diff options
Diffstat (limited to 'main.tex')
| -rw-r--r-- | main.tex | 47 |
1 files changed, 21 insertions, 26 deletions
@@ -121,7 +121,7 @@ chandra_hastatic_2013, harrison_hidden_nodate, ikeda_emergent_2012} propose a variety of possibilities. Our work here seeks to unify two experimental observations: one, the $\Bog$ ``nematic" elastic susceptibility $(C_{11}-C_{12})/2$ softens anomalously from room temperature down to -T$_{\mathrm{HO}}=17.5~$ K \brad{find old citations for this data}; and two, a +T$_{\mathrm{HO}}=17.5~$ K \cite{de_visser_thermal_1986}; and two, a $\Bog$ nematic distortion is observed by x-ray scattering under sufficient pressure to destroy the \ho\ state \cite{choi_pressure-induced_2018}. @@ -140,8 +140,8 @@ under pressure \cite{choi_pressure-induced_2018}. Above 0.13--0.5 $\GPa$ (depending on temperature), \urusi\ undergoes a $\Bog$ nematic distortion. While it is still unclear as to whether this is a true thermodynamic phase transition, it may be related to the anomalous softening of the $\Bog$ elastic -modulus---$(c_{11}-c_{12})/2$ in Voigt notation---that occurs over a broad -temperature range at zero-pressure \brad{cite old ultrasound}. Motivated by +modulus---$(C_{11}-C_{12})/2$ in Voigt notation---that occurs over a broad +temperature range at zero-pressure \cite{wolf_elastic_1994, kuwahara_lattice_1997}. Motivated by these results, hinting at a $\Bog$ strain susceptibility associated with the \ho\ state, we construct a phenomenological mean field theory for an arbitrary \op\ coupled to strain, and the determine the effect of its phase transitions @@ -157,7 +157,7 @@ predicts uniform $\Bog$ strain at high pressure---the same distortion which was recently seen in x-ray scattering experiments \cite{choi_pressure-induced_2018}. This theory strongly motivates future ultrasound experiments under pressure approaching the Lifshitz point, which -should find that the $(c_{11}-c_{12})/2$ diverges once the uniform $\Bog$ +should find that the $(C_{11}-C_{12})/2$ diverges once the uniform $\Bog$ strain sets in. @@ -515,20 +515,18 @@ Orthorhombic symmetry breaking was recently detected in the \afm\ phase of \urusi\ using x-ray diffraction, a further consistency of this theory with the phenomenology of \urusi\ \cite{choi_pressure-induced_2018}. -{\color{blue} New paragraph inserted by Mike} Second, as the -Lifshitz point is approached from low pressure, this theory predicts that the -modulation wavevector $q_*$ should vanish continuously. Far from the Lifshitz -point we expect the wavevector to lock into values commensurate with the space -group of the lattice, and moreover that at zero pressure, where the \rus\ data -here was collected, the half-wavelength of the modulation should be -commensurate with the lattice spacing $a_3\simeq9.68\,\A$, or -$q_*=\pi/a_3\simeq0.328\,\A^{-1}$ \cite{meng_imaging_2013, +Second, as the Lifshitz point is approached from low pressure, this theory +predicts that the modulation wavevector $q_*$ should vanish continuously. Far +from the Lifshitz point we expect the wavevector to lock into values +commensurate with the space group of the lattice, and moreover that at zero +pressure, where the \rus\ data here was collected, the half-wavelength of the +modulation should be commensurate with the lattice spacing $a_3\simeq9.68\,\A$, +or $q_*=\pi/a_3\simeq0.328\,\A^{-1}$ \cite{meng_imaging_2013, broholm_magnetic_1991, wiebe_gapped_2007, bourdarot_precise_2010}. In between these two regimes, the ordering wavevector should shrink by jumping between ever-closer commensurate values in the style of the devil's staircase \cite{bak_commensurate_1982}. -{\color{blue} New paragraph inserted by Mike} This motivates future \rus\ experiments done at pressure, where the depth of the cusp in the $\Bog$ modulus should deepen (perhaps with these commensurability jumps) at low pressure and approach zero @@ -592,19 +590,16 @@ in the associated elastic modulus. In this picture, the \ho\ phase is characterized by uniaxial modulated $\Bog$ order, while the \afm\ 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 \afm\ phase is consistent -with recent diffraction experiments \cite{choi_pressure-induced_2018} -{\color{blue} - except for the apparent earlier onset in temperature of the $\Bog$ symmetry - breaking than AFM, which we believe to be due to fluctuating order above - the actual phase transition. -} -%\brad{needs a caveat about temperature, so that we're being transparent}. -This work motivates both further theoretical work regarding a microscopic theory -with modulated $\Bog$ order, and preforming \rus\ experiments at pressure that -could further support or falsify this idea. +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 \afm\ 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 than AFM, which we believe to be +due to fluctuating order above the actual phase transition. This work +motivates both further theoretical work regarding a microscopic theory with +modulated $\Bog$ order, and preforming \rus\ experiments at pressure that could +further support or falsify this idea. \begin{acknowledgements} This research was supported by NSF DMR-1719490 and DMR-1719875. |