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 or PDW order can generically give way to a SDW or 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 .
- Received 17 February 2015
DOI:https://doi.org/10.1103/PhysRevX.5.031008
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Published by the American Physical Society
Popular Summary
Spontaneous breaking of translational symmetry, known as density-wave order, is observed in a large number of electronic systems. In the presence of imperfections (i.e., nonmagnetic impurities), which are inherent to any real system, the nature of these states changes dramatically, and new phases of matter arise. These new phases exhibit properties that lie midway between the possible thermal phases expected in hypothetical clean realizations of the same system. One common example is given by collinear spin-density-wave order, which has been observed in a large number of materials ranging from conventional metals to more complicated systems such as cuprates. There the magnetic moments of the electrons exhibit a periodically modulated pattern in space, oscillating between alignment and antialignment with a spontaneously chosen axis. Such states break both translation symmetry and spin-rotation symmetry, and their interplay with disorder leads to a number of striking effects that we analyze here in both two and three dimensions.
Using analytical arguments supported by numerical simulations, we uncover and characterize new phases of matter that we refer to as spin-density-wave glasses (and closely analogous pair-density-wave glasses). Crucially, the magnetic moments remain aligned or antialigned to a spontaneously chosen axis even as the periodic spatial modulations are lost. As a consequence, these systems are both spin glasses and symmetry broken phases at the same time; their measured nature depends on the experimental probe. Since any solid-state experiment necessarily includes disorder, spin-density-wave glasses are likely to be a common phenomenon. These glasses present a natural starting point for interpreting experiments in any system where spin-density-wave order is observed.
Similar effects arise in systems with spatially modulated superconductivity, which have important consequences for recent theoretical and experimental work on the cuprate .