Angle-Resolved Cryogenic Brillouin-Mandelstam Spectroscopy of Surface and Bulk Acoustic Phonons in Diamond

Referee: [Abstract] Abstract: The statement that all three surface acoustic phonon frequencies 'agree with the theoretical values within the experimental uncertainty' is not accompanied by details on uncertainty estimation, mode identification procedure, or data exclusion criteria. This renders the central agreement claim unverifiable from the provided information.

Authors: We agree that the abstract is too concise to convey these details. In the revised manuscript we will expand the Methods section with a dedicated subsection on data analysis. Uncertainty estimation will be described as the quadrature sum of Lorentzian peak-fitting standard errors (typically 0.5–1.5 MHz) and the 0.2° angular-resolution contribution to velocity uncertainty. Mode identification is performed by matching measured phase velocities to dispersion curves calculated from literature Cij values, cross-checked against established diamond SAW velocities in the literature. Data exclusion criteria (SNR < 5 or peaks contaminated by stray light or bulk-mode overlap) will be stated explicitly. A one-sentence reference to these procedures will be added to the abstract if length permits. revision: yes

Referee: [Results (surface mode identification)] Results section on surface modes: Assignment of observed peaks to Rayleigh, shear-horizontal, and pseudo-longitudinal branches rests exclusively on matching extracted phase velocities to dispersion curves computed from fixed literature elastic constants. No independent verification (polarization selection rules, direct comparison to bulk-mode velocities, or temperature-adjusted Cij) is described, which is load-bearing because the pseudo-longitudinal mode is a leaky resonance whose visibility depends on damping and geometry.

Authors: Phase-velocity matching to calculated dispersion relations is the standard and primary identification method in angle-resolved Brillouin-Mandelstam spectroscopy because the scattering geometry fixes the polarization selection rules. We will add explicit text noting that our backscattering configuration selects the sagittal-plane modes (Rayleigh and pseudo-longitudinal) and the shear-horizontal mode via the appropriate polarization. Measured velocities are compared to bulk transverse and longitudinal velocities to confirm they lie below the respective sound lines, consistent with surface localization. For the pseudo-longitudinal (leaky) resonance we will cite its established visibility in low-damping diamond and note that its damping is small enough for clear observation in our geometry. Temperature-adjusted Cij will be addressed in the response to the third comment. revision: partial

Referee: [Temperature dependence and comparison to theory] Temperature dependence analysis: The theoretical reference curves treat elastic constants as temperature-independent, yet the data exhibit up to 1.6% frequency shift between 10 K and 300 K. Any unaccounted dCij/dT would systematically shift the comparison curves and must be quantified to support the agreement claim.

Authors: We acknowledge the need to quantify this effect. Published temperature derivatives for diamond’s elastic constants are small (dC11/dT ≈ −0.014 GPa K⁻¹, dC44/dT ≈ −0.007 GPa K⁻¹). Propagating these values over 10–300 K produces a maximum frequency shift of ~0.4 %, well below our experimental uncertainty of ~1–2 % arising from fitting and alignment. In the revision we will add a supplementary note containing this estimate and show that the fixed-Cij theoretical curves remain within the measured error bars at all temperatures. The observed 1.6 % shift is therefore still consistent with the literature-based prediction once experimental uncertainty is taken into account. revision: yes