Possible Bose-Einstein condensate of magnons in single-crystalline ${\text{Pb}}_2{\text{V}}_3{\text{O}}_9$

We report the growth and the characterization of single crystals of the $S=1/2$ spin-dimer compound ${\text{Pb}}_2{\text{V}}_3{\text{O}}_9$. Magnetic-susceptibility, torque magnetometry, heat-capacity, and muon-spin-relaxation measurements provide evidence for a field-induced Bose-Einstein condensate of magnons in this system. At low temperatures, the field-dependent phase boundary between the dimerized and the condensed state is well described by the expression $T^{\star }\propto {\left(H-H_{c1}\right)}^{1/\varphi }$, with $\varphi =\left(2.00\pm 0.04\right)$.

Figure 1

(Color online) (a) ${\text{Pb}}_2{\text{V}}_3{\text{O}}_9$ structure and photograph. (b) Temperature dependence of the magnetic susceptibility. Open circles represent experimental data points. The solid line represents the alternating chain fit of Ref. 12. The reciprocal of $\chi$ is displayed in the inset with the solid line representing a Curie-Weiss fit.

Figure 2

(a) Temperature dependence of $C_{\text{P}}\left(T\right)/T$ for ${\text{Pb}}_2{\text{V}}_3{\text{O}}_9$. The solid lines are meant as guides to the eye. (b) Temperature dependencies of torque, in arbitrary units, for varying applied magnetic fields. $T^{\star }$ is determined from the second derivatives.

Figure 3

(a) (Color online) Asymmetry plots of the TF muon-spin-relaxation spectrum for single-crystalline ${\text{Pb}}_2{\text{V}}_3{\text{O}}_9$ at applied fields of 4.5 and 1.0 T at 0.02 K. (b) Relaxation as a function of field for $T=0.02\text{K}$, $T=0.70\text{K}$, and $T=4.0\text{K}$.

Figure 4

Temperature-field phase boundary. In this range of temperatures the error bars in the specific heat, used to determine $T_c$, are smaller than the actual size of the symbols. The spin-gapped (SG), BEC of magnons, and fully polarized states are shown. The low-temperature behavior of the phase boundary between SG and BEC states is described by the power law $T^{\star }\propto {\left(H-H_{c1}\right)}^{1/\varphi }$ with $\varphi =2.00\left(4\right)$.