Goldstone-Mode Phonon Dynamics in the PyrochloreCd2Re2O7

Abstract

We have measured the polarized Raman scattering spectra of Cd2Re2O7, the first superconducting pyrochlore, as a function of temperature. For temperatures below the cubic-to-tetragonal structural phase transition (SPT) at 200K, a peak with B1 symmetry develops at zero frequency with divergent intensity. We identify this peak as the first observation of the Goldstone phonon in a crystalline solid. The Goldstone phonon is a collective excitation that exists due to the breaking of the continuous symmetry with the SPT. Its emergence coincides with that of a Raman-active soft mode. The order parameter for both features derives from an unstable doubly-degenerate vibration (with Eu symmetry) of the O1 atoms which drives the SPT.

A parity-breaking electronic nematic phase transition in the spin-orbit coupled metal Cd 2 Re 2 O 7

“…3C), obscuring the 2 order parameter. The relative faintness of the 2 signal is consistent with a nematic instability that predominantly affects states only near the Fermi level and naturally explains the absence of any detectable 2 distortion by structure-sensitive probes (19)(20)(21)(22).Distinguishing a genuine electronic nematic phase transition from a simple ferrodistortive transition is a well-known experimental challenge (11) because the electronic and structural order parameters are typically coupled and have a concurrent temperature onset, as is the case for Cd2Re2O7. The task of disentangling primary from secondary order parameters can be approached by studying the critical exponents of the order parameter temperature scaling law |1 − / | .…”

“…Detailed Raman scattering (19), x-ray (20,21) and neutron (22) diffraction, and optical secondharmonic generation (SHG) (23) studies have shown that at critical temperature (Tc) ~ 200 K, the material undergoes a continuous phase transition from a centrosymmetric cubic structure (space group 3 � ) to a noncentrosymmetric tetragonal structure (space group 4 � 2) that breaks threefold rotational symmetry about the 〈111〉 axis (Fig. 1, B and C).…”

Phenomenology of the Neutral-Ionic Valence Instability in Mixed Stack Charge-Transfer Crystals

“…Thus the diffuse X-ray of TTF-CA and DMeTTF-CA can be interpreted [39,42] analogously to the well-known Kohn anomaly of 1D metals [43]. The search for the so-called Goldstone mode [44] was among the motivations of the detailed study of intensity changes close to the exciting line of the Raman spectrum of TTF-CA and DMeTTF-CA. The Goldstone mode is a collective very low-frequency mode associated with the spontaneous breaking of a (continuous) symmetry, in the case of crystals the breaking of the translational order.…”

Evidence of an Improper Displacive Phase Transition in Cd2Re2O7Harter1, Kennes2, Chu3 et al. 2018Phys. Rev. Lett.250250View full textAdd to dashboardCite

“…1(a). Such a scenario is supported by Raman spectroscopy experiments [12], which detect the apparent softening of an E u phonon near T c , as well as by density functional theory calculations that find an unstable oxygen E u phonon at zero temperature [16].A competing hypothesis is that the phase transition is driven by an electronic order. Specific theoretical proposals include an odd-parity electronic nematic order [17,19,20], which arises from a Pomeranchuk instability in the p-wave spin interaction channel [17], as well as a combination of odd-parity quadrupolar and even-parity octupolar magnetic orders [18].…”

“…Unlike many other pyrochlore 5d transition metal oxides such as Cd 2 Os 2 O 7 [2] or members of the R 2 Ir 2 O 7 (R ¼ rare earth) family [3], which undergo paramagnetic metal-to-antiferromagnetic insulator transitions below a similar temperature scale, the phase transition in Cd 2 Re 2 O 7 is from metal to metal [4-6] and does not appear to be accompanied by any longrange magnetic order [7][8][9]. Extensive efforts to determine the underlying mechanism of the phase transition in Cd 2 Re 2 O 7 using x-ray diffraction [1,6,10,11], local magnetic probes [7][8][9], optical spectroscopy [12][13][14], and various theoretical approaches [15][16][17][18] have produced conflicting pictures.For many years, the leading hypothesis was that the transition is driven by the freezing of a soft zone-centered phonon mode with E u symmetry [15]. This mechanism is described by a Landau free energy FðΦÞ¼aðT=T c −1ÞΦ 2 þ bΦ 4 , where Φ is the structural order parameter, and requires the natural frequency of the E u phonon to monotonically approach zero near T c , as illustrated in Fig.…”