Peer review of: Non-monotonic pressure dependence of high-field nematicity and magnetism in CeRhIn5 (2020)

Reviewers' comments: 

Reviewer #1 (Remarks to the Author): 

Report on manuscript NCOMMS-20-03079 Non-monotonic pressure dependence of high-field 
nematicity and magnetism in CeRhIn5 

This paper describes the experimental study of the different phases of the heavy fermion 
antiferromagnetic and superconducting system CeRhIn5 tuned with a combination of high pressure, 
low temperature and extremely high pulsed magnetic fields 
This is an impressive feat and the described technique using a FIB to prepare the sample with a 
suitable geometry but also to perform much of the setting up of the sample on the diamond anvil is 
innovative and impressive. This technique has undoubtedly huge potential for many studies. 
The paper reports 3 major findings. 1) The reinforcement of antiferromagnetic order with pressure as 
the field induced critical point shifts to higher fields as pressure is increased. 2) the emergence of a 
re-entrant antiferromagnetic state in applied field at pressures above the critical pressure. And 3) the 
disappearance of the field induced anisotropy of the in plane resistivity, previously attributed to a 
nematic phase, at a pressure close to Pc 

I find the first 2 points convincing. The authors provide an explanation for the re-entrant magnetic 
phase which could be valid, though it is not clear from the discussion whether this “extended Doniach 
diagram” has a solid theoretical basis or is a phenomenological picture drawn from this particular 
experimental result. It is also not immediately clear to me why, as indeed a magnetic field will weaken 
the Kondo screening, it will not similarly weaken the RKKY interaction, as the same exchange J is at 
the basis of both effects. And indeed if it were so simple many more similar cases should be found 
which is not the case as the authors point out. The authors should clarify this part of the discussion. 

The experimental result supporting the 3rd point is also solid. However I don’t find the discussion 
totally convincing and I am surprised that this point is put forward as the main result of the paper, 
probably because nematicity is a fashionable keyword at the moment. The fact that this phase 
vanishes close to Pc suggests to me that, contrary to what the authors state, there could be a 
connection between the AFM order and the “nematic state”. In the archetypal system Sr3Ru2O7 it was 
shown that the ‘nematic behaviour’ could be explained by the magnetic field control of the SDW 
domains. The magnetic structure of CeRhIn5 is complex, and it’s true that no strong effect is seen in 
the magnetization, but can a similar explanation really be ruled out ? In fact wouldn’t it be surprising 
that a magnetic field with an in-plane component would have no effect on the in plane magnetic 
anisotropy with a natural feed back on the resistivity. I believe the authors should at the minimum 
open the discussion to a connection between magnetic order and the behavior so far attributed to 
nematicity. 

My final criticism is the lack of a clear figure regrouping all the main results. This in principal is 
contained in the 3D plot of fig 7, where the authors have made a laudable effort to include the 
experimental points, but I would like in addition or instead a 2D (p-B) plot at zero or base 
temperature, with all the different phases clearly labeled. This would capture the essential physics and 
results, as the temperature effects are not really discussed except to obtain an extrapolation to low 
temperatures. 
I think with substantial modification of the discussion the paper certainly warrants publication, and the 
innovative and impressive techniques used to perform these challenging experiments make the paper 
suitable for Nature Communications 

Reviewer #2 (Remarks to the Author): 

The manuscript by Helm et al. reports a detailed magnetoresistivity measurement of CeRhIn5 under 
high magnetic field and high pressure, which is indeed a challenging experiment. Based on these 
results, the authors constructed a three dimensional T-B-p phase diagram, showing that the critical 
field Bc(p), required to suppress the AFM order, increases with increasing pressure, which is surprising 
because pressure suppresses the AFM order around 23kbar. Furthermore, the authors also found that 
the so-called nematic phase shifts to higher field with increasing pressure and then suddenly vanishes 
around 20 kbar. In my opinion, there is short of evidence to support such a conclusion and the current 
manuscript is not suitable for publication in Nature Communications. 

Below are some detailed comments. 
The starting and central point of this work is the field-induced nematicity. As addressed by the authors 
in the introduction, the broken C4 symmetry is naturally expected to be reflected by a small lattice 
distortion. If this is the case, the tetragonal lattice symmetry changes to orthorhombic above B*. Can 
one still be able to define the broken symmetry/in-plane anisotropy as nematicity? If not, the direction 
of the conclusion is questionable. In addition, even in a tetragonal system, why should the resistivity 
between a and b* axis be the same? 

The crucial point is that the determination of the critical fields of B_c(p) is not clear and sometimes 
sounds arbitrary for me. For example, there is no obvious feature for B_c in Fig . 6a. In Fig. S6, the 
situation is even worse for B//a, as B_c is defined as the peak, dip or shoulder in the second derivative 
of rho(B). A self-consistent definition is needed to determine B_c(p). If we look at the 
magnetoresistivity curves in the figures, typically each data set shows several “features” and therefore 
it is difficult to pick up one as the critical point. As a result, the derived phase diagram is questionable 
and it has to be confirmed by other experiments. 

The experimental signatures of the last two points in the phase diagram (around 80T and 30kbar 
along the B_c line) are missing. From the figures, it seems that all the measurements end at 60 T. 
These two data points are critical. Without them, the AFM phase may abruptly vanish around p_c, like 
the nematic phase. 
In the discussion part, scenario 1, the authors suggest that the nematic transition occurs in the light 
bands, without changes in the 4f1 states. How is it compatible with the observed changes of the 
dHvA/SdH frequencies from heavy quasiparticle bands at B*? The heavy quasiparticles should have 
significant contributions to the resistivity. 

Some minor points: 
Page 4, right column, line 12. There is a typo “showcase”; 
Page 6, fig. 5, what are the humps around 10 T; 
Page 6, left column, line 6. The definition of “reentrant magnetic order” above p_c is misleading, since 
AFM phase does not enter above p_c in zero field and the AFM phase dome is continuous in Fig. 7. 
Alternatively speaking, p_c should be a function of B. 
Page 9, left column, line 15 to the bottom, there should be a typo in “B_c(p, T) and B_c(p, T)” 



Reviewer #3 (Remarks to the Author): 

The manuscript entitled ‘Non-monotonic pressure dependence of high-field nematicity and magnetism 
in CeRhIn5’ by Helm et al. reports on magnetoresistivity measurements carried out at extreme 
conditions on the correlated metal CeRhIn5. Notably, the measurements were carried in the 
challenging combination of pulsed high magnetic fields up to 60 T with high pressures of up to 40 
kbars at low temperatures. CeRhIn5 is a protoypical heavy fermion material in which the hybridization 
of localized f-electrons with conduction electrons results in a highly tunable strongly correlated 
metallic quantum state from which a multitude of quantum matter states ranging from complex and 
frustrated antiferromagnetism, unconventional superconductivity, and an electronic state with a large 
nematic susceptibility emerge. As such it is a crucial model system for our understanding of metallic 
quantum matter more generally. In their measurements Helm et al. address the relationship of two 
distinct magnetic quantum critical points (QCPs) that can be access by tuning the antiferromagnetic 
ground state of CeRhIn5 with pressure and magnetic fields, respectively. The unconventional 
superconducting state in CeRhIn5 appears around the pressure-accessible QCP, whereas the electronic 
state with high nematic susceptibility is observed as a function of applied magnet field. Because in 
other quantum materials that exhibit superconductivity and electronic nematic order these states are 
typically observed in the vicinity of the same QCP, clarifying the relationship between these two 
quantum states in CeRhIn5 is crucial for our understanding of quantum matter. As such, the results 
reported by Helm et al. in this manuscript are highly-relevant for scientific community working on 
quantum materials and certainly justify publication in Nature Communications. 

Further, I would like to point out that the data reported in this manuscript appears to be of high 
quality, which is particularly notable considering the complex sample environment (high field & high 
pressure at low temperature) required to obtain the data. This alone, makes the reported work highly 
remarkable and interesting to the community, as this technical achievement will likely open up 
ground-breaking studies of other relevant metallic quantum materials. To summarize, I strongly 
support the publication of this manuscript. However, before it can be published, I would like to authors 
to consider my comments and suggestions listed below. 

Spelling and other simple corrections: 

1. In the abstract, CeRhIn5 is spelled twice without the subscript for the number 5. Please correct. 
2. In the caption of Fig. 1, the expression “specific heat capacity” is used. I think that this quantity is 
either referred to as “heat capacity” or as “specific heat”. Please correct. 
3. Figure 7, panel (a). The label ‘0’ of the pressure and temperature axis overlap. I would correct this 
as it makes the figure hard to read. Further is also a purple region in the figure that does not have a 
label in the figure or the caption. This should be the fluctuating nematic phase, and should be labelled. 
4. Section “Field-induced magnetic order”. In this section Ref. [26] cites previous reports of magnetic 
order being stabilized by magnetic field. I think that Ref [24] is the first report of such behavior. 
Please correct. 
5. Ref [43] is used to state that CeRhIn5 exhibits frustrated magnetic interactions. However, this 
neutron diffraction study mostly points out that the ordered moment even at ambient pressure is 
strongly suppressed because of strong Kondo interaction. The manuscript that report frustrated 
magnetic interactions are Pinaki Das et al. Phys. Rev. Lett. 113, 246403 (2014) and D. M. Fobes et al. 
Nature Physics 14, 456–460 (2018). Please correct. 

More general comments that need to be addressed: 

1. The entire text is rather lengthy and is at times tedious to read. I would strongly recommend to try 
to shorten some parts. 
2. The term “nematic phase” is used rather loosely throughout the entire text. For example, in the 
abstract, it is not stated that the nature of the nematicity it electronic. Further, it should be clarified at 
the beginning that this phase does note spontaneously exhibit electronic nematic symmetry breaking, 
but that the symmetry needs to be explicitly broken via a small magnetic field component in the 
tetragonal ab-plane of CeRhIn5. As such, the phase is not a electronic nematic phase per se, but a 
phase with a large electronic nematic susceptibility. This is why the experiments, for example, require 
a special orientation of the sample in the DAC as shown in Fig,. 1. This should be clearly introduced in 
the introduction, and used in that sense throughout the text. 
3. In the discussion as well as in Fig. 7(b) a relationship between the applied magnetic field and the 
RKKY interaction is used. I would like to point out that in Fobes et al. Nature Physics 14, 456–460 
(2018) it is shown that at already small magnetic field (compared to the fields used in this study) the 
nearest-neighbor exchange terms change by about 30% compared to zero applied fields. This means 
that the field axis and the “J” axis in Fig. 7(b) can’t be perpendicular, and the true phase diagram is 
likely more complicated. This is also what the authors observe. In addition, the RKKY exchange is 
highly frustrated and competes with a substantial induced Ising anisotropy due to the applied field 
(see same paper). I think this needs to be considered here. 
4. The electronic phase above B* shows a large nematic susceptibility. However, it is clearly connected 
to the observed AFM phase. Notably, the nematic phase seems to only be exist within the AFM phase. 
Further, similarly to the electronic behavior, the magnetic phase AFM III (or up-up-down-down phase) 
that coexists with the fluctuating nematic phase (due to the tilted magnetic phase) breaks the same 
C4 inversion symmetry by aligning all spins perpendicular to the applied field. This is, for example, 
also discussed in Ref. [18], which states that likely the symmetry coming from the localized f-electron 
wave function is transferred onto the conduction electrons via Kondo coupling. Similar ideas are 
suggested in Fobes et al. Nature Physics 14, 456–460 (2018). I think this possibility should at least be 
discussed in the manuscript, as the strong relationship between magnetism and the fluctuating 
nematic phase cannot be neglected.