Magnetoelastic Coupling through the Antiferromagnet-to-Ferromagnet Transition of Quasi-Two-Dimensional $[\mathrm{Cu}({\mathrm{HF}}_2)(\mathrm{pyz}{)}_2]{\mathrm{BF}}_4$ Using Infrared Spectroscopy

We investigated magnetoelastic coupling through the field-driven transition to the fully polarized magnetic state in quasi-two-dimensional $[\mathrm{Cu}({\mathrm{HF}}_2)(\mathrm{pyz}{)}_2]{\mathrm{BF}}_4$ by magnetoinfrared spectroscopy. This transition modifies out-of-plane ring distortion and bending vibrational modes of the pyrazine ligand. The extent of these distortions increases with the 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.

Figure 1

(a) 300 K crystal structure of $[\mathrm{Cu}({\mathrm{HF}}_2)(\mathrm{pyz}{)}_2]{\mathrm{BF}}_4$ [18]. This rendering emphasizes the quasi-two-dimensional nature of the Cu-pyrazine network. The bifluoride anions that link the Cu centers along $c$ run into (and out of) the Letter. (b) and (c) Spin density distribution calculated for the AFM and FM state, respectively. Shading denotes different spins.

Figure 2

Close-up views of selected vibrational modes in the absorption spectrum at 300 and 4 K. These include: (a) low frequency Cu-pyrazine lattice modes, (b) out-of-plane pyrazine ring deformation, out-of-plane pyrazine bend, and $\mathrm{BF}_4{}^{-}$ bend, (c) pyrazine out-of-plane C-H bend, (d) C-C stretch, (e) a combination-overtone mode, and (f) C-H stretching modes.

Figure 3

(a) and (b) Close-up views of the absolute absorption spectra at $H=0$ and 33 T at 4.2 K in the range of several pyrazine-related vibrational modes. (c) and (d) Close-up views of the 4.2 K absorption difference spectra [$\alpha (H)-\alpha (0\mathrm{T})$] in the range of these same modes. Data in (c) and (d) are offset along the $y$ axis for clarity. The double-headed arrows correspond to an absorption difference of $100{\mathrm{cm}}^{-1}$. With this scale bar, we see that 33 T absorption differences near $490{\mathrm{cm}}^{-1}$ are on the order of $400{\mathrm{cm}}^{-1}$. This corresponds to a 13% change in the out-of-plane pyrazine bending mode in a 33 T field.

Figure 4

Integrated area of the absolute value of the absorption difference spectra for the indicated frequency ranges as a function of applied magnetic field compared with 1.5 and 4.2 K magnetization data from Goddard et al. in Ref. 8. The black dotted lines guide the eye.