From 55e5c7d53f73d905c49fbdf3b438be8cf6067634 Mon Sep 17 00:00:00 2001
From: mfm94 <mfm94@cornell.edu>
Date: Fri, 13 Dec 2019 16:37:26 +0000
Subject: Update on Overleaf.

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 main.tex | 43 ++++++++++++++++++++++++++++---------------
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index a9ed1ff..4c35f1b 100644
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@@ -546,17 +546,21 @@ This motivates future ultrasound experiments done under
 pressure, where the depth of the cusp in the $\Bog$ modulus should deepen
 (perhaps with these commensurability jumps) at low pressure and approach zero
 as $q_*^4\sim(c_\perp/2D_\perp)^2$ near the Lifshitz point. 
-{\color{blue}
-    Moreover, 
-}
-\brad{Should also
-motivate x-ray and neutron-diffraction experiments to look for new q's -
-mentioning this is important if we want to get others interested, no one else
-does RUS...} Alternatively, \rus\ done at ambient pressure might examine the
+%\brad{Should also
+%motivate x-ray and neutron-diffraction experiments to look for new q's -
+%mentioning this is important if we want to get others interested, no one else
+%does RUS...} 
+Moreover, experiments that can probe the entire correlation function such as 
+x-ray and neutron scattering should be able to track the development of new
+$q$'s along the modulated to uniform order transiiton.
+Alternatively, \rus\ done at ambient pressure might examine the
 heavy fermi liquid to \afm\ transition by doping. Previous studies 
-{\color{blue} [cite]} considered Rhodium doping 
-\brad{We have to be careful,
-someone did do some doping studies and it's not clear exactly what's going on}.
+{\color{blue} [cite]} considered Rhodium doping, however, due to the magnetic
+nature of Rhodium ions, we would suggest a dopant that would only exert chemical
+pressure such as phospherous. This way we could more accurately explore the pressure
+axis of the phase diagram without aritificially promoting magnetic phases.
+%\brad{We have to be careful,
+%someone did do some doping studies and it's not clear exactly what's going on}.
 The presence of spatial commensurability is known to be irrelevant to critical
 behavior at a one-component disordered to modulated transition, and therefore
 is not expected to modify the thermodynamic behavior otherwise.\cite{garel_commensurability_1976} 
@@ -605,11 +609,20 @@ the phase diagram of \urusi\ are $\Bog$ and $\Btg$. Of these, only a staggered
 $\Bog$ \op\ is consistent with zero-pressure \rus\ data, with a cusp appearing
 in the associated elastic modulus. In this picture, the \ho\ phase is
 characterized by uniaxial modulated $\Bog$ order, while the high pressure phase
-is characterized by uniform $\Bog$ order. \brad{We need to be a bit more
-explicit about what we think is going on with \afm - is it just a parasitic
-phase? Is our modulated phase somehow "moduluated \afm" (can you modualte AFM
-in such as way as to make it disappear? Some combination of orbitals?)} The
-corresponding prediction of uniform $\Bog$ symmetry breaking in the high
+is characterized by uniform $\Bog$ order. 
+%\brad{We need to be a bit more
+%explicit about what we think is going on with \afm - is it just a parasitic
+%phase? Is our modulated phase somehow "moduluated \afm" (can you modualte AFM
+%in such as way as to make it disappear? Some combination of orbitals?)} 
+This is compelling, but our mean field theory does not make any explicit 
+connection between the high-pressure orthorhombic phase and AFM.
+This is not unreasoable as correlations commonly realize AFM as
+a secondary effect such as in many Mott insulators. A 
+more careful electronic theory may find that
+the AFM observed in \urusi\ is indeed reproduced in the high-pressure
+orthorhombic phase associated with uniform $\Bog$ order. 
+
+The corresponding prediction of uniform $\Bog$ symmetry breaking in the high
 pressure phase is consistent with recent diffraction experiments,
 \cite{choi_pressure-induced_2018} except for the apparent earlier onset in
 temperature of the $\Bog$ symmetry breaking, which we believe to be due to
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