Magnetic skyrmions as information carriers

Magnetic skyrmions

Magnetic skyrmions

Chun-pon Chui and Yan Zhou, Department of Physics, The University of Hong Kong; Wenqing Liu, Department of Electronic Engineering, Royal Holloway University of London; and Yongbing Xu, Electronics Department, University of York

Magnetic skyrmions as information carriers Recent theoretical and computational studies of magnetic skyrmions have opened the door to state-of-the-art magnetic storage and processing devices

W

ith the current information explosion, the demand for smaller and faster data storage and processing units is rapidly increasing. As such, the magnetic skyrmion has become a prime candidate and rising star for the future of information transfer technology, drawing great attention in the quantum computation sector. So what is a magnetic skyrmion? In short, it is a spin texture in the form of a particle-like topological soliton. In contrast to a skyrmion that has a spin texture with a quantized topological number, the non-topological magnetic droplet soliton has a topological number equal to zero.

Figure 1: (Left) Time variation of a DMS in the presence of DMI, DDI or Oersted field. The skyrmion experiences both chiral and hedgehog states. Breathing occurs as well, as indicated by the change in the shaded core region. (Right) Uniform precession of a DMS when the DDI or DMI vanishes, though continuous change of spin texture between chiral and hedgehog states still occurs3

This non-topological magnetic droplet was first experimentally observed in 2013, despite having been theoretically predicted 36 years ago. Since then, a large number of papers have focused on both skyrmions and droplet solitons. The focus of this article is the dynamical magnetic skyrmion (DMS), an entirely unexpected, novel and intriguing dynamic magnetic object that combines the properties of droplets and skyrmions. The contents include (1) developing both an analytical theory and micromagnetic simulations for studying the dynamics of droplet solitons and DMS in geometries of finite dimensions, and (2) developing new mechanisms for creating and manipulating magnetic skyrmions in magnetic nanostructures. These novel magnetic nano-objects have tremendous potential for fundamental science and applied research development. The magnetic skyrmions are expected to be promising information carriers in next-generation information storage and processing technologies that are low cost, have ultra-low energy efficiency and enhanced performance.

Analytical theory and simulation of DMS It was believed that the Dzyaloshinskii-Moriya interaction (DMI) or dipole-dipole interaction (DDI) is required for nucleating a magnetic skyrmion.1-2 However, DMS is a more convenient mechanism of skyrmion nucleation because the DMI or DDI are not necessary.3 In doing so, manufacturers of magnetic storage can employ a wider choice of nanomaterials in future memory and processing devices. This proposal has been numerically confirmed by micromagnetic simulation and the findings are highlighted below. At the perimeter of a DMS, a full-circle rotation of local spin occurs

1

16

TECHNOLOGY INTERNATIONAL 2017

2

such that a DMS transforms between the vortex-like texture and the hedgehog texture. After the current and damping of the materials are removed, a DMS can maintain its precession because of the absence of energy dissipation. When the Oersted field created by the spinpolarized current is present, a DMS contracts and expands periodically; it means that a DMS ‘breathes’. When the DMI, DDI or Oersted field diminishes, precession continues but breathing ceases. The breathing process is shown in the left-hand panel of Figure 1, and the disappearance of breathing under vanishing DDI or DMI is shown in the right-hand panel. A DMS is not an excited state of a static skyrmion; rather it is a generic solution of the magnetic state without DMI or DDI. The time variation of a DMS radius and the polar angle of local spins are governed by interactions such as DDI, DMI and Oersted field, material damping, the applied spin torque supplied by a spin-polarized current, and the nanocontact radius used to nucleate a DMS. The radius is easiest to determine when all the interactions are absent, because it would converge to a fixed value. When there is no spin torque, i.e. no input current, a DMS continues to dissipate its energy and shrinks toward annihilation. If there is any type of interaction, the polar angle is found to wander between a minimum and maximum value. That means a DMS breathes when interaction is present. A DMS can be transported along a nanotrack even when DMI is absent. As a DMS leaves a

Figure 2: (a) Nucleation of magnetic skyrmions on six nanotracks that have the same magnetic field source but different current density profiles. The current density profile j(t) is shown in (b). The dashed lines indicate the time instant at which the snapshots in (a) are taken5

nanocontact that nucleates it, and drifts due to an in-plane current, its radius decreases before the DMS is captured by another nanocontact. After it reaches a nanocontact, the DMS resumes its initial radius. When more nanocontacts are placed along a long nanotrack, a DMS can travel for a long distance without being dissipated entirely. In fact a DMS can still be nucleated in the presence of DMI. In this situation there is a transformation between static skyrmion and DMS. When the external magnetic field is switched off, a DMS skyrmion dissipates and becomes a DMIstabilized skyrmion. When the field is switched on again, the DMI-stabilized skyrmion transforms back to a DMS reversibly. In addition, a DMS can also be nucleated manipulating the current density instead of the magnetic field. In the first stage, a magnetic droplet is produced when the current density is large enough. After a short time, the energy of the spin transfer torque can trigger fluctuation of the topology and form a DMS. On the other hand, a sufficiently small current density would turn the DMS spin texture to the ferromagnetic (FM) state. In short, the current density is able to manipulate the spin texture between the DMS, droplet and uniform states. The magnetic field can help to manipulate the static skyrmion state in addition to the states obtained by varying the current density. A larger field strength stiffens a DMS and gives a smaller radius and a higher precession frequency. When the current density is high, a DMS would expand and generate a lower frequency. Also, a DMS is found to be more sustainable than a droplet because of its topological protection. A DMS in a nanocontact spin-transfer oscillator (NC-STO) is useful in microwave frequency generation as it makes use of the perpendicular


17

Magnetic skyrmions

Magnetic skyrmions

3 4

magnetoresistance when each local spin rotates in a full circle. This property is superior to using droplets, where only the magnetization at their perimeter generates the largest magnetoresistance and the largest power. The output power of NCSTOs using DMS can then be raised while maintaining a large current density tunability. In addition to the analytical formulation of DMS, conversion between a domain wall pair (DW pair) and a magnetic skyrmion contributes to the development of next-generation information carriers.4 The narrower portion of a nanotrack creates a domain wall pair in the presence of a spin-polarized current. After the DW pair arrives at the wider portion, it transforms to a skyrmion with topological number Q equal to 1. More importantly, this conversion is continuously reversible. It implies that skyrmions can be transmitted through thin nanowires by transforming to DW pairs beforehand. Such a conversion is possible if DMI is present; otherwise, a non-topological magnetic droplet soliton (Q = 0) is generated and the droplet soliton disperses as spin waves. Indeed, the conversion to a skyrmion is more feasible because it requires a lower current density than a DW pair to travel along a nanotrack. A typical application of this conversion mechanism is a hybrid of a DW pair and a skyrmion. The source of this device, which is a thin nanowire, writes DW pairs. The DW pairs are then driven to the thicker skyrmion channel before they reach a thin drain. The drain reads the DW pair as data bits.

18


Figure 3: The schematic diagram of a voltage-gated skyrmionic transistor. The source and drain are essentially MTJs that respectively write and read a magnetic skyrmion. The application of a gate voltage, in addition to the charge current JHM, determines the travel of a skyrmion6

Skyrmions in magnetic nanostructures In theory, creation of multiple skyrmions in a nanotrack is achievable by applying the conversion between a domain wall and a magnetic skyrmion, as mentioned in the previous section.5 The idea has been validated by micromagnetic simulation. A microwave antenna attached to a thin nanotrack generates domain walls. The DW pairs are driven by the spin-polarized current toward the thicker nanotrack portion, where a magnetic skyrmion is nucleated. The period of a skyrmion chain and the spacing of successive skyrmion chains inside a nanotrack can be increased by lowering the applied magnetic field frequency. In this setup, the velocity of skyrmion travel can increase with the applied current density. Once a magnetic skyrmion approaches the boundary of a magnetic nanostructure, it annihilates as its topology is destroyed by the nanotrack boundary. Multiple nanotracks using one shared antenna and different pulsed spin-polarized currents along each nanotrack can become a system of ultradense information storage. While DW pairs are synchronously produced by this setting, the period and spacing of each skyrmion chain depends on the duration of the high and low current density pulses. Figure 2 exhibits an example of multiple nanotracks. A merit of the skyrmion chains is that the skyrmions are topologically protected, such that their uniformity is not destroyed in the course of travel along a nanotrack. Furthermore, micromagnetic simulation has supported the

design of voltage-gated skyrmion transistors, which can incorporate into novel skyrmionic circuits.6 Applying a gate voltage switches off a transistor by varying the perpendicular magnetic anisotropy (PMA) of the gate region. This action increases the energy barrier that prevents a skyrmion from further movement. The source region of a skyrmion transistor is a magnetic tunnel junction (MTJ) acting as a writer, from which a magnetic skyrmion is created. When the gate voltage is absent, a spin-polarized current along the nanotrack drives the skyrmion toward the drain region, which is another MTJ used for the read action. On the other hand, the presence of the gate voltage prevents a skyrmion from entering the gate region. In this case, the skyrmion cannot complete its travel from the source to the drain. Figure 3 shows the schematic diagram of the transistor design. Specifically, a skyrmion can still reach the drain in the presence of a gate voltage if the magnitude of the current density and DMI are sufficiently large to overcome the energy barrier created by the gate voltage. In addition, the radius of a skyrmion in a transistor decreases with increasing PMA at the gate region. The skyrmion transistor model is found to be scalable; the physical phenomena are reproducible in smaller transistor dimensions. Reversible conversion between a skyrmion and a magnetic DW pair has become the design basis of the skyrmion logic gates.7 The logical OR

Figure 4: (Left) Skyrmionic OR gate. The presence of a skyrmion is denoted by ‘1’ and its absence by ‘0’. Two input skyrmions can become one skyrmion at the output due to the merging mechanism. (Right) Skyrmionic AND gate. When only one skyrmion is present at the input side it is converted to a meron, which is destroyed at the central portion of the logic gate. A stable skyrmion can result when both inputs have skyrmions initially7

operation, that is, 1 + 0 = 1, 0 + 1 = 1 and 1 + 1 = 1, is achievable by the proposed skyrmion-based device in the left-hand panel of Figure 4. In the lefthand column, the skyrmion in input A is converted into a magnetic DW pair in the central narrow nanotrack. Then the magnetic DW pair is converted into a skyrmion again in the wider output branch. The conversion process in the middle column is similar to the case in the left column. In the right column, two skyrmions in the input branch are converted into two DW pairs in a narrow nanotrack. These two magnetic DW pairs are merged into one magnetic DW pair in the central narrow nanotrack. The DW pair is subsequently converted into one skyrmion in the output branch. The logical AND operation, that is, 1 + 0 = 0, 0 + 1 = 0, and 1 + 1 =1, can also be realized in this proposed skyrmion-based device with a slight difference in the nanotrack width. See the righthand panel of Figure 4. In the left-hand column, the skyrmion in input A is converted into a magnetic DW pair as it moves toward the output. The magnetic DW pair is destroyed in the central wide nanotrack, which is different from the case of the OR gate. Consequently there is no skyrmion formed in the output branch. In the middle column, the realization of 0 + 1 = 0 is similar to the case of 1 + 0 = 1. The case of 1 + 1 = 1 is demonstrated in the right-hand column of Figure 4. There are two skyrmions in the input branch that are converted into magnetic DW pairs and then merged into one


19

Magnetic skyrmions

Magnetic skyrmions

Figure 6: Motion of an isolated AFM (FM) skyrmion in a two-dimensional AFM (FM) nanotrack driven by a vertically injected spin-polarized current. (a) AFM skyrmion velocity and FM skyrmion velocity (v) as functions of current density (j) with the current-perpendicular-to-plane geometry. The open symbol denotes the destruction of the FM skyrmion due to the SkHE. (b) top-views of vertical current-driven AFM skyrmion and FM skyrmion at selected current densities and times9

IT IS ENVISAGED THAT DMS, TOGETHER WITH THE COMBINATION OF A NUMBER OF THE ABOVEMENTIONED DESIGNS, COULD BECOME THE BASIC SETUP OF REAL PROTOTYPES OF SKYRMIONIC DEVICES IN THE FORESEEABLE FUTURE.

magnetic DW pair in the central wide nanotrack. As it moves toward the output branch, the magnetic DW pair is converted into a skyrmion. Movement of skyrmions in magnetic nanostructures is a technical problem of skyrmionic devices because the driving spinpolarized current produces the Magnus force and bends the skyrmion trajectory. This is referred to as the skyrmion Hall effect (SkHE). To suppress the SkHE, the antiferromagnetically (AFM) exchange-coupled bilayer system has been proposed.8 Two perpendicularly magnetized FM

5

20


Figure 5: Current-induced motion of skyrmions in the top and bottom FM layers of an AFM exchange-coupled bilayer nanotrack. Top views of the motion of skyrmions at selected interlayer exchange coupling constants and times driven by spin currents with the currentperpendicular-to-plane (CPP) injection geometry8

sublayers are AFM exchange-coupled with a heavy-metal layer beneath the bottom FM layer. As one skyrmion is created in the top FM layer, the other skyrmion in the bottom FM layer will be created simultaneously when the interlayer AFM exchange coupling is strong enough. The strong interlayer AFM exchange interaction can tightly bind the two skyrmions with opposite skyrmion numbers in the top and bottom FM layers. Accordingly, the Magnus forces on the skyrmions are canceled when they are driven by the spin-polarized current. Figure 5 illustrates the motion of skyrmions driven by the spin-polarized current in the AFM exchange-coupled and decoupled bilayers. In the AFM exchange-coupled bilayer, the skyrmions in the top and bottom FM layers move together in a straight line without showing the SkHE. On the contrary, the skyrmions in the top and bottom FM layers in the decoupled bilayer move in opposite transverse directions due to the SkHE. When t = 0.22ns, the skyrmion in the bottom FM layer is destroyed by touching the edge. These results show that the proposed AFM exchange-coupled bilayer system is able to suppress SkHE effectively. Another promising strategy to suppress the SkHE is to construct the skyrmion in AFM materials.9 The current-driven isolated AFM and FM skyrmions are demonstrated in Figure 6. Figure 6a shows their velocities as functions of the driving current density. For a small driving current, the velocities are proportional to the driving current density. When the current density is large enough, the FM skyrmion is destroyed (indicated by the open symbol in Figure 6a). By contrast, the AFM skyrmion can move at a high velocity while remaining stable at a high current density of 1012A/m-2. In Figure 6b it can be seen that the FM skyrmion is destroyed by touching the edge due to the SkHE. Keeping the same driving current density, the AFM skyrmion can move straight without transverse motion as there is no SkHE. The AFM skyrmion is promising as it hosts the topological protection but shows no SkHE.

Concluding remarks The theory of DMS has opened an area of skyrmion formation without the use of DMI. As a result of this, more materials can be adopted for future skyrmionic research and applications. In addition to this, skyrmionic applications are abound with many practical functions, such as the creation of skyrmion chains, skyrmion-based transistors, logic circuits and minimizing the SkHE. It is envisaged that DMS, together with the combination of a number of the above-mentioned designs, could become the basic setup of real prototypes of skyrmionic devices in the foreseeable future. n

6

References 1) J Sampaio, V Cros, S Rohart, A Thiaville and A Fert, Nucleation, stability and current-induced motion of isolated magnetic skyrmions in nanostructures, Nature Nanotechnology, vol 8, pp839-844, 2013 2) N Nagaosa and Y Tokura, Topological properties and dynamics of magnetic skyrmions, Nature Nanotechnology, vol 8, pp899-911, 2013 3) Y Zhou, E Iacocca, A A Awad, R K Dumas, F C Zhang, H B Braun and J Åkerman, Dynamically stabilized magnetic skyrmions, Nature Communications, vol 6, p8193, 2015 4) Y Zhou and M Ezawa, A reversible conversion between a skyrmion and a domain wall pair in a junction geometry, Nature Communications, vol 5, p4652, 2014 5) F Ma, M Ezawa and Y Zhou, Microwave field frequency and current density modulated skyrmion-chain in nanotrack, Scientific Reports vol 5, p15154, 2015 6) X Zhang, Y Zhou, M Ezawa, G P Zhao and W Zhao, Magnetic skyrmion transistor: skyrmion motion in a voltage-gated nanotrack, Scientific Reports vol 5, p11369 2015 7) X Zhang, M Ezawa and Y Zhou, Magnetic skyrmion logic gates: conversion, duplication and merging of skyrmions, Scientific Reports, vol 5, p9400, 2015 8) X Zhang, Y Zhou and M Ezawa, Magnetic bilayer-skyrmions without skyrmion Hall effect, Nature Communications, vol 7, p10293, 2016 9) X Zhang, Y Zhou and M Ezawa, Antiferromagnetic skyrmion: stability, creation and manipulation, Scientific Reports, vol 6, p24795, 2016


21