Magnetoelastic coupling through the antiferromagnetic - to - ferromagnetic transition in quasi-two-dimensional [Cu(pyz)$_2$HF$_2$]BF$_4$ using infrared spectroscopy*

We investigated magneto-elastic coupling through the field-driven transition to the fully polarized magnetic state in quasi-two-dimensional [Cu(HF$_2$)(pyz)$_2$]BF$_4$ by magneto-infrared spectroscopy. This transition modifies out-of-plane ring distortion and bending vibrational modes of the pyrazine ligand. The extent of these distortions increases with field, systematically tracking the low temperature magnetization. These distortions weaken the antiferromagnetic spin exchange, a finding that provides important insight into magnetic transitions in other copper halides.