Interplay of triplets and lattice degrees of Freedom in the coupled spin dimer system $\mathrm{K}\mathrm{Cu}{\mathrm{Cl}}_3$

We report inelastic light scattering measurements of the three-dimensional coupled spin dimer system $\mathrm{K}\mathrm{Cu}{\mathrm{Cl}}_3$ with a spin gap of $\Delta =31\mathrm{K}$. We observe several distinct features, (i) equally intense two- and three-magnon continua, showing substantial temperature dependence of spectral weight and onset energy, and (ii) nonmonotonic temperature dependence of optical phonon modes and the presence of pronounced multiphonon scattering. The former points to the significance of delocalized triplets while the latter uncovers substantial lattice anomalies. This suggests that the studied system, showing the Bose-Einstein condensation of triplets, is characterized by an intriguing interplay between delocalized triplets and lattice degrees of freedom.

Figure 1

Raman spectra of $\mathrm{K}\mathrm{Cu}{\mathrm{Cl}}_3$ in three different polarizations and at $T=5\mathrm{K}$ and $T=295\mathrm{K}$, in the lower and upper curve, respectively.

Figure 2

Multiphonon scattering up to fourth order in the $\left(xx\right)$ polarization at 5, 100, and $200\mathrm{K}$. The spectra are shifted for clarity.

Figure 3

(Color online) (a) The ratio of higher- and first-order scattering intensity at 546, 1092, 1637, and $2181{\mathrm{cm}}^{-1}$ as a function of temperature. (b) Temperature dependence of the relative frequency shift at 123, 307, and $543{\mathrm{cm}}^{-1}$ modes, which is defined as $\nu \left(\mathrm{K}\right)–\nu \left(295\mathrm{K}\right)$. It should be noted that phonon anomalies in frequency occur around 10, 55, and $100\mathrm{K}$.

Figure 4

Two low-energy magnetic excitations observed in the $\left(xx\right)$ polarization for temperatures below $150\mathrm{K}$. Note that we have fitted the weak phonon modes at 55 and $75{\mathrm{cm}}^{-1}$ to a Lorentzian profile and then subtract them from the raw spectrum for clarity. As a result, the presented spectrum consists of pure magnetic excitations.

Figure 5

(Color online) (a) Temperature dependence of the onset of the two magnetic continua. (b) Temperature dependence of integrated intensity of the two magnetic continua. The LEM (HEM) stands for the lower (higher)-energy continuum. The solid line is a fit to a Bose-Einstein factor at low temperature region.