Spin Fluctuations in Magnetically Coupled Bi-layer Cuprates

We propose a possible mechanism of pseudo spin gap anomaly(PSGA) in magnetically coupled bi-layer cuprates without any fermion pairing instability. In our proposal PSGA does not necessarily require the spin-charge separation or the breakdown of the Fermi liquid description of a normal state of the cuprate superconductor.The low energy magnetic excitations are mainly governed by the {\it itinerant nature of the intra-layer system} and {\it the inter-layer antiferromagnetic coupling}. No matter how weak the bare inter-layer coupling is, it can be dramatically enhanced due to the intra-layerspin fluctuations. As the temperature decreases near the antiferromagnetic phase boundary the strongly enhanced inter-layer correlation induces the inter-layer particle-hole exchange scattering processes that tend to enhance the inter-layer spin singlet formation and kill the triplet formation. We propose that the coupling of spin fluctuations on the adjacend layers via the strong repulsive interaction between parallel spins travelling on each layer give rise to the dynamical screening effects. As a result the low energy part of the spin excitation spectrum is strongly suppressed as the temperature decreases near the antiferromagnetic phase boundary. We ascribe PSGA to this dynamical screening effects.Comment: 30 page, latex, figures are available upon reques

Spin-fluctuation mechanism of superconductivity in cuprates

The theory of superconductivity within the t-J model, as relevant for cuprates, is developed. It is based on the equations of motion for projected fermionic operators and the mode-coupling approximation for the self-energy matrix. The dynamical spin susceptibility at various doping is considered as an input, extracted from experiments. The analysis shows that the superconductivity onset is dominated by the spin-fluctuation contribution. We show that T_c is limited by the spin-fluctuation scale $\Gamma$ and shows a pronounced dependence on the next-nearest-neighbor hopping t'. The latter can offer an explanation for the variation of T_c among different families of cuprates.Comment: Color figure

Quantum fluctuations in the effective pseudospin-1/2 model for magnetic pyrochlore oxides

The effective quantum pseudospin-1/2 model for interacting rare-earth magnetic moments, which are locally described with atomic doublets, is studied theoretically for magnetic pyrochlore oxides. It is derived microscopically for localized Pr^{3+} 4f moments in Pr_2TM_2O_7 (TM = Zr, Sn, Hf, and Ir) by starting from the atomic non-Kramers magnetic doublets and performing the strong-coupling perturbation expansion of the virtual electron transfer between the Pr 4f and O 2p electrons. The most generic form of the nearest-neighbor anisotropic superexchange pseudospin-1/2 Hamiltonian is also constructed from the symmetry properties, which is applicable to Kramers ions Nd^{3+}, Sm^{3+}, and Yb^{3+} potentially showing large quantum effects. The effective model is then studied by means of a classical mean-field theory and the exact diagonalization on a single tetrahedron and on a 16-site cluster. These calculations reveal appreciable quantum fluctuations leading to quantum phase transitions to a quadrupolar state as a melting of spin ice for the Pr^{3+} case. The model also shows a formation of cooperative quadrupole moment and pseudospin chirality on tetrahedrons. A sign of a singlet quantum spin ice is also found in a finite region in the space of coupling constants. The relevance to the experiments is discussed.Comment: 18 pages including 14 figures; Comparison with the magnetization curve on Pr2Ir2O7 included; to appear in Phys. Rev.

Theory of magnetic excitations in iron-based layered superconductors

Based on the effective four-band model we analyze the spin response in the normal and superconducting states of the Fe-pnictide superconductors. While the normal state spin excitations are dominated by the continuum of the interorbital antiferromagnetic fluctuations and the intraband spin density wave fluctuations, the unconventional superconductivity yields different feedback. The resonance peak in form of the well-defined spin exciton occurs {\it only} for the interband scattering at the antiferromagnetic momentum ${\bf Q}_{AFM}$ for the $s_\pm$ (extended s-wave) superconducting order parameter and it disappears rapidly for ${\bf q} < {\bf Q}_{AFM}$. The resonance feature is extremely weak for the $d_{x^2 -y^2}$-wave order parameter due to specific Fermi surface topology of these compounds. The essential difference between $s_\pm$-wave and $d_{x^2 -y^2}$-wave symmetries for the magnetic excitations can be used for experimental determination of the superconducting wave function symmetry.Comment: 5 pages, 3 figures, published versio

Phenomenological theory of spin excitations in La- and Y-based cuprates

Motivated by recent inelastic neutron scattering (INS) experiments on La-based cuprates and based on the fermiology theories, we study the spin susceptibility for La-based (e.g., La$_{2-x}$Sr$_x$CuO$_4$) and Y-based (e.g., YBa$_2$Cu$_3$O$_y$) cuprates, respectively. The spin excitation in YBa$_2$Cu$_3$O$_y$ is dominated by a sharp resonance peak at the frequency 40 meV in the superconducting state. Below and above the resonance frequency, the incommensurate (IC) peaks develop and the intensity of the peaks decreases dramatically. In the normal state, the resonant excitation does not occur and the IC peaks are merged into commensurate ones. The spin excitation of La$_{2-x}$Sr$_x$CuO$_4$ is significantly different from that of Y-based ones, namely, the resonance peak does not exist due to the decreasing of the superconducting gap and the presence of the possible spin-stripe order. The spectra are only enhanced at the expected resonance frequency (about 18 meV) while it is still incommensurate. On the other hand, another frequency scale at the frequency 55 meV is also revealed, namely the spectra are commensurate and local maximum at this frequency. We elaborate all the results based on the Fermi surface topology and the d-wave superconductivity, and suggest that the spin-stripe order be also important in determining the spin excitation of La-based cuprates. A coherent picture for the spin excitations is presented for Y-based and La-based cuprates.Comment: 8 pages, 8 figure

Double dispersion of the magnetic resonant mode in cuprates

The magnetic excitation spectra in the vicinity of the resonant peak, as observed by inelastic neutron scattering in cuprates, are studied within the memory-function approach. It is shown that at intermediate doping the superconducting gap induces a double dispersion of the peak, with an anisotropy rotated between the downward and upward branch. Similar behavior, but with a spin-wave dispersion at higher energies, is obtained for the low-doping case assuming a large pairing pseudogap.Comment: 4 LaTeX pages, 4 figure

Doping dependance of the spin resonance peak in bilayer high-TcT_c superconductors

Motivated by a recent experiment on the bilayer Y$_{1-x}$Ca$_{x}$Ba$_2$Cu$_3$O$_y$ superconductor and based on a bilayer $t-J$ model, we calculate the spin susceptibility at different doping densities in the even and odd channels in a bilayer system. It is found that the intensity of the resonance peak in the even channel is much weaker than that in the odd one, with the resonance position being at a higher frequency. While this difference decreases as the doping increases, and both the position and amplitude of the resonance peaks in the two channels are very similar in the deeply overdoped sample. Moreover, the resonance frequency in the odd channel is found to be linear with the critical temperature $T_c$, while the resonance frequency increases as doping decreases in the even channel and tends to saturate at the underdoped sample. We elaborate the results based on the Fermi surface topology and the d-wave superconductivity.Comment: 6 pages, 5 figure

Spin susceptibility in bilayered cuprates: resonant magnetic excitations

We study the momentum and frequency dependence of the dynamical spin susceptibility in the superconducting state of bilayer cuprate superconductors. We show that there exists a resonance mode in the odd as well as the even channel of the spin susceptibility, with the even mode being located at higher energies than the odd mode. We demonstrate that this energy splitting between the two modes arises not only from a difference in the interaction, but also from a difference in the free-fermion susceptibilities of the even and odd channels. Moreover, we show that the even resonance mode disperses downwards at deviations from ${\bf Q}=(\pi,\pi)$. In addition, we demonstrate that there exists a second branch of the even resonance, similar to the recently observed second branch (the $Q^*$-mode) of the odd resonance. Finally, we identify the origin of the qualitatively different doping dependence of the even and odd resonance. Our results suggest further experimental test that may finally resolve the long-standing question regarding the origin of the resonance peak.Comment: 8 pages, 5 figure

The spin resonance and high frequency optical properties of the cuprates

We argue that recently observed superconductivity-induced blue shift of the plasma frequency $\delta \omega_{pl}$ in $Bi_2Sr_2CaCu_2O_{8+\delta}$ is related to the change in the integrated dynamical structure factor associated with the development of the spin resonance below $T_c$. We show that the magnitude of $\delta \omega_{pl}$ is consistent with the small integrated spectral weight of the resonance, and its temperature dependences closely follow that of the spin resonance peak.Comment: 5 pages, 3 figure

Coexistence of magnetism and superconductivity in a t-J bilayer

We investigate coexistence of antiferromagnetic and superconducting correlations in bilayered materials using a two-dimensional t-J model with couplings across the layers using variational Monte Carlo calculations. It is found that the underdoped regime supports a coexisting phase, beyond which the (d-wave) superconducting state becomes stable. Further, the effects of interplanar coupling parameters on the magnetic and superconducting correlations as a function of hole doping are studied in details. The magnetic correlations are found to diminish with increasing interplanar hopping away from half filling, while the exchange across the layers strengthens interplanar antiferromagnetic correlations both at and away from half filling. The superconducting correlations show more interesting features where larger interplanar hopping considerably reduces planar correlations at optimal doping, while an opposite behaviour, i.e. stabilisation of the superconducting state is realised in the overdoped regime, with the interplanar exchange all the while playing a dormant role.Comment: 8 pages, 9 figures, RevTex4, Submitted to Phys. Rev.