Fig. 2: Phase diagram and magnetic excitations in YbAlO₃.

a Phase diagram of YbAlO₃ reconstructed from specific-heat and magnetization measurements for B∥[100]. Colored areas show three magnetically ordered phases; red points at low temperatures and B ≈ 0.7 T mark the position of the M_S/3 plateau. Gray dotted lines indicate crossovers between Luttinger liquid, quantum critical (QCP), and field-polarized regimes. Horizontal and vertical error bars correspond to uncertainties in the determination of the peak positions for constant-temperature and constant-field scans, respectively. b Normalized magnetization, M/M_S, measured at T = 0.05 K, and magnetization curves calculated using (QMC). The red curve shows noisy features within the spin-density wave (SDW) phase due to finite-size errors in the calculations. (c1–f1) Energy-momentum cuts along the (00L) direction measured at T = 0.05 K and in different magnetic fields (shown in each panel). All spectra show no gap within the experimental resolution of 50 μeV. Because the dispersion of magnetic excitations in YbAlO₃ has 1D character, the data were integrated over the whole available range in the orthogonal directions (K = [−2; 2] r.l.u. and H = − [0.3; 0.3] r.l.u.). (c2–f2) ENS maps within the (0KL) plane obtained by integrating the same dataset as in c1–f1 around the elastic position, E = [−0.05; 0.05] meV with H = [−0.05; 0.05]. Red arrows indicate extrinsic Bragg reflections due to the presence of the twin in the sample, which is discussed in detail in Sec. (S1) of the SI. Subtraction of the 2 T data set was applied to all spectra in c1–f2.