Short-range Antiferromagnetic Order Research Articles

Optical conductivity of high-temperature superconductors: Exact solution for a “spin - bag” model

Exact summation of all Feynman diagrams for two-particle Green's function is performed for the one-dimensional Gaussian model of static fluctuations of short-range (antiferromagnetic) order with Lorentzian correlator analogous to “spin-bag” model of Schrieffer et al. We obtain the general picture of frequency dependence of conductivity for different ranges of correlation length of short-range order. For specific values of parameters we get good qualitative agreement with experimental data on optical absorption in high-Tc superconductors.

Electronic structure and correlations of high-temperature superconducting compounds.

Calculations on negatively charged planar ${\mathrm{Cu}}_{\mathit{n}}$${\mathrm{O}}_{\mathit{m}}$ clusters are reported. Starting from a self-consistent-field calculation within a good Gaussian-type-orbital basis set, correlations are included using the local ansatz. A charge analysis reveals a Cu 3d occupation in close agreement with calculations in the local-density approximation. The electrons in the formal ${\mathrm{Cu}}_{\mathit{n}}^{2+}$${\mathrm{O}}_{\mathit{m}}^{2\mathrm{\ensuremath{-}}}$ entities are delocalized between Cu and O sites and strongly correlated. Our findings do not agree with the assumption of localized ${\mathrm{Cu}}^{2+}$ spins which is often made in models for these compounds. Spin correlations indicate strong short-range antiferromagnetic order even if electrons are removed. For them, there is no difference between O and Cu sites.

A New Approach to the Dynamics of Holes and Spins

We briefly review our recent approach towards the physics of the Hubbard t-J model. It is characterized by (i) path-integral quantization of electrons in the slave boson and fermion representation, (ii) integration over spin degrees of freedom on the odd lattice sites around the short-range antiferromagnetic order, and (iii) introduction of auxiliary collective field describing the hole pairs on nearest-neighbour links as an order parameter of superconductivity. The results obtained so far include (A) derivation of the CP1+ Dirac-fermion theory as the low-energy effective field theory in the superconducting state, (B) derivation of the U(1) lattice gauge theory with Higgs coupling as the Ginzburg-Landau theory of hole pairs, and (C) some discussions on the phase structure based on the nonlinear sigma model renormalized by holes and the solvable one-pair model.

Heat capacity of single-crystal La2CuO4 and polycrystalline La2-xSrxCuO4 (0

Heat-capacity C(T) data on the title materials, as well as on CuO for comparison, were obtained with use of a differential scanning calorimeter to a precision of \ensuremath{\simeq}0.1--1%. The measurements were carried out (i) to characterize the thermal anomaly at the tetragonal-orthorhombic transition temperature ${\mathit{T}}_{0}$ of single-crystal ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$ and polycrystalline ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Sr}}_{\mathit{x}}$${\mathrm{CuO}}_{4}$ (0\ensuremath{\le}x\ensuremath{\le}0.20) and (ii) to search for thermal anomalies at the N\'eel temperature ${\mathit{T}}_{\mathit{N}}$ of ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$ (\ensuremath{\simeq}300 K). We find a cusp-shaped anomaly with a peak at 523 K (\ensuremath{\approxeq}${\mathit{T}}_{0}$) for a single crystal of ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$ with ${\mathit{T}}_{\mathit{N}}$=304 K and find the transition to be second order, consistent with previous neutron- and x-ray-diffraction measurements. ${\mathit{T}}_{\mathit{N}}$ was determined from measurements of the anisotropic magnetic susceptibility on the same crystal, which are also presented. The C(T) anomaly at ${\mathit{T}}_{0}$ is smeared out somewhat in polycrystalline ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$.The size of the anomaly decreases with x in polycrystalline ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Sr}}_{\mathit{x}}$${\mathrm{CuO}}_{4}$ until the anomaly is no longer observable for x\ensuremath{\ge}0.10. For 0\ensuremath{\le}x\ensuremath{\le}0.08, ${\mathit{T}}_{0}$ decreases linearly with x at a rate ${\mathit{dT}}_{0}$/dx=-(2430\ifmmode\pm\else\textpm\fi{}50) K. This variation of ${\mathit{T}}_{0}$ with x is consistent with that found previously using x-ray and neutron diffraction. No features in C(T) were observed at the N\'eel temperature of single-crystal or polycrystalline ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$. This is consistent with the expectation that the magnetic entropy is very small at ${\mathit{T}}_{\mathit{N}}$, since dynamic short-range intraplanar antiferromagnetic ordering, which begins at much higher temperatures, is well developed at ${\mathit{T}}_{\mathit{N}}$. A calculation shows that the expected size of the anomaly at ${\mathit{T}}_{\mathit{N}}$ is well below the resolution of the measurements.

Antiferromagnetic fluctuations and short-range order in a Kagomé lattice.

We report neutron-scattering measurements on ${\mathrm{SrCr}}_{8\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Ga}}_{4+\mathit{x}}$${\mathrm{O}}_{19}$, a layered compound containing Kagom\'e planes of S=3/2 ${\mathrm{Cr}}^{3+}$ ions. From magnetic-susceptibility data, the Curie-Weiss constant is large and negative; ${\mathrm{\ensuremath{\theta}}}_{\mathrm{CW}}$\ensuremath{\simeq}-500 K. Even so, our measurements for a sample with x=0.87 reveal only short-range antiferromagnetic order with a correlation length \ensuremath{\xi}=7\ifmmode\pm\else\textpm\fi{}2 \AA{}\ensuremath{\approxeq}2a, where a is the inter-Cr spacing. Below 8 K, there is a spin-freezing transition to a state where the magnetic fluctuations have large amplitude and a spectrum (averaged over reciprocal space) characteristic of two-dimensional antiferromagnets with \ensuremath{\xi}\ensuremath{\gg}a.

Proton nuclear magnetic relaxation in quasi-one-dimensional S = 1 Heisenberg antiferromagnet Ni(C 2H 8N 2) 2NO 2(ClO 4)

The proton spin-lattice relaxation time T 1 in the Haldane-gap system, Ni(C 2 H 8 N 2 ) 2 NO 2 (ClO 4 ) was measured down to 0.5 K. The development of antiferromagnetic short range order was not found even at low temperatures. A relaxation process of activation type with an energy gap of 11 K has been observed.

Phase transitions in high-Tcsuperconductive oxides

Abstract Superconductivity is stabilized by the opening up of an energy gap at the Fermi Energy E F below the superconductor transition temperature T c ; any other mechanism that opens an energy gap at E F is competitive. In the high-T c bismuth oxides, a charge-density wave (CDW) is competitive; in the high-T c copper oxides the correlation splitting associated with localized electrons is competitive. In each class of oxide, stabilization of superconductivity requires the introduction of mixed valency. It is argued that suppression of a CDW or of localized magnetic moments and long-range magnetic order by the introduction of mixed valency is not a sufficient condition for high-T c superconductivity. A common feature of the superconductive phase in all the p-type high-T c oxides is a Fermi energy that cuts two bands, a [sgrave]∗ band of primarily cationic character (Bi-6s or Cu-3dx2-y2) and a π or π∗ band of primarily anionic character (O-2pπ). The transition from localized copper magnetic moments to Pauli paramagnetism is monitored in the system La2-xSrxCuO4-y; although short-range antiferromagnetic order is retained in the p-type superconductive phase of the copper oxides, a charge-transfer as against a spin-spin exchange interaction appears to be the more probable mechanism for enhancement of the Cooper pairing below T c . The recently discovered n-type superconductivity in Nd2-xCexCuO4 may involve charge transport to the rare-earth 5d bands.

Nuclear Resonance Properties of YBa 2 Cu 3 O 6+x Superconductors

Nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) results for copper-63, oxygen-17, and yttrium-89 nuclei in the superconducting composition range of YBa(2)Cu(3)O(6+x) (0.4 </= x </= 1.0) are reviewed and interpreted. Copper NMR shift and susceptibility data, combined with a simple ionic model of local magnetic properties, yield a comprehensive analysis of the normal-state anisotropic susceptibility components and full characterization of the copper spin and orbital hyperfine couplings. Data on the spin-lattice relaxation time of these three nuclear species serve to characterize the highly correlated fermion dynamics in this system. Relaxation data from YBa(2)Cu(3)O(7) (superconducting transition temperature T(c) = 90 K) and oxygen-deficient samples of this material (T(c) approximately 60 K) have been analyzed in terms of meanfield models incorporating short-range antiferromagnetic order, giving a quantitative account of (planar) relaxation for these three nuclei in terms of a single dynamical susceptibility.

Proton Spin-Lattice Relaxation in the Quasi-One-DimensionalS=1 Heisenberg Antiferromagnet Ni(C2H8N2)2NO2(ClO4)

Proton spin-lattice relaxation time T 1 in the Haldane-gap system with S =1, Ni(C 2 H 8 N 2 ) 2 NO 2 (ClO 4 ), was measured at temperatures between 1.4 K and 77 K. The relaxation rate T 1 -1 decreased over more than three orders of magnitude with decreasing temperature, thus suggesting scarce development of the antiferromagnetic short-range order. Monotonous decrease of T 1 -1 above 6 K was analyzed on the basis of the theory for insulating paramagnets using static susceptibility data. To explain the behavior of T 1 -1 below 6 K, which accompanies a rounded peak, we consider the effect of local-field fluctuation of the order of the nuclear Larmor period, which is associated with magnetic excitation from the nonmagnetic ground state.

Magnetic correlations in random anisotropy Dy xY 1− xAl 2 magnets

Coexistence of short range antiferromagnetic order and random axes of magnetic anisotropy is found in the crystalline Laves phase compounds Dy x Y 1− x Al 2, for x = 0.35. A neutron diffraction Bragg peak ( 1 2 , 1 2 , 1 2 ) , which vanishes at temperatures much higher than the RMA one, T SG, is observed, together with strong small angle neutron scattering below T SG.

Electronic charge distributions and correlations in highT c superconducting compounds

Calculations on negatively charged planar Cu n O m clusters are reported. Starting from a self-consistent field calculation within a good Gaussian-type orbital basis set, correlations are included by using the Local Ansatz. A charge analysis reveals that the Cu 3d occupation is 9.5, in close agreement with Local Spin Density calculations. The electrons in the formal ((CuO2)2−) n entities are delocalized between Cu and O sites and strongly correlated. Our findings do not agree with the assumption of localized Cu2+ spins which lead to thet-J model. Spin correlations indicate strong short-range antiferromagnetic order even when additional electrons are removed. For them, there is no difference between O and Cu sites.

Gauge field, Aharonov-Bohm flux, and high-Tc superconductivity.

In a spin-1/2 Heisenberg model with short-range antiferromagnetic order, a hole making a closed loop on one sublattice is subject to a slowly varying spin-quantization axis and picks up a phase equal to half the solid angle subtended by the spin orientation around the loop. The phase can be represented by an Aharonov-Bohm flux resulting in a U(1) gauge theory. For a finite hole density this model leads to superconductivity even in the presence of Coulomb repulsion. The gauge field also enhances low-energy particle-hole excitations, leading to a /ital T//sup 4/3/ law for the normal-state resitivity.

Critical currents at small-angle grain boundaries and antiferromagnetism in YBa 2Cu 3O 7−δ

The strong dependence of critical current density on the angle of tilt between grains of YBa 2Cu 3O 7−δ tilted about their common c-axes is readily explained using a model in which the superconducting ordering depends upon the existence of an underlying long-range or short-range antiferromagnetic order.

Spin-flip pairing in CuO 2 superconductors

It is shown that virtual 2D paramagnon exchange in a material with short-range planar antiferromagnetic order leads to triplet pairing of itinerant electrons, in analogy to singlet pairing via virtual phonon exchange in BCS theory. Values of T c for CuO 2 layered perovskites are related by the theory to the electronic density of states and to a short-range magnetic order parameter. The theory is consistent with all well-established experimental and theoretical data for these materials.

Linear dichroism study of the structural phase transition of BaMnF4.

Linear dichroism (LD) has been investigated on ferroelectric antiferromagnet BaMn${\mathrm{F}}_{4}$ in a temperature range of 15-300 K. The LD is clearly observed to reflect the order parameter of the structural phase transition (transition temperature: ${T}_{I}=252$ K) and antiferromagnetic shortrange order (N\'eel temperature: ${T}_{N}=26$ K) as in the case of linear birefringence. It is confirmed, from a jump of LD at ${T}_{I}$ and a value of critical exponent $\ensuremath{\beta}=0.23$, that a slight firstorder character is involved in the structural phase transition. No additional structural phase transition was observed below ${T}_{I}$.

Diluted magnetic semiconductors

We review the physical properties of diluted magnetic semiconductors (DMS) of the type AII1−xMnxBVI (e.g., Cd1−xMnxSe, Hg1−xMnxTe). Crystallographic properties are discussed first, with emphasis on the common structural features which these materials have as a result of tetrahedral bonding. We then describe the band structure of the AII1−xMnxBVI alloys in the absence of an external magnetic field, stressing the close relationship of the sp electron bands in these materials to the band structure of the nonmagnetic AIIBVI ‘‘parent’’ semiconductors. In addition, the characteristics of the narrow (nearly localized) band arising from the half-filled Mn 3d5 shells are described, along with their profound effect on the optical properties of DMS. We then describe our present understanding of the magnetic properties of the AII1−xMnxBVI alloys. In particular, we discuss the mechanism of the Mn++-Mn++ exchange, which underlies the magnetism of these materials; we present an analytic formulation for the magnetic susceptibility of DMS in the paramagnetic range; we describe a somewhat empirical picture of the spin-glasslike freezing in the AII1−xMnxBVI alloys, and its relationship to the short range antiferromagnetic order revealed by neutron scattering; and we point out some not yet fully understood questions concerning spin dynamics in DMS revealed by electron paramagnetic resonance. We then discuss the sp-d exchange interaction between the sp band electrons of the AII1−xMnxBVI alloy and the 3d5 electrons associated with the Mn atoms. Here we present a general formulation of the exchange problem, followed by the most representative examples of its physical consequences, such as the giant Faraday rotation, the magnetic-field-induced metal-to-insulator transition in DMS, and the properties of the bound magnetic polaron. Next, we give considerable attention to the extremely exciting physics of quantum wells and superlattices involving DMS. We begin by describing the properties of the two-dimensional gas existing at a DMS interface. We then briefly describe the current status of the AII1−xMnxBVI layers and superlattices (systems already successfully grown; methods of preparation; and basic nonmagnetic properties of the layered structures). We then describe new features observed in the magnetic behavior of the quasi-two-dimensional ultrathin DMS layers; and we discuss the exciting possibilities which the sp-d exchange interaction offers in the quantum-well situation. Finally, we list a number of topics which involve DMS but which have not been explicitly covered in this review such as elastic properties of DMS, DMS-based devices, and the emerging work on diluted magnetic semiconductors other than the AII1−xMnxBVI alloys—and we provide relevant literature references to these omitted topics.

Neutron scattering measurements of spin fluctuations in the heavy-fermion system UPt3.

We report the results of both polarized and unpolarized neutron scattering measurements on single-crystal specimens of the heavy-fermion system ${\mathrm{UPt}}_{3}$. At low temperatures (T&lt;30 K), and for the energy scales probed in these measurements (\ensuremath{\Elzxh}\ensuremath{\omega}\ensuremath{\approxeq}6--8 meV), there is antiferromagnetic short-range order between nearest-neighbor uranium-ion moments located in adjacent basal planes. Such order implies that next-nearest neighbors, located within the same basal plane, are correlated ferromagnetically. As the temperature is raised above 18 K, where the bulk in-plane susceptibility has a maximum, the antiferromagnetic correlations between nearest neighbors disappear. However, the ferromagnetic correlations in the basal plane do not vanish until T\ensuremath{\gtrsim}150 K.

Polarization-analysis study of the atomic and spin-pair correlations in Ni0.76Mn0.24.

Neutron diffuse scattering measurements were made on single-crystal Ni/sub 0.76/Mn/sub 0.24/ to determine the atomic and spin-pair correlations in the reentrant spin-glass state. The nuclear and magnetic diffuse scattering were separated by polarization analysis at T = 10 K in a field of 8.1 kOe applied parallel to Q. The nuclear cross section shows diffuse peaks at (100) and (110) due to atomic short-range order (ASRO) with a range of about 3a/sub 0/. The ASRO parameters for this quenched alloy were determined to 16 shells; these show a preference for like even-shell and unlike odd-shell neighbors. In the experimental geometry, the magnetic cross section determines the correlations between spin components transverse to the applied field, or magnetization direction. The magnetic short-range-order parameters alternate in sign for the first four shells and then remain positive at larger distances. This unusual result corresponds to the coexistence of short-range antiferromagnetic order with both short- and long-range ferromagnetic order.

Phase-transition problem and magnetic short-range order in Heisenberg spin glasses.

We report on measurements of the nonlinear susceptibility for the spin glasses ${\mathrm{Eu}}_{x}{\mathrm{Sr}}_{1\ensuremath{-}x}{\mathrm{S}}_{y}{\mathrm{Se}}_{1\ensuremath{-}y}$ which, depending on the concentration $y$, possess either ferromagnetic or antiferromagnetic short-range order. Only for the case of ferromagnetic short-range order does the nonlinear susceptibility diverge for $T\ensuremath{\rightarrow}{T}_{f0}$; for antiferromagnetic short-range order it is nearly temperature independent for $T\ensuremath{\rightarrow}{T}_{f0}$. The results are in favor of a nonequilibrium transition at ${T}_{f0}$ and demonstrate the misleading role of magnetic short-range order developing above the freezing temperature for the phase-transition problem in real spin glasses.

Magnetic properties of diluted magnetic semiconductors: A review (invited)

Diluted magnetic semiconductors (DMS) are semiconducting alloys containing a random distribution of substitutional magnetic ions (e.g., Mn++ in Cd1−xMnxSe). Magnetic properties of DMS—such as spin glass behavior due to lattice frustration, magnon excitations in a random system of spins, superexchange, and short range antiferromagnetic order—are of considerable interest in their own right. In addition, understanding these properties is important because they strongly influence the electronic phenomena in DMS via the sp-d exchange interaction between the band electrons and the localized magnetic moments. We review the most recent results concerning magnetic susceptibility, Mn++-Mn++ nearest-neighbor exchange, and magnetic short-range order in these materials. On this basis, we can present a fairly complete and unified picture of magnetic properties of DMS. In addition, we point out some of the issues and challenges that lie ahead.