One-dimensional spin glass with oscillating long-range interaction

In this paper a long-range interacgion approximation for spin glasses is proposed as an alternative to the Sherrington-Kirkpatrick model. The one-dimensional model of Ising spins with the interaction κV _O cosQ x exp (?κ|x|), where κ?c?Q (c is the spin concentration) is studied in detail. The long-range approximation enables one to describe the spin configuration in terms of slowly varying in space fields of the type of amplitude (ρ) and phase (ψ); the ψ-dependent part of the Hamiltonian is analogous to the Hamiltonian, describing the weak pinning of the charge density waves by impurities. As a result, the phase variable apears to be gaples in equilibrium thermodynamics and parametrizes different metastable states under quasiequilibrium conditions. In the mean field approximation (MFA) (κ»0) in the vicinity of the transition pointT _c =cV ₀, there is a symmetric cusp of the magnetic susceptibility ξ; at low temperatures the heat capacity is proportional toT, whereas the susceptibility does not depend on temperature. The MFA cannot be applied in the close vicinity ofT _c (|τ?(κ/c)^2/3) and at very low temperaturesT?κV ₀ when a gap appears in the distribution of the molecular fielsh ath≈0.     

Magnetic correlations in 3d ferromagnets above Tc

A review is presented of our current neutron scattering experiments on Fe and Ni above the Curie temperature. Our experimental results show that the picture of propagating spin waves above T_c, widely accepted since 1973, is incorrect. In addition, we will demonstrate that over wide ranges of ω, q and temperature, both Fe and Ni, as well as Pd₂MnSn, follow a simple paramagnetic scattering function of the spin diffusion type.     

Crystallization and melting of spin-polarized<Superscript>3</Superscript>He

The melting and growth of³He crystals, spin-polarized by an external magnetic field, are different in nature depending on whether the temperature is higher or lower than the characteristic ordering temperatures in the crystal (the Neel temperatureT _N ) and in the liquid (the superfluid transition temperatureT _c ). In the high-temperature region (T≥T _N ,T _c ) the liquid which appears upon melting has a high nonequilibrium spin density. In the low-temperature region (T?T _N ,T _c ) the melting and growth are accompanied by spin supercurrents both in the liquid and in the crystal in addition to mass supercurrents in the liquid. The crystallization waves at the liquid-solid interface should exist in the low-temperature region. With increasing magnetic field the waves change in nature, because the spin currents begin to play a dominant role. The wave spectrum becomes linear with a velocity inversely proportional to the magnetic field. The attenuation of the waves at low enough temperatures is mainly due to the interaction of the moving crystal-liquid interface with thermal spin waves in the crystal. The waves could be weakly damped at temperatures below a few hundreds microkelvins.     

Spin-pair correlations of the classical Heisenberg ferromagnet above and below the critical point: Results of self-consistent Monte Carlo calculations

The spin-pair correlation functions of the classical Heisenberg ferromagnet with simple cubic lattice have been calculated in the paramagnetic and ferromagnetic temperature range using the self-consistent Monte Carlo method. The results agree with high-temperature series expansions aboveT _c , for low temperatures with spin-wave theory. By two different approaches the divergence of the ferromagnetic homogeneous susceptibility in zero field throughout the ferromagnetic temperature range could be verified. The functional dependence of the static susceptibilityχ _T (k) upon the inverse correlation lengthκ ₁ is discussed above and belowT _c and a Fourier transform for the explicit dependence of the spin correlations upon correlation length belowT _c is given. According to these results the scaling assumptionv=v′ for the exponents of the correlation length in the critical region is consistent with a divergent ferromagnetic susceptibility.     

Experimental determination of the critical exponent η for nickel

The first unambiguous experimental determination of the critical exponent η, describing the critical point line shape of the spin correlation function, is presented for a three dimensional magnetic system. As a consequence of a finite value of η the critical scattering displays a maximum at T_max(q) above the Curie temperature T_c. The shift of the maximum with increasing scattering vector q was observed by a neutron small-angle experiment, yielding η=0.041±0.009 for a nickel single-crystal.     

NMR and NQR studies of spin dynamics and superconductivity in High-T c oxides

The magnetic and superconducting properties in the high-T _c cuprates have been investigated over a wide hole doping range by⁶³Cu,¹⁷O and²⁰⁵Tl NMR and NQR in the lightly-doped La_2?xSr_xCuO₄ (LSCO), the heavily-doped Tl₂Ba₂CuO_6+y (TBCO) and the Zn-doped YBa₂Cu₃O₇ (YBCO₇). In low doping region, the large antiferromagnetic (AF) spin correlation around the zone boundary (q=Q) causes the Curie-Weiss behavior of⁶³(1/T ₁ T) associated with that of the staggered susceptibility χ_O(T) in LSCO. In the vicinity of the hole content whereT _c has a peak, the AF spin correlation still survives, although the magnetic coherence length ξ_M is considerably short being presumably (ξ_M/a) ～ 1. The further doping destroys progressively the AF spin correlation, which is no longer present is non-superconducting TBCO compounds. These NMR evidences signify that there is an intimate relation between the presence of the AF spin correlation and the onset of the superconductivity. The local collapse of AF spin correlation is a primary cause for the unexpected strong reduction ofT _c in case of the substitution of Zn impurities into the CuO₂ plane. The superconducting properties clarified by NMR experiments cannot be accounted for by the conventional BCS model or other isotropic s-wave models. A d-wave model is applicable in interpreting consistently most of the NMR results, if the finite density of states at the Fermi level is taken into consideration and is associated with the pair breaking effect. There are increasing evidences that the magnetic mechanism for the superconductivity is promising in high-T _c cuprates.     

The CESR and spin wave studies of A-15 films in normal and superconducting states

The electron spin resonance studies have been reported for A-15 superconductors, namely Nb₃Ge, Nb₃Si and V₃Si possessing different T_c values and CESR, Platzmann-Wolff type spin waves, and spin waves of antiferromagnetic type are observed in all the samples. It is found that T_c of Nb₃Ge depends upon the presence and separation of spin wave absorptions from the CESR, and T_c is found to increase when the separation is reduced. It is concluded that the exchange interactions in the conduction band, as manifested by the behaviour of spin waves, are of antiferromagnetic type and they are responsible for superconductivity in A-15 materials studied.     

A neutron small angle scattering study of the onset of ferromagnetism in TiBe2-xCux alloys

The onset of ferromagnetic order in TiBe_2-xCu_x alloys, with x = 0.5, 0.4, 0.3, 0.2 and 0.15, has been examined using the technique of neutron small-angle scattering. The Curie temperature, T_c, for these alloys has been determined from the temperature dependence of the magnetic critical scattering. A linear extrapolation of T_c versus copper concentration yields a critical concentration for ferromagnetic order of x_c = 0.05 ± 0.02. For the alloys with x = 0.4, 0.5 the lineshape of the magnetic critical scattering, at and above T_c, is well explained by the Ornstein-Zernicke form of the spin correlation function. For the lower concentration alloys the exact form of the spin correlation function is still unclear.     

Proton spin relaxation in hexagonal ice

Measurements of the rotating frame proton spin relaxation timeT _1p in hexagonal ice single crystals as a function of temperature ? for various rotating magnetic field strengths reveal the expectedT _1p minimum at the lowest practicable field values. This allows a very precise determination of the proton correlation (? molecular jump) time τ_c and the related activation energy ΔE by means of the theoretical reasoning of relaxation spectroscopy. We find the Arrhenius-law temperature dependenceτ _c=1.99×10^?17exp(0.603/8.61×10^?5 ?)sec, which is in good agreement with our earlier indirect derivation.     

Critical dynamics in isotropic ferromagnets

Modern high resolution inelastic neutron scattering methods make very long wavelength fluctuations accessible to dynamical investigation. The new results on Fe and EuO show that: (a) the $\text{q}{}^{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$ power law is well borne out at T = T_c; (b) strong zero-wavenumber relaxation due to spin non-conserving forces can make the predicted hydrodynamic spin diffusion at T >T_c unobservable; (c) this zero-wavenumber relaxation is the only appreciable deviation from the $\text{z =}\text{5}\text{2}$ exchange scaling behaviour; (d) there is no evidence for the predicted cross-over to dipolar dynamics a finite q's.     

Effect of renormalization of magnetic fluctuations on the kinetic coefficients of high-T c superconductors

Temperature dependences of resistivity, ρ(T), and Hall coefficient, R _H (T), in a 2D doped antiferromagnet are studied for various forms of the dynamic spin susceptibility X(q, θ) (in the mean-field approximation, taking into account attenuation and renormalization of the magnetic excitation spectrum θ_q, and for so-called strongly overdamped magnons). Doped CuO₂ planes in cuprates are considered in the one-band model of the Kondo lattice. Charge carrier scattering anisotropy, which strongly depends on temperature, is taken into account using the density matrix formalism and seven-moment approximation for the nonequilibrium distribution function. It is shown that the behavior of ρ(T) and R _H (T) is completely determined by the renormalization θ_q → $\omega _q \to \tilde \omega _q $ of the spin wave spectrum (the renormalization is essentially controlled by the fulfillment of the sum rule for X(q, θ) and by the strong temperature dependence of the gap δ(T). The resultant ρ(T) and R _H (T) dependences match the experimental data for optimally doped high-T _c superconductors.     

Iron above the curie temperature

A quantitative discussion is given of recent paramagnetic diffuse neutron scattering data on bcc Fe above T_c. It is found that although the spatial spin correlation function has a weak tail of fairly long range the correlation between nearest neighbour spin directions is very small at 1.24T_c. It is concluded that the data are inconsistent with the giant short-range order hypothesis of Prange and Korenman, Capellmann and Sokoloff and another interpretation is given.     

Orientational dynamics of superfluid 3He: A “two-fluid” model. II. Orbital dynamics

We present a phenomenological theory of the homogeneous orbital dynamics of the class of “separable” anisotropic superfluid phases which includes the ABM state generally identified with ³He-A. The theory is developed by analogy with the spin dynamics described in the first paper of this series; the basic variables are the orientation of the Cooper-pair wavefunction (in the ABM phase, the l-vector) and a quantity K which we visualize as the “pseudo-angular momentum” of the Cooper pairs but which must be distinguished, in general, from the total orbital angular momentum of the system. In the ABM case l is the analog of d in the spin dynamics and K of the “superfluid spin” S_p. Important points of difference from the spin case which are taken into account include the fact that a rotation of l without a simultaneous rotation of the normal-component distribution strongly increases the energy of the system (“normal locking”), and that the equilibrium value of K is zero even for finite total angular momentum. The theory does not claim to handle correctly effects associated with any intrinsic angular momentum arising from particle-hole asymmetry, but it is shown that the magnitude of this quantity can be estimated directly from experimental data and is extremely small; also, the Landau damping does not emerge automatically from the theory, but can be put in in an ad hoc way. With these provisos the theory should be valid for all frequencies $\text{ω ?}\text{Δ(T)}\text{h}\text{?}$ irrespective of the value of ωτ. (Δ = gap parameter, τ = quasi-particle relaxation time.) It disagrees with all existing phenomenological theories of comparable generality, although the disagreement with that of Volovik and Mineev is confined to the “gapless” region very close to T_c.The phenomenological equations of motion, which are similar in general form to those of the spin dynamics with damping, involve an “orbital susceptibility of the Cooper pairs” χ_orb(T). We give a possible microscopic definition of the variable K and use it to calculate χ_orb(T) for a general phase of the “separable” type. The theory is checked by inserting the resulting formula in the phenomenological equations for ωτ ? 1 and comparing with the results of a fully microscopic calculation based on the collisionless kinetic equation; precise agreement is obtained for both the ABM and the (real) polar phase, showing that the complex nature of the ABM phase and the associated “pair angular momentum” is largely irrelevant to its orbital dynamics. We note also that the phenomenological theory gives a good qualitative picture even when ω ～ Δ(T), e.g., for the flapping mode near T_c. Our theory permits a simple and unified calculation of (1) the Cross-Anderson viscous torque in the overdamped regime, (2) the flapping-mode frequency near zero temperature, (3) orbital effects on the NMR, both at low temperatures and near T_c, (4) the orbit wave spectrum at zero temperature (this requires a generalization to inhomogeneous situations which is possible at T = 0 but probably not elsewhere). We also discuss the possibility of experiments of the Einstein-de Haas type. Generally speaking, our results for any one particular application can be also obtained from some alternative theory, but in the case of orbital and spin relaxation very close to T_c (within the “gapless” region) our predictions, while somewhat tentative and qualitative, appear to disagree with those of all existing theories. We discuss briefly how our approach could be extended to apply to more general phases.     

Ultrasonic attenuation determination of Hc1 and Hc2 for ErRh4B4 at 1.5 K

The attenuation coefficient of longitudinal sound waves propagating in ErRh₄B₄ has been measured as a function of applied magnetic field where the propagation direction (q) of the sound waves was oriented either parallel or perpendicular to H_applied. For both orientations there is evidence of a type II-1 superconducting transition at H_c1 for T ≈ 1.5 K. In addition, when q ⊥ H an increase in attenuation is evident at H_c2, which does not appear when q 6 H, consistent with theories developed by Tachiki et al. utilizing supercurrent screening of the internal magnetic fields.     

Magnetic correlations in disordered MncZn1−cTe alloys

The spin correlations between Mn ions in Zn_1?cMn_cTe alloys have been measured as a function of temperature and concentration. The spin correlations follow the same sign sequence as for a type III antiferromagnet out to seven shells of neighbours. Complete long range magnetic order was not observed for any c or T.     

Spin-orbit effects in carbon nanotubes – Analytical results

We report a study of the normal and superconducting state properties of the Ti _x V_1?x alloys for x = 0.4, 0.6, 0.7 and 0.8 with the help of dc magnetization, electrical resistivity and heat capacity measurements along with the electronic structure calculation. The superconducting transition temperature T _c of these alloys is higher than that of elemental Ti and is also higher than elemental V for x ≤ 0.7. The roles of electron density of states, electron-phonon coupling and spin fluctuations in the normal and superconducting state properties of these alloys have been investigated in detail. The experimentally observed value of T _c is found to be considerably lower than that estimated on the basis of electron density of states and electron-phonon coupling in the x = 0.4, 0.6 and 0.7 alloys. There is some evidence as well for the preformed Cooper pair in all these Ti-V alloys in the temperature regime well above T _c . Similar to x = 0.6 [Md. Matin, L.S. Sharath Chandra, R.K. Meena, M.K. Chattopadhyay, A.K. Sinha, M.N. Singh, S.B. Roy, Physica B 436, 20 (2014)], the normal state properties of the x = 0.4 alloy showed the signature of the presence of spin fluctuations. The difference between the experimentally observed T _c and that estimated by considering electron density of states and electron-phonon coupling in the x = 0.4, 0.6 and 0.7 alloys is attributed to the possible influence of these spin fluctuations. We show that the non-monotonous variation of T _c as a function of x in the Ti _x V_1?x alloys is due to the combined effects of the electron-phonon coupling and the spin fluctuations.     

Role of inter-site exchange and hybrid interactions in itinerant ferromagnetism

In this work, we study the magnetic properties of itinerant electron systems using the Hubbard-like tight binding Hamiltonian along with inter-site exchange and hybrid interactions. We have used the mean-field approximation to deal with the exchange and hybrid interactions. It is found that hybrid interaction is more effective than exchange interaction for the on-set of ferromagnetic state. We have studied the effect of hybrid interaction on various physical quantities at different temperatures. The effective mass (m*/m) of up spin electrons increases slowly as the temperature decreases but below the critical temperature (T_c), it decreases rapidly. For down spin electrons effective mass increases slowly as the temperature decreases and below T_c, it increases more rapidly. Spectral weight (n/m*) for up spin electrons decreases slowly upto T_c and below T_c, it increases rapidly. For down spin electrons spectral weight decreases slowly upto T_c and below T_c, it decreases rapidly. Our results for both the effective mass and spectral weight are in good agreement with recently observed experimental behaviour in itinerant ferromagnet Ga_1−xMn_xAs [Phys. Rev. Lett. 89 (2002) 097203]. We have also studied variation of the spectral weight and optical absorption with temperature in presence of magnetic field. We found that these two quantities for up spin electrons increase as applied magnetic field increases at all temperatures (∼4T_c). For down spin electrons these two quantities decrease as applied magnetic field increases.     

Scaling function for order-parameter correlations in expansion to order 1/n: I. Short-range interactions

The order-parameter correlation function $\text{G}\text{?}\text{(}\text{q}\text{, ξ}{}_1\text{)}$ is calculated in the critical region of momentum space $\text{q}$ in terms of a second-moment correlation length ξ₁ by means of perturbation expansion to order 1/n, for an n-vector system with short-range interactions, in zero field above T_c, for 2 < d < 4. The scaling function of the $\text{q}$ dependence is obtained in closed form with a precisely identified cutoff-dependent factor which is the amplitude of the correlation-length dependence of the susceptibility. Both the exponents and the coefficients of the expansion for fixed q as t = (T?T_c)/T_c → 0 are given explicitly and the former are shown to be in accordance with the operator product expansion. The coefficients of order 1/n in the terms associated with a t^k(1?α) dependence of the energy density, for integer k ≥ 1, are expected to be explicitly cutoff-dependent and this is verified by the detailed calculations for k = 1. The behaviour for fixed t and q → 0 is shown to be markedly different from the Ornstein-Zernike approximation. Detailed comparison is provided with the scaling function of the t dependence of the correlations appearing in parallel work.     

Temperature dependence of the magnetization in the mixed state of superconducting alloys

The theory of Abrikosov of the immediate subcritical region in the mixed state is extended by means of the generalized Ginzburg-Landau theory to temperatures belowT _c and arbitrary mean free pathl of the electrons. The results for the magnetization and the free energy can still be presented in the form derived by Abrikosov apart from the fact thatκ is replaced by a new parameterκ ₂(T). The slope of the curveκ ₂/κ versust=T/T _c att=1 is found to decrease monotonically from ?0.105 to — (1.367-0.136κ ^?2) asl increases from zero to infinity. The results for short mean free paths are consistent with experiment, in particular,κ ₂ is always larger thanκ in the vicinity ofT _c . But the experimental temperature dependence ofκ ₂/κ in pure Nb is much higher than the theoretical one.     

Spin correlations in Ni-Mn-Ga

Results of measuring small-angle neutron scattering and neutron depolarization in a Ni_49.1Mn_29.4Ga_21.5 single crystal in the temperature range 15<T<400 K and in the range of magnetic fields 0<H<4.5 kOe are presented. The characteristic temperatures of the alloy were found to be as follows: T _C=373.7 K and the martensite transition temperature T _m=301–310 K. The magnetic critical scattering at T _C and the scattering at T<T _C were adequately described by the relationship I _m=A(q ²+κ²)^?2 (q is the transferred wave vector and R _c=1/κ is the correlation radius), and the temperature dependences of the A and R _c scattering parameters were determined. Left-right asymmetry was observed at 150<T< T _m in the scattering of neutrons polarized along or opposite to the applied field. This asymmetry was due to the inelastic magnetic interaction of neutrons in the sample. The magnetization of the alloy at T _m, critical scattering at T?T _C, anomalies in scattering, and the softening of magnetic excitations at 150 <T<T _m are discussed.