Fig. 2: Detecting surface magnetization from the tunnelling spectra.

a, Sketch of the crystal structure of the top layers and magnetization of the bulk (M_B) and surface layer (M_S). In the ferromagnetic ground state²⁶, both M_S and M_B point in the same direction parallel to the c axis (left). When the direction of one of them (here M_B) is flipped (right), the exchange force results in an increase in the distance between the surface trilayer and the bulk (increase in the distance is exaggerated). b, Tunnelling spectra measured for parallel (black; M_S↑↑M_B) and antiparallel (purple; M_S↑↓M_B) alignment of the magnetizations of the bulk and surface layer. The spectra are normalized (norm.) by the value of g(V) at V = 8 mV. Two peaks are observed just below the Fermi level: P_I and P_II. The energy of peak P_I (E_PI) depends sensitively on the relative magnetization of the bulk and surface layer. It is 750 μV higher in energy when M_B and M_S are antiparallel compared with when they are parallel. The energy of peak P_II (E_PII) remains the same. c, Change in M_S and M_B observed in the tunnelling spectra taken between 0.41 T and –1.06 T, after having polarized the overall magnetization with B_z = 1.3 T. Triangles indicate P_I, as in b. The energy of peak P_I jumps abruptly to higher energies when M_B switches between –0.13 T and –0.17 T, resulting in M_S and M_B being antiparallel. The peak jumps back when the surface layer switches between –0.96 T and –1.06 T. The spectra are offset vertically for clarity. d, Energy E_PI of peak P_I as a function of field B_z, taken by cycling the field from 1.3 T to –1.06 T and then back to 1.05 T. The direction of the triangles indicates the direction of the ramp of the field. P_I changes abruptly at –0.16 T and –0.98 T when ramping to negative fields, and at 0.20 T and 0.96 T when ramping to a positive field. e, Energy E_PI as a function of field B_z, taken by cycling B_z between –0.25 T and +0.25 T after aligning M_B and M_S with a field of B_z = –1 T. All data are taken at T = 80 mK (set-point conditions: V_set = 10 mV, I_set = 450 pA; lock-in modulation amplitude: V_L = 125 μV). The points in d and e were extracted from a fit of two Lorentzian peaks to the spectra and the error bars are the 95% confidence intervals. The red and blue arrows illustrate the orientation of local moments at the surface (top line) and bulk (bottom line) along the cycle.