Spin-orbit (SO) coupling, the interaction between spin and orbital magnetic moments due to relativistic effects, is an important and interesting parameter due to its key action on a variety of physical situations, including spectral lines splitting and effects on electronic band structures. It is also important in spintronics and for topological phases formation. [1] A solid understanding of spin-orbit effects in solids must take applied pressure into account since high pressures may intensely modify interatomic distances and thus affect the way atomic orbitals hybridize to form bands. However, probing SO coupling under such conditions is very challenging due to physical limitations imposed by high pressure instrumentation. In this way, exploring the limits of high pressure characterization techniques applicability to SO probing is a highly relevant scientific goal.

X-ray absorption spectroscopy (XAS) is a major technique for probing electronic properties with element and orbital selectivity and is well stablished in high pressure studies using diamond anvil cells. Since it allows us to probe excitations from spin-orbit split energy levels, such as 2p1/2 and 2p3/2 (L2/L3 absorption edges), it is well suited for SO coupling investigation under high pressure. Indeed, it is known that the L3/L2 white line intensity ratio (branching ratio) is directly proportional to the SO operator expectation value < L.S >. [2] Such approach has already been used for studying spin-orbit interactions in 5d transition elements under ambient and high pressure. [3–5] Here, we seek using metallic Hf for testing the capabilities of XAS to explore correlations between SO coupling and the emergence of superconductivity (SC) at applied pressure. Hafnium poses an interesting case for its high orbital moment 5d2 electronic configuration, which should favor superconductivity at ambient pressure (while spin moment is, in turn, expected to diminish SC).  Although orbital moment suppression would be expected at higher pressures, a rise in superconducting critical temperature is observed, from 0.12 K at ambient pressure to 8.6 K at 62 GPa. [6] The mechanism behind this surprising behavior should involve spin and orbital moments interaction, making Hf a great candidate for XAS probing of SO interaction influences on the emergence of SC phases.

We acknowledge financial support by FAPESP (SP-Brazil) under contracts No. 2018/10585-0 and No. 2010/19979-9. Work at Argonne is supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC- 02-06CH11357

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