Experimental observation of hydrogen in a mixed state of order-disorder and displacive behavior in squaric acid

H₂C₄O₄ (Squaric acid, henceforth abbreviated by SQA) is one of the most studied hydrogen-bonded anti-ferroelectrics in the KH₂PO₄ (KDP) family. Here, we report the static hydrogen lineshape which shows a mixed state behavior of order-disorder and a displacive feature in the anti-ferroelctric (AFE)/paraelectric (PE) phase transition of SQA. We obtained the dipolar splitting data from the nonlinear fitting curve of the static hydrogen lineshape. The calculated proton-proton distance showed an increase at temperatures above the transition temperature T_c. As temperature increases through T_c, the inter-atomic distance shows a peculiar S-shape variation. This S-shape variation around T_c is also observed in other NMR reports for SQA, where the chemical shift variation is used to characterize the deformation of the C₄O₄ squarate group. Here, we used the dipolar interaction, instead of the chemical shift information, to detect the geometrical change of the hydrogen. Below the transition temperature T_c, the proton interactions showed long-range order whereas it showed short range order at temperatures above T_c. The peculiar S-shape variation from the hydrogen lineshape analysis can be understood as another piece of experimental evidence for a mixed state for the phase transition in SQA.