J1−J2J_1-J_2 Quantum Heisenberg Antiferromagnet: Improved Spin-Wave Theories Versus Exact-Diagonalization Data

We reconsider the results cocerning the extreme-quantum $S=1/2$ square-lattice Heisenberg antiferromagnet with frustrating diagonal couplings ($J_1-J_2$ model) drawn from a comparison with exact-diagonalization data. A combined approach using also some intrinsic features of the self-consistent spin-wave theory leads to the conclusion that the theory strongly overestimates the stabilizing role of quantum flutcuations in respect to the N\'{e}el phase in the extreme-quantum case $S=1/2$. On the other hand, the analysis implies that the N\'{e}el phase remains stable at least up to the limit $J_{2}/J_{1} = 0.49$ which is pretty larger than some previous estimates. In addition, it is argued that the spin-wave ansatz predicts the existence of a finite range ($J_{2}/J_{1}<0.323$ in the linear spin-wave theory) where the Marshall-Peierls sigh rule survives the frustrations.Comment: 13 pages, LaTex, 7 figures on reques

High Frequency Asymptotics for the Spin-Weighted Spheroidal Equation

We fully determine a uniformly valid asymptotic behaviour for large $a \omega$ and fixed $m$ of the angular solutions and eigenvalues of the spin-weighted spheroidal differential equation. We fully complement the analytic work with a numerical study.Comment: The .tar.gz file should contain 1 tex file, 24 figures in .ps format and 1 bibliography file in .bbl format. All these files are located in the same director

Instability of antiferromagnetic magnons in strong fields

We predict that spin-waves in an ordered quantum antiferromagnet (AFM) in a strong magnetic field become unstable with respect to spontaneous two-magnon decays. At zero temperature, the instability occurs between the threshold field $H^*$ and the saturation field $H_c$. As an example, we investigate the high-field dynamics of a Heisenberg antiferromagnet on a square lattice and show that the single-magnon branch of the spectrum disappears in the most part of the Brillouin zone.Comment: RevTeX, 4 pages, 3 figures, accepted to PR

Transport Properties, Thermodynamic Properties, and Electronic Structure of SrRuO3

SrRuO$_3$ is a metallic ferromagnet. Its electrical resistivity is reported for temperatures up to 1000K; its Hall coefficient for temperatures up to 300K; its specific heat for temperatures up to 230K. The energy bands have been calculated by self-consistent spin-density functional theory, which finds a ferromagnetic ordered moment of 1.45$\mu_{{\rm B}}$ per Ru atom. The measured linear specific heat coefficient $\gamma$ is 30mJ/mole, which exceeds the theoretical value by a factor of 3.7. A transport mean free path at room temperature of $\approx 10 \AA$ is found. The resistivity increases nearly linearly with temperature to 1000K in spite of such a short mean free path that resistivity saturation would be expected. The Hall coefficient is small and positive above the Curie temperature, and exhibits both a low-field and a high-field anomalous behavior below the Curie temperature.Comment: 6 pages (latex) and 6 figures (postscript, uuencoded.) This paper will appear in Phys. Rev. B, Feb. 15, 199

Collective excitations in ferrimagnetic Heisenberg ladders

We study ground-state properties and the low-lying excitations of Heisenberg spin ladders composed of two ferrimagnetic chains with alternating site spins $(S_1>S_2)$ by using the bosonic Dyson-Maleev formalism and Lanczos numerical techniques. The emphasis is on properties of the ferrimagnetic phase which is stable for antiferromagnetic interchain couplings $J_{\perp}\geq 0$. There are two basic implications of the underlying lattice structure: (i) the spin-wave excitations form folded acoustic and optical branches in the extended Brillouin zone and (ii) the ground state parameters (such as the on-site magnetizations and spin-stiffness constant) show a crossover behavior in the weak-coupling region $0<J_{\perp}<1$. The above peculiarities of the ladder ferrimagnetic state are studied up to second order in the quasiparticle interaction and by a numerical diagonalization of ladders containing up to N=12 rungs. The presented results for the ground-state parameters and the excitation spectrum can be used in studies on the low-temperature thermodynamics of ferrimagnetic ladders.Comment: 9 pages, 9 figure

Electron-Phonon Interaction and Ultrasonic Attenuation in the Ruthenate and Cuprate superconductors

This article derives an electron-phonon interaction suitable for interpreting ultrasonic attenuation measurements in the ruthenate and cuprate superconductors. The huge anisotropy found experimentally (Lupien et al., 2001) in Sr2RuO4 in the normal state is accounted for in terms of the layered square-lattice structure of Sr2RuO4, and the dominant contribution to the attenuation in Sr2RuO4 is found to be due to electrons in the gamma band. The experimental data in the superconducting state is found to be inconsistent with vertical lines nodes in the gap in either (100) or (110) planes. Also, a general method, based on the use of symmetry, is developed to allow for the analysis of ultrasonic attenuation experiments in superconductors in which the electronic band structure is complicated or not known. Our results, both for the normal-state anisotropy, and relating to the positions of the gap nodes in the superconducting state, are different from those obtained from analyses using a more traditional model for the electron-phonon interaction in terms of an isotropic electron stress tensor. Also, a brief discussion of the ultrasonic attenuation in UPt3 is given.Comment: 12 pages. Comments have been added to the original version of this article showing how, for the ultrasonic attenuation for a hexagonal crystal (which must be isotropic with respect to rotations about the c axis) our approach reproduces the results of the traditional isotropic electron stress tensor mode

Thermodynamics of isotropic and anisotropic layered magnets: renormalization group approach and 1/N expansion

The O(N) model of layered antiferro- and ferromagnets with a weak interlayer coupling and/or easy-axis anisotropy is considered. A renormalization group (RG) analysis in this model is performed, the results for N=3 being expected to agree with those of the 1/M expansion in the CP^{M-1} model at M=2. The quantum and classical cases are considered. A crossover from an isotropic 2D-like to 3D Heisenberg (or 2D Ising) regime is investigated within the 1/N expansion. Analytical results for the temperature dependence of the (sublattice) magnetization are obtained in different regimes. The RG results for the ordering temperature are derived. In the quantum case they coincide with the corresponding results of the 1/N expansion. The numerical calculations on the base of the equations obtained yield a good agreement with experimental data on the layered perovskites La2CuO4, K2NiF4 and Rb2NiF4, and the Monte Carlo results for the anisotropic classical systems.Comment: 13 pages, RevTeX, 4 figure

Possible Pairing Symmetry of Three-dimensional Superconductor UPt3_3 -- Analysis Based on a Microscopic Calculation --

Stimulated by the anomalous superconducting properties of UPt$_3$, we investigate the pairing symmetry and the transition temperature in the two-dimensional(2D) and three-dimensional(3D) hexagonal Hubbard model. We solve the Eliashberg equation using the third order perturbation theory with respect to the on-site repulsion $U$. As results of the 2D calculation, we obtain distinct two types of stable spin-triplet pairing states. One is the $f$-wave(B$_1$) pairing around $n = 1.2$ and in a small $U$ region, which is caused by the ferromagnetic fluctuation. Then, the other is the $p_x$(or $p_y$)-wave(E$_1$) pairing in large $U$ region far from the half-filling ($n = 1$) which is caused by the vertex corrections only. However, we find that the former $f$-wave pairing is destroyed by introduced 3D dispersion. This is because the 3D dispersion breaks the favorable structures for the $f$-wave pairing such as the van Hove singularities and the small pocket structures. Thus, we conclude that the ferromagnetic fluctuation mediated spin-triplet state can not explain the superconductivity of UPt$_3$. We also study the case of the pairing symmetry with a polar gap. This $p_z$-wave(A$_1$) is stabilized by the large hopping integral along c-axis $t_z$. It is nearly degenerate with the suppressed $p_x$(or $p_y$)-wave(E$_1$) in the best fitting parameter region to UPt$_3$ ($1.3 \le t_z \le 1.5$). These two p-wave pairing states exist in the region far from the half-filling, in which the vertex correction terms play crucial roles like the case in Sr$_2$RuO$_4$.Comment: 15 pages, 12 figure

Band-theoretical prediction of magnetic anisotropy in uranium monochalcogenides

Magnetic anisotropy of uranium monochalcogenides, US, USe and UTe, is studied by means of fully-relativistic spin-polarized band structure calculations within the local spin-density approximation. It is found that the size of the magnetic anisotropy is fairly large (about 10 meV/unit formula), which is comparable with experiment. This strong anisotropy is discussed in view of a pseudo-gap formation, of which crucial ingredients are the exchange splitting of U 5f states and their hybridization with chalcogen p states (f-p hybridization). An anomalous trend in the anisotropy is found in the series (US>>USe<UTe) and interpreted in terms of competition between localization of the U 5f states and the f-p hybridization. It is the spin-orbit interaction on the chalcogen p states that plays an essential role in enlarging the strength of the f-p hybridization in UTe, leading to an anomalous systematic trend in the magnetic anisotropy.Comment: 4 pages, 5 figure

Comparison of superconductivity in Sr_2RuO_4 and copper oxides

To compare the superconductivity in strongly correlated electron systems with the antiferromagnetic fluctuations in the copper oxides and with the ferromagnetic fluctuations in Sr_2RuO_4 a t-J-I model is proposed. The antiferromagnetic coupling J results in the superconducting state of d_{x^2-y^2} symmetry and the ferromagnetic coupling constant I results in the spin-triplet p-type state. The difference in the gap anisotropies provides the large difference in T_c values, for the typical values of the coupling constants: T_c of order of 1K for the ruthenate and T_c of order of 100K for the cuprates.Comment: 4 pages, RevTEX, 3 figs. Submitted to Phys. Rev. Let