Magnetic Skyrmion Transistor Operated with Microwaves

Jing Xia,1, 2 Yangqi Huang,3, 4 Xichao Zhang,1, 2 Wang Kang,4, 5 Chentian Zheng,3, 4 Weisheng Zhao,3, 4, ∗ and Yan Zhou1, 2, †

1Department of Physics, University of Hong Kong, Hong Kong, China2School of Electronics Science and Engineering, Nanjing University, Nanjing 210093, China

3Fert Beijing Institute, Beihang University, Beijing, China4School of Electronic and Information Engineering, Beihang University, Beijing, China

5School of Computer Science and Engineering, Beihang University, Beijing, China(Dated: July 2, 2018)

Magnetic skyrmion is a topologically protected magnetic domain-wall structure in nanoscale, which mightbe a basic building block for advanced spintronic devices. Here, we propose the microwave-driven motion of amagnetic skyrmion in a voltage-gated nanotrack, where the transistor-like function of the magnetic skyrmion isinvestigated from the point of view of micromagnetic calculation. It is demonstrated that the microwave fieldcan lead to the motion of the magnetic skyrmion by exciting propagating spin waves, where the motion of themagnetic skyrmion is also governed by a gate voltage. We also investigate the microwave-assisted nucleationof a magnetic skyrmion, which is dedicated to supporting the operation of the magnetic skyrmion transistoron the source terminal. It shows that the microwave current with an appropriate frequency can significantlyreduce the threshold current density required for the nucleation of the magnetic skyrmion. We hope that theproposed magnetic skyrmion transistor operated with the microwave field and current will be useful in futureskyrmion-based spintronic circuits.

PACS numbers: 75.78.Fg, 75.78.Cd, 85.70.-w, 85.75.-d

I. INTRODUCTION

The magnetic skyrmion is an exotic magnetic texture whichhas a nanoscale vortex-like magnetization structure that is pro-tected by topological invariance [1–3]. In the recent decade,the magnetic skyrmion has been experimentally observed inmagnetic materials [4–15], semiconductors [16], multifer-roic [17] and ferroelectric [18] materials, which indicate thatthere are diverse potential applications of magnetic skyrmionsin the field of spintronics. Indeed, the magnetic skyrmionas the information carrier attracts increasing interest for de-veloping the next-generation data storage devices due to itsremarkable stability, extremely small size, and low-currentdepinning property [19–28]. Concurrently, many other ap-plications of the magnetic skyrmions has been proposed anddemonstrated, such as skyrmion-based logic devices [29], os-cillators [30, 31], and electronic devices [32, 33].

For the applications of the magnetic skyrmion, it is re-quired to generate and control the isolated magnetic skyrmionin a feasible way. The magnetic skyrmion can be createdwith some kinds of energy injection, such as by applyinga spin-polarized current [14, 20], a local heating [34], anda laser [35]. The magnetic skyrmion can also be nucleatedwith the nano-patterning [36] and be converted from the mag-netic domain wall [23]. For the manipulation of the mag-netic skyrmion, one can use the spin current [19, 21], the spinwave [37–40], as well as the thermal gradient [41–43] to drivethe magnetic skyrmion.

Recently, the magnetic skyrmion transistor has been pro-posed and studied in Refs. [32, 33], in which the mag-netic skyrmion is driven by spin current in a voltage-gated

∗ weisheng.zhao@buaa.edu.cn† yanzhou@hku.hk

nanotrack. In this paper, we propose and study the mag-netic skyrmion transistor operated with microwaves, that is,the microwave-field-driven motion and microwave-current-assisted nucleation of the magnetic skyrmion in a voltage-gated nanotrack, where the perpendicular magnetic anisotropyof the gate region is determined by the applied voltage. Themicrowave field excites propagating spin waves that drives themotion of the magnetic skyrmion from the source region tothe drain region. The generation of the magnetic skyrmion atthe source region is performed by applying a spin-polarizedcurrent with an additional microwave current. Our studyshows that the motion of the magnetic skyrmion, which isgoverned by the gate voltage, can also be controlled by thefrequency and amplitude of the microwave field, which ex-cites the propagating spin wave. Meanwhile, it shows thatthe microwave current with a certain frequency can signifi-cantly reduce the critical current density required for the nu-cleation of the magnetic skyrmion. The results indicate thatthe proposed microwave-field-driven and microwave-current-assisted methods are effective approaches for building theskyrmion-based transistor. The magnetic skyrmion transistoroperated and controlled by the microwave field and currentwill be beneficial for the future skyrmion-based spintronic cir-cuits.

II. MODEL AND SIMULATION DETAILS

The three-dimensional (3D) micromagnetic simulation isperformed by using the 1.2a5 release of the Object Ori-ented MicroMagnetic Framework (OOMMF) software devel-oped at the National Institute of Standards and Technology(NIST) [44]. The simulation is handled by the OOMMF ex-tensible solver (OXS) objects of the standard OOMMF dis-tribution with the OXS extension module for including the

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FIG. 1. The microwave-driven magnetic skyrmion transistor at different working states (initial state, ON state, and OFF state). Thelength along the x-axis, width along the y-axis, and thickness along the z-axis of the magnetic nanotrack are equal to 600 nm, 60 nm and 1nm, respectively. The PMA of the nanotrack Ku = 0.8 MJ m−3. The DMI of the nanotrack D = 3.5 mJ m−2. A magnetic skyrmion is firstcreated and relaxed at the left (source) side of the nanotrack (x = 100 nm). An electrode is placed on the center (gate) of the nanotrack (200nm < x < 400 nm) for locally changing PMA. An oscillating magnetic field B = B0sin(2πft) along the y-direction is applied at the left endof the nanotrack (0 nm < x < 15 nm) by a microwave antenna (here, B0 = 500 mT, f = 75 GHz). At the initial state, both the microwaveantenna and voltage gate are turned off. The magnetic skyrmion keeps it position on the source side. At the ON state, the microwave antenna isturned on but the voltage gate is turned off. The magnetic skyrmion driven by the microwave-excited spin wave (SW) passes the voltage-gatedregion and reaches the right (drain) side of the nanotrack. At the OFF state, both the microwave antenna and voltage gate are turned on. Themicrowave-excited SW drives the magnetic skyrmion moving toward the right, while the gate voltage, which results in the change of PMAin the voltage-gated region, leads to the stop of the magnetic skyrmion when it approaches the gate-induced potential barrier. The magneticskyrmion cannot reach the drain side at the OFF state. The cones represent the magnetization, of which the out-of-plane component mz isdenoted by the orange-white-green color scale and the in-plane component mx is denoted by the blue-gray-yellow color scale.

interface-induced Dzyaloshinskii-Moriya interaction (DMI),that is, the Oxs_DMExchange6Ngbr class [45–48].

The interfacial DMI in the ultra-thin magnetic film withperpendicular magnetic anisotropy (PMA) placed on theheavy-metal substrate with high spin-orbit coupling is ex-pressed as [46]

EDM =∑〈i,j〉

dDM(uij × z) · (Si × Sj), (1)

with dDM the DMI coupling energy, uij the unit vector be-tween spins Si and Sj , and z the normal to the interface,oriented from the heavy-metal substrate to the magnetic layer.In the continuous micromagnetic model, the DMI reads

EDM = b

∫D[(mx

∂mz

∂x−mz

∂mx

∂x)

+(my∂mz

∂y−mz

∂my

∂y)]d2r, (2)

with D the continuous DMI constant, b the magnetic samplethickness. mx, my and mz are the components of the reducedmagnetization m, where m = M/MS. The link between Dand dDM is dDM/ab for a (001) interface and dDM

√3/ab for a

(111) interface with a the atomic distance [45], of which thelatter case is employed in this paper.

The 3D time-dependent magnetization dynamics in thesimulation is controlled by the Landau-Lifshitz-Gilbert (LLG)equation including the spin-transfer torque (STT) term [44,49]. Specifically, when no spin-polarized current is injectedinto the simulated system, that is, the STT term is deactivated,the LLG equation reads

dM

dt= −γ0M ×Heff +

α

MS(M × dM

dt), (3)

where M is the magnetization, Heff is the effective field, t isthe time, α is the Gilbert damping coefficient, and γ0 is thegyromagnetic ratio. The effective field Heff is expressed asfollows

Heff = −µ−10

∂E

∂M. (4)

The average energy density E is a function of M specified by

E = A[∇(M

MS)]2 −K (n ·M)2

M2S

− µ0M ·H

− µ0

2M ·Hd(M) + ωDM, (5)

3

FIG. 2. The typical trajectories of the magnetic skyrmion motion in the microwave-driven transistor at the ON and OFF states. (a) Themagnetic skyrmion transistor is in the ON state, where the microwave antenna is turned on (B0 = 500 mT, f = 75 GHz, similar hereinafter),and the voltage gate is turned off. The PMA in the voltage-gated region (Kuv) equals that of the outside region (Ku). The magnetic skyrmionreaches the drain side within 10 ns driven by the propagating spin waves. (b) The magnetic skyrmion transistor is in the OFF state, wherethe microwave antenna and the voltage gate are turned on. The PMA in the voltage-gated region is larger than that of the outside region(Kuv = 1.025Ku). The magnetic skyrmion cannot surmount the left potential barrier induced by the voltage gate, and relaxes near it. (c)The magnetic skyrmion transistor is in the OFF state, where the microwave antenna and the voltage gate are turned on. The PMA in thevoltage-gated region is smaller than that of the outside region (Kuv = 0.975Ku). The skyrmion cannot penetrate the right potential barrierinduced by the voltage gate, and relaxes near it. The dots denote the center of the magnetic skyrmion. The simulation time is 30 ns, which isindicated by the color scale. The red and blue regions stand for the regions where the microwave antenna and the voltage gate are deployed,respectively.

where A and K are the exchange and anisotropy energy con-stants, respectively. H and Hd(M) are the applied andmagneto-static self-interaction fields while MS = |M(r)| isthe saturation magnetization. The ωDM is the energy densityof the DMI, which has the form

ωDM =D

M2S

(Mz∂Mx

∂x+Mz

∂My

∂y−Mx

∂Mz

∂x−My

∂Mz

∂y),

(6)where the Mx, My and Mz are the components of the mag-netization M . The five terms at the right side of equation (5)correspond to the exchange energy, the anisotropy energy, theapplied field (Zeeman) energy, the magneto-static (demagne-tization) energy and the DMI energy, respectively. For thesimulated system in the presence of the spin-polarized currentwith the injection of current-perpendicular-to-the-plane (CPP)geometry, that is, the in-plane STT torque is activated, whichis written as

τin-plane = −ubm× (m× p), (7)

where u = γ0~jP2µ0eMS

, j is the current density, P is the spin po-larization, p is the unit electron polarization direction. Thus,the LLG equation (3) of magnetization motion augmentedwith STT terms reads

dm

dt= −γ0m×heff+α(m×dm

dt)− γ0~jP

2µ0ebMS[m×(m×p)],

(8)where heff is the reduced effective field, that is, heff =Heff/MS. The models built in the micromagnetic simulationare divided into regular cells with the constant size of 2 nm× 2 nm × 1 nm, which allows for a trade-off between nu-merical accuracy and computational efficiency. In the currentinjection geometry of CPP, the spin current polarized alongthe +y-direction flow toward the top in the magnetic layer,induced by the charge current flowing in the heavy-metal sub-strate. The polarization rate (P ) of the spin-polarized currentis equal to 0.4. The Oersted field is neglected in the simula-tion for simplicity due to its minor contribution to the effectfield.

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FIG. 3. The working windows of the microwave-driven skyrmiontransistor. (a) The working window at different gate voltages andmicrowave antenna excitation frequencies with a fixed microwaveantenna excitation amplitude of 500 mT. (b) The working window atdifferent gate voltages and microwave antenna excitation amplitudeswith a fixed microwave antenna excitation frequency of 75 GHz. Thesquare denotes the ON state, that is, the magnetic skyrmion passesthe voltage-gated region moving from the source side to the drainside. The circle denotes the OFF state, that is, the magnetic skyrmioncannot pass the voltage-gated region and stops at the rest of the drainside.

For micromagnetic simulations, the parameters of the mag-netic layer are adopted from Refs. [19, 20, 22]: the Gilbertdamping coefficient α = 0.02 and the value for the gyromag-netic ratio γ = −2.211 × 105 m A−1 s−1. Saturation mag-netization MS = 580 kA m−1, intralayer exchange stiffnessA = 15 pJ m−1, DMI constant D = 0 ∼ 4 mJ m−2 and PMAKu = 0.8 MJ m−3 unless otherwise specified.

The stable magnetic skyrmion stabilized by the interface-induced DMI is the hedgehog-like skyrmion, which has a ra-dial in-plane magnetization profile. It is characterized by thePontryagin number Q [23, 29], namely the topological chargein the planar system, which is defined by

Q =

∫dxdyρsky(x), (9)

where the ρsky reads

ρsky(x) = − 1

4πm(x) · (∂xm(x)× ∂ym(x)). (10)

The number Q is referred to as the skyrmion number. Whenthe background magnetization and the skyrmion core arepointing in the +z-direction and the −z-direction, respec-tively, the skyrmion number Q equals +1. Otherwise, whenthe background magnetization and the skyrmion core arepointing in the −z-direction and the +z-direction, respec-tively, the skyrmion number Q equals −1. In this paper, aswe are assuming that the background magnetization is alignedalong the +z-direction at the initial state, thus the skyrmionnumber of the relaxed (stable/metastable) skyrmion equalsone, Q = +1.

III. MAGNETIC SKYRMION TRANSISTOR DRIVEN BY AMICROWAVE FIELD

First, we study the magnetic skyrmion transistor driven by amicrowave field under the framework of micromagnetics. As

FIG. 4. The effect of Dzyaloshinskii-Moriya interaction (DMI)on the working window of the microwave-driven skyrmion tran-sistor. (a) The working window at different DMI and microwaveantenna excitation frequencies with fixed Kuv = 1.020Ku andB0 = 500 mT. (b) The working window at different DMI and mi-crowave antenna excitation amplitudes with fixed Kuv = 1.020Ku

and f = 75 GHz. (c) The working window at different DMI and mi-crowave antenna excitation frequencies with fixed Kuv = 0.995Ku

and B0 = 500 mT. (d) The working window at different DMI andmicrowave antenna excitation amplitudes with fixedKuv = 0.995Ku

and f = 75 GHz. The square denotes the ON state, that is, themagnetic skyrmion passes the voltage-gated region moving from thesource side to the drain side. The circle denotes the OFF state, thatis, the magnetic skyrmion cannot pass the voltage-gated region andstops at the rest of the drain side.

shown in Figure 1, the magnetic skyrmion transistor is basi-cally constructed by a nanotrack with the size of 600 nm ×60 nm × 1 nm, which has a PMA value of Ku = 0.8 MJ m−3

and a DMI constant of D = 3.5 mJ m−2. The magnetic nan-otrack is sandwiched between the voltage gate electrode andthe heavy-metal substrate, where the a voltage-gated regionis between x = 200 nm and x = 400 nm. The PMA valuewithin the voltage-gated region Kuv can be tuned by applyingan electric field Egate based on the relationship of Kuv = Ku+ ∆KuvEgate [50–52], where the transition regions betweenKu and Kuv span 10 nm. The regions in the nanotrack at theleft and right sides of the voltage-gated region are referredto as the source and drain sides, respectively. A microwaveantenna is deployed at the left end of the nanotrack (0 nm< x < 15 nm), which can generate a sinusoidal microwavemagnetic field B = B0sin(2πft) along the y-direction, whereB0 is the microwave amplitude and f is the microwave fre-quency. The relaxed magnetization of the nanotrack is almostmagnetized along the +z-direction in our setup. A magneticskyrmion is created and relaxed at the source side of the nan-otrack (x = 100 nm) by a skyrmion injector, which can befabricated by placing a magnetic tunnel junction (MTJ) uponthe source side of the nanotrack [26].

5

Figure 1 shows the initial, ON and OFF states of the mag-netic skyrmion transistor. At the initial state, both the mi-crowave antenna and the voltage gate are turned off, theskyrmion keeps its position on the source side at x = 100nm. At the ON state, the antenna is turned on (B0 = 500mT, f = 75 GHz) but the voltage gate is turned off. Themicrowave field pulse applied at the left end of the nanotrackexcites spin waves propagating toward the drain side of thenanotrack, driving the magnetic skyrmion into motion. Themoving skyrmion passes the voltage-gated region and reachesthe drain side of the nanotrack at t = 9 ns, which can be de-tected by the skyrmion reader at the drain side [26]. At theOFF state, both the microwave antenna and the voltage gateare turned on. The spin waves excited by the microwave fielddrive the magnetic skyrmion moving toward the right. Onthe other hand, the gate voltage, which results in the changeof the PMA value Kuv in the voltage-gated region, leads tothe stop of skyrmion when it approaches the gate-induced po-tential barrier. As shown in Figure 1, when the PMA valuein the voltage-gated region is larger than that of the intrinsicvalue, i.e. Kuv = 1.025Ku, the skyrmion stops at the poten-tial barrier at the boundary between the source side and thevoltage-gated region. When the PMA value in the voltage-gated region is smaller than that of the intrinsic value, i.e.Kuv = 0.975Ku, the skyrmion stops at the potential barrier atthe boundary between the voltage-gated region and the drainside. For both OFF states, the skyrmion reaches the equilib-rium state within t = 30 ns under the driving force from themicrowave-induced spin waves and the repulsive force fromthe potential barrier.

Figure 2 shows the trajectories of the skyrmion motion inthe magnetic skyrmion transistor driven by the microwave-induced spin waves at the ON and OFF states. As shownin Figure 2(a), the magnetic skyrmion transistor is in the ONstate, where the microwave antenna is turned on (B0 = 500mT, f = 75 GHz), and the voltage gate is turned off. ThePMA value in the voltage-gated region equals that of the in-trinsic value, i.e. Kuv = Ku. The skyrmion moves from thesource side to the drain side within 10 ns. It is worth men-tioning that the transverse motion of the skyrmion in the y-direction is caused by the skyrmion Hall effect [24]. Due tothe decay of the microwave-induced spin waves and the repul-sion from the edge at the right end of the nanotrack, the mag-netic skyrmion is finally relaxed at the drain side at t = 30 ns.When the magnetic skyrmion transistor is in the OFF state,as shown in Figure 2(b), where the microwave antenna andthe voltage are turned on, the PMA value in the voltage-gatedis larger than that of the intrinsic value, i.e. Kuv = 1.025Ku.The magnetic skyrmion driven by the microwave-induced spinwaves moves toward the drain side. However, the magneticskyrmion cannot surmount the potential barrier at the bound-ary between the source side with lower PMA and the voltage-gated region with higher PMA. It can be seen that the centerof the magnetic skyrmion can enter the voltage-gated regionfor a short time driven by the strong excited spin wave emit-ted from the microwave antenna. Nevertheless, the magneticskyrmion is repelled by the potential barrier. The combinedeffects of the driving force supplied from the microwave an-

tenna, the repulsive force provided by the voltage gate andthe Magnus force exerted on the magnetic skyrmion lead tothe motion of the magnetic skyrmion in a spiral trajectory.The skyrmion eventually reaches equilibrium and stops nearthe boundary between the source side and the voltage-gatedregion. Figure 2(c) shows the other OFF state, where the mi-crowave antenna and the voltage are turned on, the PMA valuein the voltage-gated is smaller than that of the intrinsic value,i.e. Kuv = 0.975Ku. The magnetic skyrmion driven by themicrowave-induced spin waves moves toward the drain side.In contrast to the OFF state shown in Figure 2(b), the magneticskyrmion passes the boundary between the source side withhigher PMA and the voltage-gated region with lower PMA,where a potential well is induced. However, the magneticskyrmion cannot penetrate the potential barrier at the bound-ary between the voltage-gated region with lower PMA and thedrain side with higher PMA. Similar to the OFF state shownin Figure 2(b), the magnetic skyrmion shows a spiral trajec-tory of motion, and finally stops near the boundary betweenthe voltage-gated region and the drain side.

Figure 3 shows the working windows of the magneticskyrmion transistor driven and controlled by the microwaveantenna and the voltage gate. As shown in Figure 3(a), theexcitation field amplitude of the microwave antenna is fixedat B0 = 500 mT, while the excitation field frequency of themicrowave antenna is varied in the range between f = 72GHz and f = 78 GHz. Obviously, when the voltage gate isturned off, i.e. Kuv = Ku, the magnetic skyrmion transistor isalways in the ON state, where the magnetic skyrmion movesfrom the source side to the drain side in a certain time. Whenthe voltage gate is turned on, which adjusts theKuv to be in therange of 0.995Ku and 1.015Ku, the magnetic skyrmion tran-sistor is still in the ON state, as the gate-induced potential bar-rier is not strong enough to stop the magnetic skyrmion frommoving. When the Kuv is further increased to be larger than1.02Ku or decreased to be smaller than 0.99Ku, the workingstate of the magnetic skyrmion transistor switches to the OFFstate at f = 72 GHz. However, it can be seen that when fincreases to 78 GHz, the magnetic skyrmion under strongerdriving force provided by the microwave antenna can over-come the potential barrier induced by the voltage gate in therange of Kuv = 0.99Ku and Kuv = 1.03Ku. Because thepotential barrier at the boundary between the source side withlower PMA and the voltage-gated region with higher PMA iscloser to the antenna than the one at the boundary between thevoltage-gated region with lower PMA and the drain side withhigher PMA, the skyrmion experiences stronger driving forcewhen it is approaching the former potential barrier. Thus, thepotential barrier at the boundary between the source side withlower PMA and the voltage-gated region with higher PMA iseasier to be penetrated by the magnetic skyrmion at the sameB0 and f . Similar results are shown in Figure 3(c), where theexcitation field frequency of the microwave antenna is fixedat f = 75 GHz, while the excitation field amplitude of themicrowave antenna is varied in the range between B0 = 350mT and B0 = 650 mT.

Figure 4 shows the working windows of the magneticskyrmion skyrmion transistor at different DMI constants and

6

microwave antenna parameters with a fixed voltage gate-induced PMA valueKuv. Figure 4(a) and Figure 4(b) show theworking state of the magnetic skyrmion transistor at Kuv =1.020Ku as functions of the DMI constant D and antennafrequency f , and as functions of DMI constant D and an-tenna amplitude B0, respectively. Figure 4(c) and Figure 4(d)show the working state of the magnetic skyrmion transistor atKuv = 0.995Ku as functions of the DMI constant D and an-tenna frequency f , and as functions of DMI constant D andantenna amplitude B0, respectively. It can be seen that themagnetic skyrmion in a nanotrack with a smaller DMI con-stant D is easier to overcome the potential barrier at givenKuv, B0 and f .

IV. NUCLEATION OF THE MAGNETIC SKYRMIONASSISTED BY A MICROWAVE CURRENT

With respect to the generation of the magnetic skyrmion atthe source terminal of the magnetic skyrmion transistor, wealso implement the microwave-current-assisted nucleation ofthe magnetic skyrmion. For the sake of low computationalcomplexity, here we consider the model of a nanodisk insteadof the nanotrack studied in last section. As shown in Fig-ure 5(a), a magnetic nanodisk initially magnetized along +z-direction is built in the simulation, which has a diameter of 80nm and a thickness of 1 nm. The current contact is of 24 nmin diameter and set in the central region of the nanodisk.

In order to create the magnetic skyrmion in the nanodisk,we utilize a microwave-assisted vertical spin-polarized cur-rent, which can be expressed as jtotal = j0 sin 2πft + jDC.Here, j0 is the amplitude of the microwave current, fAC isthe frequency of the microwave current, and jDC is the cur-rent density of the DC current. As jDC dominates the energyconsumption in case of jDC > j0, we focus on the thresholdcurrent density jth defined as the minimal jDC required to nu-cleate the magnetic skyrmion. The applied current duration isfixed to 2 ns.

Figure 5 shows the nucleation process of the magneticskyrmion in the presence and absence of the microwave cur-rent. As shown in Figure 5(a), the DC current density jDCis fixed at jDC = 1.8 × 1012 A m−2, and the frequency ofthe microwave current is set as fAC = 53 GHz. In order toindicate the nucleation of the magnetic skyrmion, we calcu-late and show the skyrmion number Q as a function of time.When the nucleation current is injected from t = 0 ns, theskyrmion numberQ starts to fluctuate while the magnetizationstays quasi-uniform with a spin wave transferring from thecenter to the edge, which expresses the injection of energy. Att = 0.39 ns, the magnetization of the central region reverses ina very short time (∼ 0.01 ns), and generates a stable magneticskyrmion, resulting in a rapid jump of the skyrmion numberfrom Q = −0.1 to Q = 0.9. After this rapid change, theskyrmion number stabilizes at Q ∼ 1, marking a success ofthe skyrmion nucleation. It should be noted that we also findthe breathing of the magnetic skyrmion after its nucleation,which can be seen from the snapshots at t = 0.39 ∼ 0.60 ns.At t = 0.60 ns, the magnetic skyrmion stops breathing and

FIG. 5. The microwave-current-assisted nucleation of the mag-netic skyrmion. (a) The skyrmion nucleation assisted by a mi-crowave current with a selected frequency of fAC = 53 GHz. Thediameter of the nanodisk equals 80 nm. The diameter of the currentinjection region equals 24 nm, which is denoted by the dashed circlein (a). A spin-polarized DC current is applied in conjunction withan additional microwave current, that is, jtotal = j0 sin 2πft + jDC,to nucleate the magnetic skyrmion. Here, j0 = 1 × 1012 A m−2 isthe amplitude of the microwave current, jDC = 1.8× 1012 A m−2 isthe current density of the DC current. A magnetic skyrmion can benucleated successfully even jDC is lower than the threshold currentdensity, jth = 2 × 1012 A m−2. (b) The skyrmion nucleation byapplying only a DC spin current of jDC = 1.8 × 1012 A m−2. Inthe absence of the microwave current, the DC spin current itself ofjDC = 1.8× 1012 A m−2 is unable to create the magnetic skyrmion.Only a subtle fluctuation of the skyrmion number Q is detected dur-ing the 2-ns-long current pulse, which is caused by the slight motionof the magnetization. The initial magnetization state of the nanodiskis along the +z-direction, and the polarization of the spin current isaligned along the −z-direction.

becomes a stable magnetic skyrmion. Figure 5(b) shows thecase in the absence of the assistance of the microwave current.With the identical DC current density, no magnetic skyrmionis formed in the nanodisk in the absence of the microwavecurrent. We also calculate the skyrmion number Q and find aslight fluctuation during the time within which the DC currentis applied. The skyrmion number is equal to Q ∼ 0 dur-ing the simulation. It indicates that the DC current density of1.8× 1012 A m−2 is smaller than the threshold current.

Figure 6 shows the threshold current density jth as functionsof the amplitude j0 and frequency fAC of the microwave cur-rent. As shown in Figure 6(a), the frequency of the microwavecurrent is fixed at fAC = 53 GHz, while the amplitude of themicrowave current is in the range of j0 = 0 ∼ 2 × 1012

A m−2. The circles denote the threshold current density jthcorresponding to different microwave current amplitudes j0.Obviously, jth decreases as the amplitude of the microwave

7

FIG. 6. The effects of the amplitude and frequency of the mi-crowave current on the threshold current density needed to cre-ate the magnetic skyrmion. (a) The threshold current density jth

and j2th + j20 /2 as functions of the microwave current amplitude j0.The microwave frequency fAC is fixed to 53 GHz. A linear fit isshown for the relation between the microwave amplitude j0 and thethreshold current density jth. (b) The threshold current density jth

as a function of the microwave current frequency fAC with a fixedamplitude of j0 = 1.3 × 1012 A m−2. The assistance effect of themicrowave current varies with its frequency fAC, and the most effec-tive frequency in this case is around 53 GHz, which is indicated bygreen shadow in (b).

current j0 increases. A linear fit, which is expressed asjth = −0.36j0 + 1.98×1012 A m−2, is used to characterizingthe relation between jth and j0. Since the energy consump-tion E ∝ j2total, where jtotal = j0 sin 2πft+ jth, we can obtainthe relation between E, jth and j0 as E ∝ j2th + j20 /2. Thevalue of j2th + j20 /2 is also denoted as triangle in Figure 6(a).When j0 < 1.2 × 1012 A m−2, we find a decrease of theenergy consumption while the amplitude of the microwavecurrent increases. The energy consumption reaches a mini-mum at the j0 = 1.2 × 1012 A m−2. However, further in-creasing microwave current amplitude leads to an increasingenergy consumption. The results can be understood as fol-lows. When j0 < jth, jth dominates the energy consumption.The increase of j0 leads to a decrease of jth as well as theenergy consumption. When j0 > jth, j0 is dominant in theenergy consumption. A higher j0 increases the energy con-sumption. We can see that the additional microwave currentwith j0 = 1.2 × 1012 A m−2 saves 31% of the energy con-sumption compared with the case where only the DC currentis applied. Besides, we study the relation between jth andthe frequency fAC of the microwave current with a fixed mi-

crowave amplitude j0 = 1.3× 1012 A m−2, as shown in Fig-ure 6(b). The most effective microwave frequency is foundaround fAC = 53 GHz, where the corresponding jth reachesits lowest value. Indeed, a clear peak of jth appears in therange of fAC = 50 ∼ 55 GHz, which is indicated by greenshadow in Figure 6(b).

V. CONCLUSION

In summary, we have proposed a magnetic skyrmion tran-sistor operated and controlled by microwaves. It is demon-strated that the microwave field can lead to the motion of themagnetic skyrmion by exciting propagating spin waves, wherethe motion of the magnetic skyrmion is well governed by agate voltage. Besides, the creation of the magnetic skyrmionat the source region of the magnetic skyrmion transistor isalso assisted by a microwave current. It shows that the mi-crowave current can remarkably reduce the energy consump-tion required for the nucleation of the magnetic skyrmion. Ourresults on the magnetic skyrmion transistor operated and con-trolled by the microwave field and microwave current mightbe useful in the design of future skyrmion-based spintroniccircuits.

ACKNOWLEDGMENTS

Y.Z. acknowledges the support by National Natural Sci-ence Foundation of China (Project No. 1157040329), the SeedFunding Program for Basic Research and Seed Funding Pro-gram for Applied Research from the HKU, ITF Tier 3 fund-ing (ITS/171/13 and ITS/203/14), the RGC-GRF under GrantHKU 17210014, and University Grants Committee of HongKong (Contract No. AoE/P-04/08). W.S.Z. acknowledges thesupport by the projects from the Chinese Postdoctoral ScienceFoundation (No. 2015M570024), National Natural ScienceFoundation of China (Projects No. 61501013, No. 61471015and No. 61571023), Beijing Municipal Commission of Sci-ence and Technology (Grant No. D15110300320000), andthe International Collaboration Project (No. 2015DFE12880)from the Ministry of Science and Technology of China. X.Z.was supported by JSPS RONPAKU (Dissertation Ph.D.) Pro-gram.

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