Spin-lattice interactions through the quantum critical transition in Cu(pyz)(NO$_3$)$_2$*

We measured the magneto-infrared response of the quasi-one-dimensional quantum Heisenberg antiferromagnet Cu(pyz)(NO$_3$)$_2$ to investigate local lattice distortions through the field-driven transition to the fully polarized magnetic state. This magnetic quantum critical transition involves changes in the out-of-plane N and C-H bending modes of pyrazine with field that directly track the magnetization. We discuss our results in terms of calculated spin densities, scaling laws, and extracted spin-phonon coupling constants, the latter of which are remarkably large due to the softness of the pyrazine ligand.