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Circularly-polarized extreme UV and X-ray radiation provides valuable access to the structural, electronic and magnetic properties of materials. To date, this capability was available only at largescale X-ray facilities such as synchrotrons. Here we demonstrate the first bright, phase-matched, extreme UV circularly-polarized high harmonics and use this new light source for magnetic circular dichroism measurements at the M-shell absorption edges of Co. We show that phase matching of circularly-polarized harmonics is unique and robust, producing a photon flux comparable to the linearly polarized high harmonic sources that have been used very successfully for ultrafast element-selective magneto-optic experiments. This work thus represents a critical advance that makes possible element-specific imaging and spectroscopy of multiple elements simultaneously in magnetic and other chiral media with very high spatial and temporal resolution, using tabletop-scale setups. IntroductionCircularly polarized radiation in the extreme ultraviolet (EUV) and soft X-ray spectral regions has proven to be extremely useful for investigating chirality-sensitive light-matter interactions. It enables studies of chiral molecules using photoelectron circular dichroism 1 , ultrafast molecular decay dynamics 2 , the direct measurement of quantum phases (e.g. Berry's phase and pseudo-spin) in graphene and topological insulators 3-5 and reconstruction of band structure and modal phases in solids 6 . For magnetic materials, circularly polarized soft x-rays are particularly useful for X-ray Magnetic Circular Dichroism (XMCD) spectroscopy 7 . XMCD enables element-selective probing as well as coherent imaging and holography of magnetic structures with nanometer resolution [8][9][10] . Moreover, it can also be used to extract detailed information about the magnetic state by distinguishing between the spin and orbital magnetic moments of each element. Thus, time-resolved XMCD can probe the element-specific dynamics of the spin and orbital moments when interacting with the electronic and phononic degrees of freedom in a material [11][12][13][14] . However, the time resolution available to date for XMCD has been > 100 fs, limited by the pulse duration and timing jitter of synchrotron pulses [15][16][17] . To date it has not been possible to probe spin dynamics of multiple elements simultaneously within the same sample, because the photon energy must be tuned across the various absorption edges at the large-scale facilities where these experiments are currently performed.2 Table-top soft x-ray sources based on high harmonic upconversion of femtosecond laser pulses represent a viable alternative to large-scale sources for many applications, due to their unique ability to generate bright, broadband, ultrashort and coherent light with an energy spectrum reaching into the keV region 18 . High harmonic generation (HHG) not only enables coherent imaging of nanometer structures with a spatial resolution approaching the diffraction limit 19 , but also accesses...

Strong-field ionization provides fundamental insight into light-matter interactions, encoding the structure of atoms and molecules on the sub-Ångström and sub-femtosecond scales. In this Letter, we explore an important new regime: strong-field ionization by two-color circularly polarized laser fields. In contrast to all past work using linearly polarized drivers, we probe electron trajectories that are driven in a 2D plane, thus separating the tunneling angle from the rescattering angle. This allows us to make several new findings. First, we observe a single-lobed electron distribution for co-rotating fields, and a three-lobed distribution for counter-rotating fields, providing the first experimental validation of the theoretical model explaining the generation of circularly polarized high harmonic light. Second, we discover that there is significant electron-ion rescattering using counter-rotating fields, but not with co-rotating fields. Finally, we show that the rescattered electrons are well separated from the directly-ionized electrons, in striking contrast to similar low-energy structures seen with linearly polarized fields. These findings help overcome the long-standing problem of how to decouple the tunneling and rescattering steps in strong-field ionization, which will enable new dynamic probes of atomic and molecular structure.