Discrete Hall resistivity contribution from N{e}el skyrmions in multilayer nanodiscs

Discrete Hall resistivity contribution from Néel skyrmions in multilayer nanodiscs Katharina Zeissler1*, Simone Finizio2, Kowsar Shahbazi1, Jamie Massey1, Fatma Al Ma’Mari1,3, David M. Bracher2, Armin Kleibert2, Mark C. Rosamond4, Edmund H. Linfield4, Thomas A. Moore1, Jörg Raabe2, Gavin Burnell1, and Christopher H. Marrows1 1School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, United Kingdom
2Swiss Light Source, Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland 3Department of Physics, Sultan Qaboos University, 123 Muscat, Oman 4School of Electronic and Electrical Engineering, University of Leeds, Leeds LS2 9JT, United Kingdom
*Correspondence to k.zeissler@leeds.ac.uk

Magnetic skyrmions are knot-like quasiparticles. They are candidates for non-volatile data storage in which information is moved between fixed read and write terminals. Read-out operation of skyrmion-based spintronic devices will rely upon electrical detection of a single magnetic skyrmion within a nanostructure. Here, we present Pt/Co/Ir nanodiscs which support skyrmions at room temperature. We measured the Hall resistivity whilst simultaneously imaging the spin texture using magnetic scanning transmission x-ray microscopy (STXM). The Hall resistivity is correlated to both the presence and size of the skyrmion. The size-dependent part matches the expected anomalous Hall signal when averaging the magnetisation over the entire disc. We observed a resistivity contribution which only depends on the number and sign of skyrmion-like objects present in the disc. Each skyrmion gives rise to 22±2 nΩ cm irrespective of its size. This contribution needs to be considered in all-electrical detection schemes applied to skyrmion-based devices. The non-trivial topology of a skyrmion leads to an improved stability against external perturbations1, 2, 3, 4, 5. The topology of the spin texture is characterised by the skyrmion winding number S, which takes integer values6. Mathematically, S is given by 1, 𝑆= 1 4𝜋∫𝒎∙( 𝜕𝒎 𝜕𝑥× 𝜕𝒎 𝜕𝑦) 𝑑𝑥𝑑𝑦, (1) where m is a unit vector pointing along the local magnetisation direction. Individual cylindrical skyrmions have a winding number of ±1. S is an integer invariant for all mutually continuously deformable skyrmions. Hence, the associated topological Hall effect is also invariant under continuous deformation. A consequence of this, in the context of Néel skyrmions, is that the winding number is magnetic domain size and shape independent as long as the domain is wrapped by an unbroken Néel domain wall 1. In multilayer films the formation of Néel type skyrmions is energetically favourable due to perpendicular magnetic anisotropy, interface Dzyaloshinskii-Moriya and dipolar interaction 7, 8 9, 10, 11. In thin film multilayers they are stable at room temperature 11, 12, 13
and can be moved using spin-torques 14, 15, 16, 17, 18, with the expectation that the current densities needed can eventually be as low as the 106-107 A/m2 observed in cryogenic measurements on single crystal materials 19, 20, 21. This permits very low energy manipulation of information22. Whilst current- induced movement of skyrmions is needed to manipulate the encoded information, electrical detection of single skyrmions is essential to read back the stored information.
Here we have measured the Hall resistance of Pt/Co/Ir multilayer discs of 1 µm diameter while simultaneously imaging the magnetic configuration within it using STXM with x-ray magnetic circular dichroism (XMCD) contrast. STXM is a high resolution imaging technique which is magnetically non- invasive. The conclusions that we draw are twofold. The variation in skyrmion size with field leads to 2

a signal that matches that expected from the anomalous Hall effect tracking the change in magnetisation. Furthermore, an additional magnetisation-independent Hall signal of 22±2 nΩ cm associated with the presence, number, and sign of individual skyrmion-like objects was found. Its size is comparable to the anomalous Hall signal for skyrmions with a radius smaller than 150±30 nm. This skyrmion number-dependent resistivity cannot qualitatively be explained with conventional Berry phase theories of the topological Hall effect, suggesting that further theoretical development is needed.
Skyrmions and skyrmion-like domains were stabilised in an electrically connected 1 μm diameter discs from [Pt/Co/Ir]x10 multilayer stacks (see supplementary information , Fig. S1, for device, magnetic and electrical information). A current and field nucleation protocol was used to nucleate an integer number of skyrmions in the disc (see methods section and supplementary information, Fig. S2 for details). The Hall resistance was measured as a function of out-of-plane field. From the XMCD contrast images the normalised magnetisation, Mz/MSat, was computed by counting the number of black, white, and grey pixels in the disc and assigning them

…(Full text truncated)…