Manipulation of magnetic Skyrmions with a Scanning Tunneling Microscope
MManipulation of magnetic Skyrmions with a Scanning TunnelingMicroscope
R. Wieser
1. International Center for Quantum Materials,Peking University, Beijing 100871, China2. Collaborative Innovation Center of Quantum Matter, Beijing 100871, China (Dated: October 23, 2018)
Abstract
The dynamics of a single magnetic Skyrmion in an atomic spin system under the influenceof Scanning Tunneling Microscope is investigated by computer simulations solving the Landau-Lifshitz-Gilbert equation. Two possible scenarios are described: manipulation with aid of a spin-polarized tunneling current and by an electric field created by the scanning tunneling microscope.The dynamics during the creation and annihilation process is studied and the possibility to movesingle Skyrmions is showed.
PACS numbers: 75.78.-n, 75.10.Jm, 75.10.Hk a r X i v : . [ c ond - m a t . o t h e r] S e p agnetic Skyrmions have been intensively studied during the last period of time due tothe possibility to use them as potential candidates for data storage [1–3], for logic devices [4],or as Skyrmion transistor [5]. The idea to use local changes in the magnetic structure is notnew: Bubble domains in thin film structures [6], magnetic domain walls in nanowires drivenby an electric current [7], and magnetic vortices [8, 9] have been considered as candidates fordata storage and / or logic devices. However, due to the stability as result of their topology(topological protected) and their dimension (just a view nanometer) magnetic Skyrmionsare promising candidates for future spintronic devices.Furthermore, magnetic Skyrmions can be found in thin film systems on the microscopic[10–12] but also on the atomic length scale [13, 14]. In the moment most of the focus lieson the magnetic Skyrmions at the microscopic length scale. The reason can be found in thepossibility to observe these Skyrmions at room temperature and with several experimentaltechniques like e.g. magnetic transmission X-ray microscopy [11] or magneto-optical Kerreffect microscopy [10, 15]. For Skyrmions at the atomic length scale this is not the case.Here, a scanning tunneling microscope and low temperatures ( T ≈ L x × L y = 26 .
325 nm × H = − J (cid:88) (cid:104) n,m (cid:105) S n · S m − (cid:88) (cid:104) n,m (cid:105) D nm · ( S n × S m ) − µ S B z (cid:88) n S zn . The first two terms are the ferromagnetic exchange and Dzyaloshinky-Moriya interaction(DMI) where J = 7 mev and | D nm | = 2 . D nm are oriented in-plane (film plane) perpendicular to the lattice vector r nm = r m − r n pointing from lattice site n to m . The third term describes the influence ofan external magnetic field perpendicular to the film plane in z -direction.Without magnetic field B z = 0 T the system shows a maze like spin spiral structure [17].With external field the magnetic configuration provides Merons [19] and at larger fields ( B z approximately in between 4 and 10 T) Skyrmions which due to the in plane orientationof D nm show a hedgehog structure with magnetic moments pointing to the center of theSkyrmion. For B z ≥
10 T the ferromagnetic state is the ground state and Skyrmions areno longer existent. The Skyrmionic structure as well as the color coding of the picturesare given in Fig. 1. All figures have the same camera position and therefore the same colorcoding even if the focus varies. The diameter of the Skyrmion depends on the strength ofthe external field. During the simulations B z = 7 T (Skyrmion creation and destruction)and B z = 4 . IG. 1: (color online) Single Skyrmion in the Skyrmion gas phase [19] at B z = 7 T. Left: triangularlattice hedgehog structure, right: corresponding continuum (color) picture. diameter are d ≈ .
24 nm ( B z = 7T) and d ≈ .
26 nm ( B z = 4 . ∂ S n ∂t = − γ (1 + α ) µ S S n × [ H n + α ( S n × H n )] − S n × [ A T n + B ( S n × T n )] . The first and second term are the precessional and relaxation term of the conventional LLGequation with the effective field: H n = − ∂ H /∂ S n + ξ n , where ξ n is a white noise whichsimulates the effect of temperature. For the description of the manipulation via electricfields underneath the tip (radius r ≈ . . γ = 1 . ·
11 1
T s ,the magnetic moment µ S = 3 . µ B in Bohr magneton µ B , and the dimensionless Gilbertdamping constant α = 0 .
02. The third and fourth term are spin transfer torques describingthe influence of an spin polarized current. These terms have been modified to describe thetunnel current of a spin-polarized scanning tunneling microscope: A = 0 .
05 and B = 1 . T n = − I e − κ √ ( x n − x tip ) +( y n − y tip ) + h P , where P = ± ˆ z is the polarization of the tip, I the strength of the current, κ = 0 . · IG. 2: (color online) Creation and annihilation of a Skyrmion with current pulses from a spin-polarized STM tip. Left column: creation with tip polarization P = − ˆ z , right column: annihilationwith tip polarization P = +ˆ z . r tip = ( x tip , y tip , h ) T is the tip positionwhich is time dependent, and r n = ( x n , y n ,
0) the position vector within the lattice.Fig. 2 provides a sequence of pictures showing the creation and annihilation of a magneticSkyrmion with a spin-polarized tunnel current. The starting configuration with a ferromag-netic orientation of the magnetic moments underneath the STM tip is given in Fig. 2a).After a current pulse of 8 ps with I max0 = 1 . · P is assumed5 IG. 3: (color online) Manipulation of a single Skyrmion with a spin-polarized STM. Left column:slow tip velocity and “normal” tunnel current strength, right column: huge tip velocity and largetunnel current. The Roman and Arabic numerals give the positions of the original and new createdSkyrmions. Due to the interaction a clear change in the order can be seen. to be in − z -direction which is opposite to the orientation of the ferromagnetically alignedmagnetic moments. After a short moment the Skyrmion configuration is created and theSkyrmion grows with the time. The size of the Skyrmion overpasses the size of the finalconfiguration before it shrinks. During the shrinking the Skyrmion shows first a nonlin-ear excitations: fuzzy oscillation which becomes a breathing mode [20, 21] with frequency f ≈ H a reversed central spin with 6nearest neighbors will set free an energy of ∆ E = 6 J + 2 µ S B z .Despite the creation and annihilation of Skyrmions the scanning tunneling microscope canbe also used to move Skyrmions. The possibility to shift domain walls has been discussed in[22, 23]. Fig. 3a) shows a sequence of pictures where the movement of a single Skyrmion witha moving scanning tunneling tip is demonstrated. The tip has a polarization in − z -directionwhich is opposite to the orientation of the ferromagnetic surrounding of the Skyrmion butparallel to the orientation in the center. In the former publications it has been shown thata tip polarization parallel to the magnetization in the center of the domain wall is the bestchoice. In the case of the Skyrmion a tip polarization parallel to the central magnetization isthe best decision and has been used during the simulations. Furthermore, I has been set to I = 2 . · I = 2 . · D nm = D nm + ω nm ( E × r nm ) . D nm is the original DMI without electric field, E is the electric field vector, r nm = r n − r m is the vector pointing from lattice site n to lattice site m , and ω nm is a constant. If, as inthe experiment the electric field is given by a vector pointing in ± z -direction (perpendicularto the film plane) E × r nm will be parallel/antiparallel to the DMI vector and increases ordecreases the effect of the DMI. This means especially if the electric field is oriented in such away that it neglects the DMI the Skyrmion gets annihilated. Without DMI the ferromagneticconfiguration is the ground state and the magnetic field which has stabilized the Skyrmionbefore destroys it now. The dynamics here is similar to the one described in [18]. Twophases can be observed: first the reduction of the Skyrmion size and then the reversal of thecenter of the Skyrmion. During this reversal process the Skyrmion releases energy whichcan be seen in form of a concentric shock wave running through the system. During the firstphase (reduction of the radius) the Skyrmion shows a twist of the magnetic moments whichends with the annihilation of the Skyrmion. The creation process of a Skyrmion is a littlebit more complex. Here, the electric field strengthens the DMI. However, this is not enoughto create the Skyrmion. To create the Skyrmion and the corresponding topology first thesymmetry of the ferromagnetic order needs to be broken. In other words first a singularitywhich becomes the center of the Skyrmion has to be created. Here, temperature fluctuationsand especially the Joule heating helps. Koshibae and Nagaosa have shown that a locallyincreased temperature can be used to create a Skyrmion [29]. 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