Magnetic-Field-Induced Condensation of Triplons in Han Purple Pigment ${\mathrm{B}\mathrm{a}\mathrm{C}\mathrm{u}\mathrm{S}\mathrm{i}}_2{\mathrm{O}}_6$

Besides being an ancient pigment, ${\mathrm{B}\mathrm{a}\mathrm{C}\mathrm{u}\mathrm{S}\mathrm{i}}_2{\mathrm{O}}_6$ is a quasi-2D magnetic insulator with a gapped spin dimer ground state. The application of strong magnetic fields closes this gap, creating a gas of bosonic spin triplet excitations. The topology of the spin lattice makes ${\mathrm{B}\mathrm{a}\mathrm{C}\mathrm{u}\mathrm{S}\mathrm{i}}_2{\mathrm{O}}_6$ an ideal candidate for studying the Bose-Einstein condensation of triplet excitations as a function of the external magnetic field, which acts as a chemical potential. In agreement with quantum Monte Carlo numerical simulations, we observe a distinct lambda anomaly in the specific heat together with a maximum in the magnetic susceptibility upon cooling down to liquid helium temperatures.

Figure 1

(a) ${\mathrm{C}\mathrm{u}}^{2+}$-dimer plane in ${\mathrm{B}\mathrm{a}\mathrm{C}\mathrm{u}\mathrm{S}\mathrm{i}}_2{\mathrm{O}}_6$ in a square lattice arrangement. $J$ and $J^{\prime }$ are the intradimer and interdimer exchange constants. (b) Evolution of the isolated dimer spin singlet and triplet with an applied magnetic field $H$. (c) Partially occupied hard core boson lattice. Occupation (chemical potential) is given by the external magnetic field. (d) Transmission-light picture of a ${\mathrm{B}\mathrm{a}\mathrm{C}\mathrm{u}\mathrm{S}\mathrm{i}}_2{\mathrm{O}}_6$ single crystal.

Figure 2

(a) Magnetization vs field at different temperatures from 0.4 to 40 K, measured in both 65 T short-pulse and 45 T midpulse capacitor driven pulsed magnets. (b) Magnetic susceptibility vs temperature from measurements in (a), and from our model using a quantum Monte Carlo algorithm.

Figure 3

Specific heat vs temperature at constant magnetic fields $H$. A low temperature $\lambda$ anomaly is evident at $H\ge 28\mathrm{T}$. The anomaly first moves to higher temperatures with increasing magnetic fields, it reaches a maximum at $H=36\pm 1\mathrm{T}$, and then decreases for $37<H<45\mathrm{T}$. Inset: specific heat vs $T$ at $H=37\mathrm{T}$ after subtraction of a small contribution due to the $S^z=0$ triplet level only relevant at higher temperatures, and phonons. Also displayed is the result of our Monte Carlo calculation.

Figure 4

Left $y$ axis: magnetization normalized to the saturation value ($M/M_{\mathrm{s}\mathrm{a}\mathrm{t}}$) vs magnetic field along the $c$ axis, measured at 1.5 K (red line). Results for the model discussed in the text (green line). Right $y$ axis: transition temperature from specific heat vs temperature, magnetocaloric effect (MCE) and magnetization vs field data. Black lines are the sample temperature measured while sweeping the magnetic field quasiadiabatically.