Bose-Einstein condensation of triplons close to the quantum critical point in the quasi-one-dimensional spin-$1/2$ antiferromagnet NaVOPO${}_4$

Abstract

Structural and magnetic properties of a quasi-one-dimensional spin-$1/2$ compound NaVOPO${}_4$ are explored by x-ray diffraction, magnetic susceptibility, high-field magnetization, specific heat, electron spin resonance, and ${}^{31}$P nuclear magnetic resonance measurements, as well as complementary \textit{ab initio} calculations. Whereas magnetic susceptibility of NaVOPO${}_4$ may be compatible with the gapless uniform spin chain model, detailed examination of the crystal structure reveals a weak alternation of the exchange couplings with the alternation ratio $\alpha \simeq 0.98$ and the ensuing zero-field spin gap ${\Delta }_0/k_{\mathrm{B}}\simeq 2.4$~K directly probed by field-dependent magnetization measurements. No long-range order is observed down to 50\,mK in zero field. However, applied fields above the critical field $H_{c1}\simeq 1.6$\,T give rise to a magnetic ordering transition with the phase boundary $T_{\mathrm{N}}\propto (H-H_{c1}{)}^{\frac{1}{\varphi }}$, where $\varphi \simeq 1.8$ is close to the value expected for Bose-Einstein condensation of triplons. With its weak alternation of the exchange couplings and small spin gap, NaVOPO${}_4$ lies close to the quantum critical point.

15 pages, 15 figures, 2 tables