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Percolating Puddles in Rich Quantum Landscapes

Complex electronic and atomic structures often produce nanoscale phases that draw materials into the quantum world, where unique and anomalous properties can emerge. For example, charge density waves (CDWs), which may occur in atomic layers or low-dimensional materials, are periodic modulations of electronic charge that are relevant to sought-after properties such as high-temperature superconductivity.

“Although previous studies have demonstrated that CDW order appears in many materials,” said Gaetano Campi of the Institute of Crystallography in Rome, “our knowledge of the rich quantum landscapes in these materials—crucial to understanding how structure is related to function—remains limited, especially when multiple competing orders exist simultaneously.”

Here, Campi and colleagues studied La2−xSrxNiO4+y (LSNO), a material with the same crystal structure as a known cuprate high-temperature superconductor, but with nickel atoms in place of copper. In LSNO, as with the superconducting cuprate, both spin- and charge-ordered phases develop upon cooling and then start to decay at lower temperatures, below 65 K.

The study made innovative use of two experimental methods. First, the nanoscale dynamics of CDWs were visualized using resonant soft x-ray photon correlation spectroscopy (XPCS) at Advanced Light Source (ALS) Beamline 12.0.2. Second, the CDW spatial inhomogeneity was visualized using scanning micro x-ray diffraction (SµXRD) at the Petra III synchrotron in Germany.

“The measurements were taken and fluctuations determined over a broad temperature range, and the temporal measurements were directly correlated with the spatial data,” said ALS staff scientist and Scattering Program lead, Sujoy Roy. “The results showed that, in different temperature ranges, the material displays different types of dynamics.”

This first direct visualization of the spatial and temporal evolution of CDW domains called “puddles” revealed motions occurring at two different characteristic time scales: small puddles actively “percolate” (fluctuate in size and shape), while large puddles are more static.

The spatiotemporal pattern of percolating small dynamic CDW puddles competing with large static CDW puddles represents a novel form of nanoscale phase separation and provides new information that may help scientists disentangle the competing factors that affect the appearance and disappearance of anomalous properties in quantum materials.

Top left shows experiment setup; top right shows domain delay time vs temperature. Bottom left shows spatial distribution of temporal data at three temperatures; bottom right shows number of clusters vs fluctuation rates—two peaks reveal the two phases.
(a) Experimental scheme for the XPCS measurements using coherent x-rays. A time series of x-ray coherent diffraction images captures the temporal evolution of the CDW. (b) The time delay, τ, of CDW fluctuations increases by a factor 100 from the static region to the dynamic region at low temperature. (c) Maps of CDW peak frequency, τ-1, at T = 35K, 50K, and 65K, obtained by scanning the sample over an area of 66 × 100 μm2. (d) Number of forming clusters calculated for the maps in (c). Cluster analysis allows characterization of the static and dynamic CDW. In the static regime, a larger number of clusters forms at lower fluctuation rates, τ−1.

G. Campi, A. Bianconi, B. Joseph, S.K. Mishra, L. Müller, A. Zozulya, A.A. Nugroho, S. Roy, M. Sprung, and A. Ricci, “Nanoscale inhomogeneity of charge density waves dynamics in La2−xSrxNiO4,” Sci. Rep. 12, 15964 (2022), doi:10.1038/s41598-022-18925-y.