Magnetoelastic coupling in the organic radical $\beta -p-$NCC${}_6$F${}_4$CNSSN

Resonant ultrasound spectroscopy (RUS) was used to analyze the elastic and anelastic behavior associated with canted antiferromagnetic ordering at 36 K in the radical, $\beta$-$p$-NCC${}_6$F${}_4$CNSSN, 1. On cooling through the magnetic ordering transition there is anomalous elastic behavior away from the expected uniform stiffening with decreasing temperature, consistent with magnetoelastic coupling. The excess in the elastic stiffness follows the magnetic order parameter linearly below the magnetic ordering temperature. A much larger change in elastic properties is associated with short-range ordering between $T_{\mathrm{c}}$ and 150 K which appears to correlate with an excess heat capacity (and entropy). Thus it appears that the onset of long-range order to this spin canted system might only be a partial contribution to the whole phase transition.

Figure 1

Structure of 1 viewed down the crystallographic $b$ axis with unit cell displayed. Carbon atoms are displayed in gray, nitrogen in blue, sulfur in yellow, and fluorine in green. One of each atom is labeled in black. Short contacts between sulfur atoms in the heterocyclic ring and nitrogen atoms in the cyano group are labeled as dashed lines. A single unit cell is marked with $c$ horizontal and $a$ vertical.

Figure 2

Stack of RUS spectra for 1 between 12 and 52 K. The spectrum recorded at the magnetic ordering temperature 36 K is shown in blue and labeled on the right of the figure.

Figure 3

Evolution of the square of the frequency and the acoustic dissipation for two peaks at 513 (blue circles) and 463 kHz (red squares). Variations in $f^2$ are represented by open symbols and variations in $Q^{-1}$ by closed symbols. Dashed line displays the magnetic ordering temperature 36 K. Solid curve is a baseline fit of Eq. (4) data above 150 K with ${\theta }_{\mathrm{s}}$ set at 21 K.

Figure 4

Fit of Eq. (4) to the low temperature values of $f^2$ with $a_1=2.19\times {10}^{11}$, $a_2=-3.56\times {10}^8$, and ${\theta }_{\mathrm{s}}=21$ K. Magnetic ordering temperature is represented by dashed line at 36 K.

Figure 5

Plot of the reduced excess of $f^2$ (proportional to excess elastic constant) calculated from the fit in Fig. 4 as a baseline (blue open circles), and the magnetic order parameter for $S=\frac{1}{2}$ (solid curve), along with corresponding experimental data for the order parameter determined from spontaneous magnetization (red crosses), antiferromagnetic resonance studies (open black squares), and muon spin relaxation experiments (solid purple circles). Within experimental error the variation of $\Delta f^2$ is indistinguishable from the variation of $Q_{\mathrm{m}}$.

Figure 6

Original heat capacity data from Palacio et al.[10, 17] (black crosses) showing original baseline (blue, upper solid line) and new baseline (red, lower solid line).

Figure 7

Plot of the excess elastic constant squared (red crosses) and excess entropy (curve) below 150 K extracted from heat capacity data. Transition temperature is represented by solid vertical line for comparison.