Abstract
Spontaneous breaking of translational symmetry---known as `density wave' order---is common in nature. However such states are strongly sensitive to impurities or other forms of frozen disorder leading to fascinating glassy phenomena. We analyze impurity effects on a particularly ubiquitous form of broken translation symmetry in solids: a Spin Density Wave (SDW) with spatially modulated magnetic order. Related phenomena occur in Pair Density Wave (PDW) superconductors where the superconducting order is spatially modulated. For weak disorder, we find that the SDW / PDW order can generically give way to a SDW / PDW glass---new phases of matter with a number of striking properties, which we introduce and characterize here. In particular, they exhibit an interesting combination of conventional (symmetry-breaking) and spin glass (Edwards-Anderson) order. This is reflected in the dynamic response of such a system, which---as expected for a glass---is extremely slow in certain variables, but---surprisingly---is fast in others. Our results apply to all uniaxial metallic SDW systems where the ordering vector is incommensurate with the crystalline lattice. In addition, the possibility of a PDW glass has important consequences for some recent theoretical and experimental work on $La_{2-x}Ba_xCu_2O_4$.
Highlights
A variety of electronic solids settle into equilibrium states that spontaneously break the translational symmetry of the underlying crystal [1]
Despite the common occurrence of spin-density-wave ordering, surprisingly little attention has been devoted to impurity effects on spin density wave (SDW) systems, and this is the subject of this paper
Questions closely related to the ones we study arise in considering the effects of impurities on pair-density-wave (PDW) superconductors of the kind proposed to be realized in the high-temperature superconductor La2−xBaxCu2O4
Summary
A variety of electronic solids settle into equilibrium states that spontaneously break the translational symmetry of the underlying crystal [1]. Density wave orders have been found in conventional metals as well as in strongly correlated systems like the underdoped cuprates, iron pnictides and organic materials. They are intertwined with many other fascinating phenomena such as high temperature superconductivity. It is important to distinguish between collinear SDWs, where the spin orientation oscillates in space along a fixed common direction, and spiral SDWs, where the spin rotates around an axis as a function of space while the magnitude jS~ðrÞj is constant Both kinds of SDW order break both spin-rotation and lattice-translation symmetries, but the latter retains a combination of the two as a symmetry. A fluctuating version of the PDW state appears as a “mother” state that controls the physics of the pseudogap regime in the cuprates in a recently proposed theory [7]
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