Merge branch 'master' of https://git.overleaf.com/5cf56f861d72e9071d1a343c

1 files changed, 17 insertions, 4 deletions

diff --git a/referee_comments.txt b/referee_comments.txt
index 87f2116..18fd524 100644
--- a/referee_comments.txt
+++ b/referee_comments.txt
@@ -88,9 +88,22 @@ The behaviour of c/a is indeed interesting, but our model only considers the cou
 > simplest framework of localized f-electrons, what ionic moments would 
 > fit the present proposal?
 
-In a picture of localized U-5f electrons this
-This is a consistent with hexadecapolar order 
-[Mike, can you help with this?] [Yes I think he can! And it's a good point]
+We thank the referee for bringing up this point. We have added a discussion of possible physical 
+realizations to the conclusion section of our manuscript, which we believe broadens the appeal of our
+work by connecting it to the large body of research concerning microscopic theories of hidden order.
+The U-5f electrons in URu$_2$Si$_2$ exhibit a moderate degree of localization [cite], which is
+reflected in partial occupancy of many electronic states. Motivated by the results of refs [cite],
+we assume that the dominant U state consists of $j = 5/2$ electrons in the U-5f2 configuration, which has 
+total angular momentum $J = 4$. Within the $J=4$ multiplet, the precise energetic ordering
+of the $D_{4h}$ crystal field states still remains a matter of debate [cite]. In a simple
+framework of localized $j = 5/2$ electrons in the 5f2 configuration, our phenomenological theory
+is consistent with the ground state being the B$_{1g}$ crystal field state with
+hexadecapolar order parameter 
+\[
+    H = \eta (J_x^2 - J_y^2)
+\]
+where here $\eta$ is taken to be modulated at $\vec{Q} = (0, 0, 1)$. 
+The result of non-zero $\eta$ is a nematic distortion of the B1g orbitals, alternating along the c-axis.
 
 > ----------------------------------------------------------------------
 > Report of the Second Referee -- BN13654/Kent-Dobias
@@ -123,7 +136,7 @@ What our manuscript provides is a new way of interpreting a very clear experimen
 > T_HO. Thus, the fitting is not regarded as the decisive evidence on 
 > the validity of the model. 
 
-There are a couple of very important distinctions to be made between our work and the work of ref. 25 (K.  Kuwahara et al.), which as the referee points out, also identified softening in (c11-c12)/2. First, the data in ref. 25 (figure 2c) appear to be contaminated by the c66 mode, based on the fact that the peak in c66 appears around 60 K. In the work of T. Yanagisawa et al (Journal of the Physical Society of Japan 82 (2013) 013601), the peak is at 130 K, and the elastic constant softens back down to its room-temperature value by T_HO. The data we show in figure 2b, obtained with resonant ultrasound, also shows a maximum at around 130 K, and also softens to its room-temperature value by T_HO. The contamination in ref. 25 is likely an artifact of the pulse-echo ultrasound technique, which can mix between c66 and (c11-c12)/2 when the crystal is not perfectly aligned. Perhaps more importantly, the fit shown in figure 4 of ref 25 does not show very good agreement with the data at any temperature. The model used is one for thermally-populated crystal field levels, and has nothing to do with the phase transition at T_HO. This model does not produce the sharp change in slope of (c11-c12)/2 at T_HO, which is an essential singularity in the thermodynamic free energy and must appear in the elastic moduli, and it does not produce 1/(T-T_0) strain susceptibility above T_HO, which is a signature of strain and order parameter coupling. 
+There are a couple of very important distinctions to be made between our work and the work of ref. 25 (K.  Kuwahara et al.), which as the referee points out, also identified softening in (c11-c12)/2. First, the data in ref. 25 (figure 2c) appear to be contaminated by the c66 mode, based on the fact that the peak in c66 appears around 60 K. In the work of T. Yanagisawa et al (Journal of the Physical Society of Japan 82 (2013) 013601), the peak is at 130 K, and the elastic constant softens back down to its room-temperature value by T_HO. The data we show in figure 2b, obtained with resonant ultrasound, also shows a maximum at around 130 K, and also softens to its room-temperature value by T_HO. The contamination in ref. 25 is likely an artifact of the pulse-echo ultrasound technique, which can mix between c66 and (c11-c12)/2 when the crystal is not perfectly aligned. Perhaps more importantly, the fit shown in figure 4 of ref 25 does not show very good agreement with the data at any temperature. The model used is one for thermally-populated crystal field levels, and has nothing to do with the phase transition at T_HO. This model [this being thermally populated crystal field levels, right?] does not produce the sharp change in slope of (c11-c12)/2 at T_HO, which is an essential singularity in the thermodynamic free energy and must appear in the elastic moduli, and it does not produce 1/(T-T_0) strain susceptibility above T_HO, which is a signature of strain and order parameter coupling. 
 
 > 3) The agreement of C[B1g] in the region T<T_HO is poor, though only 
 > the cusp at T_HO seems qualitatively consistent with the experiment.