Skyrmions in magnetic multilayers

TLDR: In this article, the fundamental topological physics underlying these chiral spin textures, the key factors for materials optimization, and current developments and future challenges are discussed, and a few promising directions that will advance the development of skyrmion based spintronics will be highlighted.

About: This article is published in Physics Reports.The article was published on 2017-08-23 and is currently open access. It has received 417 citations till now. The article focuses on the topics: Magnetic skyrmion & Spin engineering.

Figures

Fig. 27. Stabilization of atomic scale magnetic skyrmions in a Fe/Ir(111) bilayer. A-1 illustrates the onset of a four-spin antiferromagnetic exchange interaction that facilitates the formation of a square skyrmion lattice, in sharp contrast to the hexagonal skyrmion lattice in the B20 compounds. Reproduced with permission [124]. Copyright 2011, Nature Publishing Group. (B) Shows topological transport in an inversion asymmetric heterostructure consisting of a layer of nonmagnetic topological insulator and a layer of magnetically doped topological insulator. Shown in 2 is the anomalous Hall measurement in a 7 nm thick Crx(Bi1-ySby)2-xTe3 layer. Shown in 3 is a bilayer of thickness 3nm/5nm and of composition Crx(Bi1-ySby)2-xTe3/(Bi1-ySby)2-xTe3 respectively. Shown in 4 is a bilayer of thickness 2nm/5nm and of the same composition. The measured Hall signal shows the onset of a topological Hall contribution that signifies the chiral spin textures. The associated phase diagram is summarized and presented in the part 5. Reproduced with permission [289]. Copyright 2016, Nature Publishing Group.

Figure 22. Skyrmion Hall angle and accumulation. (A) Phase diagram of the skyrmion Hall angle as a function of the current density and sign of the topological charge, obtained by tracking the motion of several tens of skyrmions in wires of dimension 80 (width) ×100 (length) µm+ patterned from a Ta/CoFeB/TaOx trilayer. In the low current density regime, the skyrmion Hall angle 𝛷 Û exhibits a linear dependence. Further increase of current density 𝑗- > 8 × 10? A/cm+ results in the saturation of the skyrmion Hall angle. By alternating the sign of driving electron current density (±𝑗-) and the sign of topological charge (±𝑄), a phase diagram for the four different regimes was determined. Namely, for a negative topological charge (under positive magnetic fields), regime I(+𝑗-, −𝑄) with positive 𝛷 Û and regime III(−𝑗-, −𝑄) with negative 𝛷 Û were identified by changing the polarity of electron current. For skyrmions with a positive topological charge (under negative magnetic fields) a positive 𝛷 Û in regime II(−𝑗-, +𝑄), and negative 𝛷 Û in regime IV(+𝑗-, +𝑄) were detected. The decrease of the skyrmion Hall angle from 𝛷 Û ≈ 32 ± 2° to 𝛷 Û ≈ 28 ± 2° is demonstrated by increasing the skyrmion diameter from 𝑑 = 800 ± 300 nm (+0.54 mT/-0.52 mT) to 𝑑 = 1100 ± 300 nm (+0.48 mT/-0.46 mT). (B) Polar MOKE microscopy images demonstrating skyrmion (𝑄 = −1) accumulation at the edge of the device (of width 60 µm and length 500 µm). This is achieved by repetitively applying 50 current pulses of duration 50 µs at a frequency of 1 Hz with a current density 𝑗- = −6 × 10? A/ cm+ and an applied field of +0.54 mT. (C) Reversing the magnetic field from positive (+0.54 mT) to negative (-0.52 mT) leads to the accumulation of skyrmions with positive topological charge 𝑄 = +1 at the opposite edge. Reproduced with permission [95]. Copyright 2016, Nature Publishing Group.

Fig. 18. Evolution of complex domain patterns in [Co0.4nm/Pt0.7nm]X multilayers. Shown in the upper panel are the corresponding magnetic force microscopy images acquired after ac demagnetization. The size of each figure is 5 µm2. X denotes the number of repetition. The calculated magnetostatic energy versus domain wall energy is shown in the lower panel of (G), from which a minimum domain size is found around X » 20. Reproduced with permission [228]. Copyright 2007, Elsevier.

Fig. 9. Uniqueness of skyrmions stabilized in magnetic heterostructures with a broken inversion symmetry. (A) illustrates the inversion asymmetric bilayer composing of a HM/FM bilayer where the strong SOC of the HM layer, together with the ultra-thin FM, result in a non-collinear spin chirality determined by the interfacial DMI vector. Reproduced with permission [32]. Copyright 2013, Nature Publishing Group. As a result of this interfacial DMI contribution, Néel-type skyrmions can be stabilized, shown in (B). Its topological representation is further projected onto a unit sphere as a hedgehog shape. A slice across the center of the Néel-type skyrmion, is shown to reveal the presence of spin chirality by placing a mirror in the center of the spin chain. Only by performing a mirror operation can spins on the left and on the right, can be overlapped which thus underlies the name of chiral magnetic skyrmion. Reproduced with permission [189]. Copyright 2015, Nature Publishing Group. (C) illustrates the accompanied spin Hall effect. The strong SOC of HM layer creates a spin dependent scattering that splits the spin-up and spin-down electrons preferentially, which leads to a spin accumulation at the interface, enabling electrical control of the adjacent magnetization dynamics. An oxidized layer can be deposited on top of HM/FM bilayer for protecting stack from further oxidization that degrades the desired properties, and also for breaking inversion symmetry. The marriage of spin-orbit torques and interfacial DMI stabilized skyrmion consequently results in an efficient electrical manipulation of Néel-type magnetic skyrmions. The electron current (𝑗-) induced effective spin-orbit fields (𝐵 Ã), beared by spins on the right and on the left, act constructively, producing a motion of skyrmion with velocity vskyrmion along the same direction, as illustrated in (D). The motion of the skyrmion follows the electron current direction in the case of a negative spin Hall angle (-𝜃 Ã), together with left-handed chirality of Néel-type skyrmion. Reproduced with permission [41]. Copyright 2015, AAAS.

Fig. 13. Performance of magnetic skyrmions in a racetrack. (A) shows micromagnetic simulation results with stabile 10-nm Néel-type skyrmions. In a nanoscale racetrack, the coherent motion of a row of magnetic skyrmions with a velocity of 57 m/s was deterministically produced using a train of current pulses with a current density of 5 ×106 A/cm2. Reproduced with permission [32]. Copyright 2013, Nature Publishing Group. Experimental demonstration using Polar MOKE microscopy images of the motion of a single magnetic skyrmion along a wire in a Ta/ CoFeB/TaOx trilayer, shown in (B). It can be seen that the magnetic skyrmion, with a diameter ≈ 1 μm, is displaced by about 10 μm for each 100-μs long current pulse of amplitude 5×105 A/cm2, which yields a velocity of 0.1 m/s. Reproduced with permission [208]. Copyright 2016, AIP Publishing.

Figure 5 (A) Dependence of 𝐸UVW 𝑚 + (black line) as well as local magnetic moment per atom (red line) averaged over 3𝑑 /5𝑑 interfaces vs. 3𝑑 adlayer, where 𝐸UVW is the DMI energy and 𝑚 is spin magnetic moment. All values are averaged based on the data of 5𝑑 metals from tungsten to platinum. (B) Shown on the left are the filling of 3𝑑 orbitals of the typical transition metal elements guided by Hund’s first rule. On the right is the spin-split band positions of 3𝑑 states with respect to the 5𝑑 state of the W substrate. Reproduced with permission [144]. Copyright 2016, American Physical Society.

Frequently asked questions

Q1. What are the contributions in "Skyrmions in magnetic multilayers" ?

In this review article, the fundamental topological physics underlying these chiral spin textures, the key factors for materials optimization, and current developments and future challenges will be discussed. This review article is organized as follows: 1. Topological physics of magnetic skyrmions 1. 1 Origin of spin topology 1. 2 Real space topological physics In the end, a few promising directions that will advance the development of skyrmion based spintronics will be highlighted. 

Q2. Why does the spin of the conduction electron always follow the spatial distribution of the magnetization vector?

Due to the large Hund’s rule exchange coupling, between conduction electrons and local magnetization vectors, which is generally on the scale of eV, the spin of the former always tries to follow adiabatically the spatial distribution of the latter. 

Q3. What is the role of the Hall effect in the study of skyrmions?

Enhanced topological transport, in particular the topological Hall effect, is also beneficial for efficient electrical readout of magnetic skyrmions, which is a pivotal step towards the future of skyrmion based electronics. 

Q4. How can a magnetization m and topological charge be reversed?

The sign reversal of magnetization 𝒎 and concomitant topological charge can be done by reversing the polarity of the perpendicular magnetic fields. 

Q5. How was the magnetic nanodot used to assess the skyrmion spin texture?

Very recently, a single electron spin in diamond with a nitrogen vacancy center was used as a probe to assess the vectorial spin profile of skyrmion, as well as the associated spin topology [138]. 

Q6. How can the authors study the formation of magnetic skyrmions in the absence of an applied field?

Utilizing the exchange bias generated by an AFM layer, it is then possible to investigate the formation of magnetic skyrmions in the absence of applied field at room temperature. 

Q7. Why are these magnetic skyrmions forming a square lattice?

due to the onset of four-spin antiferromagnetic exchange interactions, these magnetic skyrmions are forming a square lattice, rather than the typically observed triangular lattice. 

Q8. What is the way to generate and delete nanometer-sized skyrmions?

nanometer-sized skyrmions can be generated and deleted both locally and reversibly on demand by a spin-polarized tunneling current (of amplitude 1 nA) from the STM tip. 

Q9. Why is the DMI energy independent of the thickness of the film?

This is because the stray field energy will increase with increasing film thickness whereas the DMI energy is usually independent of the film thickness. 

Q10. What is the directional dependence of the skyrmion bubbles?

This directional dependence suggests that spatially divergent currents and SOTs are most likely responsible for transforming the chiral band domains into magnetic skyrmion bubbles. 

Q11. How can a topologically protected magnetic skyrmion be manipulated?

As previously mentioned, topologically protected magnetic skyrmions in metallic chiral magnets can efficiently be manipulated by a spin transfer torque using the spin-polarized electric current [24, 130]. 

Q12. How has the concept of hybrid skyrmion structure been proposed?

Very recently, a concept of hybrid skyrmion structure has been proposed by patterning magnetic nanodisks onto a B20 skyrmion material, in which the enhanced stability of skyrmion state and suppression of skyrmion Hall effect have been revealed through a micromagnetic simulation study [281]. 

Q13. How can the nanoscale skyrmions be addressed locally?

More interestingly, by passing a vertical current from the STM tip, these nanoscale skyrmions can be addressed locally through spin transfer torques [53]. 

Q14. How does the orientation of the spin plane within the wall affect the stray field energy cost?

The orientation of the spin rotation plane within the wall depends on the stray field energy cost associated with the magnetic domain wall geometry: the width of the domain wall and height of the wall (equivalent to the thickness of the film 𝑡t). 

Q15. Why can't the authors use the evolution of domain width and hence the domain wall surface energy as?

In these systems, due to the competition between the interfacial DMI, magneto-static, Zeeman energy terms, one can use the evolution of domain width and hence the domain wall surface energy as a function of perpendicular magnetic field (𝐻 ) to determine the strength of DMI [42].