Spin fluctuations and high temperature superconductivity

Theory of spin fluctuations for itinerant magnetism and its application to high temperature superconductivity are reviewed. After a brief introduction to the whole subject the developments of the self-consistent renormalization theory of spin fluctuations are summarized with particular emphasis on critical properties at the quantum phase transitions. Most of the anomalous properties in the normal state of high-T_c cuprates are understood as due to the critical behaviours for the two dimensional antiferromagnetic metals. By analysing the nuclear magnetic relaxation rate and the T-linear term of resistivity, the set of parameters to specify the spin fluctuations are determined. It is shown that by using the parameters thus obtained one can describe other quantities as well, e.g. optical conductivity. Then we proceed to the theory of superconductivity by the spin fluctuation mechanism. After some discussion on the weak coupling treatments, the strong coupling theory is reviewed. It is shown that the set of parameters determined by the normal state properties of the high-T _c cuprates just give a transition temperature of the right order of magnitude. Among the parameters, the most sensitive one for T _c is the frequency spread of the spin fluctuations. This fact enables us to present a possible unified picture of the antiferromagnetic spin fluctuation-induced superconductors, including heavy fermion superconductors and organic superconductors. This point of view may be confirmed to a certain extent by microscopic calculations based on the fluctuation exchange approximation for the two-dimensional Hubbard models representing not only the cuprates but also organic and trellis lattice compounds. The review is concluded with some discussions on future problems, e.g. the pseudo spin-gap in the under-doped region.     

Spin fluctuations in metals: Application to the actinides

We present here a review of the spin fluctuation theory and of its applications to transition and actinide systems, with a particular emphasis to the latter where some very anomalous properties find an explanation in terms of spin fluctuation effects. Firstly, we summarize the development of the spin fluctuation model which had been initially applied to transition metals and alloys such as palladium or Pd–Ni alloys. Then, we present the extension of the paramagnon model to nearly magnetic actinide systems by taking into account explicitly the temperature dependence of the Stoner susceptibility, because the 5f-band of actinides is much narrower than the d-band of transition metals. As a result the paramagnon contribution to the resistivity departs from the usual T ² and T power laws at temperatures higher than the spin fluctuation one and saturates at high temperatures, with eventually the presence of a maximum at intermediate temperatures. We present also the calculation of the other properties of actinide systems, namely the thermal resistivity, the thermoelectric power, the magnetic susceptibility, the specific heat capacity and the NMR relaxation rate, which are generally enhanced by the presence of paramagnons. Finally, we have introduced the concept of ‘antiferromagnetic-like’ spin fluctuations which have a maximum of the q-dependent susceptibility _χ(q) at a q value different from q =0, in contrast to the regular ferromagnetic spin fluctuations; both types of spin fluctuation give the same resistivity behaviour, while they yield a markedly different behaviour of the magnetic susceptibility, in agreement with experiment. The spin fluctuation theory is applied successfully to the different properties of neptunium and plutonium metals and of many nearly magnetic compounds such as UAl₂.     

Cooperative order and excitation spectra in the bicomponent spin networks

A ferrimagnetic spin model composed of S = 1/2 spin-dimers and S = 5/2 spin-chains is studied by combining the bond-operator representation (for S = 1/2 spin-dimers) and Holstein-Primakoff transformation (for S = 5/2 spins). A finite interaction J _DF between the spin-dimer and the spin chain makes the spin chains ordered antiferromagnetically and the spin dimers polarized. The effective interaction between the spin chains, mediated by the spin dimers, is calculated up to the third order. The staggered magnetization in the spin dimer is shown proportional to J _DF. Due to the triplon-magnon interaction, the degeneracy of the triplons is lifted and the hybridized triplon-like excitations show different behaviors near the vanishing J _DF. A mode with longitudinal polarization is identified. The hybridized magnon-like excitations are also studied. These results are compared with the experiments on Cu₂Fe₂Ge₄O₁₃.     

Density of states,level-statistics and localization of fractons in 2- and 3-dimensional disordered systems

We calculate by the Lanczos method the density of spin wave states, and its fluctuation properties on the infinite percolating cluster of a randomly site-dilute Heisenberg ferromagnet. Our results demonstrate that the averaged density follows the fracton laws with spectral dimension valuesd _s =1.32 andd _s =1.30 in two and three dimensions, respectively, and is smooth at the magnon-fracton crossover. Similar laws are also shown in the case of continuous disorder on the bonds of the clusters. The density fluctuations are studied via the nearest energylevel-spacing distribution functionP(S), which is shown to obey the Wigner surmise with level-repulsion far from the percolation thresholdp _c and an almost Poisson law with uncorrelated spectrum atp _c . The localization properties of excitations are investigated by considering the density of states fluctuations and also via the participation ratio of the eigenvector amplitudes. It is seen that the fracton states are sharply localized. Our results are further discussed in connection to previous theories and numerical data.     

Spin liquid in an almost ferromagnetic Kondo lattice

A theory of stabilization of a spin liquid in a Kondo lattice at temperatures close to the temperature of antiferromagnetic instability has been developed. Kondo exchange scattering of conduction electrons leads to emergence of a state of the spin liquid of the resonating valence bonds (RVB) type at T>T _K. Owing to this stabilization, low-energy processes of Kondo scattering with energies below T _K are frozen so that the “singlet” state of the Kondo lattice is not realized; instead a strongly correlated spin liquid with developed antiferromagnetic fluctuations occurs. A new version of the Feynman diagram technique has been developed to describe interaction between spin fluctuations and resonant valence bonds in a self-consistent manner. Emergence of a strongly anisotropic RVB spin liquid is discussed. Zh. éksp. Teor. Fiz. 112, 729–759 (August 1997)     

Dynamical interaction of antiferromagnetic subsystems: a neutron scattering study of the spinwave spectrum of the garnet Fe2Ca3(GeO4)3

The Fe³⁺ ions in the garnet Ca₃Fe₂Ge₃O₁₂ form two identical antiferromagnetic subsystems. The interaction between the two subsystems is vanishing within molecular field approximation forq=0. A coupling appears due to the spin fluctuations. The dynamics of the system is described by the Hamiltonian for a Heisenberg antiferromagnet. Symmetry requirements impose two exchange parameters between the sublattices (nearest neighbours)J ₁ in the direction of the 3-fold axis andJ' ₁ in the other three space diagonals. The interaction within each sublattice (second nearest neighbours) is described by the exchange parameterJ ₂. The measured spin wave dispersion curves for the three principal symmetry directions are very well reproduced by a model calculation withJ ₁=-0.909(9) K,J' ₁=-0.307(8) K andJ ₂=-0.615(2)K. The observed intensities are in agreement with predictions from the model. Forq0 the model predicts two acoustic branches going towards zero frequency. A calculation beyond linear spin wave theory forq=0 predicts a quantum gap for the lower acoustic branch. This gap has been found at 0.033(4) THz. An anisotropy gap of 0.007 THz has been taken from the literature.     

Spin correlations in REAl2 compounds aboveT c

Transverse fieldSR measurements in the paramagnetic region on polycrystalline samples of CeAl₂, NdAl₂, PrAl₂, GdAl₂, ErAl₂, HoAl₂, DyAl₂ and TmAl₂ are reported. We have observed increased damping rate and frequency shifts of the muon precession signal asT _c is approached from above. The shifts are linear in applied magnetic field, while the damping rates are more complicated functions of magnetic field strength and temperature.We interpret the damping as being partly due to inhomogeneous broadening proportional to the magnetic susceptibility, and partly due to apparent slowing down of RE spin fluctuations. These slow fluctuations are ascribed to the existence of correlations between the RE spins also at temperatures well aboveT _c. The variations of shifts and damping rates within the series of REAl₂ compounds will be discussed.     

Effect of asymmetry of CuO2 layers in copper oxides on the anomalous neutron scattering near T c

Reasons for critical magnetic scattering of neutrons near T _c in copper oxides with CuO₂ layers whose nearest environment has no “up-down” symmetry are discussed. The intracrystalline electric field, which threads the CuO₂ planes on account of the asymmetry, induces coupling between the spin and momentum of the current carriers. This coupling is shown to result in a manifestation of virtual Cooper pairs in the imaginary part of the spin susceptibility. Thus spin density fluctuations as well as current fluctuations should participate in the scattering. A way of experimentally distinguishing between the two mechanisms is pointed out. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 5, 363–368 (10 March 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Resonant amplification of quantum fluctuations in a spinor gas

Bose-Einstein condensates of atoms with non-zero spin are known to constitute an ideal system to investigate fundamental properties of magnetic superfluids. More recently it was realized that they also provide the fascinating opportunity to investigate the macroscopic amplification of quantum and classical fluctuations. This is strikingly manifested in a sample initially prepared in the m _F = 0 state, where spin-changing collisions triggered by quantum fluctuations may lead to the creation of correlated pairs in m _F = ±1. We show that the pair creation efficiency is strongly influenced by the interplay between the external trapping potential and the Zeeman effect. It thus reflects the confinement-induced magnetic field dependence of elementary spin excitations of the condensate. Remarkably, pair production in our experiments is therefore characterized by a multi-resonant dependence on the magnetic field. Pair creation at these resonances acts as strong parametric matter-wave amplifier. Depending on the resonance condition, this amplification can be extremely sensitive or insensitive to the presence of seed atoms. We show that pair creation at a resonance which is insensitive to the presence of seed atoms is triggered purely by quantum fluctuations and thus the system acts as a matter-wave amplifier for the vacuum state.     

Influence of a nonmagnetic impurity on the properties of the quasi-one-dimensional antiferromagnet CsNiCl3

Various magnetic properties of the diluted quasi-one-dimensional antiferromagnet CsNi_1−x MgxCl₃ are investigated experimentally for several impurity concentrations. The antiferromagnetic resonance spectrum and the phase diagrams are found to depend significantly on the amount of added Mg. The field and temperature dependences of the static magnetization is measured for crystals with two different contents x. A substantial increase in the magnetization is observed at low temperature, where the additional susceptibility is approximately proportional to the concentration. The physical mechanisms underlying the observed strong influence of magnetic defects formed at breaks in the spin chains in a quasi-one-dimensional antiferromagnet on its magnetic properties in the ordered state and for T<T _N are discussed. Zh. éksp. Teor. Fiz. 112, 209–220 (July 1997)     

Quantum temperature fluctuations in the magnetization of antiferromagnetic semimetals

It is shown that in semimetallic, low-temperature antiferromagnetic materials located in a quantizing magnetic field, the part of the band magnetization M _∼ which oscillates in H can have a nonmonotonic temperature dependence. This non-Fermi liquid behavior will show up experimentally in the form of quantum temperature fluctuations of the magnetization when the decrease with rising temperature is oscillatory, rather than the usual monotonic decrease. It is shown that the magnetization from an individual spin electron (or hole) subband has the form of weakly damped periodic oscillations as a function of T ². This result makes it possible to develop an efficient method for studying the electronic structure of antiferromagnetic semimetals based on an examination of the quantum temperature fluctuations. Calculations show that quantum temperature fluctuations can be observed, for example, in the cerium monopnictides CeP and CeAs, which are strongly correlated, antiferromagnetic, compensated semimetals with low Neel temperatures. Fiz. Tverd. Tela (St. Petersburg) 40, 1674–1680 (September 1998)     

Electronic phase separation in a low-temperature tetragonal phase of lanthanum-strontium cuprates according to 139La NQR data

A nonuniform electron density distribution is observed in La_{1−x− y} Nd_ySr_xCuO₄ and La_1−x−y Eu_ySr_xCuO₄, and long-lived magnetic fluctuations in these compounds are studied. The dynamics of the magnetic fluctuations depends strongly on the magnetic properties of the rare-earth ions, which stabilize the low-temperature tetragonal phase. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 5, 344–349 (10 March 1998)     

EPR investigation of the spin-spin interactions in a Cu(II)-Gd(III)-Fe(III) heterospin system

The spin-spin interactions in a system that contains three different spin carriers, [{LCu}Gd(H₂O)₃×{Fe(CN)₆}] _n ·4nH₂O (1) [L²⁻, N,N-propylenedi(3-methoxysalicylideneiminato)], were investigated by electron paramagnetic resonance spectroscopy. Additional information was obtained by analyzing the discrete heterobinuclear system [LCu(OH₂)Gd(O₂NO)₃] (2), which contains the Cu(II)-Gd(III) pair also existing in the structure of 1, and the compounds [{LCu}Gd(H₂O)₃{Co(CN)₆}] _n ·3.5nH₂O and [{LCu}La(H₂O)₃×{Fe(CN)₆}] _n ·4nH₂O, which are isostructural with 1 and in which the paramagnetic low-spin Fe(III) and Gd(III) ions were replaced by diamagnetic low-spin Co(III) and La(III), respectively. The investigations were carried out in the temperature range of 293–4 K in both X- and Q-bands and also using a dual-mode X-band. The experimental spectra of the Cu(II)-Gd(III) pairs in 2 were interpreted as the sum of spectra of the ground spin state with total S = 4 and the excited state with S = 3 appearing due to the ferromagnetic exchange interaction between Cu(II) and Gd(III) ions. By fitting the experimental and simulated spectra, the zero-field splitting parameters of the Gd(III) ion are estimated and it is shown that no influence of the anisotropic interaction is detected. The magnetic properties of 1 are discussed from the perspective of the interaction of the Cu(II)-Gd(III) binuclear fragments with the Fe(III) ions.     

Excited high spin states of novel π conjugated verdazyl radicals: photoinduced spin alignment utilizing the excited molecular field

This paper reports the excited quartet (S = 3/2) and quintet (S = 2) states arising from the intramolecular radical-triplet pair in the purely organic π conjugated spin systems. A previous paper reported the excited quartet and quintet states of 9-anthracene-(4-phenyliminonitroxide) and 9,10-anthracene-bis(4-phenyliminonitroxide), respectively, in which iminonitroxide radicals are linked to the phenyl- or diphenylanthracene moiety (a spin-coupler) through the π conjugation. The similar excited quartet and quintet states were observed for the 9-anthra-cene-(4-phenylverdazyl) radical (1) and 9,10-anthracene-bis(4-phenylverdazyl) diradical (2) by time resolved electron spin resonance (TRESR). The TRESR spectrum was analysed by the ordinary spin Hamiltonian with the Zeeman and fine structure terms. For the quartet state of 1, the g value, fine structure splitting, and relative population of the Ms sublevels have been determined to be g = 2.0035, D = 0.0230 cm^?1, E = 0.0, P _1/2′ = P _?1/2′ = 0.5 and P _3/2′ = P _?3/2′ = 0.0, respectively, by spectral simulation. The spin Hamiltonian parameters of the quintet state of 2 were determined to be g = 2.0035, D = 0.0128 cm^?1, E = 0.0, P _2′ = P _?2′ = 0.0, P _1′ = P _?1′ = 0.37 and P _0′ = 0.26, respectively. Direct observation of the excited high spin state showed that photoinduced intramolecular spin alignment is realized between the excited triplet state (S = 1) of the phenyl- or diphenylanthracene moiety and the doublet spin (S = 1/2) of the dangling verdazyl radicals. Ab initio MO calculations (DFT) were carried out in order to clarify the mechanism of the photoinduced spin alignment.     

Electronic, magnetic and transport properties of Co2TiZ (Z=Si, Ge and Sn): A first-principle study

We have studied the electronic structure, magnetic and transport properties of some Co based full Heusler alloys, namely Co₂TiZ (Z=Si, Ge and Sn), in the frame work of first-principle calculations. The calculations show that Co₂TiZ (X=Si, Ge and Sn) are to be half-metallic compounds with a magnetic moment of 2 μ_B, well consistent with the Slater-Pauling rule. The electronic structure results reveal that Co₂TiZ has the high density of states at the Fermi energy in the majority-spin state and show 100% spin polarization. Our results also suggest that both the electronic and magnetic properties in these compounds are intrinsically related to the appearance of the minority-spin gap. The origin of energy gap in the minority-spin states is discussed in terms of the electron splitting of Z (Z=Si, Ge and Sn) and 3d Co atoms and also the d-d hybridization between the Co and Ti atoms. The transport properties of these materials are discussed on the basis of Seebeck coefficients, electrical conductivity coefficients and thermal conductivity coefficients.     

Mechanism of giant magnetoresistance in intermetallic compounds of rare-earth ions and actinides

Giant positive or negative magnetoresistance is calculated in a band model. The spectra of the band electrons in a two-sublattice antiferromagnetic intermetallic compound depend on the antiferromagnetism vector L(T,H). The metamagnetic transition to the ferromagnetic phase is accompanied by splitting with respect to the spin σ, displacement of the energy bands, and a decrease in the effective masses of the band electrons. This mechanism of giant negative magnetoresistance is also accompanied by an increase in the relaxation time τ_jσ. Scattering by chemical-bond fluctuations is considered as the main relaxation mechanism. Giant positive magnetoresistance results from a four-subband model of 4f and 5f intermetallic compounds. The electron effective masses m _jσ(J _jT ) of the (j,σ) bands increase with the mean angular momentum J _1T (T,H) of an ion in the jth sublattice of 4(5)f ions. The thermodynamics of such a four-sublattice model, the nonlinear magnetization and magnetoresistance curves, and the nonmonotonic dependence of the specific heat C _m(T,H) on the field H are calculated. Fiz. Tverd. Tela (St. Petersburg) 39, 1806–1814 (October 1997)     

Giant intrinsic magnetic hardness

Crystallographically partly randomized materials with high magnetic anisotropy exhibit anisotropy and exchange fluctuations. Possibly the most dramatic consequence of these interaction fluctuations is the presence of giant intrinsic magnetic hardness observed, especially at cryogenic temperatures. This magnetic hardness (resistance to demagnetization) is anintrinsic solid state property, quite in contrast with hardness in technologically important materials based on the presence of fine particles or precipitate phases. It introduces rather a further variety in the phenomenology of interaction fluctuation materials such as spin glasses, representing the extreme case of high anisotropy and high moment concentrations. In this paper the phenomenon of strong intrinsic magnetic hardness is reviewed, and some new experimental data are presented for homogeneous pseudobinary regions of composition on the basis of such compounds as SmNi₅, SmCu₅, SmCo₅, TbFe₂ and others. Magnetic hardness in some of these cases reaches the highest values found so far for any class of materials. For instance, maximum values of coercive force of aboutH _c=230 kOe are observed for SmCo_5−xNi_x. Even higher values are extrapolated in other cases. Maximum values ofH _c are observed in materials with ordering temperatures of order 60–200 K. A strong temperature and a weaker time dependence ofH _c is observed and discussed on the basis of theories involving thermal activation of domain propagation. Comparisons are drawn with effects generally observed in magnetically hard materials, and the relationship of intrinsic magnetic hardness to technologically interesting materials is discussed. Tentative conclusions as to the details of the origins of giant intrinsic magnetic hardness are drawn and areas of future interest are indicated. This study was supported by a grant from the National Science Foundation.     

Covalent magnetism in the RFe <Emphasis Type="Bold">6</Emphasis>Ge <Emphasis Type="Bold">6</Emphasis> series

The electronic structure of the RFe ₆ Ge ₆ compounds ( R = Sc, Lu, Ti, Zr, Hf and Nb) of HfFe ₆ Ge ₆ -type structure has been studied using the muffin-tin Korringa-Kohn-Rostoker method in a non-relativistic approach. The chemical bonding is analyzed based on the l-decomposed site projected densities of states. Spin-dependent changes in the R nd- Fe 3d covalent bond are shown to be responsible for the experimentally observed rise in the Fe moment and hyperfine field upon increasing the R valency. The limited quantitative agreement between theoretical and experimental values is interpreted as being due to a non-negligible orbital moment and to a significant asphericity in the spin density at the iron site. The theoretical results also forecast a strong increase of the Ge(2e) transferred hyperfine field with the R valency. Received 20 December 2002 Published online 4 June 2003 RID="a" ID="a"e-mail: Thomas.Mazet@lcsm.uhp-nancy.fr RID="b" ID="b"Associé au CNRS (UMR 7555)     

Crystal field effects on the saturation magnetic moment of Sm3+ ion in ferronagnetic samarium compounds

The effects of cubic crystal fields on the saturation magnetic moment of Sm³⁺ ion in ferromagnetic compounds have been investigated. In samarium compounds with magnetic elements, the exchange fieldH _ex acting on Sm³⁺ ion is taken to be proportional to the sublattice magnetization of the magnetic element, while in compounds with nonmagnetic elementsH _ex is taken to be proportional to the spin average of the Sm³⁺ ion and is determined self-consistently. In both types of compoundsH _ex is assumed to be along [001] direction. The saturation magnetic moment is calculated by taking into account the admixture of excited (J=7/2 andJ=9/2) levels into the ground (J=5/2) level of Sm³⁺ ion by crystal fields and exchange fields. It is shown that depending upon the strength, the crystal fields quench or enhance the magnetic moment from the free ion value, and in some cases force Sm³⁺ ion to behave effectively like an (L+S) ion rather than an (L−S)ion. The crystal fields may have important bearing on the performance of samarium compounds as permanent magnet materials.     

Solitons on a discrete ferromagnetic spin chain

Discrete ferromagnetic spin chains with planar single-ion and exchange anisotropy and with an externaldc fieldB applied in the easy plane are considered in the classical limit. We find two different static in-plane kink structures, which are symmetric with respect to a given spin or to a given bond of the chain, respectively. The first structure is unstable against in-plane fluctuations for all applied fields. The second one, on the other hand, exists (independent of the anisotropy parameters) only up to a critical fieldB _e and is stable against in-plane fluctuations in its whole domain of existence. Depending on the anisotropy parameters, this latter configuration may, however, become unstable against out-of-plane fluctuations at a critical valueB _c <B _e of the external field. Both types of kink structures can also move along the chain, by developing an out-of-plane spin component. With increasing velocity, the kink motion leads to a rapid reduction of the critical field marking the existence limit of these spin structures. The discreteness is found to have substantial influence on the spectrum of the solitons.Work supported by the Bundesministerium für Forschung und TechnologieWork supported by Schweizerischer Nationalfonds