Field-concentration phase diagram of a quantum spin liquid with bond defects

The magnetic susceptibility of the gapped quantum spin liquid compound (C${}_4$H${}_{12}$N${}_2$)Cu${}_2$Cl${}_6$ and its chemically disordered derivatives (C${}_4$H${}_{12}$N${}_2$)Cu${}_2$(Cl${}_{1-x}$Br${}_x$)${}_6$ are systematically studied in magnetic fields of up to 45 T, as a function of Br concentration. The corresponding field-temperature and field-concentration phase diagrams are determined. Measurements on the disorder-free parent compound are not fully consistent with previously published results by other authors. The effect of Br/Cl substitution on the magnetic properties is superficially similar to that of finite temperature. However, important differences are identified and discussed with reference to the previously studied magnetic excitation spectra.

Figure 1

(a) Dynamic susceptibility, $\chi \left(H\right)$ of PHCC at fields up to 14 T from $T=2$ K to 4 K, measured in $\mathrm{H}\parallel \mathrm{c}$ orientation. (b) Temperature dependence of magnetization $M\left(T\right)$ at constant fields. Black hollow circles indicate positions of $M\left(T\right)$ minima. (c) Measured $H-T$ phase diagram of PHCC. Symbols correspond to peaks in $C\left(H\right)$ (hollow triangles),[16] $C\left(T\right)$ (filled triangles),[16] $\chi \left(H\right)$ (squares), and dips in M(T) (circles). Data from Ref. 19 are shown by hollow and filled star symbols corresponding to specific heat and susceptibility anomalies, respectively. The error bars indicate the largest uncertainty found from Ref. 19 for the temperature range plotted here. The dashed line is a guide to the eye.

Figure 2

Relative increase of lattice parameters and unit cell volume (a), and Br/Cl occupancies at the three unique positions in unit cell (b), as a function of nominal Br concentration in PHCX. Thin lines are guide to the eye and indexes refer to Cl position as shown in (c). The solid orange line is a linear fit to the average Br occupancy at Cl sites shown by orange circles. (c) A projection of the Cu${}_2$Cl${}_6$ layers onto a plane perpendicular to the crystallographic $b$ axis in the structure of PHCC. Blue filled circles are the magnetic Cu${}^{2+}$ ions. Shaded circles correspond to three crystallographically unique halide ion positions.

Figure 3

Dynamic susceptibility of PHCX at $T=2$ K for 0 to 7.5% Br content up to 14 T applied in $\mathrm{H}\parallel \mathrm{c}$ orientation. Arrows indicate the local susceptibility maxima.

Figure 4

Magnetic susceptibility at fields below the critical field of three-dimensional ordering. Blue triangles, red circles, and green squares correspond to ac susceptibility values shown in Fig. 3 at 0, 4, and 8 T fields, respectively. The solid line is a guide for the eye.

Figure 5

Magnetic susceptibility of PHCX measured at 1.5 K in pulsed fields for several Br concentrations. The magnetic field was applied in $\mathrm{H}\parallel {\mathrm{a}}^{*}$ orientation.

Figure 6

False color map of magnetic susceptibility of PHCX plotted vs magnetic field and nominal Br content. Triangles and circles indicate positions of susceptibility maxima in pulsed field and ac measurements, respectively. Squares indicate the critical fields obtained from specific heat measurements in Ref. 16. Lines are guide to the eye.