The Higgs mechanism, first invoked to describe spontaneous symmetry breaking in superconductors, has since proven successful in describing masses of the W and Z bosons in the standard model1, in describing collective excitations in superconducting condensates and superfluids2, and in describing quantum magnets close to criticality3,4. In these scenarios, Higgs modes of scalar nature are a crucial component of spontaneous symmetry breaking. Very recently, axial Higgs modes have been discussed in the context of condensed matter physics, where the spontaneous and simultaneous breaking of different symmetries gives rise to the interplay of multiple order parameters5. As axial Higgs modes may be highly relevant for models describing physics beyond the standard model, e.g., dark matter6,7, correlated electron systems with entangled degrees of freedom can serve as excellent playgrounds to explore exotic, non-scalar amplitude-Higgs modes and test proposed models5.

Among correlated electron systems, 4d transition metal oxides (TMOs) provide exceptional platforms for exploring complex emergent phenomena due to their intricate interplay of spin and orbital degrees of freedom8,9. Examples include spin fractionalization into Majorana fermions due to bond-dependent exchange frustration in Kitaev honeycomb magnets9,10,11,12,13, unconventional superconductivity14, spin-ice states with emergent magnetic monopoles and unique quantum electrodynamics15,16,17,18, and materials with topologically non-trivial electronic and magnon band structures19,20,21, to name a few. Particularly, the family of 4d transition metal pyrochlore oxides exhibits a diverse array of exotic phenomena, driven by the interplay between geometrical frustration, electronic interactions, spin-orbit coupling, and lattice instabilities22,23.

The diverse physical properties of these 4d TMO pyrochlores with the general chemical formula A2M2O7 are determined by the choice of A-site ions and transition metal ions M. The Mott insulators A2Ru2O7 with a series of rare-earth elements (A = Pr – Lu, Y), in which Ru4+ ions (electron configuration 4d4) are expected to carry S = 1 spins and angular moment L = 1 according to Hund’s rule, are of special interest as candidate materials to study magnetic properties of frustrated spin-1 antiferromagnetism24,25,26,27. Particularly, a number of different spin structures both with and without topological magnons may be realized in this class of materials, depending on microscopic details22. Yet, the lack of high quality single crystals of the A2Ru2O7 series has hindered a systematic experimental exploration of their exact ground states and emergent magnetic anisotropies so far. Additional complications arise from the fact that spin-orbit coupling is comparable to the super-exchange scale. Therefore, a magnetic condensation of Van Vleck excitons may occur3,28, which will behave as the magnetic degrees of freedom and lead to either spin-nematic or amplitude fluctuations.

The compound of our interest, Nd2Ru2O7, consists of Ru4+ ions octahedrally coordinated by O2− ions to form larger Ru tetrahedra building blocks. Below TN = 147 K, Ru magnetic moments order antiferromagnetically (see Supplementary Note 1, and Supplementary Figs. 1 and 2), although a dispute exists about the nature of the ordering – while some experiments point towards a long-range ordered state29, an earlier neutron diffraction study on powder samples of Nd2Ru2O7 suggested a spin-glass or short-range ordered state30.

Here, we employ polarization-resolved Raman spectroscopy to study the symmetry and the temperature-dependence of magnetic and phonon excitations in high quality Nd2Ru2O7 single crystals. Below the Néel temperature TN = 147 K of the Ru ions we uncover an extended temperature regime of spin-lattice coupled fluctuations that result in a second phase transition T* = 97 K and give rise to an anomalous, well-defined low-energy amplitude excitation. Our observations suggest that at intermediate temperatures Nd2Ru2O7 is dominated by bond energy fluctuations from which a collective excitation emerges, which is consistent with a Higgs-type nematic amplitude mode.


Magnetic excitations

Below 1.8 K, Nd3+ spins are found to order in an all-in-all-out state31. In our study we only focus on temperatures above 5 K, therefore we can consider the Nd spins to be paramagnetic29 and thus assign all magnetic excitations in our study to Ru ions. In Fig. 1a, b we plot Bose-corrected Raman data obtained at 300 and 5 K in two different scattering geometries, distinguishing between the three allowed symmetry channels A1g+T2g and Eg (see also Supplementary Note 2 and Supplementary Fig. 3). All spectral features in the energy range 33–90 meV can be assigned to phonon modes, which we will discuss in more detail below. Three low-energy excitations emerge below TN at 32, 25, and 3 meV, marked by asterisks in Fig. 1a.

Fig. 1: Temperature dependence of magnetic modes.
figure 1

a, b Bose-corrected Raman intensity (Imχ) measured at 5 K (blue curve) and 300 K (red curve) in the A1g+T2g (ein = eout = [110]) and the Eg (\({{{{\bf{e}}}}}_{{{{\rm{in}}}}}=[110],{{{{\bf{e}}}}}_{{{{\rm{out}}}}}=[\bar{1}10]\)) symmetry channels, respectively. Arrows mark the T2g phonon a and the Eg phonon b. The insets plot the angular dependent intensity of excitation A at 5 K in parallel and crossed polarization. c Color contour plot of the temperature dependence in Eg symmetry. Note that the Raman shift is shown on a logarithmic scale to emphasize low lying excitations. Square symbols trace the evolution of excitation A. The dashed lines mark TN and T*. d Raman spectra measured in Eg symmetry at selected temperatures through TN (full circles). The emergent quasi-elastic scattering (QES) and excitation A are shaded. eg Temperature dependence of the energy, linewidth, and intensity of the low-energy excitation A (red squares) together with the one-magnon excitation at 25 meV (pale green diamonds). The solid red curve is a mean-field fit to the energy (see text for details). The blue circles in g show the intensity of quasi-elastic scattering. The dashed green line marks TN. Error bars in eg indicate ± 1 standard deviation around the mean value.

We can assign the two higher-lying excitations at 32 and 25 meV to one-magnon modes, based on their symmetry, their energies (see Supplementary Note 3 and Supplementary Fig. 4), and their temperature dependence discussed below. Based on our analysis of symmetry-allowed spin configurations on the S = 1 pyrochlore lattice, the best description of the 32 and 25 meV one-magnon modes in terms of energy and number of branches at q = 0 is achieved for the all-in-all-out ordered state of Ru magnetic moments. This result is somewhat at odds with previous powder neutron diffraction results30, where a spin-glass state or XY spin structure was assigned to Nd2Ru2O7. Our assignment is based on experiments restricted to q = 0. Furthermore, additional terms added to the Hamiltonian, such as substantial spin-orbit coupling, may modify this scenario and other spin configurations may be better candidates to describe our experimental data. Eventually, a detailed temperature-dependent inelastic neutron scattering study on high-quality phase-pure single crystalline Nd2Ru2O7 will help to settle this issue.

Phenomenologically similar one-magnon excitations have been reported in the spin-1/2 pyrochlore compound Y2Ir2O732, as well as in recent Raman scattering experiments from powder samples of A2Ru2O7 (A = Y, Sm, Eu, Ho, Er)33. In addition, the overall small intensities of these modes relative to other phonon modes can support our assignment, as magnetic Raman scattering processes are generally less intense than phononic Raman scattering processes.

In contrast to these one-magnon modes of weak scattering intensities, the peak at 3 meV (in the following referred to as the A-mode) dominates the Raman spectra at low temperatures. The angular dependence of its intensity, measured at T = 5 K, is plotted as a function of light polarization within the ab plane with parallel polarization (inset of Fig. 1a) and crossed polarization (inset of Fig. 1b). Its two-fold symmetry in the parallel polarization and the modulation of the lobe’s amplitudes in the cross polarization are incompatible with expected A1, T2, or E irreducible representations of the Td lattice point group of the pyrochlore lattice, and require a Raman tensor with antisymmetric tensor elements. Therefore these results are also different from the four-fold symmetries expected and observed for conventional (i.e., one-magnon or two-magnon) magnetic modes (see Supplementary Notes 4, 5, and Supplementary Fig. 5 for a detailed symmetry analysis).

To better understand the nature of this unconventional excitation, we now turn to an analysis of its thermal evolution. The temperature dependent Raman data is shown in a color contour plot in Fig. 1c (see Supplementary Note 6 and Supplementary Fig. 6 for details on the fitting procedure). As we approach TN from the high temperature side, there is a continuous increase in a broadened spectral weight at the left shoulder of the Eg phonon around 40 meV (see the green-colored background between 10 and 40 meV). In agreement with previous Raman studies on pyrochlore magnets34, we assign this continuum to paramagnetic fluctuations. Once TN is reached and crossed, this spectral weight is transferred towards zero energies, forming an increasing quasi-elastic scattering signal. Note that the spectral weight is not necessarily a conserved quantity through the transition process. Nonetheless, the transfer of spectral weight suggests an intimate link between the two signals. The quasi-elastic signal can be well fitted by a single Lorentzian line-shape centered at E = 0, as demonstrated in Fig. 1d for the temperatures 110–140 K. Such behavior is characteristic for a phase transition and originates from increasing zero-energy density fluctuations of the order parameter, which diverge through a phase transition35,36,37,38,39,40.

Only below a second transition temperature T* = 97 K does the quasi-elastic scattering intensity decrease, giving rise to a massive excitation, marked by the pale red shaded area in Fig. 1d for a few selected temperatures. The peak position determined from the fit is shown with pale red squares in Fig. 1c. Interestingly, neither bulk magnetization, nor specific heat shows any hint of this phase transition T* (see Supplementary Fig. 1 and Supplementary Note 1). Despite these missing fingerprints, the dispersion of the A peak suggests that this mode may be linked to some bond spin-nematic order parameter η, which lowers the crystalline symmetry of the pyrochlore lattice below T*.

The full temperature evolution of the A-mode is given in the panels of Fig. 1e–g, where we analyze frequency, line width, and intensity of this excitation. Figure 1g additionally plots the intensity over temperature of the quasi-elastic signal for direct comparison. Comparing the thermal evolution of the A-mode (red squares) with that of the 25 meV one-magnon mode (green diamonds), we notice a fundamentally different behavior. The nearly temperature-independent energy of the one-magnon excitation stands in stark contrast to the dramatic softening of mode A, which instead follows an order-parameter-like behavior that can be described by a critical exponent, i.e., ω(T) = αT − T*β, with α being a scaling factor, T* = (97 ± 5) K the critical temperature, and β = 0.4 ± 0.1 the critical exponent. Likewise, while the linewidth of the one-magnon mode at 25 meV remains close to constant over a wide temperature range and up to TN, the width of the A-mode broadens significantly with increasing temperature. Finally, the intensity of the 25-meV mode gradually drops off and approaches 0 around TN, indicating a decreasing magnetic moment of the Ru ions upon approaching TN. The A-mode, instead, evidences a quick drop in intensity with increasing temperature and disappears at T*. As detailed in Supplementary Note 7 and Supplementary Fig. 7, the thermal evolution of the 32 meV excitation mirrors that of the 25-meV one.

Considering all of the above, we can confidently rule out a one-magnon scattering process to be related to the A-mode. Likewise, a purely phononic origin of this mode might be ruled out, since preliminary neutron scattering data on powder samples show no hint of a phonon mode at 3 meV at 1.5 K, although ultimately neutron data at higher wave vector and higher temperature might be needed [S. Choi, private communication]. We also emphasize that neither optical phonons, nor zone-folded acoustic phonons would be expected at such low energies in pyrochlore systems with this or similar elemental composition41. Zone-folding effects can be further discarded by taking the dominating spectral weight of the A-mode into account, which would require a significant degree of lattice anharmonicity. No other structural refinement method however has lead to the observation of such dramatic structural effects. In addition, the rather sharp linewidth of the mode at base temperature underlines the coherent nature of the corresponding excitations, which agrees with the picture of fluctuation of some magnetic order parameter.

Lattice dynamics and its connection to the bond nematic amplitude mode

Evidence for the A-mode arising through fluctuations of a nematic order parameter can be also found in the lattice dynamics. To uncover such spin-related phonon anomalies, we now investigate the enhanced lattice dynamics in Nd2Ru2O7 which we observe down to about half of TN. As the Eg phonon involves twisting motions of the RuO6 octahedra, it is rather susceptible to the changes in the Ru-O-Ru bond angle. Therefore, it justifies a strong spin-elastic coupling between the Eg phonon and Ru magnetic moments, and such coupling serves as a sensitive local probe to the onset of magnetic order or even to an enhancement of spin-spin correlations within Ru tetrahedra. In Fig. 2a we present the mid-energy range of the Eg symmetry channel, which is dominated by the Eg phonon at 40 meV. The arrows at 35 and 52 meV mark small leakage of phonons from the T2g channel. Below TN a giant softening of the phonon frequency is observed, followed by a highly dynamical, fluctuating regime in which the phonon splits into a dominating low-energy mode ( ~ 38 meV) and a weaker high-energy shoulder ( ~ 41 meV). Below T*, the lattice dynamics resumes its rather static behavior.

Fig. 2: Giant spin-phonon coupling in Nd2Ru2O7.
figure 2

a Color contour plot of the mid-energy range focusing on the thermal evolution of the Eg channel. Arrows mark leakage of phonons from the T2g channel. b Phonon spectra of the Eg channel measured at 5 K and at 300 K (symbols) together with asymmetric Fano fits to the dominating Eg phonon mode (solid lines). c-f Temperature-dependence of the phonon parameters frequency, linewidth (FWHM), peak intensity, and Fano asymmetry for the Eg phonon. The solid red lines are fits to the frequency and linewidth, corresponding to anharmonic softening and broadening, respectively (see text for details). Deviations from this anharmonic behavior are shaded in pale-green. TN and T* are marked by dashed lines. Error bars in (c-f) indicate ± 1 standard deviation around the mean value.

Figure 2b highlights the lineshape of the Eg phonon, which is highly asymmetric and can be described by a Fano lineshape at room temperature. The 5 K spectrum evidences a nearly symmetric Lorentzian phonon lineshape. The appearance of an asymmetric Fano lineshape is generally ascribed to the interference of a discrete (phonon) mode with an underlying, broad continuum of excitations42. A similar temperature dependence has been observed in the all-in-all-out pyrochlore compound Cd2Os2O743, where it was related to a metal-insulator transition driven by spin-charge-lattice coupling. We recall that Nd2Ru2O7 remains electrically insulating across the investigated temperature regime29, therefore we rule out an electronic continuum as the origin (for details on the electronic band structure, see44). Instead, incoherent spin fluctuations of the paramagnetic phase (T > TN) are a natural candidate for the broad continuum, as reported in the pyrochlore iridate Eu2Ir2O734. Upon passing through TN, the spectral weight of the continuum is transferred towards quasi-elastic scattering and eventually to the low-energy A-mode. Thus, below T* the interference between the broad magnetic continuum and the Eg phonon mode disappears and the phonon approaches a symmetric Lorentzian lineshape at low temperatures.

An analysis of the phonon peak parameters frequency, linewidth, intensity, and Fano asymmetry is presented in Fig. 2c–f. Both frequency and linewidth can be described by anharmonic behavior for T > TN (see solid red line and Supplementary Note 8 for details)45. Below TN, this anharmonic behavior is abruptly halted and replaced by an enormous energy softening, peak broadening, and line splitting. A softening of the Eg phonon with the onset of magnetic order is commonly observed in pyrochlore magnets46,47,48. The giant softening from 41 meV down to 38 meV, present in Nd2Ru2O7, however, exceeds these common values by about one order of magnitude. The dramatically enhanced linewidth in between the transition temperatures signals the opening of an effective decay channel in the form of additional spin fluctuations. Simultaneously, the intensity of the dominating line starts to increase monotonically, and the Fano asymmetry drops and approaches zero towards lowest temperatures. All these phonon anomalies underline the existence of a highly dynamical lattice that strongly couples to spin degrees of freedom, which settle in modulated or canted spin structures and culminate in the formation of an amplitude mode, i.e., the A-mode at 3 meV.

Broken symmetries

With the dynamic aspect of various Raman modes, we now turn to an analysis of the symmetry properties of various excitations in Nd2Ru2O7. As we already detailed in Fig. 1a, b, the A-mode displays a striking two-fold symmetry in both parallel and crossed scattering configurations, which is at odds with the given cubic crystal structure. If the anomalous lattice dynamics of the Eg mode is indeed from coupling to magnetic bond-energy fluctuations, there should be some evidence of this coupling in its symmetry properties as well. Therefore, we now investigate the symmetries of the phonon modes.

Figure 3 a shows polar plots of phonon intensities of different symmetries, measured at T = 5 K in parallel (xx, red circles) and crossed (xy, black squares) polarization (see Supplementary Fig. 3 for the full data set). The experimental data for the A1g and T2g modes match their fits very well, which are denoted by solid lines based on the respective Raman tensors given in Supplementary Note 2. In contrast, the splitting of the Eg phonon mode into ω1 and ω2 lowers the symmetry of the resulting branches observed in parallel polarization from four-fold to two-fold rotationally symmetric (Fig. 3b), thus pointing towards a lowering symmetry of the RuO6 octahedra. Without structural distortion, such lowering symmetry can be triggered from a spin bond order parameter 〈fη〉 = (〈f1〉, 〈f2〉), where \({f}_{1}=[({{{{\bf{S}}}}}_{1}+{{{{\bf{S}}}}}_{2})\cdot ({{{{\bf{S}}}}}_{3}+{{{{\bf{S}}}}}_{4})-2{{{{\bf{S}}}}}_{1}\cdot {{{{\bf{S}}}}}_{2}-2{{{{\bf{S}}}}}_{3}\cdot {{{{\bf{S}}}}}_{4}]/\sqrt{12}\) and f2 = (S1 − S2)  (S3 − S4)/2, as proposed in49. Such spin bond order parameter measures bond energy differences within the Ru tetrahedron, and couples directly to the Eg phonon mode through the spin-elastic coupling \({{{{\bf{f}}}}}_{\eta }\cdot {{{{\bf{u}}}}}_{{E}_{{{{\rm{g}}}}}}\). In crossed polarization, both branches still appear with the same four-fold symmetry (see Fig. 3b and Supplementary Fig. 3]. Both the splitting and the symmetry reduction are reminiscent of a nematic-like phase transition50. We can rule out any significant misalignment of the crystal or contributions from (potentially existing) neighboring domains as sources for these distorted polar plots, since all other phonons closely follow their expected rotational symmetry and only the Eg mode is affected.

Fig. 3: Evidence for symmetry breaking in Nd2Ru2O7.
figure 3

a Polarization plots for phonons of A1g, T2g, and b Eg symmetry measured in parallel (red circles) and in crossed (black squares) configuration at T = 5 K. The solid red and gray lines trace the theoretical rotational anisotropy following the respective Raman tensors. c The nematic order parameter η(T) as extracted from the phonon frequencies shown in Fig. 2c. d Arrows sketch the ionic displacement patterns of the doubly degenerate Eg mode. Error bars in c indicate ± 1 standard deviation around the mean value.

In Fig. 3c we quantify the energy difference between ω1 and ω2 by introducing η = (ω1 − ω2)/(ω1 + ω2), a phonon anisotropy parameter51, which can be associated with the spin bond order parameter 〈fη〉, and we treat η as the nematic order parameter. Figure 3d sketches the ionic displacement patterns corresponding to the two-fold degenerate Eg phonon mode. Upon distortion of the local octahedral environment within a unit cell, this two-fold degeneracy may be lifted, resulting in a splitting of the Eg phonon. Previous studies on Nd2Ru2O7 have not found any indication of a structural phase transition within our temperature range of interest, with experimental methods ranging from synchrotron and x-ray diffraction29,52, to neutron diffraction31. However, a pronounced, non-monotonic decrease in the Ru-O-Ru angle was observed between 150 and 100 K52. This can indicate a gradual canting or rearrangement of spins in a (short-ranged) antiferromagnet or a transition among two neighboring phases with decreasing temperature, accompanied by strong bond-energy fluctuations and manifested by the observed entangled spin-lattice instabilities. This concept of competing bond configurations has also been explored, e.g., in breathing pyrochlores53,54, while spin-lattice coupling in a 2D magnet lead to the splitting of an Eg phonon, albeit of smaller magnitude55. The temperature dependence of η closely follows that of the A-mode, hence its emergence below 97 K indicates the onset of nematic order. Also, the fact that the two-fold, distorted Eg polar plot resembles the rotational symmetry of excitation A, as shown in Fig. 1a and b, suggests a direct correlation between the amplitude A-mode and lattice degrees of freedom of the RuO6 octahedra.


With the broken symmetry identified, we wish to discuss the origin of the A-mode. In the related antiferromagnet Ca2RuO43,56 a broader Higgs mode at high energies (centered around 40 meV) is reported to stabilize through a condensation of J = 1 excitons per Ru site28. This single-ion picture may however not be relevant for the stabilization of the A-mode in Nd2Ru2O7, given its smaller energy scale and the fact that it emerges through a second phase transition within the magnetically-ordered phase. Instead, narrow spectral features at low energies with dominating scattering intensity—strikingly similar to the A-mode—have been observed via Raman spectroscopy and interpreted as Higgs-type amplitude modes in the charge-density-wave compounds GdTe35, 2H-TaS257, and NbSe258.

Based on these considerations and on the observed lattice dynamics, we can pinpoint the following scenario for the formation of the A-mode: At TN, when the order of the Ru magnetic moments develops and translational symmetry breaks, the spin bond order parameter 〈fη〉 remains zero, since the magnetic energy of the six bonds in a single tetrahedron is uniform. However, through the spin-elastic coupling to the Eg phonon, the magnetic energy of the system can be further lowered. This drives the development of the spin-nematic bond order, an example of vestigial order which grows out of the magnetic fluctuations, and in the temperature range between 97 K and 147 K leads to strong quasi-elastic scattering (Fig. 1d). Below 97 K, the energy of the A-mode grows as an order parameter (Fig. 1c). This order breaks the discrete rotational symmetry since it leads to inequality between bond energies on the Ru tetrahedron but preserves the translational symmetry, i.e., it is a q = 0 order. The consequences of the spin nematic order also have a feedback to the lattice, causing the splitting of the Eg phonon with reduced two-fold symmetry through the spin-elastic coupling \({{{{\bf{f}}}}}_{\eta }\cdot {{{{\bf{u}}}}}_{{E}_{{{{\rm{g}}}}}}\). Within this picture, T* is the spin-nematic transition further lowering the symmetry of the system.

Remarkably, a two-fold symmetric amplitude Higgs mode was recently reported in the charge-density-wave ordered GdTe3 in Raman scattering experiments of both parallel and crossed polarization configurations5. As such low symmetry is also inconsistent with the scalar nature of the Higgs mode, a polarization-dependent mechanism of constructive/destructive pathway interference was invoked, which instead yields an exotic axial Higgs mode. The striking similarities between GdTe3 and Nd2Ru2O7 raise the exciting prospect of stabilizing an axial Higgs mode of magnetic nature in pyrochlore systems with multiple spontaneously broken symmetries, e.g., both magnetic and nematic order. A deeper insight into the spin dynamics and requires a temperature-dependent study of the magnon band structure, e.g., via inelastic neutron scattering or resonant elastic x-ray scattering experiments. In addition, second-harmonic generation studies may shine further light on the nature of broken symmetries. However, these methods require sizable single crystals with flat or cleavable surfaces. Given the availability of suitable single crystals, such future studies will be essential to unambiguously uncover the nature of the observed amplitude mode in Nd2Ru2O7.

In summary, we uncover a wide temperature regime of coupled spin and lattice fluctuations in the pyrochlore ruthenate Nd2Ru2O7 via Raman spectroscopy that result in a second phase transition T*, which has been elusive in other thermodynamic probes. A low-energy excitation emerging out of these fluctuations with a distinct symmetry and a peculiar temperature evolution is interpreted as a coherent amplitude mode out of nematic order. Future studies under extreme conditions, such as high pressure and magnetic fields, are envisaged to tune these fluctuations and further pinpoint the nature of the low-energy Higgs mode.


Sample growth

Single crystals of Nd2Ru2O7 were synthesized using the KF flux method59. Typical resulting crystals of about 30 × 30 × 30 μm3 volume exhibit shiny triangular- and rectangular-shaped as-grown surfaces, corresponding to [111] and [100] facets, respectively. Based on our obtained Raman spectra and basic thermodynamic characterization [see Supplementary Note 1] we can rule out any inclusion of a secondary Nd3RuO7 phase, commonly found in pyrochlore ruthenates29,60.

Raman scattering

Raman spectroscopic experiments have been carried out using a λ = 532 nm solid state laser (Cobolt Samba) with a spot diameter of about 10 μm and an incident laser power at the sample position below 0.35 mW to reduce local laser heating effects. The scattered light passed through a volume Bragg grating notch filter set (Optigrate) to discriminate the laser line and to access Raman signals with energies as low as 0.8 meV. The sample was mounted via silver epoxy onto the cold finger of a He-cooled open-flow cryostat (Oxford Microstat HiRes). The Raman-scattered light was dispersed through a single-stage Horiba iHR 320 spectrometer with a 1800 gr/mm grating onto a Horiba Synapse CCD. In this configuration, a spectral resolution of about 1.2 cm−1/pixel is achieved. A constant background (dark current) of 117 counts was subtracted from each spectrum. Where indicated, Bose-corrected Raman intensity Imχ(ω) is plotted. It is related to the as-measured Raman intensity I(ω) via the fluctuation-dissipation theorem by I(ω) = [1 + n(ω)]Imχ, where n(ω) is the Bose factor.