Local Defect in Metallic Quantum Critical Systems

Abstract

We present a theory of a single point, line or plane defect coupling to the square of the order parameter in a metallic system near a quantum critical point at or above its upper critical dimension. At criticality, a spin droplet is nucleated around the defect with droplet core size determined by the strength of the defect potential. Outside the core a universal slowly decaying tail of the droplet is found, leading to many dissipative channels coupling to the droplet and to a complete suppression of quantum tunneling. We propose an NMR experiment to measure the impurity-induced changes in the local spin susceptibility. 75.10.Jm,75.10.Nr,75.70.Kw,76.30.Da The behavior of 'droplets' of local order in a nonordered background is an issue of wide relevance in condensed matter physics. One particularly interesting subclass of problems concerns 'droplets' induced by defects in nearly critical systems. A long-standing problem in heavy fermion physics concerns the very small magnetic moments which have been observed in several materials [1,2] and may be related to grain boundaries and other structural defects [3][4][5]. In a colossal magnetoresistance material, magnetic order was observed to be enhanced near grain boundaries.[6] A related issue is the magnetism induced in high temperature superconductors by apparently non-magnetic substituents such as Zn [7], which have been interpreted [8,9] as spin droplets induced in a nearly critical system (although other interpretations exist also [10]). Nucleation of regions of charge density wave order around defect sites on the surface of a 'correlated' material was reported by [11]. 'Quantum Griffiths' effects and 'Kondo disorder' are presently of intense interest. [12][13][14][15]. The problem bears on the fundamental issue of the Kondo effect near a quantum critical point [16]. Finally, recording of information involves the polarization of small domains, whose long time dynamics and stability are of great importance.This Letter presents the theory of the local polarization ('droplet') induced by a single defect in an otherwise nondisordered system which is near a quantum critical point at or above it upper critical dimension, d u . These restrictions allow a controlled theoretical treatment and apply to a wide range of systems including metallic magnets in dimensions d = 2, 3 [17,18] and "quantum paraelectric" (i.e. nearly ferroelectric) systems in d = 3 [19]. We study defects which couple to the square of the order parameter, i.e. change the 'local T c ', and thus create small regions where order is more favored than in the pure system. We address three questions: under which circumstances does the defect create a 'droplet', a region about the defect in which the order parameter is non-vanishing (at least on short time scales)? What is the size and general properties of the droplet? What are the relevant fluctuations? Our work is complementary to that of Vojta and Sachdev [20], who studied a linear coupling of the defect to the order parameter in a quantum critical system...

Quantum Griffiths effects in metallic systems

“…Therefore, (9) and (10) are very similar (the difference in the exponents is due to the different nature of the percolation in the two problems) and show that N ξ diverges as ξ → ∞. It should be clear at this point that the two main elements of the theory, namely the tunneling splitting and its distribution, although calculated in very different way, are essentially the same in both theories.…”

“…Using the Hertz theory of quantum critical phenomena [8] and treating the problem of an Ising field theory in the presence of a single impurity, Millis, Morr, and Schmalian (MMS) [9] have cast doubts on the possibility of Griffiths singularities in these materials based on the over-damping of the cluster (droplet) dynamics due to the electronic degrees of freedom. This effect is the result of the slow decay of the droplet profile in the single impurity case.…”

Impurities near an antiferromagnetic-singlet quantum critical point

“…Impurities reduce order, but also nucleate ordered domains which, when sufficiently proximate, coalesce to create long range order. [33][34][35] We brought together exact QMC calculations of the effect of impurities on spin correlations/domains and the NMR relaxation rate, as a system is tuned through a QCP.…”

Interacting Antiferromagnetic Droplets in Quantum CriticalCeCoIn5

“…As the Fermi surface evolves with hole doping, either superconductivity or antiferromagnetism may emerge, depending on the quantity JN 0 in much the same way that pressure changes the ground state by modifying J [1]. An alternative to this global interpretation is that the Cd acts as a local defect that nucleates antiferromagnetism in a quantum critical system [5,6]. In a system close to a QCP, a local perturbation can induce droplets of local antiferromagnetic order.…”