Nonlinear optical signatures of the tensor order in Cd2Re2O7 

Abstract

G rowing evidence indicates that the superconducting pyrochlore Cd 2 Re 2 O 7 exhibits a structural phase transition at T c = 200 K with an unusual tensor character 1-3 . The structural order parameter for this state is two-dimensional, and spanned by distinct but nearly degenerate crystallographic structures I4 1 22 and I4m2 (ref. 1). Symmetry rules imply that the low-energy excitations of the ordered state are Goldstone phonons, or long wavelength fluctuations between the two crystal structures. These are the structural equivalents of magnons in an XY antiferromagnet, with the two crystal structures analogous to orthogonal spin directions in the xy-plane. Goldstone phonons have been observed in Raman spectroscopy 3 , but high-resolution X-ray and neutron scattering experiments have produced conflicting assignments of the static low-temperature structure 4-6 . Here, we use optical secondharmonic generation with polarization sensitivity to assign the I4m2 structure unambiguously and verify an auxiliary condition on the structure that is implied by the order parameter symmetry. We also show that the temperature dependence of the order parameter is consistent with thermal occupation of the Goldstone mode. The methodology may be applied more widely in characterizing ordered states in matter.Various experimental probes show a continuous cubic-totetragonal transition in Cd 2 Re 2 O 7 at T c (refs 1,2,4-10). However, as Anderson and Blount pointed out over 40 years ago 11 , a less conventional order parameter, possibly with ferroelectric character, must accompany strain to make any cubic-to-tetragonal transition continuous. Experiments have indeed ruled out strain as the primary order parameter for Cd 2 Re 2 O 7 (ref. 2), and both X-ray and neutron diffraction reveal broken inversion symmetry below T c (refs 4-6). Theoretical analysis indicates that the true order parameter is a second-rank pseudotensor, corresponding to the E u representation of the cubic point group 1,2 , shown in Fig. 1. The more familiar types of order all have lower rank: vectors for ferroelectricity, inversion-symmetric pseudovectors for ferromagnetism and second-rank tensors for ferroelasticity. Like the vector order of ferroelectricity, E u tensor order in In 0 Out

Successive spatial symmetry breaking under high pressure in the spin-orbit-coupled metal Cd2Re2O7Yamaura1, Takeda2, Ikeda3 et al. 2017Phys. Rev. B251270View full textAdd to dashboardCite

“…It undergoes a successive structural transition from high-temperature cubic Fd−3m (phase I) to tetragonal I−4m2 (phase II) at T s1 = 200 K and to tetragonal I4 1 22 (phase III) at T s2 = 120 K [13][14][15][16][17][18][19]. The T s1 transition of the second-order type is considered as a band Jahn-Teller transition lifting the highly degenerate bands, because there are large changes in the electronic properties in spite of the tiny tetragonal distortion at T s1 [23,30] On the other hand, the origin of the T s2 transition, which is of the first-order, is thus far unclear [15,31].…”

Nature of the tensor order in Cd2Re2O7

“…In this subsection, we shall apply them to the case of the 4m2 point group of the low-temperature phase of Cd 2 Re 2 O 7 , as well as to some of its subgroups, in order to explain the SHG experiments. We first make an important notational remark: throughout this paper we label the SHG susceptibilities, χ xyz , with x, y and z referred to the cubic axes of F d3m, in keeping with previous papers [17,19]. This corresponds, in principle, to the 42m point group, not 4m2, the two being just a different description of the same geometry related by a 45…”

“…As we will show below, the OP of E u symmetry detected in both SHG experiments conducted on Cd 2 Re 2 O 7 [17,19] is not the E u OP proposed in [12], but rather an axial toroidal quadrupole of x 2 − y 2 symmetry (in the cubic F d3m coordinates, with z along the tetragonal c axis). Concerning the primary OP, we find that a time-reversal even scenario is not the only possibility.…”

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

“…To measure how quickly the electron and lattice subsystems thermally equilibrate in Cd 2 Re 2 O 7 , we performed time-resolved SHG measurements. The second-order electric-dipole susceptibility has been shown to couple linearly to the E u structural order parameter below T c [13,14]; therefore, the SHG intensity can be used as a sensitive measure of the lattice temperature. Figure 5 acquired at T ¼ 175 K. For all pump fluences tested, we observe the SHG intensity drop to a lower value quickly upon pump excitation, indicating a rapid heating of the lattice, and then stay nearly constant at this value for over 100 ps.…”

“…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.…”