BO₃)₂, a quasi-two-dimensional metal oxide compound with a spin gap, were studied at low temperatures. In the temperature interval 0.4<T<3.2 K, the thermal conductivity of a single crystal sample in the ab plane varies according to the power law κ∝T ^2.73. As the temperature increases further, a deep minimum is observed in the region of T _min≈9.8 K. This behavior is explained by the scattering of phonons—the major heat carriers—on the fluctuations of the spin subsystem.     

Nuclear magnetic resonance study of the heavy-fermion system URu2Si2

Nuclear magnetic resonance (NMR) and relaxation studies on ²⁹Si have been carried out on the heavy Fermion system URu₂Si₂. Above the Kondo temperature of about 60 K, the nuclear relaxation time T₁ is nearly temperature independent, which is consistent with the occurrence of fluctuations of localized U moments. Below about 60 K T₁ is inversely proportional to temperature suggesting that the system behaves like a Fermi liquid. A sharp increase in T₁ occurs below 17 K which is probably associated with the opening of an energy gap at the Fermi surface due to the formation of a spin density wave state. Below about 10 K, T₁ reacquires the inverse temperature dependence observed in the 17 K ∼ 60 K temperature range.     

Photoexcited Eu2+ spin dynamics in EuFe2As2

Employing temperature dependent time-resolved optical femtosecond spectroscopy, we investigated the quasiparticle and Eu²⁺ spin relaxation dynamics in EuFe₂As₂ (EFA). As previously reported in other undoped iron-based pnictides, we observe the quasiparticle relaxation bottleneck due to the charge gap opening in the spin density wave (SDW) state below T _SDW = 189 K. Below the Eu²⁺ antiferromagnetic (AFM) spin ordering temperature, T _AFM = 19 K, we observe another slower relaxation component, which we attribute to the Eu²⁺ AFM order dynamics. The slow dynamics of this component suggests a weak coupling between the Eu²⁺ spins and the carriers in the Fe-d derived bands.     

Flow equations for the ionic Hubbard model

Taking the site-diagonal terms of the ionic Hubbard model (IHM) in one and two spatial dimensions, as H₀, we employ Continuous Unitary Transformations (CUT) to obtain a “classical” effective Hamiltonian in which hopping term has been renormalized to zero. For this Hamiltonian spin gap and charge gap are calculated at half-filling and subject to periodic boundary conditions. Our calculations indicate two transition points. In fixed Δ, as U increases from zero, there is a region in which both spin gap and charge gap are positive and identical; characteristic of band insulators. Upon further increasing U, first transition occurs at U=Uc₁, where spin and charge gaps both vanish and remain zero up to U=Uc₂. A gap-less state in charge and spin sectors characterizes a metal. For U>Uc₂ spin gap remains zero and charge gap becomes positive. This third region corresponds to a Mott insulator in which charge excitations are gaped, while spin excitations remain gap-less.     

Spin gap, phase separation and d-wave pairing as revealed by electron spin-lattice relaxation in 123 and 124 YBaCuO systems doped with Gd3+

With an original modulation technique, the Gd³⁺ electron spin-lattice relaxation has been investigated in normal and superconducting states of YBa₂Cu₃O_6+x (123) and YBa₂Cu₄O₈ (124) compounds doped with 1% Gd. In the 123 sample withx = 0.9T _c = 90 K), theT ₁ behavior within 50 <T< 200 K reveals the [1 ? tanh²(Δ/2kT)]/T dependence typical of a spin gap opening with Δ ≈ 240 K. Below 50 K, the exponential slowing down ofT ₁ is limited by the Korringa-like behaviorT ₁ T = const); the same Korringa-like law is found in the 123 sample withx = 0.59 (T _c = 56 K) within the total 4.2–200 K temperature range. This is interpreted in terms of microscopic separation of the normal and superconducting phases allowing for the electron spin cross-relaxation between them. In the 124 sample (T _c = 82 K), the Gd³⁺ relaxation rate below 60 K is found to obey a power lawT _n with an exponentn ≈ 3. Such a behavior (previously reported for nuclear spin relaxation) is indicative of the d-wave superconducting pairing. Additional paramagnetic centers characterized by relatively slow spin-lattice relaxation are found in both 123 and 124 systems. A well-pronounced change in theT ₁ temperature dependence atTT* ≈ 180–200 K is observed for these slowly relaxing centers as well as for the conventional, fast-relaxing Gd³⁺ ions, suggesting microscopic phase separation and a change in the relaxation mechanism due to electronic crossover related with the opening of the spin gap. This hypothesis is supported by some “180 K anomalies” previously reported by other authors.     

Nuclear spin-lattice relaxation of protons in low-dimensional Ising-like system: [(CH3)3NH]CoCl3 · 2H2O

The nuclear spin-lattice relaxation times of protons in a low-dimensional Ising-like system [(CH₃)₃NH]CoCl₃ · 2H₂O were measured from 1.2 to 4.2 K in zero field and in an external magnetic field applied along the spin easy-axis. The calculation for the two-magnon Raman process was carried out with respect to a ferromagnetic layer of the bc-plane. By taking the gap energy to be 14.0 K, the best fit of the theoretical curves with the data was obtained from 1.2 K to about 2.0 K. The experimental results at high temperatures deviate seriously from the prediction of this process, which is discussed in terms of a tentative model for the nuclear relaxation process associated with magnon bound states.     

Spin gaps and spin dynamics in superconducting cuprates

Spin gap effects, consisting of a declining uniform susceptibility and spin paramagnetic NMR shift at low temperaturesin the normal state and associatedT ₁ behavior, are discussed and documented in several cuprate superconductors. Dynamic spin magnetism in these systems is further reviewed in the light of mean-field models, where we note that detailed results from the model by Millis, Monien, and Pines are not borne out in recent neutron data on YBa₂Cu₃O_6.92.T ₁ data on¹⁷O in La_1.85Sr_0.15CuO₄ are presented, showing consistency with neutron dynamic susceptibility data forT≧80 K, but exhibiting a strong spin gap character below 80 K which is not present in the neutron data. Data for Zn-doped YBCO withT _c≈60 K are also presented, showing strong RKKY broadening from localized moments in the planes, but no spin gap effect such as that found in theT _c=60 K oxygen-deficient phase.     

Electron spin resonance in the Heusler alloy YbRh2Pb

An electron spin resonance (ESR) signal was observed in a concentrated Kondo lattice, Heusler alloy YbRh₂Pb. It is attributed to the combined effect of the 4f local magnetic moments of Yb³⁺ and conduction electrons. It is shown that the significant broadening and disappearance of the ESR line at temperatures above 20 K is caused by the processes of the spin-lattice relaxation of the Yb³⁺ ions through the first excited Stark doublet with an activation energy Δ ≈ 73.5 K. A comparison of the ESR data for YbRh₂Pb and some other undoped intermetallic compounds based on ytterbium, cerium, and europium indicates that hybridized electronic states occurring as the result of hybridization between the localized 4f electrons and the collectivized conduction electrons constitute a fundamentally new source of ESR.     

Tunable electronic structure in stained two dimensional van der Waals g-C2N/XSe2 (X = Mo,W) heterostructures

The electronic structure of the strained g-C₂N/XSe₂ (X=Mo, W) van der Waals heterostructures are investigated by first-principles calculations. The g-C₂N/MoSe₂ heterostructure is an indirect band gap semiconductor at a strain from 0% to 8%, where its band gap is 0.66, 0.61, 0.73, 0.60 and 0.33 eV. At K point, the spin splitting is 186, 181, 39, 13 and 9 meV, respectively. For g-C₂N/WSe₂ heterostructures, the band gap is 0.32, 0.37, 0.42, 0.45 and 0.36 eV, and the conduction band minimum is shifted from Г-M region to K-Г region as the strain increases from 0% to 8%. Its spin splitting monotonically decreases as a strain raises to 8%, which is 445, 424, 261, 111 and 96 meV, respectively. Moreover, at a strain less than 4%, the conduction band mainly comes from g-C₂N, but it comes from XSe₂ (X=Mo, W) above 6%. Our results show that the g-C₂N/XSe₂ heterostructures have tunable electronic structures, which makes it a potential candidate for novel electronic devices.     

Shubnikov-de haas effect in n-CdSnAs2

Shubnikov-de Haas oscillations in the transverse magnetoresistance of single-crystalline n-type CdSnAs₂ have been recorded at temperatures between 2 and 25 K in magnetic fields up to 5T. The electron concentration of the samples ranged from 2 × 10¹⁷ to 2 × 10¹⁸ cm^?3. The angular dependences of the oscillation periods and cyclotron effective masses showed that the conduction band exhibits an energy dependent anisotropy, obeying the Kildal band structure model. For the low-temperature values of the band parameters we found: a band gap E_g = 0.30 eV, a spin-orbit splitting Δ = 0.50 eV, a crystal field splitting parameter δ = ?0.09 eV, and an interband matrix element P = 8.5 × 10^?8eV cm. This simple four-level model was found to be not adequate to describe quantitatively the observed electronic effective g-factor for a sample with low electron concentration.     

Modeling Spectroscopic Properties of Ni2+ Ions in the Haldane Gap System Y2BaNiO5

Modeling of spin Hamiltonian parameters enables correlation of crystallographic, spectroscopic, and magnetic data for transition ions in crystals. In this paper, based on the crystallographic data and utilizing the point-charge model and superposition model, the crystal field parameters (CFPs) are estimated for Ni²⁺(3d ⁸) ions in the Haldane gap system Y₂BaNiO₅. The CFPs serve as input for the perturbation theory expressions and the crystal field analysis package for microscopic spin Hamiltonian modeling of the zero-field splitting parameters (ZFSPs) D and E. Results of an extensive literature search of the pertinent crystallographic data, experimental ZFSPs, and model parameters are briefly outlined. The modeling aims at verification of the experimental ‘single ion anisotropy’ parameters and explanation of the controversy concerning the maximal rhombic distortion |E/D| ≈1/3 reported for Ni²⁺ ions in Y₂BaNiO₅. The preliminary results call for reanalysis of some magnetic studies of the Haldane gap systems.     

High field ESR measurements of spin gap system MCu2(PO4)2

Submillimeter and millimeter wave ESR measurements of spin gap systems SrCu₂(PO₄)₂ and PbCu₂(PO₄)₂, which have four kinds of dimers, have been performed to investigate the magnetic properties of spin gap systems using the pulsed magnetic field up to 35T. The observed ESR spectra of powder sample SrCu₂(PO₄)₂ show sharp and single peak in the temperature range from 4.2 to 80 K. The anisotropy of the g-values turned out to be very small compared to the usual anisotropic powder spectra of copper compounds. The dynamical properties will be discussed from the temperature dependence measurements.     

Electron spin-lattice relaxation in noncommon metals YBa2Cu3Ox and Rb1C60

Using an original modulation technique, the electron spin-lattice relaxation have been investigated in two noncommon metals: YBa₂Cu₃O_x, high-T_c material doped with 1% Gd, and Rb₁C₆₀, linear polymer phase fulleride. In the first case, the Korringa-like temperature dependence of the Gd³⁺ longitudinal relaxation time T₁, is found forx = 6.59 in a wide temperature range 4.2 <T < 200 K, both above and below T_c = 56 K. Atx = 6.95 (T_c = 90 K), the T₁ behavior within 50 <T < 200 K is evidently affected by spin gap opening with the gap value of about 240 K. At 200 K, an unexpected acceleration of the relaxation rate takes place, suggesting some change in the relaxation mechanism. The data are discussed in terms of the Barnes-Plefke theory with allowance made for microscopic separation of the normal and superconducting phases. In Rb₁C₆₀, the evolution of the ESR line and relaxation rates have been studied accurately in the range of the metal-insulator transition (below 50 K). Interpretation is suggested which takes into account breaking down the relaxation bottleneck due to opening of the energy gap near the Fermi surface. The gap value of about 100 cm^?1 is estimated from the analysis of relaxation rates, lineshape and spin susceptibilities.     

Negative boron isotope effect of a ‘2Δ’ gap peak in Raman spectra from non-magnetic borocarbide superconductors

The nickel borocarbides RNi₂B₂C, R=Y or Lu, have a superconducting T_c of 15-16 K and exhibit properties consistent with an anisotropic s-wave gap. We briefly review their properties. Electronic Raman scattering results are presented on YNi₂B₂C containing ¹¹B or ¹⁰B. In A_1g and B_1g Raman symmetries, there is no shift in the position of the ‘2Δ’ peak with B-isotope. There is a distinct negative shift, however, in B_2g symmetry. This is interpreted as a negative isotope shift for the gap Δ on that portion of the Fermi surface where the magnitude of the B_2g Raman vertex is large.     

The temperature evolution of the magnetic correlations in pure and diluted spin ice Ho2−xYxTi2O7

Diffuse polarized neutron scattering studies have been carried out on single crystals of pyrochlore spin ice Ho_2−xY_xTi₂O₇ (x=0, 0.3, and 1) to investigate the effects of doping and anisotropy on spin correlations in the system. The crystals were aligned with the (1 −1 0) orientation coincident with the direction of neutron polarization. For all the samples studied the spin flip (SF) diffuse scattering (i.e. the in-plane component) reveals that the spin correlations can be described using a nearest-neighbour spin ice model (NNSM) at higher temperatures (T=3.6 K) and a dipolar spin ice model (DSM) as the temperature is reduced (T=30 mK). In the non-spin flip (NSF) channel (i.e. the out-of-plane component), the signature of strong antiferromagnetic correlations is observed for all the samples at the same temperature as the dipolar spin ice behaviour appears in the SF channel. Our studies show that the non-magnetic dopant Y does not significantly alter SF or NSF scattering for the spin ice state, even when Y doping is as high as 50%. In this paper, we focus on the experimental results of the highly doped spin ice HoYTi₂O₇ and compare our results with pure spin ice Ho₂Ti₂O₇. The crossover from a dipolar to a nearest-neighbour spin ice behaviour and the doping insensitivity in spin ices are briefly discussed.     

Enhancement of the anomalous Hall effect and spin glass behavior in the bilayered manganite La2−2xSr1+2xMn2O7

The Hall resistivity and magnetization have been investigated in the ferromagnetic state of the bilayered manganite La_2−2xSr_1+2xMn₂O₇ (x=0.36). The Hall resistivity shows an increase in both the ordinary and anomalous Hall coefficients at low temperatures below 50 K, a region in which experimental evidence for the spin glass state has been found in a low magnetic field of 1 mT. The origin of the anomalous behavior of the Hall resistivity relevant to magnetic states may lie in the intrinsic microscopic inhomogeneity in a quasi-two-dimensional electron system.     

Charge density wave transition in Na2Ti2Sb2O probed by 23Na NMR

Herein we investigated the electronic properties of layered transition-metal oxides Na2Ti2Sb2O by23Na nuclear magnetic resonance(NMR)measurement.The resistivity,susceptibility and specific heat measurements show a phase transition at approximately 114 K(TA).No splitting or broadening in the central line of23Na NMR spectra is observed below and above the transition temperature indicating no internal field being detected.The spin-lattice relaxation rate divided by T(1/T1T)shows a sharp drop at about 110 K which suggests a gap opening behavior.Below the phase transition temperature zone,1/T1T shows Fermi liquid behavior but with much smaller value indicating the loss of large part of electronic density of states(DOS)because of the gap.No signature of the enhancement of spin fluctuations or magnetic order is found with the decreasing temperature.These results suggest a commensurate charge-density-wave(CDW)phase transition occurring.     

The exact ground state and the origin of the spin gap in the distorted mixed spin (1, 1/2) diamond chain

By using the method of exact diagonalization, we investigated the properties of the distorted mixed spin (1, 1/2) diamond chain with antiferromagnetic interactions along the rung and leg. The ground states of this model contain the sawtooth chain state and the rung dimer plus Haldane state. The research on the origin of the spin gap of the model discloses that there are three different types of spin excitations at different parameter regimes due to the competition among the interactions J₁, J₂ and J₃.     

Stoner excitations in the strong itinerant amorphous ferromagnets FexNi80−xB18Si2 and Fe80B20

Accurate measurements of the static magnetization of the amorphous ferromagnets Fe_xNi_80?xB₁₈Si₂ (x = 15, 20, 40, 60%) and Fe₈₀B₂₀ are reported. The results are analyzed in terms of spin-wave and Stoner excitations, and the latter indicate strong itinerant ferromagnetism with a Stoner gap Δ varying between 20 and 60 K. The other fitting parameters give values of the spin-wave stiffness and a quantity simply related to the saturation magnetization. The well-known anomaly regarding the spin-wave stiffness observed in earlier measurements in thus explained quantitatively.     

Chemical-potential dependence of the pairing gap in a nuclear-matter slab

The equation for the pairing gap Δ in a slab of nuclear matter governed by the Paris nucleon-nucleon potential is solved for various values of the chemical potential μ in the range from −8 MeV, which corresponds to stable nuclei, to −0.1 MeV, which corresponds to nuclei in the vicinity of the nucleon drip line. The slab is placed in a one-dimensional Woods-Saxon potential whose parameters are set to values typical of nuclei. Two models are considered. In the first, the potential-well depth is fixed at U ₀ = −50 MeV, the density within the slab growing as |μ| is reduced. In the second model, the density is fixed at the center of the slab, |U ₀| decreasing as |μ| is reduced. The behavior of the gap Δ as a function of μ is model-dependent. In the first model, Δ decreases with decreasing |μ|, while, in the second, it increases. At the same time, the effect of the surface enhancement of Δ becomes more pronounced with decreasing |μ| in both models. Original Russian Text ? S.S. Pankratov, E.E. Saperstein, M.V. Zverev, 2006, published in Yadernaya Fizika, 2006, Vol. 69, No. 12, pp. 2052–2063.