Fig. 2: Evidence for nonreciprocal directional dichroism.

a Absorption coefficient (A) spectra (k_X > 0, E^ω||Y) at 4.2 K. The blue- and the red-colored data were obtained after ME cooling procedure with E_Z = +100 kV m⁻¹ and −100 kV m⁻¹, respectively, and μ₀H_Y = +0.15 T. The inset shows an experimental geometry. b Difference absorption spectra, ΔA = A(+100 kV/m) − A(−100 kV/m), for k_X > 0 (purple) and k_X < 0 (dark yellow). c ΔA spectra at various temperatures above and below T_N = 44 K. d The temperature dependence of ΔA at 1.65 eV, where ΔA takes the maximum in the spectra. In (a–d), the cooling electric and magnetic fields applied during the ME cooling were removed before each measurement. e Schematic hole-energy spectrum of Cu(3d)-O(2p) bonding molecular orbitals of the square-planar CuO₄⁶⁻ unit partly reproduced from ref. [³⁸]. a(z²) is omitted for clarity. An electric-dipole (magnetic-dipole) transition with a Y-(Z-)axis electric (magnetic) field of light, allowed in C4 symmetry, is denoted by a green (red) arrow. A spin–orbit coupling term l_xs_x + l_ys_y hybridizes b(xy) and e(xz) [e(yz)].