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Nanoscale phase coexistence and inhomogeneity are ubiquitous in correlatedelectron materials, existing in doped Mott insulators, manganites, andhigh-temperature superconductors. The small length scales and lack of contrastmechanisms make it extremely challenging to measure real-space images of thephase coexistence with high resolution. Yet, images aid our understanding ofhow phase coexistence and domain boundaries dictate the exotic materialproperties. Here we show that resonant soft-X-ray holography, previouslyemployed to image magnetic domains, can be used to image phase separation onthe nanoscale. We observe nucleation and growth of nanometre-sized metallicdomains out of the insulating phase of the prototypical correlated materialVO2, using linearly polarized coherent synchrotron radiation. By spectrallyresolving the holograms, we extract differential soft X-ray absorption spectrawith 50 nm spatial resolution. Furthermore, when combined with ultra-bright andultra-short X-ray sources, X-ray holography could capture both nanoscalespatial variations and temporal fluctuations that occur close to the transitiontemperatures or are induced by femtosecond light pulses that cannot be observedwith alternative imaging methods.

Nanoscale spectroscopic imaging of phase separation in a correlated material by resonant X-ray holography