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Physical review. B, Condensed matter

Nonmagnetic impurity in the spin-gap state

Naoto Nagaosa, Tai Kai Ng

Published Jun 1, 1995• 31 citations
Publisher

Abstract

The effects of nonmagnetic strong scatterers (unitary limit) on magnetic and transport properties are studied for resonating-valence-bond states in both the slave-boson and slave-fermion mean-field theories with the gap for the triplet excitations. In the d-wave pairing state of the slave-boson mean-field theory in two dimensions, there is no true gap for spinons, but the Anderson localization occurs, which leads to the local moment when the repulsive interaction is taken into account. In the slave-fermion mean-field theory, local moments are found bound to nonmagnetic impurities as a result of (staggered) gauge interaction. However, in both theories, localization of spinon does not appear in the resistivity, which shows the classical value for the holon.

DOI
10.1103/physrevb.51.15588

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The effects of nonmagnetic strong scatterers (unitary limit) on magnetic and transport properties are studied for resonating-valence-bond states in both the slave-boson and slave-fermion mean-field theories with the gap for the triplet excitations. In the d-wave pairing state of the slave-boson mean-field theory in two dimensions, there is no true gap for spinons, but the Anderson localization occurs, which leads to the local moment when the repulsive interaction is taken into account. In the slave-fermion mean-field theory, local moments are found bound to nonmagnetic impurities as a result of (staggered) gauge interaction. However, in both theories, localization of spinon does not appear in the resistivity, which shows the classical value for the holon.
We study the effect of a small density n_{v} of quenched nonmagnetic impurities, i.e., vacancy disorder, in gapped short-range resonating valence bond (RVB) spin liquid states and valence bond solid (VBS) states of quantum magnets. We argue that a large class of short-range RVB liquids are stable to vacancy disorder at small n_{v} on the kagome lattice, while the corresponding states on triangular, square, and honeycomb lattices are unstable to vacancy disorder at any nonzero n_{v} due to the presence of emergent vacancy-induced local moments. In contrast, VBS states are argued to be generically unstable (independent of lattice geometry) to vacancy disorder at any nonzero n_{v} due to such a local-moment instability. Our arguments rely in part on an analysis of the statistical mechanics of maximally packed dimer covers of the diluted lattice, and are fully supported by our computational results on O(N) symmetric designer Hamiltonians. These arguments also imply that short-range RVB spin liquid states are generically unstable to bond dilution on all these lattices.
We discuss the effects of nonmagnetic impurities (static holes) in the S=1/2S=1/2S=1/2 Heisenberg model on a two-dimensional (2D) square lattice, and on two- and three-leg ladders. Results of quantum Monte Carlo simulations show that a free localized moment is induced around an isolated impurity only in the spin-gapped two-leg ladder, in agreement with previous theoretical expectations. The localization length of the S=1/2S=1/2S=1/2 impurity moment in a two-leg ladder with isotropic couplings is $\ensuremath{\approx}1.5$ lattice spacings. In gapless ladders (odd number of legs) and in the 2D lattice, no free moments are induced. However, in the 2D system, which has antiferromagnetic long-range order at T=0T=0T=0 and a gap for longitudinal fluctuations, the impurity leads to a localized distortion of the magnetization in the direction of the broken symmetry, with total Sz=1/2.{S}^{z}=1/2.Sz=1/2. The shape of the distortion is in close agreement with previous spin-wave calculations. For all the systems, a staggered moment is induced by the impurity. For the gapped two-leg ladder this is exponentially localized within a length equal to the spin correlation length of the ladder ($\ensuremath{\approx}3.2$ lattice spacings). For the three-leg ladder, the integrated staggered moment diverges as the system size goes to infinity, but the staggered magnetization at a given site appears to vanish. In 2D, we discuss the behavior seen in finite systems both with and without additional symmetry-breaking mechanisms. We also discuss the effect of impurities on the NMR Knight shift and the bulk magnetic susceptibility.
We reconsider the problem of separation of spin and charge in one-dimensional quantum antiferromagnets. We show that spin and charge separation in one-dimensional strongly correlated systems cannot be described by the slave-boson or fermion representation within any perturbative treatment of the interactions between the slave holons and slave spinons. The constraint of single occupancy must be implemented exactly. As a result the slave fermions and bosons are not part of the physical spectrum. Instead, the excitations that carry the separate spin and charge quantum numbers are solitons. To prove this result, it is sufficient to study the pure spinon sector in the slave-boson representation. We start with a short-range resonating-valence-bond state spin liquid mean-field theory for the frustrated antiferromagnetic spin-1/2 chain. We derive an effective theory for the fluctuations of the Affleck-Marston and Anderson order parameters. We show how to recover the phase diagram as a function of the frustration by treating the fluctuations nonperturbatively.
We study the effect of nonmagnetic impurities in the superconducting state of the t–J model. The Bogoliubov de Gennes equation is derived using a slave-boson mean-field approximation, and we solve it numerically at T = 0. The dx2-y2-wave order parameter is suppressed near an impurity and the extended s-wave component is induced. We also find the local CDW-like feature due to the Friedel oscillations. This leads to the splitting of the expected zero-energy Andreev bound state. Therefore the system is unlikely introducing a localized state of other symmetry such as superconductivity with broken time reversal symmetry or antiferromagnetism.
We examine the effect of a nonmagnetic impurity in a two-dimensional spin liquid in the spin-gap phase, employing a drone-fermion representation of spin-1/21/21/2 operators. The properties of the local moment induced in the vicinity of the impurity are investigated and an expression for the nuclear-magnetic-resonance Knight shift is derived, which we compare with experimental results. Introducing a second impurity into the spin liquid an antiferromagnetic interaction between the moments is found when the two impurities are located on different sublattices. The presence of many impurities leads to a screening of this interaction as is shown by means of a coherent-potential approximation. Further, the Kondo screening of an impurity-induced local spin by charge carriers is discussed.