diff options
Diffstat (limited to 'main.tex')
| -rw-r--r-- | main.tex | 40 |
1 files changed, 23 insertions, 17 deletions
@@ -537,21 +537,27 @@ 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} - -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. -Alternatively, \rus\ done at ambient pressure might examine the heavy Fermi -liquid to \afm\ transition by doping. 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 otherwise modify the thermodynamic behavior.\cite{garel_commensurability_1976} +broholm_magnetic_1991, wiebe_gapped_2007, bourdarot_precise_2010, hassinger_similarity_2010} In between +these two regimes, mean field theory predicts that the ordering wavevector +shrinks by jumping between ever-closer commensurate values in the style of the +devil's staircase.\cite{bak_commensurate_1982} In reality the presence of +fluctuations may wash out these transitions. + +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. 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 rhodium dopants likely +promote magnetic phases. A non-magnetic dopant such as phosphorous may more +faithfully explore the transition out of the HO phase. 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}, @@ -592,7 +598,7 @@ 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. +is characterized by uniform $\Bog$ order. The staggered nematic of \ho\ is similar to the striped superconducting phase found in LBCO and other cuperates.\cite{berg_striped_2009} The coincidence of our theory's orthorhombic high-pressure phase and \urusi's \afm\ is compelling, but our mean field theory does not make any explicit @@ -614,7 +620,7 @@ 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, Danilo Liarte, and Jim + grateful for helpful discussions with Sri Raghu, Steve Kivelson, 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} |