Fig. 4

Magnetic-order-induced frequency difference for phonon P₂. a Polarized Raman spectra of bulk NiPS₃ as a function of the temperature. b Peak positions of P₂ and P₆ obtained in parallel (black squares, \({P}_{\mathrm{2}}^{{\mathrm{||}}}\) and \({P}_{\mathrm{6}}^{{\mathrm{||}}}\)) and cross (red circles, \({P}_2^ \bot\) and \({P}_6^ \bot\)) polarization configurations as a function of the temperature. c Temperature dependences of phonon frequency difference ΔP₂ (\({\mathrm{\Delta }}P_2 \equiv \left| {P_{\mathrm{2}}^{{\mathrm{||}}} - P_2^ \bot } \right|\), blue circles) and susceptibility of bulk NiPS₃. The error bars indicate experimental uncertainties. d Schematics of lattice-vibration patterns associated with A_g and B_g modes near ~180 cm^–1. Black arrows indicate the direction of atomic displacement and thick red arrows indicate spin orientations of Ni atoms below T_N