Evidence for a conical spin spiral state in the Mn triple-layer on W(001): spin-polarized scanning tunneling microscopy and first-principles calculations

The spin structure of a Mn triple layer grown pseudomorphically on surfaces is studied using spin-polarized scanning tunneling microscopy (SP-STM) and density functional theory (DFT). In SP-STM images a c$(4 \times 2)$ super structure is found. The magnetic origin of this contrast is verified by contrast reversal and using the c$(2 \times 2)$ AFM state of the Mn double layer as a reference. SP-STM simulations show that this contrast can be explained by a spin spiral propagating along the [110] direction with an angle close to $90^\circ$ between magnetic moments of adjacent Mn rows. To understand the origin of this spin structure, DFT calculations have been performed for a large number of competing collinear and non-collinear magnetic states including the effect of spin-orbit oupling (SOC). Surprisingly, a collinear state in which the magnetic moments of top and central Mn layer are aligned antiparallel and those of the bottom Mn layer are aligned parallel to the central layer is the energetically lowest state. We show that in this so-called "up-down-down" ($\uparrow \downarrow \downarrow$) state the magnetic moments in the Mn bottom layer are only induced by those of the central Mn layer. Flat spin spirals propagating either in one, two, or all Mn layers are shown to be energetically unfavorable to the collinear $\uparrow \downarrow \downarrow$ state even upon including the Dzyaloshinskii-Moriya interaction (DMI). However, conical spin spirals with a small opening angle of about $10^\circ$ are only slightly energetically unfavorable within DFT and could explain the experimental observations. Surprisingly, the DFT energy dispersion of conical spin spirals including SOC cannot be explained if only the DMI is taken into account. Therefore, higher-order interactions such as chiral biquadratic terms need to be considered which could explain the stabilization of a conical spin spiral state.