Abstract
Current-controlled magnetic domain wall motion has opened the possibility of a novel type of shift register memory device, which has been optimistically predicted to replace existing magnetic memories. Owing to this promising prospect, intensive work has been carried out during the last few decades. In this article, we first review the progress in the study of current-induced magnetic domain wall motion. Underlying mechanisms behind the domain wall motion, which have been discovered during last few decades, as well as technological achievements are presented. We then present our recent experimental results on the real-time detection of current-driven multiple magnetic domain wall motion, which directly demonstrates the operation of a magnetic domain wall shift register.
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1. Introduction
Modern magnetic information storage devices utilize magnetic domains as digital memory bits, for example, "1" for a magnetic domain with magnetization pointing "up" and "0" for one pointing "down". Naturally, the controlled switching of magnetization vectors has been considered as a key to realizing memory devices. In nanowire geometries, such magnetization switching occurs by the motion of a magnetic domain wall (DW). Therefore, the controlled motion of a magnetic DW along a nanowire is an important prerequisite for the realization of DW-motion-based memory devices. To achieve controlled magnetic DW motion, magnetic-field-based control was investigated in the early stage of research.1–4) However, a magnetic field is not able to drive multiple DWs along the same direction and thus, is hardly applicable to DW-motion-based memory devices. In 1996, Berger showed in his seminar paper that an electric current can move multiple DWs along the same direction.5) This pioneering work attempts to develop a novel concept of memory devices that utilize the current-induced motion of multiple DWs, which is conceptually similar to a shift register memory.6) After the prediction by Berger,5) researchers strived to demonstrate current-induced DW motion (CIDWM). Below we give an overview of it, attempts to use CIDWM as a shift register memory device.
We first review the key physics and concepts regarding the DW driving forces that were actively discussed in the first stage of research on CIDWM. In the first stage, CIDWM was investigated for ferromangets with in-plane magnetic anisotropy. The effects of spin transfer torque (STT) were discussed vigorously during this period. The second stage of research on CIDWM began with a change in the material system from in-plane magnetized materials to materials with perpendicular magnetic anisotropy (PMA). Much better device performances were obtained using PMA materials. However, the physics behind CIDWM remained a mystery because in some PMA materials, the DW moves in the opposite direction to the electron flow, contradicting the orthodox theory of STT. This mystery was successfully resolved when the spin–orbit torque (SOT) was proposed in ferromagnet (FM)/heavy metal (HM) bilayer structure, which marked the start of the third stage of research on CIDWM. The SOT naturally invokes a chiral DW structure that is formed by the interfacial Dzyaloshinskii–Moriya interaction (DMI). The SOT and DMI have also triggered fundamental interest in topological spin structures, such as skyrmions and Bloch lines, which are also able to be used in memory devices. After reviewing the progress in the understanding of CIDWM, we finally present our recent experimental results on the real-time detection of current-induced multiple DW motion, which directly demonstrates the operation of a DW-motion-based shift register. This article ends by providing future research directions for CIDWM.
2. Progress in study of current-induced domain wall motion
2.1. STT-driven DW motion in materials with in-plane magnetic anisotropy: first stage of research on CIDWM
Since the seminar paper by Berger,5) theoretical works have continued.7–14) In these theoretical works, the authors have pointed out that spin-polarized electric currents in ferromagnets can transfer their spin angular momentum to local magnetization via the s–d exchange interaction and generate torques on local magnetizations, resulting in the motion of magnetic DWs. This phenomenon which can be understood in terms of the conservation of global angular momentum was termed as a STT. STT is often considered as an effective field that is proportional to the non equilibrium carrier spin polarization s, and hence STT has the general form T = dM/dt = M × s, where M is the local magnetization of the ferromagnet. In the limit of the long carrier spin lifetime, the injected carrier spins precess around the local magnetization. In this case, the resulting s depends on M as s = M × p, where p is the polarization of the injected spin current. The corresponding STT has the form T = M × (M × p) and is referred to as "adiabatic STT". On the other hand, in the limit of the short carrier spin lifetime relative to the spin precession time in a ferromagnet, s is independent of M and is proportional to the polarization p of the injection spin current. Hence the STT is described by T = M × p, which is known as the "non-adiabatic STT". Two STTs, the adiabatic STT and non-adiabatic STT, can be readily incorporated in the Landau–Lifshitz–Gilbert (LLG) equation which describes the magnetization dynamics of a ferromagnet. The LLG equation including STT terms then reads
where γ is the gyromagnetic ratio, α is the Gilbert damping parameter, MS is the saturation magnetization, and Heff is the total effective field including the external field, anisotropy field, and exchange field. β is the phenomenological non-adiabatic STT parameter. u has the dimension of velocity and scales with the electrical current density J:
where g is the Lande factor, μB is the Bohr magnetron, e is the electron charge, and P is the spin polarization of the current in the ferromagnet. Considering vector coordinates, Eq. (1) indicates that the adiabatic STT [third term in the right-hand side (RHS) of Eq. (1)] contribute or competes with the Gilbert damping term [second term in the RHS of Eq. (1)] depending on the sign of the current, whereas the direction of non-adiabatic STT [final term in the RHS of Eq. (1)] is collinear with that of the field torque term [first term in the RHS of Eq. (1)]. This yields additional terminology for STTs, that is, the adiabatic STT is referred to as a damping-like torque and the non-adiabatic STT is referred to as a field-like torque.
To understand the DW dynamics more analytically, a one-dimensional DW model was developed.11–15) In an approximation of rigid DW motion, in which the DW maintains its shape during the motion, the DW dynamics is described by two dynamical variables, the DW position q(t) along the x-axis and the DW tilting angle φ(t) in the xy plane (see Fig. 1). By using the procedure developed by Thiele,15) one can derive, from the LLG equation, the equations of motion for the two collective coordinates q(t) and φ(t),
where α is the Gilbert damping parameter, Δ is the DW width, γ is the gyromagnetic ratio, MS is the saturation magnetization, Ω is the cross-sectional area of the nanowire, is the DW potential energy, and u is spin drift velocity described by Eq. (2). The signs in Eqs. (3) and (4) are chosen in such a way that positive H and u drive the DW toward the positive q-direction. The DW potential energy consists of a disorder potential energy V(q) and the DW anisotropy energy 2ΩΔKd sin2 φ, where Kd is the strength of the DW anisotropy (the DW anisotropy is the energy difference between a Bloch DW and Néel DW). Here φ is defined in such a way that φ = 0 for the preferential tilting angle for the DW anisotropy. Equations (3) and (4) indicate that the DW position and angle are coupled with each other, so that when the DW moves, both the translational motion and rotational motion occur simultaneously. This DW motion is in analogy to the motion of a charged particle in a magnetic field, which exhibits both translational and rotational motion.16)
One can solve Eqs. (3) and (4) for the case of CIDWM with V(q) = 0, H = 0 to obtain
Equations (5) and (6) indicate the DW dynamics under an electric current. For the case of β = 0, that is, when only adiabatic STT exists, the threshold current can be defined as uC = ΔγKd/MS. For u < uC, Eqs. (5) and (6) have a solution when , indicating that the DW cannot have any translational or rotational motion. Note that this argument holds even when there is no extrinsic disorder in the nanowire [i.e., V(q) = 0], indicating that the threshold behavior originates from the intrinsic DW anisotropy Kd (this is the reason why the DW anisotropy Kd is called intrinsic pinning). If β has a finite value, on the other hand, Eqs. (5) and (6) have a solution when = finite, = 0 even in the case of u < uC. This implies that the DW is able to move without precession below the threshold current with the help of non-adiabatic STT. Figure 2 show the DW velocity as a function of current density for several β based on a one dimensional 1D model.9) For β = 0, the threshold current required to move the DW is clearly observed. For β ≠ 0, on the other hand, a finite DW velocity is observed even below the threshold current. It is worth noting that the trend of the DW velocity is strongly affected by the value of the non-adiabaticity β. Therefore, the existence of non-adiabatic STT and its strength were important and debated issues at the first stage of research on CIDWM. Naturally, experimental investigations of CIDWM have followed.
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Standard image High-resolution imageThe first experimental demonstration of CIDWM was reported in 2004 by Yamaguchi et al.,17) who created a DW in curved in-plane NiFe (permalloy, Py) wires and moved it by applying a current pulse [Fig. 3(a)]. A DW velocity of about 3 m/s was obtained for a current density of 7 × 1011 A/m2 [Fig. 3(b)]. CIDWM was also observed in a magnetic semiconductor at a low temperature, for which a much lower threshold current density was realized.18–20) However, the slow DW velocity as well as the low-temperature characteristics of magnetic semiconductors prevented its direct application. For this reason, much attention was devoted to metallic systems such as Py. The pioneering work done by Yamaguchi et al. sparked a tremendous number of studies on CIDWM. The underlying mechanism of CIDWM was first investigated. The microscopic structure of a DW was observed by using advanced imaging techniques,21–23) from which it was found that there are four types of DWs: transverse and vortex DWs with clockwise and counterclockwise spin rotation. It was revealed that among the DW types, the vortex DW is more mobile than the transverse one.22) Issues related to non-adiabatic STT were also actively discussed. At the time, most of the CIDWM results were assumed to be predominantly governed by the non-adiabatic STT because the current densities required to move the DW were much smaller than the threshold value predicted theoretically on the basis of intrinsic pinning. This raised a question on the strength of the non-adiabatic STT, but a clear consensus was not reached because of large scattering of the values of the reported non-adiabatic STT parameter β,24–30) which probably originated from the complex internal DW structures. The precessional behavior of DW motion31,32) as well as the acceleration/deceleration of DWs33–35) was also presented. In particular, the acceleration/deceleration behavior triggered a debate on the existence of DW mass.36,37) From a technological aspect, high-speed DW motion of up to 100 m/s was obtained for a current density of 1.5 × 1012 A/m2,38) a comparable speed to that of existing hard disk drives (HDDs). Controlled DW motion using multiple current pulses was successfully demonstrated and a proof-of-concept experiment for the operation of a 3-bit shift register was also reported.39) These technological achievements showed the feasibility of DW-motion-based devices. As a result, research on CIDWM began to be carried out by researchers in diverse fields, not only academic researchers but also scientific engineers.
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Standard image High-resolution imageDespite the seemingly successful demonstrations, however, there were some fundamental problems that need to be solved for device application. A complex DW structure limited the comparison between experiment and theory.21) Transformations between a transverse DW and vortex DW, and vice versa, made it difficult to control the DW position by a current pulse.22) A relatively large DW (∼a few hundreds nm) was thought to limit the density of devices.21,40) An extremely large driving current density (>1012 A/m2) was the greatest barrier for device application since it causes stochastic DW motion40,41) as well as severe Joule heating.42,43) Naturally, researchers turned their interest to another magnetic materials to solve the problems raised.
2.2. STT-driven DW motion in materials with perpendicular magnetic anisotropy: second stage of research on CIDWM
While the in-plane magnetic anisotropy of NiFe mostly depends on the shape of the device, perpendicular magnetic anisotropy (PMA) generally originates from the interfacial orbital anisotropy, therefore PMA is independent of the shape of the device.44) This property of PMA materials is generally highly beneficial for device miniaturization as demonstrated by magnetic recording media (e.g., HDDs) with PMA. For the case of magnetic DW motion, PMA materials have much smaller DWs (∼a few nm) than their in-plane counterparts (∼a few hundreds nm). Furthermore, the DW has a simple transverse structure, thus it can be categorized into a Bloch or Néel DW depending on its internal magnetization direction (see Fig. 4). Owing to this simplicity, DW dynamics in PMA materials can be well explained by a theoretical model.
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Standard image High-resolution imageIn 2008, Jung et al. predicted that intrinsic pinning behavior could be observed in metallic ferromagnetic nanowires with PMA by varying the wire geometry.12,45,46) This prediction was based on the fact that the intrinsic pinning, i.e., the energy difference between Bloch and Néel DWs, can be varied by changing the width or thickness of the wire. Hence, the threshold current, which is proportional to the intrinsic pinning, can also depend on the wire geometry. This prediction was experimentally demonstrated in Co/Ni multilayered nanowires with PMA by Koyama et al. in 2011.47) In this study, they cleverly demonstrated the intrinsic pinning nature of CIDWM by showing the wire width dependence of the threshold current density. They observed that the threshold current density decreases upon reducing the wire width due to the reduction of intrinsic pinning, while the depinning field increases for a narrower wire. This was exactly consistent with the theoretical prediction based on adiabatic STT-driven CIDWM with a negligible non-adiabatic STT parameter β. The same group also demonstrated that the threshold current density is independent of the external field and temperature, further confirming the intrinsic nature of CIDWM.48,49)
Such the intrinsic nature of CIDWM provides unique energy barriers to DW motion. Kim and coworkers attempted to quantify the energy barriers of a magnetic DW trapped at a single defect.50,51) They obtained a perfect exponential distribution for the depinning time, which enabled the identification of the energy barrier to DW motion. They repeatedly measured the energy barrier for current- and/or magnetic-field-driven DW motion. Interestingly, when the DW overcomes the energy barrier by both the magnetic field and the current, the electric current was found to generate quadratic contributions to magnetic-field-driven DW depinning even after the effect of Joule heating was eliminated.50) This result was clearly different from the effect of non-adiabatic STT, which was predicted to generate a linear contribution to magnetic-field-driven DW depinning. Consequently, Kim and coworkers concluded that the quadratic contribution to the energy barrier arises from the adiabatic STT due to the intrinsic nature of CIDWM. Taking their research a step further, Kim et al. quantified the energy barriers for magnetic-field- and current-driven DW motion separately.51) The obtained energy barriers for the magnetic field and current were clearly different; the energy barrier for the current (intrinsic energy barrier) does not strongly depend on the defects in the wire, whereas that for the magnetic field (extrinsic energy barrier) strongly depends on the defects. This finding again demonstrated that CIDWM is dominated by intrinsic pinning. These results suggest that the energy barriers for the current and field can be separately designed. The result of these investigations on the energy barriers have important implications for the practical application of DW motion; achieving a high thermal stability and a low threshold current simultaneously, which is generally not possible in conventional magnetic memory devices, is possible in DW-motion-based devices because the thermal stability and threshold current density depend on the extrinsic and intrinsic energy barriers, respectively.51)
PMA nanowires have exhibited much better technical performances than their in-plane counterparts. A threshold current as low as 3 × 1011 A/m2 was achieved while maintaining thermal stability over 60kBT.47,51) The multibit control of CIDWM was demonstrated and the successful operation of 4-bit shift register was also presented.52,53)
This unprecedented successes of CIDWM in PMA materials accelerated the development of DW-motion-based memory devices. For example, a three-terminal magnetization switching device that utilized magnetic DW motion was proposed.54) Despite the successful technological progress in research on DWs in PMA materials, however, the driving mechanism behind DW motion remained a mystery because in some materials, such as Pt/Co/AlOx and Pt/Co/Pt nanowires, the DW moves in the opposite direction to the electron flow,53,55) contradicting the orthodox theory of STT. This mystery implied that an as yet unrevealed mechanism of CIDWM existed. A novel spin torque originating from spin–orbit coupling resolved this mystery.
2.3. SOT and DMI in FM/HM bilayers: third stage of research on CIDWM
As described in the previous section, STT is an efficient tool for manipulating magnetic DW motion. STT occurs when the current flows along ferromagnetic materials because ferromagnets have inherent spin polarization. However, there is an alternative way to produce nonequilibrium spin polarization of the conduction electrons: using spin–orbit coupling and structural inversion asymmetry. The Rashba effect56) and spin Hall effect57,58) are representative examples that exhibit a nonequilibrium spin polarization originating from the spin–orbit coupling in materials. When an electron moves under an electric field E, the theory of relativity predicts that the electric field E is converted to an orthogonal effective magnetic field Beff in the electron's rest frame. Such an effective magnetic field couples to the electron spin and generates a spin polarization. In general, electrons moving in an interface or surface where an electric field exists due to the structural inversion asymmetry experience an effective magnetic field. This is also the case in electron orbital motion where the moving electron is subjected to a central electric field. As a result, the spin–orbit coupling can generate nonequilibrium spin accumulation inside materials.
Figure 5 shows a schematic diagram of the Rashba effect and spin Hall effect in a FM/HM bilayer structure. In the Rashba picture [Fig. 5(a)],56) the electrons moving at the FM/non-magnet (NM) interface with momentum effectively experience a transverse magnetic field of due to the inversion symmetry breaking. Here is a unit vector parallel to E, i.e., the inversion symmetry breaking direction, and αR is the Rashba constant which depends on the strength of the spin–orbit coupling. This effective field couples to the spins of an electron, σ, at the interface, resulting in spin accumulation. Therefore, the longitudinal charge current, je, generates transverse spin accumulation. In the spin Hall picture [Fig. 5(b)],57,58) on the other hand, the charge current, je, flowing in the HM layer partly experiences spin-dependent scattering, causing the flow of the pure spin current orthogonal to the charge current direction. It should be noted that the spin quantization axis is orthogonal to both the charge current and spin current directions. Therefore, the transverse spins, σ, accumulate at the FM/NM interface, similar to the Rashba effect. Although the Rashba effect arises from the interface while the spin Hall effect takes place inside the HM layer, both effects generate spin accumulation at the interface between the FM and HM. The accumulated spins can then diffuse into the FM, resulting in a spin torque to the magnetization of the FM due to the exchange interaction. This torque is referred to as SOT. Here, we remark on a difference between STT and SOT. STT arises from the exchange interaction between conduction electron and local magnetization and is driven by the current flowing along the FM. However, SOT originates from the spin–orbit coupling and exchange interaction, and is realized by the current at the interface or in the HM, not in the FM.
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Standard image High-resolution imageIn 2010, Miron et al. reported the first observation of SOT-induced magnetization dynamics in FM/HM metallic bilayers where the structural inversion symmetry was broken.59) They found a strong effective transverse magnetic field Beff originating from the Rashba effect. Using this Rashba-induced effective field, they further demonstrated that the DW velocity becomes much greater than that predicted from the STT.60) It was also successfully explained why the DW moved in the opposite direction to the electron flow in some PMA materials.61) This concept of the Rashba-effect-induced SOT was extended to a magnetization switching behavior, in which the magnetization can be effectively switched by SOT in the presence of an in-plane bias field.62)
Later, a similar magnetization switching behavior was also observed in different materials,63,64) whose origin was attributed to the spin Hall effect. As explained above, the spin Hall effect also generates spin accumulation at an FM/NM interface and induces a torque to the FM, similar to the Rashba effect. However, the explanation based on the spin Hall effect was initially disputed because the spin Hall angle, θSH, was expected to be negligibly small (θSH < 0.001).65,66) Here, θSH represents the spin accumulation efficiency, which is defined as the ratio between the in-plane charge current and the out-of-plane spin current. However, successive experiments found that the spin Hall angle can be significantly large (up to θSH > 0.1) in some heavy metals such as Pt, Ta, and W due to the strong spin–orbit coupling.67–71) Such a large spin Hall effect in heavy metals successfully explained the magnetization switching behavior. Furthermore, such results implied that the spin Hall effect can be used as a DW driving force.
Soon after, study began on CIDWM using the spin Hall effect. However, there was an unclarified point in spin-Hall-effect-driven CIDWM. The DW in nanowires is generally the Bloch type, that is, the magnetization direction of the DW aligns along the transverse direction of the wire [see Fig. 4(a)]. In this case, the spins diffused by the spin Hall effect are collinear with the magnetization direction, thus, no torque is exerted on the DW (note that the spin torque is described by T = M × s). Therefore, for the spin Hall effect to drive the DW, it is necessary to apply an in-plane magnetic field, which tilts the magnetization of the DW. In this case, however, two DWs move in the opposite directions similarly to magnetic-field-driven DW motion, which is unfavorable for shift-register-based DW memory application.72)
In 2012, Thiaville et al. predicted that the Dzyaloshinskii–Moriya interaction (DMI) plays a crucial role in CIDWM in FM/HM bilayers.73) The DMI is an antisymmetric exchange interaction and can be expressed as , where S1 and S2 are two localized atomic spins. Such interactions are induced because of the lack of inversion symmetry in lattices or at the interface between magnetic films. For example, in FM/HM bilayers, the interfacial DMI can exist owing to the structural inversion asymmetry. Importantly, at the interface between the FM and HM, the DMI generates a chiral spin structure, which stabilizes the Néel DW rather than the Bloch DW. This implies that the spin Hall effect can induce a torque on a DW because the magnetization of the Néel DW is orthogonal to the direction of the injected spin moment. In 2013, two groups independently demonstrated spin-Hall-effect-driven CIDWM in the presence of the interfacial DMI.74,75) By examining the in-plane-field dependence, they clearly showed that the chiral Néel DW is formed by the DMI and is moved by the spin Hall effect. Owing to the DMI-induced chiral DW structure, it is possible to move multiple DWs in the same direction using the spin Hall effect. This result also suggested that the direction of DW motion can be selectively chosen by tuning the sign of the DMI and the spin Hall angle, which explains why the DW moves in the direction of the current flow in some PMA materials. The chiral Néel DW structure was directly observed by spin-polarized low-energy electron microscopy (SPLEEM).76)
The emergence of interfacial DMI has triggered fundamental interest in the spin textures in magnetic materials. In most ferromagnetic materials the magnetization can rotate without a preferred chirality. However, the DMI with inversion symmetry breaking can lift the chiral degeneracy, leading to topological spin textures such as spin spirals and skyrmions.77,78) The dynamics of such topological spin textures became major areas of interest immediately after discovery of skyrmion. The possibility of current-driven skyrmion motion has been tested theoretically and soon be demonstrated experimentally.79–81) The low driving current and high stability of skyrmion motion was also demonstrated. The effect of the DMI on DW dynamics has also been studied. Yoshimura et al. investigated fast DW dynamics by developing a real-time DW detection technique and found that a strong DMI suppresses the velocity breakdown known as the Walker breakdown.82) Here, the Walker breakdown refers to the DW velocity breakdown that can be observed with increasing magnetic field due to the change in the dynamic mode of DW motion from steady motion to precessional motion. Yoshimura et al. demonstrated that a strong DMI lifts the degeneracy of vertical Bloch lines (VBLs), which are topological spin structures located inside a DW (see Fig. 6), leading to the unidirectional collision of VBLs, which increases the DW velocity without velocity breakdown.
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Standard image High-resolution imageThere have been technological advances in SOT period. High-speed DW motion of up to 400 m/s has been achieved.60) In order to increase the driving efficiency, it has been investigated whether it is possible to combine STT and SOT. Ueda and coworkers have shown that the relative strengths of STT and SOT can be tailored by tuning the thickness of layers.83,84) They showed that since the STT originates from the FM layer while the SOT and DMI arise from the interface or HM, one can selectively choose the desired driving force or effectively add the driving forces by tuning the layer thickness. Taniguchi et al. have demonstrated experimentally that the position of a DW can be precisely controlled by tuning the current pulse length.85) They demonstrated that multiple current pulses can place the DW at a desired position within 10% error. However, Kim et al. have pointed out that it may be difficult to reduce the threshold current density while maintaining the thermal stability because the SOT-driven CIDWM is governed only by extrinsic pinning.86) Their work implies that novel materials with much higher spin Hall efficiency are required. Regarding the issue of the shift-register application, the remaining but the most important question is whether it is possible to move multiple DWs by SOT and to detect them in real-time. In the following, we show our recent experimental result on this important issue.
3. Real-time detection of current-induced multiple DW motion
3.1. Sample and measurement setup
For this study, Si/Ta (4 nm)/Pt (2 nm)/Co (0.3 nm)/Ni (0.6 nm)/Co (0.3 nm)/MgO (1 nm)/Pt (2 nm)/Ta (4 nm) films were prepared by DC magnetron sputtering. An MgO layer was inserted to break the structural inversion symmetry. This breaking of the structural inversion symmetry generated an interfacial DMI in the film. The perpendicular magnetic anisotropy (KU) and saturation magnetization (MS) of the film were 1.31 × 106 J/m3 and 8.37 × 105 A/m, respectively. Figure 7(a) shows a schematic illustration of the device with the measurement setup. 500-nm-wide nanowires were fabricated by electron beam lithography and Ar ion milling. Au (100 nm)/Ti (5 nm) metallic electrodes (labeled A–D) were fabricated. Electrodes A and D were used for the flow of DC current to drive the DW. Electrode B was used for writing the DW by using a current-induced local Oersted field. To prevent current shunting between electrode B and the nanowire, that is, to separate the writing and driving currents, SiO2 (30 nm) was inserted between electrode B and the nanowire as shown in Fig. 7(a). Electrode C was in contact with to the Hall bar structure, which was designed to detect the DW motion by change in the anomalous Hall resistance RH. The length between electrode B and the Hall bar was set to 3 µm.
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Standard image High-resolution imageWe first explain the real-time domain writing and driving scheme. A strong out-of-plane magnetic field of 4 kOe is first applied along the −z-direction to saturate the magnetization state in the downward direction. Subsequently, a driving current, Id, is injected into the nanowire along the +x-direction, then spins with moments m aligned along the −y-direction accumulate at the interface due to the spin Hall effect of the HM [red arrows in Fig. 7(b)]. Such accumulated spins diffuse into the FM and exert torque on the magnetization of the FM. Since the magnetization of the FM [pink arrows in Fig. 7(b)] is aligned along the −z-direction (), the resulting torque () is directed along the −x-direction. Therefore, no magnetization reversal occurs. However, if we apply an in-plane longitudinal field Hx along the −x-direction and tilt the magnetization slightly, then the magnetization can be switched. This is the so called spin Hall-induced deterministic switching process, which has been reported in recent works.61,62) Note that a small in-plane bias field Hx is necessary to switch the magnetization. In our scheme, however, such an in-plane field is generated by the DW writing current pulse, Iw, which is injected along electrode B [see Fig. 7(a)]. This pulse Iw generates a local Oersted field underneath the electrode and tilts the magnetization along the −x-direction. As a result, the local area underneath the electrode is reversed. Using this scheme, a domain can be formed whenever we inject a writing current pulse Iw (along electrode B) in the presence of driving current Id (between electrode A and D). The created domain (or two DWs) is then moved by the driving current Id, which has already been applied between electrodes A and D. Using this technique, we can create and move multiple DWs.
3.2. Results
We first check whether or not the writing process is successfully performed. Figure 8 shows the result of Hall measurement. The anomalous Hall resistance, RH, is measured by sweeping the magnetic field along the z-direction in the presence of a weak dc current (0.1 mA). When the magnetic field is zero (HZ = 0), we inject both a driving current (Id = 6 mA, current density of Jd = 9 × 1011 A/m2) and a writing current pulse (Iw = 70 mA, 50 ns) simultaneously, which are required for spin-Hall-effect-induced domain switching. If the domain is created by Id and Iw, then the coercive field will decrease because magnetization reversal occurs as a result of the DW motion (note that the DW propagation field is much smaller than the switching field). Figure 8(a) shows the result of RH measurements under the application of +Id and +Iw. A clear asymmetric coercive field is observed; the switching field for a negative-to-positive sweep (∼10 mT) is much smaller than that for a positive-to-negative sweep (∼150 mT). This indicates that spin-Hall-induced magnetization switching occurs during the negative-to-positive field sweep, as expected from the spin-Hall-induced deterministic switching. To further confirm the deterministic writing, we reverse the sign of the writing current pulse (i.e., +Id and −Iw) and find that the asymmetry in the coercive field is exactly inverted as shown in Fig. 8(b). Therefore, Fig. 8 clearly demonstrates that domain writing is possible by combining the spin Hall effect (induced by Id) and the local Oersted field (induced by Iw).
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Standard image High-resolution imageWe then attempt the real-time measurement of current-induced motion of multiple DWs. We first inject a driving current Id (Jd = 9 × 1011 A/m2) into the nanowire. This driving current is used to drive the DW as well as to create the domain (i.e., two DWs). Subsequently, two successive writing current pulses (Iw = 70 mA), whose durations are respectively 100 and 50 ns, are injected into electrode B. Figure 9(a) shows the writing current pulses recorded by an oscilloscope. One can expect that domains, whose length depends on the writing pulse duration, will be formed in the nanowire by the spin-Hall-induced switching and moved immediately by Id. To detect the real-time DW motion, the Hall voltage is recorded by the oscilloscope through a differential amplifier. The details of the real-time Hall measurement technique are described in Ref. 82. We repeat the measurement 30 times to obtain a sufficiently high signal-to-noise ratio. Figure 9(b) shows the measured Hall voltage. Two square-shaped signals, which have exactly the same duration as the writing pulses, are observed. This implies that the created DWs are moved along the nanowire by Id. The time lag between the writing current pulse and the detected Hall voltage is about 60 ns, which corresponds to the DW travel time between electrode B and the Hall bar. The DW velocity is calculated from the DW travel time (60 ns) and travel distance (3 µm) to be 50 m/s, which is consistent with a previous report.86)
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Standard image High-resolution image3.3. Discussion
The observation in Fig. 9 clearly indicates the real-time process of multiple DW motion, that is, multiple DWs are created by writing current pulses, immediately moved by the driving current, and directly detected by the Hall voltage in real-time. This suggests that the shift register operation is indeed possible using CIDWM. Here, we further discuss the implications of our experimental results. Figure 9 shows that the transient time of Hall signal is about 10 ns, which is clearly longer than that of the DW writing current pulse (∼1 ns). One possible reason for this is the DW velocity distribution. Because the signal is averaged over 30 repeated measurements, the DW velocity distribution can induce a distribution in the DW arrival time, resulting in a transient time during the averaging process. The other possible reason is the stochasticity in the DW writing process since we do not know the exact time of DW nucleation during the writing current pulse. To elucidate the origin of the transient time of the Hall signal, it is necessary to perform a one-shot measurement without averaging. From Fig. 9, one can also infer the distance between two moving DWs. Considering the DW velocity (50 m/s) and the writing pulse duration (50 ns), the distance between two DWs is about 2.5 µm. To compete with existing memories, it is necessary to greatly reduce the DW spacing, which may be achievable by reducing the writing pulse duration. We confirmed the successful movement of multiple DWs using a 20 ns writing pulse, but we find that achieving DW motion becomes elusive below 20 ns due to the transient time in the Hall signal. Therefore, further work is needed to definitively demonstrate the shift register operation of real-time CIDWM.
4. Conclusions
In this article, we have reviewed the progress and current status of CIDWM study. We have also shown our state-of-the-art experimental results, which demonstrate the real-time shift register operation of CIDWM. Although memory application using CIDWM has almost been realized, there are still several technical hurdles which must be solved to realize devices. The most urgent problem is reducing the threshold current density required to move the DW. The threshold current density has been reduced down to the order of 1011 A/m2 by using PMA materials, but it is still too high and should be reduced by at least one more order. However, This reduction of the threshold current density will inevitably also decrease the DW velocity. Thus, it is necessary to increase the DW velocity at the same time. To solve these technical problems, it is necessary to survey novel materials beyond the ferromagnets. Considering that the threshold current density is inversely proportional to the magnetization of materials, materials with low magnetization are promising for future study. Ferrimagnets or antiferromagnets may be alternatives because they have much lower magnetization or even zero magnetization.87) Recently, a low threshold current has indeed been reported in ferrimagnetic compounds.88,89) Furthermore, a high DW velocity was also been predicted for antiferromagnets90,91) and experimentally reported for synthetic antiferromagnets and a ferrimagnet.92) The DMI and spin Hall effect have also been found in ferrimagnet/heavy metal bilayers.93,94) These results therefore undoubtedly signal that exploring appropriate antiferromagnetic or ferrimagnetic materials may be a key to realizing DW-motion-based shift register devices.
Acknowledgments
This work was partly supported by JSPS KAKENHI Grant Numbers 15H05702, 26870300, 26870304, 26103002, 25220604, 2604316, and the Collaborative Research Program of the Institute for Chemical Research, Kyoto University, the Cooperative Research Project Program of the Research Institute of Electrical Communication, Tohoku University, and R&D project for ICT Key Technology of MEXT from the Japan Society for the Promotion of Science (JSPS). KJK was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2017R1C1B2009686) and by the DGIST R&D Program of the Ministry of Science, ICT and Future Planning (17-BT-02).