Disorder-Induced Static Antiferromagnetism in Cuprate Superconductors

Abstract

Using model calculations of a disordered d-wave superconductor with on-site Hubbard repulsion, we show how dopant disorder can stabilize novel states with antiferromagnetic order. We find that the critical strength of correlations or impurity potential necessary to create an ordered magnetic state in the presence of finite disorder is reduced compared to that required to create a single isolated magnetic droplet. This may explain why in cuprates like La2−xSrxCuO4(LSCO) low-energy probes have identified a static magnetic component which persists well into the superconducting state, whereas in cleaner systems like YBa2Cu3O 6+δ (YBCO) it is absent or minimal.PACS numbers: 74.25.Jb,74.25.Hc The occurrence of high-temperature superconductivity in cuprates near the antiferromagnetic (AF) phase of the parent compounds has prompted speculation since their discovery that superconductivity and magnetism were intimately related. For the most part, it has been assumed that the two forms of order compete and do not coexist, consistent with the vanishing of the Néel temperature T N before the onset of a superconducting critical temperature T c , and the suppression of T c near doping x = 1/8 where static stripe phases can be stable [1]. On the other hand, there have been persistent reports of static AF at low temperatures T in the superconducting phase at low doping, as measured by muon spin resonance (µSR) [2,3], nuclear magnetic resonance (NMR) [4,5], and elastic neutron scattering (NS) [6,7]. The NS experiments reveal an incommensurate (IC) ordering wavevector evident by a quartet of peaks surrounding (π, π). Since the neutron response is enhanced by an applied magnetic field [6,8,9] several authors have discussed it in terms of coexisting d-wave superconductivity (dSC) and field-induced spin density waves [10]. Recent magnetic Raman scattering data on LSCO has been discussed in terms of such effects as well [11]. However, static order also exists at zero field in the underdoped phase of LSCO [6,7], and has been attributed to disorder [6]. In optimally doped LSCO, Kimura et al. [12] did not detect ordered moments in pure and 1% Zn-substituted samples. An elastic peak similar to the pure underdoped material was observed when 1.7% Zn was added, however [12].Phenomena similar to those in LSCO have been observed in other materials, e.g. Y 1−x Ca x Ba 2 Cu 3 O 6 , and Bi 2 Sr 2 CaCu 2 O 8+x (BSCCO) where µSR directly reveals a slowing down and subsequent freezing of spin fluctuations as T is lowered [2,13]. On the other hand, experiments on optimally doped YBCO, even with significant percentages of Zn, have never detected static magnetic signals. While there have been reports of AF coexisting with dSC in underdoped YBCO, recent NS measurements on YBCO 6.5 found that AF order, while static from the point of view of NS timescales, 10 −10 s, was fluctuating faster than the timescale, 10 −6 s, for µSR. Thus, it appears that while in YBCO low-frequency AF fluctuations are present, they do not "freeze out". Recently, reports of st...

d-Wave superconductivity as a catalyst for antiferromagnetism in underdoped cuprates

“…When these droplets come close enough to interact, there is a tendency to form incommensurate, phase-coherent Néel domains whose size is sufficient to explain the observations by Lake et al [2] in zero field [12]. Such a model explains the empirical observations that both increasing disorder [17] and underdoping [9] enhance the SDW order.In this paper, we investigate the origin of the 'order by disorder' phenomenon described in [12], as well as the T evolution of the disordered magnetic state in applied magnetic field. An apparently very natural approach to the problem was developed by Demler et al [18], who constructed a Ginzburg-Landau (GL) theory for competing SDW and SC order in a magnetic field.…”

“…If doping is assumed to be correlated with the ratio of bandwidth to local Coulomb repulsion, a phase diagram very much like the one found in various cuprate materials is obtained (see figures 1(b)-(d)). We consider this a reasonable qualitative approach, since the reported changes in the Fermi surface of these materials over the 'spin-glass' doping range are small [30] and it is therefore plausible that the primary effect on the electronic structure is due to the correlationinduced band narrowing [12]. The magnetically ordered phase can be enhanced by the increase in the correlation strength or stronger disorder potentials (see figures 1(c) and (d)).…”

“…In this model, a single impurity creates, at sufficiently large Hubbard interaction U and impurity potential strength V imp , a droplet of staggered magnetization with a size corresponding to the AF correlation length of the hypothetical pure system [13][14][15][16]. When these droplets come close enough to interact, there is a tendency to form incommensurate, phase-coherent Néel domains whose size is sufficient to explain the observations by Lake et al [2] in zero field [12]. Such a model explains the empirical observations that both increasing disorder [17] and underdoping [9] enhance the SDW order.…”

“…Such an approach was proposed in a model calculation for an inhomogeneous d-wave superconductor with Hubbard-type correlations treated in the mean field [12]. In this model, a single impurity creates, at sufficiently large Hubbard interaction U and impurity potential strength V imp , a droplet of staggered magnetization with a size corresponding to the AF correlation length of the hypothetical pure system [13][14][15][16].…”

“…In this paper, we investigate the origin of the 'order by disorder' phenomenon described in [12], as well as the T evolution of the disordered magnetic state in applied magnetic field. An apparently very natural approach to the problem was developed by Demler et al [18], who constructed a Ginzburg-Landau (GL) theory for competing SDW and SC order in a magnetic field.…”