Neutron scattering study of a quasi-two-dimensional spin-$\frac{1}{2}$ dimer system: Piperazinium hexachlorodicuprate under hydrostatic pressure

We report inelastic neutron scattering study of a quasi-two-dimensional $S=\frac{1}{2}$ dimer system piperazinium hexachlorodicuprate under hydrostatic pressure. The spin gap $\Delta$ becomes softened with the increase of the hydrostatic pressure up to $P=9.0\text{kbar}$. The observed threefold degenerate triplet excitation at $P=6.0\text{kbar}$ is consistent with the theoretical prediction and the bandwidth of the dispersion relation is unaffected within the experimental uncertainty. At $P=9.0\text{kbar}$ the spin gap is reduced to $\Delta =0.55\text{meV}$ from $\Delta =1.0\text{meV}$ at ambient pressure.

Figure 1

Background-subtracted constant-$\mathit{Q}=\left(0.5,0,-1.5\right)$ scans measured at SPINS in PHCC at $T=2.3\text{K}$ (a) $P=1\text{kbar}$, (b) $P=3\text{kbar}$, and (c) $P=4\text{kbar}$. Solid lines are fits to the model as described in the text after convolution with the instrumental resolution function. Dashed lines indicate the level of zero. Inset: Raw data of constant-$\mathit{Q}=\left(0.5,0,-1.5\right)$ scan measured at $P=1\text{kbar}$. The solid line is a Gaussian and a linear term fit to account for the background contribution. Throughout error bars indicate plus minus the standard deviation, $\sigma$.

Figure 2

(Color online) The single-crystalline inelastic neutron scattering intensity along the reciprocal $\left(0.5,0,\ell \right)$ direction measured at DCS for PHCC at $T=1.5\text{K}$ and ambient pressure. Solid line is the one-triplon dispersion relation for PHCC at ambient pressure as determined from Ref. 21. The figure was obtained by averaging the data in bins of size $d\hslash \omega =0.02\text{meV}$ and $d\ell =0.02\left(\text{r}\text{.l}\text{.u}\text{.}\right)$.

Figure 3

(Color online) Background-subtracted inelastic neutron scattering intensity along the reciprocal $\left(0.5,0,\ell \right)$ direction measured at DCS for PHCC at $T=1.5\text{K}$, and (a) $P=6.0\text{kbar}$ and (b) $P=9.0\text{kbar}$. The background from solid helium excitation was subtracted as discussed in the text. Solid lines are the one-triplon dispersion relation for PHCC at ambient pressure lowered by (a) 0.30 meV and (b) 0.45 meV. The figure was obtained by averaging the data in bins of size $d\hslash \omega =0.04\text{meV}$ and $d\ell =0.04\left(\text{r}\text{.l}\text{.u}\text{.}\right)$.

Figure 4

Energy dependence of the magnetic scattering intensity for PHCC averaged over the range of $-1.6<\ell <-1.4$ from Fig. 3 at $T=1.5\text{K}$, and (a) $P=6.0\text{kbar}$ and (b) $P=9.0\text{kbar}$. Solid lines are the fits to Eq. (1) convolved with the instrumental resolution function. Dashed lines indicate the level of zero. The shaded area is excluded due to a contamination by the solid helium excitation spectrum. Throughout error bars indicate plus minus the standard deviation, $\sigma$.

Figure 5

The pressure dependence of spin gap $\Delta$ in PHCC. The spin gap at ambient pressure was reproduced from Ref. 17. The dashed line is a guide to the eye.