Raman spectroscopic signature of fractionalized excitations in the harmonic-honeycomb iridates β- and γ-Li2IrO3

The fractionalization of elementary excitations in quantum spin systems is a central theme in current condensed matter physics. The Kitaev honeycomb spin model provides a prominent example of exotic fractionalized quasiparticles, composed of itinerant Majorana fermions and gapped gauge fluxes. However, identification of the Majorana fermions in a three-dimensional honeycomb lattice remains elusive. Here we report spectroscopic signatures of fractional excitations in the harmonic-honeycomb iridates β- and γ-Li2IrO3. Using polarization-resolved Raman spectroscopy, we find that the dynamical Raman response of β- and γ-Li2IrO3 features a broad scattering continuum with distinct polarization and composition dependence. The temperature dependence of the Raman spectral weight is dominated by the thermal damping of fermionic excitations. These results suggest the emergence of Majorana fermions from spin fractionalization in a three-dimensional Kitaev–Heisenberg system.

The authors have addressed most of the points which were raised previously and now carefully state that they 'observe signatures of fractionalization' instead of 'signatures of a quantum spin liquid state'. The manuscript is vey timely and contains important new results on both the beta and gamma Li2IrO3 which further establish these 3D materials as magnetic materials dominated by the celebrated Kitaev interaction. Their -arguably indirect -evidence for fractionalization will motivate further studies and will receive a lot of attention. The agreement between the clear Raman scattering predictions of Perreault et al. Ref.[8] for the 3D Kitaev spin liquid states is not great but nevertheless several features are surprisingly consistent. In particular the temperature dependence corroborates the authors interpretation in terms of fractionalized particles.
There are additional comments and points which the authors need to clarify, see below. Once these have been addressed, I do recommend publication of this important work in Nature Communication.
-On page 3, the authors write "We provide here Raman spectroscopic evidence for weakly-confined two-Majorana spinons in..." which is unclear at this point. (The authors should replace for example 'two-Majorana spinons' simply by 'Majorana fermions from spin fractionization' or similar) -One page 3 again second paragraph, the authors claim that they observe a "magnetic Raman response not described within a conventional magnon picture" but do not give any reason. The authors should add a few sentences what distinguishes their response from conventional two magnon response.
-On page 7, the authors claim that the magnetic specific heat is related to the Raman susceptibility Cm~ X'(w)/w, which is unclear. E.g. which frequency w is assumed or is it an integral of all frequencies?
This is related to the supplementary material F: (Ref.9 is clearly not the correct one at this point but should be Reiter, PRB 13 1976) Looking at the papers of Halley 1978 and Reiter 1976 it seems that the specific heat is proportional to the integrated Raman intensity Cm~Int X'(w) and not Cm~X'(w)/w This needs to be clarified. It could explain why the specific heat in Fig.3c does not resemble anything close close to the 3D Kitaev spin liquid calculations of the pure Kitaev model Ref.9? The authors should clarify these important issues! -Very recently, an article appeared showing that the temperature dependence of the integrated Raman response could provide further evidence for fractionalisation, see arXiv:1602.05277. Did the author look at the T-dependence of the integrated Raman intensity (similar to the RuCl3 case from Sandiland et al.)?

Reviewer #3 (Remarks to the Author):
I have already reviewed this manuscript twice and witnessed its evolution through the reviewing process. Overall the authors have tried their best to adress the comments and criticism of both myself and the first referee.
As I stated previously, the present data could possibly be interpreted as fingerprints of Majorana fermions, but the evidences in terms of selection rules, compositionnal dependence and spectral lineshape, are probably too tenuous to warrant publication in a high profile journal such as Nature Communication. My opinion on this has not changed after reviewing the new version of the ms and the reply to the referees.
It is also visible that the authors did not completely take into account the previous comments and criticisms in their ms. As a results the interpretation of several experimental features is now somewhat unclear.
-For example, as pointed that by the first referee, the low energy continuum is probably dominated by spin waves of the long range magnetic orders, and not primarily from two spinon continnum. The authors seem to acknowledge that in their reply to the referee, but the manuscript does not completely reflects this important distinction. They still state on page 4, that "the magnetic continuum is assigned to two-Majorana spinon excitations".
-Another example is the interpretation of the gapped continuum in gamma compounds. The discussion on page 5 is now completely unclear. Is the gap associated to magnons continuum (as suggested by referee 1) or to anisotropic Kitaev interactions (i.e. fermions continuum) ? This again raises the problem of disentangling the magnons from the two Majorana fermions contributions to the Raman continuum. This question is obviously hard to answer given the lack of structure in the spectral lineshape.
To summarize, the work is of quality and will certainly stimulates further theoretical work on the subject. My feeling is however that it would be better suited to a more specialized journal.