Impurity-induced spin polarization and NMR line broadening in underdoped cuprates

We present a theory of magnetic (S=1) Ni and nonmagnetic Zn impurities in underdoped cuprates. Both types of impurities are shown to induce S=1/2 moments on Cu sites in the proximity of the impurity, a process which is intimately related to the spin gap phenomenon in cuprates. Below a characteristic Kondo temperature, the Ni spin is partially screened by the Cu moments, resulting in an effective impurity spin S=1/2. We further analyze the Ruderman-Kittel-Kasiya-Yosida-type response of planar Cu spins to a polarization of the effective impurity moments and derive expressions for the corresponding ^{17}O NMR line broadening. The peculiar aspects of recent experimental NMR data can be traced back to different spatial characteristics of Ni and Zn moments as well as to an inherent temperature dependence of local antiferromagnetic correlations.Comment: PRB B1 01June9

Possible isotope effect on the resonance peak formation in high-Tc_c cuprates

Starting from the three-band $p-d$ Hubbard Hamiltonian we derive an effective $t-J$ model including electron-phonon interaction of quasiparticles with optical phonons. Within the effective Hamiltonian we analyze the influence of electronic correlations and electron-phonon interaction on the dynamical spin susceptibility in layered cuprates. We find a huge isotope effect on the resonance peak in the magnetic spin susceptibility, ${Im}\chi({\bf q},\omega)$, seen by inelastic neutron scattering. It results from both the electron-phonon coupling and the electronic correlation effects taken into account beyond random phase approximation(RPA) scheme. We find at optimal doping the isotope coeffiecient $\alpha_{res} \approx 0.35$ which can be further tested experimentally.Comment: revised version, new figure is added. Phys. Rev. B 69, 0945XX (2004); in pres

Double-layer Heisenberg antiferromagnet at finite temperature: Brueckner Theory and Quantum Monte Carlo simulations

The double-layer Heisenberg antiferromagnet with intra- and inter-layer couplings $J$ and $J_\perp$ exhibits a zero temperature quantum phase transition between a quantum disordered dimer phase for $g>g_c$ and a Neel phase with long range antiferromagnetic order for $g<g_c$, where $g=J_\perp/J$ and $g_c \approx 2.5$. We consider the behavior of the system at finite temperature for $g \ge g_c$ using two different and complementary approaches; an analytical Brueckner approximation and numerically exact quantum Monte Carlo simulations. We calculate the temperature dependent spin excitation spectrum (including the triplet gap), dynamic and static structure factors, the specific heat, and the uniform magnetic susceptibility. The agreement between the analytical and numerical approaches is excellent. For $T \to 0$ and $g \to g_c$, our analytical results for the specific heat and the magnetic susceptibility coincide with those previously obtained within the nonlinear $\sigma$ model approach for $N\to \infty$. Our quantum Monte Carlo simulations extend to significantly lower temperatures than previously, allowing us to obtain accurate results for the asymptotic quantum critical behavior. We also obtain an improved estimate for the critical coupling: $g_c = 2.525 \pm 0.002$.Comment: 23 pages, 12 figure

Effect of magnetic frustration on single-hole spectral function in the t-t'-t''-J model

We examine the effect of the magnetic frustration J' on the single-hole spectral function in the t-t'-t''-J model. At zero temperature, the exact diagonalization (ED) and the self-consistent Born approximation (SCBA) methods are used. We find that the frustration suppresses the quasiparticle (QP) weight at small momentum k, whereas the QP peak at k=(pi/2,pi/2) remains sharp. We also show the temperature dependence of the single-hole spectral function by using the ED method. It is found that the lineshapes at (pi/2,0) and (pi/2,pi/2) show different temperature dependence. These findings are consistent with the angle-resolved photoemission data on Sr2CuO2Cl2, and indicate the importance of the magnetic frustration on the electronic states of the insulating cuprates.Comment: 5 pages, 3 EPS figures, REVTeX, To be published in Phys. Rev. B, Vol. 59, Num. 3 (15 Jan. 1999

Zeeman Perturbed 63^{63}Cu Nuclear Quadrupole Resonance Study of the Vortex State of YBa2_2Cu3_3O7−δ_{7-\delta}

We report a $^{63}$Cu nuclear quadrupole resonance (NQR) study of the vortex state for an aligned polycrystalline sample of a slightly overdoped high-$T_c$ superconductor YBa$_2$Cu$_3$O$_{7-\delta}$ ($T_{c}\sim$92 K) at a low magnetic field of 96 mT along the c axis, near a lower critical field $H_{c1}$. We observed the frequency distribution of the nuclear spin-lattice relaxation time $^{63}T_1$ in the Zeeman-perturbed $^{63}$Cu NQR spectrum below $T_c$. The characteristic behavior of 1/$^{63}T_1$, taking the minimum values with respect to temperature and frequency, indicates the significant role of antiferromagnetic spin fluctuations in the Doppler-shifted quasiparticle energy spectrum inside and outside vortex cores.Comment: 4 pages, 4 figure

Dispersion of the neutron resonance in cuprate superconductors

We argue that recently measured downward dispersion of the neutron resonance peak in cuprate superconductors is naturally explained if the resonance is viewed as a spin-1 collective mode in a d-wave superconductor. The reduction of the resonant frequency away from the antiferromagnetic wave vector is a direct consequence of the momentum dependence of the d-wave superconducting gap. When the magnetic correlation length becomes large, the dispersion should become magnon-like, i.e., curve upwards from (pi,pi).Comment: 4 pages, 3 inline PostScript figures. Added reference

Quasiparticle structure in antiferromagnetism around the vortex and nuclear magnetic relaxation time

On the basis of the Bogoliubov-de Gennes theory for the two-dimensional extended Hubbard model, the vortex structure in d-wave superconductors is investigated including the contribution of the induced incommensurate antiferromagnetism around the vortex core. As the on-site repulsive interaction $U$ increases, the spatial structure of charge and spin changes from the antiferromagnetic state with checkerboard modulation to that with the stripe modulation. By the effect of the induced antiferromagnetic moment, the zero-energy density of states is suppressed, and the vortex core radius increases. We also study the effect of the local density of states (LDOS) change on the site-dependent nuclear relaxation rate $T_1^{-1}({\bf r})$. These results are compared with a variety of experiments performed on high $T_c$ cuprates.Comment: 10pages, 8 figure

Quantum impurity dynamics in two-dimensional antiferromagnets and superconductors

We present the universal theory of arbitrary, localized impurities in a confining paramagnetic state of two-dimensional antiferromagnets with global SU(2) spin symmetry. The energy gap of the host antiferromagnet to spin-1 excitations, \Delta, is assumed to be significantly smaller than a typical nearest neighbor exchange. In the absence of impurities, it was argued in earlier work (Chubukov et al. cond-mat/9304046) that the low-temperature quantum dynamics is universally and completely determined by the values of \Delta and a spin-wave velocity c. Here we establish the remarkable fact that no additional parameters are necessary for an antiferromagnet with a dilute concentration of impurities, n_{imp} - each impurity is completely characterized by a integer/half-odd-integer valued spin, S, which measures the net uncompensated Berry phase due to spin precession in its vicinity. We compute the impurity-induced damping of the spin-1 collective mode of the antiferromagnet: the damping occurs on an energy scale \Gamma= n_{imp} (\hbar c)^2/\Delta, and we predict a universal, asymmetric lineshape for the collective mode peak. We argue that, under suitable conditions, our results apply unchanged (or in some cases, with minor modifications) to d-wave superconductors, and compare them to recent neutron scattering experiments on YBCO by Fong et al. (cond-mat/9812047). We also describe the universal evolution of numerous measurable correlations as the host antiferromagnet undergoes a quantum phase transition to a Neel ordered state.Comment: 36 pages, 12 figures; added reference

Resonant Raman Scattering in Antiferromagnets

Two-magnon Raman scattering provides important information about electronic correlations in the insulating parent compounds of high-$T_c$ materials. Recent experiments have shown a strong dependence of the Raman signal in $B_{1g}$ geometry on the frequency of the incoming photon. We present an analytical and numerical study of the Raman intensity in the resonant regime. It has been previously argued by one of us (A.Ch) and D. Frenkel that the most relevant contribution to the Raman vertex at resonance is given by the triple resonance diagram. We derive an expression for the Raman intensity in which we simultaneously include the enhancement due to the triple resonance and a final state interaction. We compute the two-magnon peak height (TMPH) as a function of incident frequency and find two maxima at $\omega^{(1)}_{res} \approx 2\Delta + 3J$ and $\omega^{(2)}_{res} \approx 2\Delta + 8J$. We argue that the high-frequency maximum is cut only by a quasiparticle damping, while the low-frequency maximum has a finite amplitude even in the absence of damping. We also obtain an evolution of the Raman profile from an asymmetric form around $\omega^{(1)}_{res}$ to a symmetric form around $\omega^{(2)}_{res}$. We further show that the TMPH depends on the fermionic quasiparticle damping, the next-nearest neighbor hopping term $t^{\prime}$ and the corrections to the interaction vertex between light and the fermionic current. We discuss our results in the context of recent experiments by Blumberg et al. on $Sr_2CuO_2Cl_2$ and $YBa_2Cu_3O_{6.1}$ and R\"{u}bhausen et al. on $PrBa_2Cu_3O_7$ and show that the triple resonance theory yields a qualitative and to some extent also quantitative understanding of the experimental data.Comment: 19 pages, RevTeX, 16 figures embedded in the text, ps-file is also available at http://lifshitz.physics.wisc.edu/www/morr/morr_homepage.htm

Normal-State Spin Dynamics and Temperature-Dependent Spin Resonance Energy in an Optimally Doped Iron Arsenide Superconductor

The proximity of superconductivity and antiferromagnetism in the phase diagram of iron arsenides, the apparently weak electron-phonon coupling and the "resonance peak" in the superconducting spin excitation spectrum have fostered the hypothesis of magnetically mediated Cooper pairing. However, since most theories of superconductivity are based on a pairing boson of sufficient spectral weight in the normal state, detailed knowledge of the spin excitation spectrum above the superconducting transition temperature Tc is required to assess the viability of this hypothesis. Using inelastic neutron scattering we have studied the spin excitations in optimally doped BaFe1.85Co0.15As2 (Tc = 25 K) over a wide range of temperatures and energies. We present the results in absolute units and find that the normal state spectrum carries a weight comparable to underdoped cuprates. In contrast to cuprates, however, the spectrum agrees well with predictions of the theory of nearly antiferromagnetic metals, without complications arising from a pseudogap or competing incommensurate spin-modulated phases. We also show that the temperature evolution of the resonance energy follows the superconducting energy gap, as expected from conventional Fermi-liquid approaches. Our observations point to a surprisingly simple theoretical description of the spin dynamics in the iron arsenides and provide a solid foundation for models of magnetically mediated superconductivity.Comment: 8 pages, 4 figures, and an animatio