Chemical composition induced quantum phase transition in ${\mathrm{Cs}}_{1-x}{\mathrm{Rb}}_x{\mathrm{FeCl}}_3$

The isostructural series of $S=1$ quantum magnets ${\mathrm{Cs}}_{1-x}{\mathrm{Rb}}_x{\mathrm{FeCl}}_3$ is investigated, using both thermodynamic measurements and inelastic neutron scattering experiments. It is found that with increasing Rb content the system evolves from the gapped state at $x=0$, through a quantum phase transition at $x\sim 0.35$, and to the magnetically ordered state at larger $x$. Inelastic neutron experiments for $x=0, x=0.3$, and $x=1$ demonstrate that the magnetic anisotropy and spin interactions are continuously tuned by the chemical composition. For the intermediate concentration all magnetic excitations are substantially broadened suggesting that disorder plays a key role in this species. For the two end compounds, excitations remain sharp.

Figure 1

(a) Crystal structure of ${\mathrm{Cs}}_{1-x}{\mathrm{Rb}}_x{\mathrm{FeCl}}_3$ with space group $P{6}_3/mmc$. (b) Triangular lattice in the $ab$ plane. (c) Measured lattice constants for all compounds studied in this work. Red circles and blue triangles indicate lattice constants $a$ and $c$, respectively. Shaded areas are guides for eye.

Figure 2

Heat capacity measurements for all compounds. (a) Temperature scans at zero magnetic field and (b) field scans in an applied magnetic field along the $c$ axis at $T=0.25$ K. $x$ is the content of the Rb. The solid curves in (a) are the fits proportional to $exp(-\mathrm{\Delta }/k_{\mathrm{B}}T)$. The solid curves and lines in (b) are empirical fits to estimate the positions of peaks and kinks. These are indicate by red triangles. The data are shifted by vertical offset of 0.2.

Figure 3

Magnetic susceptibility at $T=2$ K in an applied magnetic field for selected compounds. The magnetic field is applied along the $c$ axis. The solid lines are empirical fits to estimate positions of the kinks. The red triangles indicate positions of the peaks and kinks.

Figure 4

Transition fields $H_{c1}, H_{c2}$ plotted as a function of the Rb content in ${\mathrm{Cs}}_{1-x}{\mathrm{Rb}}_x{\mathrm{FeCl}}_3$, as determined from heat capacity and ac magnetic susceptibility measurements. The inset shows the behavior of the activation energy in the zero-field heat capacity experiments. The dashed solid lines are linear fits. The estimated error bars are inside the data symbols.

Figure 5

False color plots of the measured inelastic neutron intensity projected onto the $\hslash \omega -(1/3,1/3,l)$ plane for (a) ${\mathrm{CsFeCl}}_3$, (b) ${\mathrm{Cs}}_{0.7}{\mathrm{Rb}}_{0.3}{\mathrm{FeCl}}_3$, and (c) ${\mathrm{RbFeCl}}_3$ at $T\simeq 0.1$ K. The incident neutron energy is $E_{\mathrm{i}}=5.93$ meV. The spectra are integrated in the range of $0.30(a^{*}+b^{*})\le q\le 0.36(a^{*}+b^{*})$. The white bars indicate the calculated instrument energy resolution. The white area at $\hslash \omega =3.5$ meV in (b) masks a strong spurious scattering that does not originate from the sample.

Figure 6

False color plots of the measured inelastic neutron intensity projected onto the $\hslash \omega -(h,h,0)$ plane for (a) ${\mathrm{CsFeCl}}_3$, (b) ${\mathrm{Cs}}_{0.7}{\mathrm{Rb}}_{0.3}{\mathrm{FeCl}}_3$, and (c) ${\mathrm{RbFeCl}}_3$ at $T\simeq 0.1$ K. The incident neutron energies are $E_{\mathrm{i}}=5.93$ meV for ${\mathrm{CsFeCl}}_3$, and $E_{\mathrm{i}}=2.99$ meV for ${\mathrm{Cs}}_{0.7}{\mathrm{Rb}}_{0.3}{\mathrm{FeCl}}_3$ and ${\mathrm{RbFeCl}}_3$. The spectra are integrated in the range of $-0.05c^{*}\le q\le 0.05c^{*}$. The white bars indicate the instrumental energy resolutions.

Figure 7

Constant-$\mathit{q}$ cuts at (a) $(1/3,1/3,0)$ and (b) $(1/2,1/2,0)$ for ${\mathrm{Cs}}_{0.7}{\mathrm{Rb}}_{0.3}{\mathrm{FeCl}}_3$ and ${\mathrm{RbFeCl}}_3$. The spectra were integrated in the range of $0.30(a^{*}+b^{*})\le q\le 0.36(a^{*}+b^{*})$ and $-0.05c^{*}\le q\le 0.05c^{*}$ for (a), and $0.47(a^{*}+b^{*})\le q\le 0.53(a^{*}+b^{*})$ and $-0.05c^{*}\le q\le 0.05c^{*}$ for (b). The shaded areas represent the calculated instrumental energy resolution.

Figure 8

False color plots of inelastic neutron intensity measured in (a) ${\mathrm{Cs}}_{0.7}{\mathrm{Rb}}_{0.3}{\mathrm{FeCl}}_3$ and (b) ${\mathrm{RbFeCl}}_3$ at constant energy transfers of 0.2 and 0.4 meV. The data were taken with $E_{\mathrm{i}}=2.99$ meV. The spectrum was integrated in the range of $0.175\le \hslash \omega \le 0.225$ meV and $0.375\le \hslash \omega \le 0.425$ meV. The aspect ratio of the figure is scaled to units of ${\AA }^{-1}$.