Origin of temperature and field dependence of magnetic skyrmion size in ultrathin nanodots

Abstract

PACS:Understanding the physical properties of magnetic skyrmions is important for fundamental research with the aim to develop new spintronic device paradigms where both logic and memory can be integrated at the same level. Here, we show a universal model based on the micromagnetic formalism that can be used to study skyrmion stability as a function of magnetic field and temperature. We consider ultrathin, circular ferromagnetic magnetic dots. Our results show that magnetic skyrmions with a small radius-compared to the dot radius-are always metastable, while large radius skyrmions form a stable ground state. The change of energy profile determines the weak (strong) size dependence of the metastable (stable) skyrmion as a function of temperature and/or field. These results can open a path toward the design of optimal materials for skyrmion based devices.2 Non-linear localized excitations have attracted the attention of physicists for a long time.Such excitations, including solitary waves or solitons, play an important role in optics, quantum field theory, condensed matter and other fields. It is sometimes possible to associate integer numbers (topological charges) to the solitons, which are preserved in their dynamics. Topologically non-trivial magnetization configurations in ferromagnets, such as domain walls, vortices, and skyrmions are currently the focus of a lot of research activity. These spin textures are also candidates for nanoscale device applications-computational paradigms, magnetic storage and programmable logic-due to their small size [1][2][3][4][5][6][7][8][9][10][11][12][13].Skyrmion solutions were obtained first by Skyrme in the non-linear field theory [14].Subsequently chiral skyrmions were predicted [15], and discovered experimentally in noncentrosymmetric cubic B20 compounds [16][17][18][19][20] which permit an antisymmetric anisotropic interaction, namely the Dzyaloshinskii-Moriya interaction (DMI). This arises from a relativistic correction and relies on spin-orbit interactions [21,22]. Recent efforts have focused on materials with interfacial DMI-especially ultra-thin transition metal/heavy metal multilayers with large spinorbit coupling such as Co/Pt and Co/Ir [8,23,24]. The DMI, which corresponds to Lifshitz invariants in the micromagnetic energy functional, is necessary to yield axisymmetric skyrmions in ultrathin magnetic elements and the chiral skyrmions can be further stabilized by external magnetic field [8,23,24]. Temperature is usually considered to be detrimental to skyrmion stability, leading to either the transformation of the skyrmion state into a more energetically favorable state [25] or to nucleation of multiple skyrmions and labyrinth domains [8,23,24]. In addition, recent roomtemperature experiments with an external out-of-plane magnetic field [8,23], showed a strong nonlinear dependence of the skyrmion radius on the external field strength pointing out the key role of the external field. Here, we develop a theoretical approach to skyrmion stability based on minimization ...

Geometrically Tailored Skyrmions at Zero Magnetic Field in Multilayered Nanostructures

“…Our comprehensive investigation of confined Néel skyrmions offers a firm foundation tailor-made for such efforts. Second, the manifestly distinct trends in skyrmion configuration and size with variation of κ go beyond existing predictions [5,24,27,28]. While recent studies have incorporated the effects of granularity [32,41], interlayer coupling [6], and dipolar interactions [28,37], we posit that future studies of confined skyrmions would benefit from harnessing their differing behavior with thermodynamic stability.…”

“…6(b)] and H [ Fig. 6(c)] in the context of extensive predictions of these trends [5,6,24,27,28,37]. Figure 6(b) shows that the normalized size, d m sk /w, reduces monotonically with increasing D/A, with a sharp jump at κ ∼ 1.…”

“…In this light, numerous theoretical studies have examined the formation and manipulation of single Néel * anjan@imre.a-star.edu.sg † christos@ntu.edu.sg skyrmions in ultrathin nanodots, and their scalability with geometric and magnetic parameters [5,[24][25][26][27][28]. Meanwhile, experimental efforts on magnetic nanostructures have predominantly focused on Bloch skyrmions in lowtemperature helimagnets [29,30], and chiral skyrmion bubbles (larger than 150 nm), the latter stabilized by long-range dipolar interactions [7,8,31,32].…”

Diameter-independent skyrmion Hall angle observed in chiral magnetic multilayers

“…, to the spin current that exerts spin-torques on the skyrmion, G is the Gilbert damping. The skyrmions experience a velocity component, , towards the edge of the wire 9,18,19 . The skyrmion Hall angle is then given by tan Sky = − / G .…”

Bilayer skyrmion dynamics on a magnetic anisotropy gradient

“…Experimental transport measurements based on such mechanisms showed that high current densities on the order of 10 12 A m −2 are required to achieve practical speeds of about 100 m s −1 [12,13]. The elevated temperatures at such high current densities can drastically reduce the propagation speed of skyrmions while the risk of skyrmion annihilation increases significantly [14][15][16].…”