Hallmarks of Hunds coupling in the Mott insulator Ca2RuO4

A paradigmatic case of multi-band Mott physics including spin-orbit and Hund's coupling is realized in Ca2RuO4. Progress in understanding the nature of this Mott insulating phase has been impeded by the lack of knowledge about the low-energy electronic structure. Here we provide—using angle-resolved photoemission electron spectroscopy—the band structure of the paramagnetic insulating phase of Ca2RuO4 and show how it features several distinct energy scales. Comparison to a simple analysis of atomic multiplets provides a quantitative estimate of the Hund's coupling J=0.4 eV. Furthermore, the experimental spectra are in good agreement with electronic structure calculations performed with Dynamical Mean-Field Theory. The crystal field stabilization of the dxy orbital due to c-axis contraction is shown to be essential to explain the insulating phase. These results underscore the importance of multi-band physics, Coulomb interaction and Hund's coupling that together generate the Mott insulating state of Ca2RuO4.

The physical understanding of transition metal oxides is very often based on simplified models that contain the essential microscopic mechanisms to explain, e.g., the existence of characteristic phase transitions, magnetic order or even superconductivity. In any case the fundamental model parameters, however, require an independent determination either from first principle calculations or from experiment. In the present work, the authors present a detailed study on the paradicmatic Mott insulator Ca2RuO4 in the paramagnetic insulating phase, combining the results of angle resolved photoemission spectroscopy experiments together with DFT and DMFT calculations. The central aspect is the explanation of the non-uniform gap, appearing experimentally as two bands (or better: features) A and B with different binding energies below the chemical potential, and therewith the nature of the band gap. In principle, this explanation is rather simple, namely a lifting of the degeneracy of the Ru4d states.
To estimate the splitting, the authors focus on the importance of the Hund's coupling J, which is of the same order of magnitude as several other material parameters, e.g., the hybridization band width, the crystal electric field (0.6 eV), the Coulomb repulsion energy U (2.3 eV), orfinally the observed splitting of the two spectral features itself. The consideration of all these parameters in the DMFT calculation results in a reasonable well description of the experimental results.
Although the authors have structured the paper very carefully and, furthermore, a phenomenological model was introduced to support the assignment of the bands to the respective orbital character, it is very hard to assess the mingling of the many physical parameters. The interpretation given here is not unreasonable and even the stated "first direct quantitative estimate of the effective Hund's coupling from spectroscopy data" could be true. However, it remains unclear whether another parameter set, which possibly would lead to a different interpretation, does not lead to at least a similarly good description. Without ruling out other explanations in the frame of the same physical model, the conclusions remain rather speculative.
Anyway, since the topic is timely and both the data and the calculations are of very high quality, I recommend to publish the present manuscript in Nature Communications.
Reviewer #2 (Remarks to the Author): The authors report a direct observation of the controversial Mott insulating state realized in Ca2RuO4 by ARPES combined with DFT and DMFT calculations. Strong correlation effects on multi-orbital systems are indeed important and hot topics, and Ca2RuO4 is one of the most famous but still uncovered materials. Therefore, this study meets the standard of Nat. Commun. in terms of novelty and importance, but, I have one question regarding the conclusion made in this study, which should be resolved.
In page 3, the authors said "The Mott gap, defining the energy scale between lower and upper Hubbard bands, has previously been associated with an activation energy scale ~ 0.4 eV derived from resistivity measurements. Assuming that the Fermi level is centred approximately symmetrically between lower and upper Hubbard bands, our spectroscopic observation is consistent with the transport experiments". However, the band A is identified to have dxy character and is not regarded as the "lower Hubbard band" in this manuscript. At least in Fig. 4(b), we cannot find any "upper Hubbard band" for dxy (or some small weight exists?). I wonder which interpretations the authors support, "two Mott energy scale (dxy, dxz/yz)" or "band-insulating dxy and half-filled dxz/yz", because the most parts of this manuscript seem to support the latter but the sentences cited above do not. Note that if one assumes the lowest unoccupied bands to be the upper Hubbard bands of dxz/yz, U might be too small. I understand that the unoccupied states are out of range for ARPES, but it is directly related to the controversial nature of Mott insulating state of Ca2RuO4, which is a central object in this study. Could the authors make the argument presented in the above-cited sentences clearer?

REPLIES TO THE REFEREES
Referee #1 (Remarks to the Author): "Anyway, since the topic is timely and both the data and the calculations are of very high quality, I recommend to publish the present manuscript in Nature Communications." We thank referee 1 for his/her clear recommendation to publish our manuscript in Nature Communications. Below, we describe how we amended the feedback.
"Although the authors have structured the paper very carefully and, furthermore, a phenomenological model was introduced to support the assignment of the bands to the respective orbital character, it is very hard to assess the mingling of the many physical parameters. The interpretation given here is not unreasonable and even the stated "first direct quantitative estimate of the effective Hund's coupling from spectroscopy data" could be true. However, it remains unclear whether another parameter set, which possibly would lead to a different interpretation, does not lead to at least a similarly good description. Without ruling out other explanations in the frame of the same physical model, the conclusions remain rather speculative." The referee gives three suggestions for improvements: (1) More clear presentation of physical parameters.
(2) Be more careful about the claim of first direct experimental estimate of Hund coupling in the ruthenates. (3) Be more clear on the fact that even a successful theory has been presented it does not rule out all other possible explanations.
We believe that point (1) applies mainly to the first paragraph of the discussion section. To improve, we have added more description to make it easier to follow. This paragraph now reads: