Fig. 5: Beyond mean-field approach and randomness effect.
From: Double dome structure of the Bose–Einstein condensation in diluted S = 3/2 quantum magnets
a, b Low-temperature phase diagram for x = 0.25 and 0.375, respectively. The latter contains provisional suggestions on Bose-glass (BG) and Mott-glass (MG). The fittings to the power-law TN ∝ ∣H − Hc∣φ, are also shown by red dashed lines. The predicted values of (1/2)Hcross and (4/7)Hcross from the previous reports23, 28 are shown as black triangles (see text). Inset shows the temperature dependence of εa, which is used to obtain the ordering temperatures (red triangles). c Schematics of effective S = 1 XXZ model with SI easy-plane anisotropy \(D{\hat{S}}_{z}^{2}\) on a square-lattice. Original multiplet, Sz = 3/2, 1/2, −1/2 for S = 3/2 are mapped on to S = 1, Sz = 1, 0, −1 states [see Fig 1a and text]. Magnetic field hz and magnetic interaction JXXZ in S = 1 model corresponds to D + nJ/2 and 1.74J in original S = 3/2 model, respectively. d Ground state magnetic phase diagram as a function of x for diluted S = 1 XXZ model at hz = 0. Line for each D/JXXZ is reproduced from Fig. 1 in ref. 40. x* ≈ 0.35 is the critical value for D/JXXZ ≈ 3, which corresponds to BCGO.
