Weak phonon coupling to nematic quantum critical mode in BaFe2(As1-xPx)2

In this work, we investigate the softening of the in-plane transverse acoustic phonon driven by electronic nematicity in BaFe$_2$(As$_{1-x}$P$_x$)$_2$ using inelastic X-ray scattering, with a focus on the optimally doped sample ($x = 0.31$) sample, a system exhibiting signatures of a putative nematic quantum critical point and minimal disorder among iron pnictides. We observe only a modest softening of the phonon frequency and no evidence of critical damping, suggesting that the nematic quantum critical fluctuations couple only weakly to the lattice from our quantum critical model. Given the close proximity of the structural and magnetic transition temperatures in the underdoped sample, which implies that spin-nematic fluctuations couple strongly to the lattice. We conjecture that the quantum critical nematic fluctuations are predominantly orbital in origin.