Peer review of: Unconventional Hund metal in a weak itinerant ferromagnet (2020)

Reviewers' comments: 

Reviewer #1 (Remarks to the Author): 

The manuscript by X. Chen (et al.) presents a study of high-energy magnetic excitations in MnSi well 
into the Stoner continuum. The spectra in this region consist of strongly damped single-particle 
excitations, as opposed to the collective spin-waves found at low momentum and energy transfers. 
They experimentally find that the damping parameter diverges before the boundary of the magnetic 
Brillouin zone, prematurely cutting off further magnon propagation. Using density functional theory 
and dynamical mean-field theory, the authors link this effect to an additional decay channel given by 
interorbital Hund's exchange. 

The authors were able to collect high-quality experimental data of a region in the phase space of MnSi 
which is still very unexplored due to the difficulties that the measurements of such strongly damped 
and weak high-energy excitations pose. Together with their innovative theoretical interpretation, 
which establishes MnSi as an unconventional Hund metal, I recommend publication in Nature 
Communications once the following minor points have been addressed: 

(1) As the study is specific to MnSi, it would be useful to include the concrete momentum and energy 
scales in Fig. 1(a). 

(2) A DHO model is used to determine the line widths of the damped excitations that are depicted in 
Fig. 2(d). The instrumental resolution is not taken into account for these fits because the authors 
name an energy resolution of 1.6 meV for an incident neutron energy of 30 meV, i.e. ca. 10% of the 
damping constant. The instrumental resolution can nevertheless be expected to change significantly 
within the large range of energy transfers of 0..20 meV. Please ensure that it can still be neglected for 
up to 20 meV. 

(3) Have all experiments been conducted at zero magnetic field? If so, does the zero-field multi-
domain magnetic state of MnSi also play a role at high energies? In the low-energy helical state, for 
example, the presence of multiple domains leads to a complicated superposition of individual magnon 
modes, which the authors of Ref. 17 could only disentangle via resolution-deconvolution methods. 

(4) To better distinguish the modified spectrum including the Hubbard and Hund terms from the the 
pure non-magnetic DFT spectrum in Fig. 3, it might be useful to unite Fig. 3(a) and (b). For example, 
one could overplot the pure DFT lines of Fig. 3(a) in Fig. 3(b). 

(5) In the same way as it is already done for Supplementary Fig. 5, it would be helpful to add 
temperature labels to all plots showing experimental data. 



Reviewer #2 (Remarks to the Author): 

This paper studied the nature of spin fluctuations in MnSi by analyzing the magnetic susceptibility data 
measured by inelastic neutron scattering (INS). The INS data reveals that the ferromagnetic spin-
wave dispersion in MnSi becomes strongly damped inside the particle-hole continuum region. MnSi 
exhibits the strong coupling between the local magnetic moment from the Mn site and the itinerant 
bands in the Si site. Understanding the microscopic origin behind this physics is difficult due to the 
interplay between itinerant and localized nature of spin fluctuations. In this paper, DFT+DMFT is 
employed to carry out the electronic structure and the local susceptibility calculations in MnSi. 
Theoretical calculations show that the nature of many-body correlations are local spin and orbital 
fluctuations captured in DFT+DMFT and the local susceptibility is peaked at the coherence energy 
which can be computed by DFT+DMFT. This material can be considered as a Hund’s metal in which 
Hund’s J plays an important role and the non-Fermi liquid behavior is also captured within DFT+DMFT. 
Overall, this paper is a nice collaboration paper between theory and experiment to reveal important 
features in spin fluctuations of the Hund’s metal. While the data is technically sound and the 
arguments can be applicable to other similar materials, I think the following points should be clarified 
for the paper to be accepted in Nature Communications. 

1. While the paper emphasizes the importance of spin and orbital fluctuations in capturing magnetic 
fluctuation features in MnSi, I am not fully convinced about the role of orbital correlations. Is the spin 
incoherence originated from the orbital incoherence given that the spin and orbital coherence energy 
scales are very close in DFT+DMFT calculations? Why are the interorbital fluctuations with the a1g 
orbital dominant contributions? 

2. What is the origin of additional bumps in the DMFT susceptibility above the coherence temperature? 
Are they originating from the fluctuations of the Hubbard bands? Or the Hund’s coupling energy? Why 
is this feature not captured in the experimental susceptibility above the coherence temperature 
exhibiting the strong damping due to the particle-hole continuum? 

3. How do the orbital and spin coherence energy scales change at different U and J values in DMFT? 

4. The DFT+DMFT susceptibility was computed in the paramagnetic symmetry. Would the spin 
excitation and the coherence energy be still similar if it is computed using the ferromagnetic symmetry? 

5. The authors also argue that correlations beyond the local one in ferromagnetic spin waves are 
important. At the same time, Fermi liquid theory calculations including l=0 and l=1 Landau 
parameters without the multi-band effect can still explain qualitatively the spin wave dispersion with a 
gapped mode as a function of momentum (Fig.2c). The authors should clarify the role of dynamical 
correlations on the spin wave dispersion. For example, how does the local DMFT susceptibility compare 
to the Lindhard susceptibility (without dynamical vertex correction) computing using the one-particle 
DMFT spectra or the DFT spectra? 

6. In the main discussion, the authors argue that the DFT+DMFT magnetic moment is 0.3 muB while 
the experimental moment is 0.4 muB. Are those paramagnetic fluctuating moments or static 
ferromagnetic moments? It should be clarified in the text. How is this moment computed in 
DFT+DMFT? Is this moment consistent with the sum rule of the magnetic susceptibility data? 

7. Can the authors show the orbital-resolved self-energies on the real axis? Does self-energy show 
any signature of coherence energy scale? 

8. The authors claim that the Fermi surface is strongly modified due to correlations. Can the authors 
also plot the Fermi surface comparing DFT vs DFT+DMFT to show the correlation effect? 

9. The authors say that local susceptibilities within DFT+DMFT without charge-self-consistency using 
the Hirsch-Fye QMC. Does this mean that they use DFT charge density or DMFT charge density? Also, 
why didn’t they use CTQMC for computing the susceptibility? If there is any technical issue, they can 
clarify in the text. 

10. The purple color in Fig.3.(a) is not visible even in the color print. The authors should use different 
colors. 

11. The orbital figures in Suppl. Fig. 6 are hidden by other atoms. The authors should display a 
smaller number of atoms to emphasize the shape of orbitals.