Spin-polarized scanning tunneling microscopy (SP-STM) experiments in 2012 demonstrated that the spin degree of freedom contributes measurably to friction when a magnetic cobalt (Co) atom is dragged across a manganese monolayer on tungsten, W(110): the adatom spin flips between nearly antiparallel Mn rows, adding a dissipation channel that raises the simulated average friction by about 60%, and magnetic exchange coupling to the tip makes the threshold lateral forces site-dependent. The supporting Monte Carlo simulations replaced the true magnetic ground state — a left-handed cycloidal spin spiral rotating by about 173° between adjacent Mn rows and completing a full precession over roughly 45 rows (period of order 12 nm) — with a commensurate row-wise antiferromagnet, and the experiment delivered only qualitative and order-of-magnitude comparisons. The open problem is to give a quantitative account of spin friction on the real noncollinear template: how the angular dependence of the spin-dependent friction forces and the spatial variation of the manipulation-cell asymmetry change when the true spin-spiral texture is included, together with an experimental quantification of the dissipated energy per jump and of absolute lateral forces resolved simultaneously with the spin configuration. These are the prerequisites for assessing how far the identified spin-friction mechanisms — spin-flip dissipation, exchange-dependent threshold asymmetries, and the non-monotonic average friction versus tip–adatom exchange strength — generalize, in line with the paper's expectation that spin friction is "a general phenomenon occurring in a large class of systems". A quantitative account of spin friction on the real noncollinear template has not yet been reported.

Background

Friction between sliding surfaces ultimately arises from dissipative microscopic processes at contacting atoms, and scanning probe methods make it possible to study these processes one atom at a time — the field called nanotribology. In low-temperature scanning tunneling microscopy (STM), an adsorbed atom can be laterally manipulated: the attractive force of the tip apex holds the atom at one adsorption site until, at a characteristic threshold lateral force, it hops ("slips") to the next site; the energy lost in these stick–slip cycles is the friction. For nonmagnetic systems, experiments had already separated electronic from phononic dissipation (for example, friction drops when a metal becomes superconducting), and lateral forces for moving single atoms were measured at the few-hundred-piconewton level (Ternes et al., Science 319, 1066 (2008)). Whether the spin degree of freedom of magnetic atoms contributes to friction at the atomic scale was first demonstrated directly by Wolter et al. (Physical Review Letters 109, 116102 (2012)).

The experiment used spin-polarized STM (SP-STM), in which a ferromagnetic tip has a preferred magnetization so that the tunneling current depends on the relative orientation of tip and sample magnetization. Single Co adatoms were manipulated at T=8 KT=8\ \mathrm{K} across a monolayer of Mn on W(110). This Mn monolayer is a classic noncollinear magnetic surface: spin–orbit coupling in the tungsten substrate induces a Dzyaloshinskii–Moriya interaction (DMI, an exchange term that favors a fixed handedness of rotation between neighboring spins), so the ground state is a single-handedness cycloidal spin spiral — spins rotating in a plane containing the surface normal — propagating along the [11ˉ0][1\bar{1}0] direction with adjacent atomic rows rotating by about 173°, nearly antiferromagnetic row-wise, and completing a full precession over roughly 45 rows (period of order 12 nm); the spiral state persists up to at least 300 K (Bode et al., Nature 447, 190 (2007); Honolka et al., Physical Review B 103, 174419 (2021)). Locally the surface therefore looks like a row-wise antiferromagnet: rows of Mn moments alternating between nearly parallel and nearly antiparallel to any fixed axis.

Manipulation images taken with the spin-polarized tip showed an alternating pattern: the apparent height and the size of the "manipulation cell" (the tip-travel distance between adatom jumps) alternated from site to site, tracking whether the underlying Mn rows were magnetically parallel or antiparallel to the tip. A Metropolis Monte Carlo model — chemical binding represented by Morse potentials, magnetic coupling by pairwise Heisenberg exchange J S1⋅S2J\,\mathbf{S}_1\cdot\mathbf{S}_2 with surface coupling JSurf≈75 meVJ_{\rm Surf}\approx 75\ \mathrm{meV} per Mn nearest neighbor and variable tip–adatom coupling JTipJ_{\rm Tip}, the adatom position and spin relaxed after each tip increment — reproduced the alternation, and simulated tunneling currents from the spin-polarized Tersoff–Hamann approximation (a standard approach in which the current is computed from the vacuum charge density, here with tip and sample polarizations P=0.35P=0.35) matched the measured contrast. The model yielded three quantitative results: (i) threshold lateral forces of order 10−10 N10^{-10}\ \mathrm{N}, comparable to earlier measurements for Co on Pt(111), but asymmetric between the two jump directions (up to roughly a factor of two in the strong-exchange regime); (ii) an additional dissipation channel when the Co spin flips at each jump to follow the local Mn magnetization, raising the average friction force ⟨Fx⟩=EDiss/np\langle F_x\rangle = E_{\rm Diss}/np by about 60% relative to a nonmagnetic adatom at JTip=0J_{\rm Tip}=0; and (iii) a non-monotonic dependence of the average friction on JTipJ_{\rm Tip}, including a locking regime near JTip≈180 meVJ_{\rm Tip}\approx 180\ \mathrm{meV} where the adatom spin follows the tip rather than the surface. To keep the simulation tractable, the true spiral was replaced by a perfect row-wise antiferromagnet (180° between rows). Conceptually, this spin-flip dissipation connects to magnetic friction found earlier in classical spin models (Kadau et al., Physical Review Letters 101, 137205 (2008); Fusco et al., Physical Review B 77, 174426 (2008)), but the 2012 work was the first atomic-scale experimental realization.

Problem Statement

The unresolved problem, posed by the limitations of the 2012 spin-friction experiment itself, is to replace the row-wise antiferromagnetic surrogate and the qualitative, order-of-magnitude comparisons with a quantitative account of spin friction on the real noncollinear Mn/W(110) spin-spiral surface:

(1) Theory: determine quantitatively how the true noncollinear spin texture — a cycloidal spiral with about 173° rotation between adjacent Mn rows and a precession period of roughly 45 rows (of order 12 nm) — modifies the angular dependence of the spin-dependent friction forces (the variation of lateral forces and jump threshold forces with the relative orientation of tip magnetization, adatom spin, and local Mn moments, and with sliding direction relative to the spiral) and the spatial variation of the manipulation-cell asymmetry, relative to the row-wise antiferromagnetic approximation used in the original Monte Carlo model; and, correspondingly, how the identified spin-friction mechanisms — spin-flip dissipation at jumps, exchange-dependent threshold asymmetries, and the non-monotonic average friction versus tip–adatom exchange strength including the spin-locking regime near JTip≈180 meVJ_{\rm Tip}\approx 180\ \mathrm{meV} — are preserved or changed.

(2) Experiment: systematically quantify the dissipated energy per adatom jump and the absolute lateral forces, resolved simultaneously with the local spin configuration, going beyond the qualitative and order-of-magnitude comparisons of the original work.

The problem is posed as the theoretical determination (1) together with the experimental quantification (2). The experimental component requires a quantitative determination of the dissipated energy per adatom jump and of the absolute lateral forces, resolved simultaneously with the local spin configuration; where such spin-resolved force measurements are not yet available, that determination takes the form of a concrete measurement protocol and the signatures it should observe.

These two components share one scientific objective — a mechanism-level, quantitative account of spin-dependent dissipation in atomic-scale motion on the noncollinear magnetic template. Both arise from limitations the 2012 paper itself states: the row-wise antiferromagnetic surrogate adopted in the Monte Carlo model "to reduce complexity" in place of the true spin spiral, and the fact that "the variation in dissipated energy and threshold forces cannot directly be extracted from such an image", which left the experiment with qualitative and order-of-magnitude comparisons. Beyond the anchoring Mn/W(110) system, the paper's only generality statement is the expectation that spin friction is "a general phenomenon occurring in a large class of systems"; a quantitative account on the real noncollinear template is the prerequisite for assessing how far the identified mechanisms extend, but no systematic multi-system assessment, and no restriction to a particular material, geometry, or numerical threshold beyond the anchoring system, is imposed as a deliverable.

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