We discuss the universal theory of localized impurities in the paramagnetic state of 2D antiferromagnets where the spin gap is assumed to be significantly smaller than a typical exchange energy. We study the impurity spin susceptibility near the host quantum transition from a gapped paramagnet to a Néel state, and we compute the impurity-induced damping of the spin-1 mode of the gapped antiferromagnet. Under suitable conditions our results apply also to d-wave superconductors. Doped antiferromagnets (AF) have been the subject of intense studies in the context of the cuprate high-temperature superconductors and other layered transition metal compounds. We present a quantum theory of a particular class of doped AF where it is possible to neglect the coupling between the spin and charge degrees of freedom and consider a theory of the spin excitations alone. Such a theory will apply to (i) quasi-2D ‘spin gap ’ insulators like SrCu2O3 or NaV2O5 in
We discuss the universal theory of localized impurities in the paramagnetic state of 2D antiferromagnets where the spin gap is assumed to be significantly smaller than a typical exchange energy. We study the impurity spin susceptibility near the host quantum transition from a gapped paramagnet to a Néel state, and we compute the impurity-induced damping of the spin-1 mode of the gapped antiferromagnet. Under suitable conditions our results apply also to d-wave superconductors. Doped antiferromagnets (AF) have been the subject of intense studies in the context of the cuprate high-temperature superconductors and other layered transition metal compounds. We present a quantum theory of a particular class of doped AF where it is possible to neglect the coupling between the spin and charge degrees of freedom and consider a theory of the spin excitations alone. Such a theory will apply to (i) quasi-2D ‘spin gap ’ insulators like SrCu2O3 or NaV2O5 in
Dynamical properties of the impurity spin-21 in two-dimensional (2D) and quasi-2D Heisenberg antiferromagnets (AFs) at $T\ensuremath{\geqslant}0$ are discussed. The specific case of an impurity coupled symmetrically to two neighboring host spins is considered. The specific feature of this problem is that the defect is degenerate (frustrated) being located in zero molecular field. It is shown that this problem can be described by the spin-boson model without a tunneling term and with a more complex interaction. We demonstrate that the effect of the host system on the defect is completely described by the spectral function. It is found within the spin-wave approximation that for not too small $\ensuremath{\omega}$ the spectral function is proportional to ${\ensuremath{\omega}}^{2}∕{J}^{3}$, where J is the exchange constant between the host spins. The defect dynamical susceptibility is derived using Abrikosov's pseudofermion technique and diagrammatic expansion. The calculations are performed within the fourth order of the dimensionless coupling parameter f. It is found that transverse impurity susceptibility ${\ensuremath{\chi}}_{\ensuremath{\perp}}(\ensuremath{\omega})$ has a Lorenz peak, with the width proportional to f4J(T∕J)3 which disappears at T=0, and a nonresonant term. The latter term diverges logarithmically as $\ensuremath{\omega},\phantom{\rule{0.2em}{0ex}}T\ensuremath{\rightarrow}0$. The static susceptibility $\ensuremath{\chi}(0)$ has the free-spin-like contribution 1∕(4T), and a logarithmic correction proportional to f2ln(J∕T). The influence of finite concentration of the defects n on the low-temperature properties of AFs is also investigated. A logarithmic correction to spin-wave velocity of the form $n{f}^{4}\mathrm{ln}\ensuremath{\mid}J∕\ensuremath{\omega}\ensuremath{\mid}$ and an anomalous damping of spin waves proportional to $n{f}^{4}\ensuremath{\mid}\ensuremath{\omega}\ensuremath{\mid}$ are obtained. The results of the present paper can be applied to other systems with a frustrated impurity in which the spectral function is proportional to ${\ensuremath{\omega}}^{2}$.
We describe the spin distribution in the vicinity of a nonmagnetic impurity in a two-dimensional antiferromagnet undergoing a transition from a magnetically ordered N\'eel state to a paramagnet with a spin gap. The quantum critical ground state in a finite system has total spin S=1∕2 (if the system without the impurity had an even number of S=1∕2 spins), and recent numerical studies in a double layer antiferromagnet [K. H. H\"oglund et al., Phys. Rev. Lett. 98, 087203 (2007)] have shown that the spin has a universal spatial form delocalized across the entire sample. We present the field theory describing the uniform and staggered magnetizations in this spin texture for two classes of antiferromagnets: (i) the transition from a N\'eel state to a paramagnet with local spin singlets, in models with an even number of S=1∕2 spins per unit cell, which are described by a O(3) Landau-Ginzburg-Wilson field theory; and (ii) the transition from a N\'eel state to a valence bond solid, in antiferromagnets with a single S=1∕2 spin per unit cell, which are described by a ``deconfined'' field theory of spinons.
Recent scanning tunneling microscopy (STM) experiments on underdoped cuprates have displayed modulations in the local electronic density of states, which are centered on a Cu-O-Cu bond [Kohsaka et al., Science 315, 1380 (2007)]. As a paradigm of the pinning of such bond-centered ordering in strongly correlated systems, we present the theory of valence bond solid (VBS) correlations near a single impurity in a square lattice antiferromagnet. The antiferromagnet is assumed to be in the vicinity of a quantum transition from a magnetically ordered N\'eel state to a spin-gap state with long-range VBS order. We identify two distinct classes of impurities: (i) local modulation in the exchange constants and (ii) a missing or additional spin, for which the impurity perturbation is represented by an uncompensated Berry phase. The ``boundary'' critical theory for these classes is developed. In the second class, we find a VBS pinwheel around the impurity, accompanied by a suppression in the VBS susceptibility. Implications for numerical studies of quantum antiferromagnets and for STM experiments on the cuprates are noted.
Various forms of antiferromagnetic exchange interaction among quantized spins in one-dimensional and quasi-one-dimensional lattices are examined. Primary results are reported in two real compounds, the sodium vanadate NaV2O5 and the copper germanate CuGeO3, and in a class of compounds of real materials modeled as dimerized antiferromagnetically coupled spin-1/2 chains susceptible to spin-1 impurity doping and that include such examples as the strontium cuprate Sr14Cu24O41 and vanadium pyrophosphate (VO)2P2O7. Sodium vanadate, NaV2O5, a quarter-filled two-leg ladder compound that was originally thought to be composed of magnetic legs and nonmagnetic legs was subsequently shown to be a charge ordered system below room temperature. Initial models of the material as isolated antiferromagnetically coupled spin-1/2 chains can be mapped to the subsequently resolved magnetic system of the charge ordered state with the spins on molecular orbitals of V-O-V rungs antiferromagentically coupled between neighboring rungs either on the same ladder or on neighboring ladders. Comparing the model's dynamic structure factor to inelastic neutron scattering data could distinguish between the proposed spin coupling schemes and consequently reveal the details of the interaction between the lattice and the "zig-zag" charge density as well as the magnetic stabilization of the low temperature phase. Copper germanate, the first and only known inorganic spin-Peierls compound, exhibits a strong temperature dependent exchange coupling pattern among the spin-1/2 Cu2+ chains. Above the spin-Peierls transition temperature an unmodulated antiferromagnetic nearest neighbor exchange interaction J1 competes with an antiferromagnetic next nearest neighbor interaction J2. The next nearest neighbor exchange represents an effective coupling equivalent to the net effect of all longer range exchange interactions. This frustration to the nearest neighbor spin exchange produces a distinctive magnetic susceptibility χ (T) much different from the Bonner-Fisher susceptibility of the spin-1/2 Heisenberg chain with nearest neighbor antiferromagnetic exchange only. The ratio of the second to first nearest neighbor couplings α = J2/J1 ≈ 0.36 is sufficient to open a spontaneous gap in the spin-wave excitation spectrum at low temperatures. Below TSP = 14K, the dynamical structure factor is used to fit the dimerization δ and the exchange interactions J1 and J2 to the inelastic neutron scattering data of CuGeO3 at T = 10K. It is found that both δ and α increase significantly at lower temperatures, relative to the values obtained in the high temperature phase and at the onset of dimeration at 14 K. Static structure factor calculations how Scattering inconsistent with the δâJ1âJ2 model and can be attributed primarily to the phonon degrees of freedom but possibly also to the couplings between chains in the b and a directions of the crystal lattice. Structurally dimerized compounds of antiferromagnetic spin-1/2 chains possess dynamic structure factor and magnetic susceptibility features that are very sensitive to doping with magnetic and nonmagnetic impurities. It is shown that the effects of spin-1 impurities are very similar to those of nonmagnetic (S = 0) impurities if the coupling between impurity and native spin is about the same magnitude as or larger than between native S = 1/2 spins. The microscopic origins of the similarity can be appreciated with the consideration that neighboring spins to the impurity find it more energetically favorable to couple to the impurity than the other spins of the lattice. Thus the spin-1 impurity and its neighboring S = 1/2 spins decouple from the lattice, creating a nonmagnetic break in the chain. The spins that now observe a nonmagnetic cluster on one side can couple to the S = 1/2 spins on the other side with a higher AF correlation than in the pure compound since they do not have to have a ï¬uctuating dimer resonating between two neighbors. Such enhancements to the local correlations can stabilize the global AF order in one dimensional compounds as shown in theoretical and experimental studies of CuGeO3. ED calculations of the dynamic structure factor show that S(q, ω) developes states with ω = 0 in the gap at q = π. Magnetic susceptibilites in the presense of spin-1 impurities were obtained for 80 site chains by QMC simulations and for 16 site chains by ED calculations. An impurity concentration-dependent second peak in the low temperature region reveals an increasing second maximum with T as observed in doped copper germanates and suggests that the results of the study are applicable even to phonon mediated dimerization. This is not immediately apparent because spin-phonon coupling could distort the dimerization patterns. However, experimental and theoretical results show that elastic coupling between chains can stabilize the dimerization pattern due to the impurities and the results will still apply.
We present a systematic study of spin dynamics in a superconducting ground state, which itself is a doped Mott insulator and can correctly reduce to an antiferromagnetic (AF) state at half-filling with an AF long-range order (AFLRO). Such a doped Mott insulator is described by a mean-field theory based on the phase string formulation of the $t\text{\ensuremath{-}}J$ model. We show that the well-known spin wave excitation in the AFLRO state at half-filling evolves into a resonancelike peak at a finite energy in the superconducting state, which is located around the AF wave vectors. The width of such a resonancelike peak in momentum space decides a spin correlation length scale which is inversely proportional to the square root of doping concentration, while the energy of the resonancelike peak scales linearly with the doping concentration at low doping. These properties are consistent with experimental observations in the high-Tc cuprates. An important prediction of the theory is that, while the total spin sum rule is satisfied at different doping concentrations, the weight of the resonancelike peak does not vanish, but is continuously saturated to the weight of the AFLRO at zero-doping limit. Besides the low-energy resonancelike peak, we also show that the high-energy excitations still track the spin wave dispersion in momentum space, contributing to a significant portion of the total spin sum rule. The fluctuational effect beyond the mean-field theory is also examined, which is related to the broadening of the resonancelike peak in energy space. In particular, we discuss the incommensurability of the spin dynamics by pointing out that its visibility is strongly tied to the low-energy fluctuations below the resonancelike peak. We finally investigate the interlayer coupling effect on the spin dynamics as a function of doping, by considering a bilayer system.
We show that a two-dimensional (2D) metal in a superconducting (SC) state with wave-vector-dependent gap behaves as a quantum-spin liquid characterized by a collective mode of resonance type. Formally the mode exists whatever is a form of Fermi surface (FS). However, when the latter is spherical the effect is rather formal: any factor leading to an even weak electron scattering, like finite T, impurity, etc., easily kills the mode. On the contrary, for the type of FS observed in the high-Tc cuprates (characterized by a proximity to the saddle-point wave vectors) the resonance mode exists in a true sense being well separated from the electron-hole continuum and well defined. The effect is due to the effective 1D dimension in a proximity of electronic topological transition quantum critical point. The physical nature of the collective mode varies progressively between two possibilities. In the case of a weak interaction, the resonance mode is a typical effect of a two-particle bound state that appears slightly below the bottom of the two-particle continuum. The effect exists even in the case of infinitesimally weak interaction (of relevant sign). In the case of a strong or intermediate interaction, it is a critical mode existing as a precursor of spin-density wave (SDW) instability. The gap of the collective mode is not related directly to the value of the SC gap (being, however, limited by the latter from above) but rather to a proximity to SDW instability. We predict also a second collective mode lying inside the two-particle continuum. The existence of these two modes and the particular form of their dispersion in the case corresponding to the underdoped cuprates ${(d}_{{x}^{2}\ensuremath{\sim}{y}^{2}}$ symmetry of SC gap, exchange interaction of antiferromagnetic sign, etc.) allows one to understand the main features observed experimentally in the underdoped cuprates, namely the so-called ``41 meV resonance peak'' and ``24 meV incommensurability'' and their two-dimensional wave vector dependences, the doping evolution of the spin dynamics and many other features. The theory also predicts new features to be tested experimentally.