Fig. 3

A coherent, longitudinal interchain mode in Yb₂Pt₂Pb. a The field-temperature phase diagram of Yb₂Pt₂Pb deduced from specific heat measurements (see Supplementary Note 3). Symbols representing phase lines of the low field AFM order (red), gapped phase when k_BT < Δ_S (blue), and second, weaker order (green) are obtained from the magnetic field dependence of the magnetization along the (110) direction at fixed temperatures. Refer to Fig. 2a for an example. Not all of the field-induced AFM phases observed in the magnetization are shown. b–d The magnetic excitation spectrum along the q_HH direction of reciprocal space measured at T = 0.1 K and μ₀H = 1.0 T (b), 1.5 T (c), and 1.7 T (d), summed over 0 ≤ q_L ≤ 2 rlu. The fitted dispersion of the interchain mode is shown (white circles), as well as fits to the expression described in the main text (red lines). The mode dispersion and fits are only shown for q_HH > 0 for clarity (see Supplementary Note 4). The continuum boundary appears at 2Δ_M³³ (white dashed line). e Example cuts of the energy dependence at q_HH = 0.4 rlu measured at B = 1.0 (red) and 1.5 T (green). Fits are described in the text. The mode dispersions shown in b–d are extracted from such fits. (Inset) The integrated intensity of the scattering over the energy of the interchain mode extracted from the fits is shown in parts b–d as a function of momentum q_L along the chain. Magnetic fields of 1.0 T (red), 1.5 T (black), and 1.7 T (blue) are offset for clarity. q_L = 1±2k_F is shown at each field (gold stars). f The polarization of the excitations follows the projection onto the scattering vector q of the magnetic moments contributing to the scattering, indicating that all observed excitations are longitudinal (see Supplementary Note 5). Fields and integration ranges are given in the figure legend; the calculated polarization was averaged within the corresponding q_L integration range. Error bars represent one standard deviation and where not visible are smaller than symbol size