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

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