Letter pubs.acs.org/NanoLett
Magnetically Capped Rolled-up Nanomembranes Robert Streubel,*,†,‡ Dominic J. Thurmer,† Denys Makarov,*,† Florian Kronast,§ Tobias Kosub,†,‡ Volodymyr Kravchuk,∥ Denis D. Sheka,⊥ Yuri Gaididei,∥ Rudolf Schaf̈ er,¶,# and Oliver G. Schmidt†,‡ †
Institute for Integrative Nanosciences, IFW Dresden, 01069 Dresden, Germany Material Systems for Nanoelectronics, TU Chemnitz, 09107 Chemnitz, Germany § Helmholtz-Zentrum Berlin für Materialien und Energie GmbH, 12489 Berlin, Germany ∥ Bogolubov Institute for Theoretical Physics, 03143 Kiev, Ukraine ⊥ Taras Shevchenko National University of Kyiv, 01601, Kyiv, Ukraine ¶ Institute for Metallic Materials, IFW Dresden, 01069 Dresden, Germany # Institute for Materials Science, TU Dresden, 01069 Dresden, Germany ‡
ABSTRACT: Modifying the curvature in magnetic nanostructures is a novel and elegant way toward tailoring physical phenomena at the nanoscale, allowing one to overcome limitations apparent in planar counterparts. Here, we address curvature-driven changes of static magnetic properties in cylindrically curved magnetic segments with different radii of curvature. The curved architectures are prepared by capping nonmagnetic micrometer- and nanometer-sized rolled-up membranes with a soft-magnetic 20 nm thick permalloy (Ni80Fe20) film. A quantitative comparison between the magnetization reversal processes in caps with different diameters is given. The phase diagrams of magnetic equilibrium domain patterns (diameter versus length) are generated. For this, joint experimental, including X-ray magnetic circular dichroism photoelectron emission microscopy (XMCD-PEEM), and theoretical studies are carried out. The anisotropic magnetostatic interaction in cylindrically curved architectures originating from the thickness gradient reduces substantially the magnetostatic interaction between closely packed curved nanowires. This feature is beneficial for racetrack memory devices, since a much higher areal density might be achieved than possible with planar counterparts. KEYWORDS: Magnetic nanomembranes, magnetic tubular architectures, curvature, magnetic domain imaging, rolled-up nanotechnology, XMCD-PEEM, micromagnetic simulation
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information is realized by moving the magnetic domain walls coherently to the read device using a current pulse.5 It has recently been demonstrated theoretically16 that the speed of the racetrack memory can be significantly increased when using magnetic wires with cylindrical cross-section. Simulations showed that in such curved magnetic wires, a transition of the transverse domain wall into a magnetic vortex is suppressed due to the instability of magnetic vortices.17,18 Thus, the magnetic domains can be coherently moved at a much higher velocity, while maintaining the magnetic domain pattern. The most straightforward way to obtain magnetic wires with a curved surface is to deposit magnetic thin films onto nonmagnetic architectures with cylindrical cross-section. There are several templates available, such as carbon nanotubes (CNT)19 and nanowires fabricated by anodization.20 However, in reference to on-chip integration and electrical contacting, as required for reading and writing onto racetrack memory,
ver the past years, much effort has been dedicated to studying and tuning electromagnetic properties of structurally confined media. The small dimensions lead to an enhanced surface effect that reveals new physical phenomena in many fields, including plasmonics,1,2 and magnetism.3−5 In addition to conventionally applied lithography approaches, it was demonstrated that the curvature of magnetic nano-objects has substantial impact on their physical properties.6−8 The nanoscopic modification of magnetic properties influences both magnetic equilibrium domain patterns and magnetization reversal processes.9,10 This effect can be adjusted by changing the size of the curved template or the thickness of the magnetic film and provides therefore new possibilities for both fundamental investigations and applications. One of the driving forces of modern magnetism is magnetic recording. The increasing digital storage demand has led to new concepts for future fast high-density nonvolatile random access memory devices (RAM), such as vortex RAM11,12 and magnetic racetrack memory.5,13−15 In the latter approach, the information is stored in domain patterns in an elongated magnetic wire, typically of a rectangular cross-section. Accessing the © 2012 American Chemical Society
Received: March 24, 2012 Revised: June 26, 2012 Published: June 27, 2012 3961
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Figure 1. Nonmagnetic semiconductor tubes fabricated by means of the rolled-up nanotechnology and cut by focused ion beam etching. Panel a shows the SEM image of the tube segments with a diameter of 250 nm before metal deposition. The side view is shown in panel a1. Panels b and c depict the tube segments with a diameter of 250 nm and 1.7 μm capped with Ta(2 nm)/Py(20 nm)/Ta(5 nm), respectively. Panel b1 illustrates the curvature-driven thickness gradient for the case when a 100 nm Py film is deposited on a tube with a diameter of 600 nm.
approaches based on rolled-up nanotechnology21,22 are superior. Rolled-up nanotechnology is a strain-engineering technique that exploits differential strain within a planar nanomembrane. Using this approach one can fabricate rolledup architectures in the range from several nanometers23,24 to several tens of micrometers.25−27 Moreover, electrical contacting of tube arrays has already been successfully demonstrated.28−32 Here, we focus on the curvature-driven modification of the magnetic properties in soft-magnetic caps on cylindrical architectures. For this purpose, nonmagnetic rolled-up nanoand microtubes are fabricated and capped with soft-magnetic permalloy (Py, Ni80Fe20) films. We performed studies on this novel system, including experimental and theoretical investigations of magnetic equilibrium domain patterns (tube diameter versus segment length) and governing magnetization reversal processes. A substantial impact of the curvature-driven thickness gradient on magnetostatic coupling is demonstrated. In order to visualize the magnetic domain patterns on curved surfaces, X-ray magnetic circular dichroism photoelectron emission microscopy (XMCD-PEEM) at BESSY II (beamline UE49-PGM, Helmholtz-Zentrum Berlin) is applied, accompanied by regular magneto-optical Kerr effect measurements. The tubular architectures are fabricated by rolling up epitaxially grown semiconductor multilayers upon selective undereteching. To this end, a GaAs/In33Ga66As strained nanomembrane bilayer is epitaxially grown on top of an AlAs sacrificial layer. All layers are grown on semi-insulating singlecrystal GaAs(001) wafers by molecular beam epitaxy (MBE). The epitaxial growth is monitored by reflection high energy electron diffraction (RHEED) analysis to ensure high-quality crystal growth and smooth layers. The internal stress gradient depends on the film thickness and occurs due to different lattice constants of top and bottom layer. In this respect, the thickness of the In33Ga66As and GaAs layers is adjusted to obtain nonmagnetic semiconducting rolled-up nanomembranes with diameters of 250, 600, and 1700 nm. Before exposing the AlAs sacrifical layer to hydrofluoric acid (HF) for selective
Figure 2. Angle-dependent magnetization reversal of a single cap. (a) The magnetic hysteresis loop is plotted for elongated Py caps with a diameter of 600 nm and a length of 30 μm (inset) for two different inplane angles. Zero degree corresponds to a parallel alignment of the magnetic field with respect to the tube axis. (b) The normalized coercive field is fitted by hc(φ) = Hc(φ)/Hc(φ = 0) = h + (1−h)/ cos(φ) with the longitudinal coercive field constant Hc(φ = 0) = H0 and h being the ratio between anisotropy constant and longitudinal coercive field. The unmodified Kondorsky function is plotted for comparison (dashed).
underetching, deep trenches are patterned on the surface to determine the initial starting edge of the nanomembrane release from the substrate. By means of focused ion beam (FIB) milling, tube segments of varying lengths are obtained at welldefined positions (Figure 1a). Afterward, Py films (20 nm) as well as Ta buffer (5 nm) and capping (2 nm) layers are deposited via dc magnetron sputtering at room temperature (base pressure: 7 × 10−8 mbar; Ar pressure: 10−3 mbar) and shown in Figures 1b,c. By positioning a hole right above the substrate, direct deposition with flux perpendicular to the sample surface is ensured. The resulting magnetic film exhibits a thickness gradient from top toward the equator due to the effectively varying deposition angle caused by the curvature as illustrated for the case of a 100 nm thick Py deposited on a tube with a diameter of 600 nm (Figure 1, panel b1). As the angle with respect to the surface normal becomes larger, the thickness decreases reducing both exchange and magnetic stray field contributions. 3962
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Figure 4. Phase diagram for the magnetic equilibrium state of 20 nm thick Py caps on nonmagnetic tubes. The simulated states are sketched at the right. Small and large symbols indicate calculated and experimental data points, respectively. The hollow triangle represent the Landau state with vortex core. Depending on the magnetization behavior at the ends of the cylindrical cap, two longitudinal states can be distinguished: s-state for longer segments (bottom right) and flower state, which appears for smaller caps ("x"-symbols in the diagram).
particular, the angle between two adjacent elongated caps could be derived from the hysteresis loops by considering two angledependent coercive fields. As the angle φ increases, the coercive field Hc becomes larger (Figure 2b). The experimental data is fitted by applying the modified Kondorsky model,33−35 which is valid for magnetization reversal processes governed by nucleation and motion of domain walls in uniaxial media taking pinning processes into account. Although the Kondorsky model was originally derived for hard-magnetic media, it can also be applied to describe soft-magnetic planar films.36,37 Here, the magnetic anisotropy is due to the shape anisotropy of the elongated cap. The angle dependence of the normalized coercive field reads hc(φ) =
Figure 3. Magnetic equilibrium states in Py cap structures. Panels a and b depict the XMCD-PEEM contrast with corresponding PEEM image for 20 nm thick Py caps on nonmagnetic rolled-up nanomembranes (indicated by dashed rectangles) with a diameter of 250 nm and 1.7 μm, respectively. Red- and blue-colored regions refer to in-plane magnetization components with the orientation indicated by the arrows. The incidence angle of the beam is illustrated in panel a. Coming from long to short tube segments, the contrast transforms from uniform over multidomain (X-shape) to uniform (white). From the arrangement of the vortex chirality in (b), an anisotropic magnetostatic interaction between neighboring Py caps is observed due to the curvature-driven thickness gradient.
Hc(φ) 1−h =h+ Hc(φ = 0) cos(φ)
with the longitudinal coercive field Hc(φ = 0) = H0 and h being the ratio between the anisotropy constant and the longitudinal coercive field. The corresponding coefficients are H0 = 50.1 Oe and h = 0.92 for caps with a diameter of 600 nm, and H0 = 14.8 Oe and h = 0.72 for caps with a diameter of 1.7 μm and a length of 100 μm. Comparing the experimental data for softmagnetic caps with the unmodified Kondorsky function hc(φ) = 1/cos(φ) (dashed), reveals a much smaller increase of the normalized coercive field values due to the curvature of the magnetic film that leads to an increased effective shape anisotropy described by the parameter h. As direct observation of the magnetic domain patterns by optical means like magneto-optical Kerr microscopy38 is barely possible due to the small size and, particularly, the curvature of the magnetic structures, XMCD-PEEM was employed to visualize the magnetic domains. This technique has a spatial resolution of about 25 nm and is successfully applied to investigate both equilibrium states and dynamics in planar softmagnetic films.39−43 In the used setup,44 the polarized X-ray radiation hits the sample under an angle of 74° with respect to the surface normal. The photon energy is set to the L3 absorption edge of nickel (852 eV) to obtain optimal magnetic contrast. The method is sensitive to the in-plane magnetization
A first impression of the curvature-induced modification of the magnetic properties is obtained by measuring the magnetization reversal process in an elongated Py cap on rolled-up nanomembranes (inset Figure 2a) by means of magneto-optical Kerr magnetometry. The hysteresis loops obtained from a single capped tube with a diameter of 600 nm and a length of 30 μm are shown in Figure 2a for two different in-plane field angles φ; parallel alignment of the magnetic field with respect to the tube axis corresponds to φ = 0°. Although the spot size of the laser beam is ∼10 μm, the contribution of the surrounding planar Py film can be subtracted from the hysteresis curves due to significantly smaller switching fields. In 3963
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Figure 5. Vortex core displacement. (a) The images show the XMCD-PEEM contrast of Py caps with a diameter of 1.7 μm and a length of 2.4 μm while applying a magnetic field along the sketched direction. The displacement of the vortex core (indicated by black dot in panel a) is plotted in (b) and (c) for caps with a diameter of 1.7 μm and 250 nm, respectively.
component, since the transition probability depends on the polarization and direction of incidence of the X-ray radiation and the electron spin (magnetization). The emanating photoelectrons are filtered with respect to their normal momentum and detected by a CCD camera. In order to obtain the magnetic domain patterns, the PEEM signals for leftand right-circular polarized light excitation are subtracted from each other and normalized by their sum. The observed magnetic equilibrium states are shown in Figure 3 for Py caps with diameters of 250 nm and 1.7 μm and different length (indicated by dashed rectangles). Both PEEM (topography data) and XMCD images (magnetic contrast) are depicted. Red- and blue-colored regions correspond to in-plane magnetization components aligned under 13° to the tube axis (incidence direction of the beam), while white areas refer to transverse orientation. For long caps, a uniform contrast is observed that transforms into an X-shape contrast pattern with shorter segment length. As indicated by the arrows in Figure 3a, the latter pattern corresponds to a curling of the in-plane magnetization. Considering the spatial resolution of the setup, the observed magnetic domains with sizes in the order of 40 nm are already at the limit. An even further decrease of the cap size leads to a significant contribution of electrons excited by transmitted X-ray radiation that disturb the XMCD contrast. The magnetic contrast coming from the surrounding Py film on the planar substrate is also visible. However, due to a rather large separation distance between the substrate and a cap (= tube diameter), only vanishingly small magnetostatic interaction between the surrounding Py film and cap structures is present. Therefore, no strong modification of the magnetization reversal of caps is expected from the presence of the surrounding ferromagnetic film. Increasing the diameter to 1.7 μm reveals the same transition but with a different scaling (Figure 3b). Caps with a length larger than 5 μm reveal a uniformly magnetized state along the tube axis at remanence (not shown). Here, we have chosen a
double-tube configuration to study the coupling between neighboring segments. Comparing the magnetization orientation inside the two narrow cap rows, no coupling between them is observed as expected for diameters larger than 800 nm due to the thickness gradient.7,45 On the contrary, the magnetostatic interaction between adjacent caps of the same row is not suppressed due to the absence of a thickness gradient along the tube axis. As a result, vortex cores in neighboring caps nucleate during magnetization reversal process at the same side of the row to minimize long-range magnetic stray fields. In this respect, the stray field merely exists between the longitudinal edges of the cap. The corresponding anisotropy of magnetostatic interaction indicates the substantial impact of a thickness gradient, which can even be scaled down to a few tens of nanometers. Thus, a much higher areal density of wires compared to planar stripes can be achieved, which is beneficial to increase storage density of racetrack memory devices. To interpret the obtained magnetic contrast, micromagnetic simulations were performed for Py cap structures with a nominal thickness of 20 nm. For this purpose, the OOMMF code [version 1.2a4 (http://math.nist.gov/oommf/)] with the conjugate gradient method (minimizer Oxs_CGEvolve) is applied. The ground state is derived by determining the lowest energy of five different initial magnetization configurations: (i) uniformly magnetized along the cylinder axis (x-axis); (ii) uniformly magnetized along the vertical axis (z-axis); (iii) uniformly magnetized along the y-axis; (iv) uniformly magnetized along the diagonal of the cap (Lex + Rey with the length L, the radius R and the unit vectors ex,y); and (v) vortex state. All simulations are carried out at zero temperature for the material parameters of permalloy: exchange constant A = 1.3 × 10−11 J/m, saturation magnetization Ms = 8.6 × 105 A/m, and crystal anisotropy was neglected. The mesh size was varied from 2 to 5 nm depending on the sample size. For tubes with a diameter of 1.7 μm, the mesh size was set to 10 nm, which is still smaller than the vortex core diameter.4,46 Although this size 3964
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does not allow to determine the inner vortex core structure, conclusions about the ground state can still be drawn from the total energies. The resulting magnetic equilibrium states are sketched in Figure 4 at the right. A transition from longitudinal via vortex to a transverse state is apparent, which agrees well with the contrast transition observed in the experiment (Figure 3). For a quantitative analysis, the experimentally determined states are merged into the simulated phase diagram for magnetic equilibrium states in the Py caps. The hollow triangles represent Landau states with a vortex core (structured vortex states that consist of both 180 and 90° domain walls), which are also observed by micromagnetic simulations. A reasonable good agreement between experiment and theory is found. The behavior of the magnetic vortices in an applied magnetic field is experimentally examined. Figure 5 depicts the magnetic domains in Py caps with a diameter of 1.7 μm for different field values. With increasing field, the vortex is displaced and eventually expelled from the cap. The vortex core displacement as a function of the magnetic field is displayed in Figure 5b,c for caps with diameters of 1.7 μm and 250 nm, respectively. The data is approximated by a linear function. Comparing the slope of both samples reveals a difference of more than 1 order of magnitude. This finding is in agreement with the restoring force acting on the vortex core that is linear in the vortex core displacement and also depends on the aspect ratio, as known for planar disks.47 The cylindrically curved magnetic architecture represents a novel system that is, due to strongly modified magnetic properties, interesting for both fundamental studies, that is, magnetic equilibrium states, magnetostatic interaction and domain wall dynamics, and eventually applications. We prepared soft-magnetic caps deposited on top of nonmagnetic rolled-up semiconductor nano- and microtubes and investigated the impact of curvature on the magnetic properties. The magnetization reverses by domain wall motion describable by a modified Kondorsky model taking the curvature into account. We assembled the phase diagram of magnetic equilibrium states both experimentally and theoretically, showing remarkable agreement. In addition, the behavior of magnetic vortices when exposing to an external magnetic field is examined in cap structures with radii down to 250 nm. A linear restoring force acting on the displaced vortex core is determined. The crucial difference compared with planar structures is the anisotropic magnetostatic interaction in cylindrically curved architectures due to the thickness gradient. This feature allows to assemble noninteracting closely packed nanowires, as it is beneficial for racetrack memory devices, with a much higher areal density than possible with planar nanowires.
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AUTHOR INFORMATION
Corresponding Author
*E-mail: (R.S)
[email protected]; (D.M.) d.makarov@ ifw-dresden.de. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors thank I. Fiering and G. Lin (IFW Dresden) for metal deposition. This work is financed via the German Science Foundation (DFG) Grants MA 5144/1-1, MA 5144/2-1, SCHM 1298/14-1 and DFG Research Unit 1713. 3965
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