Fig. 1: Double Bose–Einstein-condensation (BEC) dome in S = 3/2 quantum magnet.
From: Double dome structure of the Bose–Einstein condensation in diluted S = 3/2 quantum magnets
a Energy diagram of the S = 3/2 spin site with easy-plane type single-ion (SI) anisotropy \(D{\hat{S}}_{z}^{2}\,(D \, > \, 0)\) in a magnetic field along the z-direction. The ground state mainly consists of single-site states \(\left|{S}_{z}=\pm 1/2\right\rangle\) in AFMI phase, and \(\left|{S}_{z}=1/2\right\rangle\) and \(\left|{S}_{z}=3/2\right\rangle\) in AFMII phase, indicated by the dark blue colored line. Above Hc3, as well as between Hc1 and Hc2, the ground state is a direct product of the single-site ground state at that field (i.e., \(\left|{S}_{z}=1/2\right\rangle\) and \(\left|{S}_{z}=3/2\right\rangle\), respectively), indicated by the pink and red-colored lines. Antiferromagnetic interaction J(>0) determines the width of magnon bands and critical fields, as schematically depicted in the inset. Each field region can effectively be described by spin Hamiltonian for Seff = 1/2 or Seff = 1 [see the discussion on Fig. 5d for the latter]. b Schematics of the phase diagram for three different strengths of J(>0). In a weakly interacting regime, two BEC domes appear, separated by the intermediate PLD phase, as shown by the dark-blue color. As J increases, two domes become larger and merge with each other at low temperature, as depicted by the light-blue color. Finally, in the strongly interacting regime, two domes merge entirely, indicated by the gray color.
