Extended Data Fig. 5: The magnon dispersion by the linear spin-wave theory.
From: Giant magnetocaloric effect in spin supersolid candidate Na2BaCo(PO4)2
a Magnon dispersion Ek calculated by the linear spin-wave theory at the supersolid transition \({B}_{{\rm{c3}}}^{* }\simeq 1.69\)(6) T, and the dashed box in a is expanded in b. The easy-axis TLAF model simulated here use the effective parameters, i.e., Jz/Jxy = 1.68, with two gapless quadratic modes at the K point. They enhance the low-energy density of states and give rise to notable entropic effect at low temperature. The results indicate a quantum critical point (QCP) with dynamical exponent z = 2. Since two order parameters, the solid order associated with lattice rotational \({{\mathbb{Z}}}_{3}\) symmetry breaking and the superfluid order with U(1) spin symmetry breaking, both vanish at the same QCP (c.f., Fig. 3b in the main text), we argue that there may exist an emergent O(4) symmetry at the QCP that include the \({{\mathbb{Z}}}_{3}\times \) U(1) as its subgroup.
