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@@ -546,24 +546,18 @@ 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. -%\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, 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} +Alternatively, \rus\ done at ambient pressure might examine the heavy fermi +liquid to \afm\ transition by doping. Though previous \rus\ studies have doped +\urusi\ with Rhodium,\cite{yanagisawa_ultrasonic_2014} the magnetic nature of +Rhodium ions likely artificially promotes magnetic phases. A dopant like +phosphorous that only exerts chemical pressure might more faithfully explore +the pressure axis of the phase diagram. Our work also motivates experiments +that can probe the entire correlation function---like x-ray and neutron +scattering---and directly resolve its finite-$q$ divergence. 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} There are two apparent discrepancies between the orthorhombic strain in the phase diagram presented by recent x-ray data\cite{choi_pressure-induced_2018} @@ -610,17 +604,14 @@ $\Bog$ \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?)} -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 coinciding of our theory's orthorhombic high-pressure phase and \urusi's +\afm\ is compelling, but our mean field theory does not make any explicit +connection with the physics of \afm. This may be reasonable since correlations +often lead to \afm\ as a secondary effect, like in many Mott insulators. An +electronic theory of this phase diagram may find that the \afm\ observed in +\urusi\ indeed follows along with a high-pressure orthorhombic phase associated with +uniform $\Bog$ electronic order. The corresponding prediction of uniform $\Bog$ symmetry breaking in the high pressure phase is consistent with recent diffraction experiments, @@ -633,7 +624,10 @@ or falsify this idea. \begin{acknowledgements} Jaron Kent-Dobias is supported by NSF DMR-1719490, Michael Matty is supported by - NSF DMR-1719875, and Brad Ramshaw is supported by NSF DMR-1752784. We are grateful for helpful discussions with Sri Raghu, \brad{People we talked to in Jim's group meeting}. + NSF DMR-1719875, and Brad Ramshaw is supported by NSF DMR-1752784. We are + grateful for helpful discussions with Sri Raghu, Danilo Liarte, and Jim + Sethna, and for permission to reproduce experimental data in our figure by + Elena Hassinger. We thank Sayak Ghosh for \rus\ data. \end{acknowledgements} \bibliographystyle{apsrev4-1} |