Study of Spin Configuration of Hexagonal Shaped Ferromagnetic Structures LUA YAN HWEE, SUNNY (B. Eng (Hons.), NUS) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY NUS Graduate School for Integrative Sciences and Engineering National University of Singapore 2008 ABSTRACT This thesis work consists of two distinct parts: the set-up of a unique characterisation system and the study of spin configurations in hexagonal ferromagnetic structures. The characterisation system developed is able to perform in-situ magnetic imaging, structural modification and electrical transport measurement on ferromagnetic structures. For the latter, hexagonal ferromagnetic structures were investigated due to its uniqueness of having a vortex state with well-defined, symmetric and moderate stray field for desirable magnetostatic interaction, which is not found in the vortices of circular disk structures. Systematic thickness reduction by in-situ FIB confirmed that the vortex structure in hexagonal elements is stable over a wide thickness range. The combined SEMPA and MFM characterisation makes it possible to determine the chirality of individual vortices. By arranging the hexagons in ring networks, we found that there is an occurrence of alternating chirality configuration in the vortices when the inter-element spacing is small. However, such alternating chirality distribution disappears in rings with either large inter-element spacings or additional / removed elements as well as in linear chains. The results imply that, in addition to the strength, the symmetry of the stray field also plays an important role in determining the relative chirality of individual hexagons. In order to explore potential applications of hexagonal elements, composite structures consisting of hexagons and a nanowire were also investigated by both magnetic-field and current-pulse induced domain wall motion measurements. The results show that it is possible to cause magnetisation reversal in the composite structures by spin-transfer torque effect. i CONTENTS ABSTRACT I CONTENTS . II LIST OF SYMBOL AND ABBREVATION XII ACKNOWLEDGMENTS . XIII 1. INTRODUCTION 1.1 Ferromagnetic Elements with Different Shapes 1.1.1 Disks . 1.1.2 Ellipses . 1.1.3 Rings . 1.1.4 Squares and rectangle elements 1.1.5 Wires . 1.1.6 Other shapes . 10 1.1.7 Dynamics study of ferromagnetic structures . 11 1.2 Potential Applications 13 1.3 Motivation and Objectives . 15 1.4 Organisation of this Thesis . 17 Chapter References . 18 2. MICROMAGNETIC MODELLING AND MAGNETIC CHARACTERISATION TECHNIQUES . 22 2.1 Introduction . 22 2.2 Domain Walls in Ferromagnetic Material . 23 2.2.1 Bloch wall . 23 2.2.2 Neél wall . 24 2.2.3 Domain walls in ferromagnetic nanowires . 25 2.3 Magnetic Energy Terms in Micromagnetism 27 2.3.1 Magnetostatic self- energy . 27 2.3.2 Magnetocrystalline anisotropy energy 28 2.3.3 Exchange energy 29 2.3.4 Zeeman energy . 30 2.4 Micromagnetic Simulation with LLG Equation 31 2.5 Magnetic Imaging Techniques . 33 2.5.1 SEMPA . 34 2.5.2 MFM . 39 2.6 Summary . 43 ii Chapter References . 44 3. EXPERIMENTAL DETAILS AND DEVELOPMENT OF ADVANCED MAGNETIC CHARACTERISATION SYSTEM . 47 3.1 Introduction . 47 3.2 Fabrication Techniques 47 3.2.1 Electron beam lithography (EBL) . 47 3.2.2 Thin film deposition process 48 3.2.3 Lift-off . 49 3.3 Integrated Ultra High Vacuum Characterisation System Setup 49 3.3.1 FIB 50 3.3.2 Nanoprobe system 51 3.4 Experimental Set-up for Current-Induced Magnetisation Reversal Study . 52 3.5 Summary . 53 Chapter References . 54 4. STUDY OF HEXAGONAL ELEMENT ARRAYS BY SEMPA 55 4.1 Introduction . 55 4.2 Experimental Details 55 4.3 Spin Configuration in a Hexagonal Element . 56 4.4 Characterisation of Arrays with Various Inter-Element Spacings 60 4.5 Mechanism of Chirality Distribution . 63 4.6 Correlation of SEMPA and MFM Imaging Results 64 4.7 Effect of Thickness Reduction by in-situ FIB on an Array of Hexagons . 65 4.7.1 Thickness reduction by in-situ FIB 65 4.7.2 X-ray photoemission spectroscopy (XPS) . 67 4.7.3 M-H curves . 68 4.7.4 Micromagnetic simulation . 70 4.8 Summary . 72 Chapter References . 73 5. SPIN CONFIGURATION OF HEXAGONAL ELEMENTS IN DIFFERENT ARRANGEMENTS 74 5.1 Introduction . 74 5.2 Hexagons in Artificial Arrangements 74 5.2.1 5.2.2 5.2.3 Ring network 74 Ring network with a missing element 78 Floral network 79 iii 5.2.4 Linear chain network . 83 5.2.5 Star network . 84 5.2.6 Triangular network 85 5.2.7 Rhomboidal network 86 5.2.8 Pyramidal network . 87 5.3 Summary . 89 Chapter References . 90 6. MAGNETOSTATIC INTERACTION OF HEXAGAONAL ELEMENTS WITH A NANOWIRE . 91 6.1 Introduction . 91 6.2 Single Hexagon in Contact with a Nanowire 91 6.2.1 Nanowire 91 6.2.2 Nanowire with a notch structure . 96 6.3 Six Hexagons in a Ring Network in Contact with a Nanowire 98 6.4 Six Hexagons in a Ring Network in Contact with Two Nanowires . 102 6.5 Current Pulse Study on Hexagons with a Nanowire . 106 6.5.1 Hexagon with a notched nanowire 107 6.5.2 Hexagons in a ring network with a notched nanowire . 110 6.5.3 Hexagons in a ring network with a nanowire . 113 6.6 Voltage-Pulse Injection Perpendicular to Ferromagnetic Structures 115 6.7 Summary . 117 Chapter References . 118 7. CONCLUSIONS AND RECOMMENDATIONS . 119 7.1 Conclusions . 119 7.2 Recommendations for future work 121 LIST OF PUBLICATIONS . 124 Journal papers: . 124 Others: 124 Conferences: . 125 Others: 125 iv LIST OF FIGURES Number Page Figure 1.1 Magnetisation distribution in a circular disk obtained by micromagnetic simulations for (a) a C-state and (b) S-state, respectively [After J. K. Ha, 2003, Ref. 7]. Figure 1.2 Experimental observations of magnetic states in circular disk structures together with the corresponding magnetisation distribution obtained by micromagnetic simulation: (a) triangle state, (b) diamond state [After C. A. F. Vaz, 2005, Ref. 10], and (c) vortex state [After T. Shinjo, 2000, Ref. 19]. Figure 1.3 Magnetic image of an elliptical structure at remanent state obtained after an in-plane magnetic field applied along (a) long and (b) short axis, with single domain and flux-closure state, respectively. Arrows represent the orthogonal magnetisation directions [After X. Liu, 2004, Ref. 32] Figure 1.4 (a) MFM images of octagonal ring structures with corresponding magnetisation distribution for SD and flux-closure states, respectively [After S. P. Li, 2001, Ref. 38]. (b) MFM images of the square rings in a horseshoe state, with magnetisation direction represented by arrows [After P. Vavassori, 2003, Ref. 42]. . Figure 1.5 Micromagnetic simulation of (a) a flower state and (b) a leaf state, in a square nanomagnet of edge length 100 nm and thickness 20 nm . [After R. P. Cowburn, 2000, Ref. 1]. Figure 1.6 (a) Foucault image of a rectangle in a S state [After J. N. Chapman, 1998, Ref. 59]. (b) Electron holography of a rectangle in a C state with its corresponding magnetisation distribution in Co, and Ni and simulated holography contours [After R. E. Dunin-Borkowski, 1998, Ref. 52]. (c) Foucault image obtained for square and rectangle with a flux-closure state and a seven-domain state [After K. J. Kirk, 2000, Ref. 55]. (d) Foucault image of two rectangles with different width having a flux-closure state and a partial flux closure [After K. J. Kirk, 1997, Ref. 51]. . Figure 1.7 (a) Foucault image of NiFe(26 nm thick) wires with two pointed ends in an array [After K. J. Kirk, 1997, Ref. 51]. (b) A plot of the coercivity as a function of the ratio of the spacing to the width when magnetic field applied along the easy axis of the wire array [After A. O. Adeyeye, 1997, Ref. 70]. 10 Figure 1.8 (a) SEM images of pentagon arrays in different sizes, 500 nm and 100 nm, respectively [After R. P. Cowburn, 2000, Ref. 1]. (b) SEM image of an array of elongated hexagons, mm long and 500 nm wide with its corresponding Magnetic hysteresis loops obtained for easy and hard axis, respectively [After G. Xiong, 2001, Ref. 74]. .11 Figure 1.9 (a) Switching probabilities as a function of excitation current frequency of NiFe disk used for vortex core polarity reversal by AC currents [After v K. Yamada, 2007, Ref. 81]. (b) Schematic setup for the magnetic vortex core reversal by AC magnetic field which consists of the NiFe sample with a flux-closure state and gold stripline [After B. Van Waeyenberge, 2006, Ref. 82]. 12 Figure 1.10 Schematics of (a) patterned media with higher storage density by having smaller patterned elements and denser packing, and (b) MRAM, respectively. 13 Figure 1.11 (a) SEM image of a NiFe nanowire with a NOT function and its corresponding magnetic signal response from a counterclockwise rotating magnetic field as a function of time [After D. A. Allwood, 2002, Ref. 87]. (b) SEM images of the left (A), center (B), and right (C) regions of two of the MQCA [After R. P. Cowburn, 2000, Ref. 89]. (c) A set of MQCA with single-domain states for majority logic gate application [After A. Imre, 2006, Ref. 90]. (d) Schematic illustration of the shift-register operation. Black squares and white squares represent head-to-head and tail-to-tail domain-walls, respectively [After M. Hayashi, 2008, Ref. 91]. .14 Figure 2.1 (a) Schematic of a ferromagnetic material containing a 180° Bloch wall and (b) its spin orientations in a uniaxial material. .24 Figure 2.2 (a) Schematic of a ferromagnetic material containing a Neél wall. (b) Magnified sketch of the spin orientations of a Neél wall in a uniaxial material. 25 Figure 2.3 Schematic of spin orientation of a (a) transverse and (b) vortex head-tohead domain wall in a soft ferromagnetic nanowire. 26 Figure 2.4 Schematic of the reduction of magnetostatic energy by forming flux closure in a ferromagnet. 28 Figure 2.5 Comparison of different types of magnetic imaging techniques [After A. Hubert and R. Schäfer, 1998, Ref. 12]. 34 Figure 2.6 Schematic of the SEMPA. Two of the four (2,0) LEED beams are shown, together with the respective electron detectors. 35 Figure 2.7 The principle of the SEMPA: An incident beam from the SEM column creates spin-polarised secondary electrons, from the surface of the ferromagnetic sample, which are subsequently spin analysed 37 Figure 2.8 Schematic of a typical MFM measurement in LiftMode. 40 Figure 2.9 (a) Schematic of an interaction between a dipole and a magnetic structure. (b) A five-dipoles approximation of the tip used for the MFM contrast modelling. .41 Figure 3.1 Schematic of the flow of the fabrication process of the mesoscopic sized ferromagnetic hexagonal elements. 48 Figure 3.2 Photographs of the integrated UHV system consisting of (i) FIB, (ii) SEMPA, (iii) nanoprobe system. .50 Figure 3.3 SEM image of a network of NiFe hexagons created using FIB. .51 Figure 3.4 Secondary electron micrographs of (a) four nanoprobes positioned on the contact pads of a device for nano-scale transport measurement and (b) a vi nanoprobe on square element (it appears as a rectangle due to large tilt angle) for current-induced magnetisation switching study. 52 Figure 3.5 Schematic of a current-induced magnetisation reversal set-up integrated with a MFM system. 53 Figure 4.1 Simulated magnetisation distribution for a permalloy (a) disk and (b) hexagon at zero magnetic field, respectively. [(c) and (d)] Calculated divergence of the magnetisation superposed with the stray field distribution (arrows), and [(e) and (f)] simulated MFM images of the corresponding elements. (g) and (h) show MFM images of a permalloy hexagonal element with CCW and CW sense of rotation, respectively. White (black) curved arrow represents the CW (CCW) chirality. .59 Figure 4.2 Simulated magnetisation orientation of the hexagonal element with a diagonal length of µm for (a) longitudinal and (b) transverse components. Arrows represent the magnetisation directions. 60 Figure 4.3 SEMPA images of the in-plane magnetisation components: (i) longitudinal (x) and (ii) transverse (y), as well as topographic images (iii), of the hexagonal elements acquired simultaneously. Each regular hexagonal element has a diagonal length of µm, with edge-to-edge separation s of (a) 100 nm, (b) 400 nm and (c) µm, respectively. .62 Figure 4.4 SEMPA images of the in-plane magnetisation components: (i) longitudinal (x) and (ii) transverse (y), as well as topographic images (iii), of the hexagonal elements with s = 200 nm. .62 Figure 4.5 Schematic of a seven-element array with (a) same chirality and (b) alternate chain of chirality distribution. Curved arrows represent the magnetisation directions. .63 Figure 4.6 (a) Topographic image of an array of hexagonal elements, with s = 100 nm, acquired by SEMPA. Magnetic images of the corresponding area obtained by SEMPA, (b), and MFM, (c), agree with each other in terms of sense of rotation, as indicated by the white (CW) and black (CCW) curved arrows. 65 Figure 4.7 SEMPA images of the in-plane magnetisation components: (i) longitudinal (x) and (ii) transverse (y), as well as topographic images (iii), of the hexagonal elements acquired simultaneously. The same sample with s = 200 nm was imaged with different FIB trimmed thicknesses: (a) 30 nm, (b) 20 nm, (c) 12 nm and (d) nm, respectively. 66 Figure 4.8 (a) Schematic of the area milled by FIB on a 30 nm thick NiFe film. XPS plot of the intensity against the binding energy of the FIB milled area over (b) a wide and (c) a narrow scan range. 69 Figure 4.9 Magnetic moment against magnetic field curves for (a) total NiFe film with and without FIB milling, and (b) FIB milled region (extracted from the total measurement). 70 Figure 4.10 A matrix of the simulated spin configurations of the regular shaped hexagonal element with a diagonal length of µm for different t and Ms. 71 vii Figure 4.11 (a) SEMPA image (x component) of an array of hexagons with diagonal lengths of µm and s = 200 nm with a thickness of about nm, trimmed by in-situ FIB. Elements with double vortex state were highlighted. (b) A simulated magnetisation configuration in x component of a hexagon with same diagonal lengths but lower Ms and thickness [Fig. 4.8(h)]. 72 Figure 5.1 (a) A scanning electron micrograph of a ring network of NiFe hexagons with diagonal lengths of m. [(b) – (h)] MFM images of the hexagons with s ranging from 100 nm to µm, respectively. White (black) curved dotted arrows represent the CW (CCW) chiralities. .75 Figure 5.2 Magnetisation configurations of hexagons in ring network with (a) same (CCW) chirality and (d) alternating chirality, together with curved arrows outside of the hexagons representing the stray field. 76 Figure 5.3 MFM images of a ring network of hexagons with s = 200 nm at remanance after having a magnetic field of 10 kOe applied at angle θ, (a) 0°, (b) 180°, (c) 120°, and (d) 300°, respectively. White (black) curved dotted arrows represent the CW (CCW) chiralities. (e) and (f) show schematics of the alignment of the magnetisation to an applied saturation field. Dotted lines with arrows indicate the direction of the magnetic flux emanating from the hexagons. .78 Figure 5.4 (a) A scanning electron micrograph of a ring network of NiFe hexagons with diagonal lengths of m and a missing element at the bottom right corner.[(b) – (h)] MFM images of the hexagons with s ranging from 100 nm to µm, respectively. White (black) curved dotted arrows represent the CW (CCW) chiralities. .79 Figure 5.5 (a) A scanning electron micrograph of a floral network of NiFe hexagons with diagonal lengths of m. [(b) – (h)] MFM images of the hexagons with s ranging from 100 nm to µm, respectively. White (black) curved dotted arrows represent the CW (CCW) chiralities. .80 Figure 5.6 (a) A scanning electron micrograph of a floral network of NiFe hexagons with diagonal lengths of m and a missing element at the bottom right corner. [(b) – (h)] MFM images of the hexagons with s ranging from 100 nm to µm, respectively. White (black) curved dotted arrows represent the CW (CCW) chiralities 81 Figure 5.7 Plot of stray field distribution away from an edge of a hexagon obtained by simulation. .82 Figure 5.8 Plot of stray field distribution away from a corner of a hexagon obtained by simulation. 83 Figure 5.9 (a) A scanning electron micrograph of a linear-chain network of NiFe hexagons with diagonal lengths of m. [(b) – (f)] MFM images of the hexagons with s ranging from 100 nm to 1.5 µm, respectively. White (black) curved dotted arrows represent the CW (CCW) chiralities. .84 Figure 5.10 (a) A scanning electron micrograph of a star network of NiFe hexagons with diagonal lengths of m. [(b) – (h)] MFM images of the viii hexagons with s ranging from 100 nm to µm, respectively. White (black) curved dotted arrows represent the CW (CCW) chiralities. .85 Figure 5.11 (a) A scanning electron micrograph of a triangular network of NiFe hexagons with diagonal lengths of m. [(b) – (h)) MFM images of the hexagons with s ranging from 100 nm to µm, respectively. White (black) curved dotted arrows represent the CW (CCW) chiralities. .86 Figure 5.12 (a) A scanning electron micrograph of a rhomboidal network of NiFe hexagons with diagonal lengths of m. [(b) – (h)] MFM images of the hexagons with s ranging from 100 nm to µm, respectively. White (black) curved dotted arrows represent the CW (CCW) chiralities. .87 Figure 5.13 (a) A scanning electron micrograph of a pyramidal network of NiFe hexagons with diagonal lengths of m. [(b) – (h)] MFM images of the hexagons with s ranging from 100 nm to µm, respectively. White (black) curved dotted arrows represent the CW (CCW) chiralities. .88 Figure 5.14 (a) A scanning electron micrograph of a pyramidal network of NiFe hexagons with diagonal lengths of m and a missing elements at centre. [(b) – (h)] MFM images of the hexagons with s ranging from 100 nm to µm, respectively. White (black) curved dotted arrows represent the CW (CCW) chiralities. 88 Figure 6.1 Simulated magnetisation distribution of the composite hexagonnanowire structure without a notch: (a) vector form, (b) longitudinal and (c) transverse components at remanent state. (d) Simulated MFM image of the composite structure. .93 Figure 6.2 Simulated magnetisation distribution of the composite hexagonnanowire structure with a separation of 60nm: (a) vector form, (b) longitudinal and (c) transverse components at remanent state. (d) Simulated MFM image of the composite structure. 94 Figure 6.3 (a) A scanning electron micrograph of a NiFe hexagon with diagonal lengths of m, in contact with a wire of 400 nm width. (b) – (d) MFM images of the hexagons after a magnetic field was applied. White (black) curved dotted arrows represent the CW (CCW) chiralities. Dotted white lines are drawn as guides to the eyes. 95 Figure 6.4 Simulated magnetisation distribution of the composite hexagonnanowire structure with a notch: (a) vector form, (b) longitudinal and (c) transverse components at remanent state. (d) Simulated MFM image of the composite structure. .97 Figure 6.5 (a) A scanning electron micrograph of a NiFe hexagon with diagonal lengths of m, in contact with a notched-wire of 400 nm width. (b) – (f) MFM images of the hexagons after a magnetic field was applied. White (black) curved dotted arrows represent the CW (CCW) chiralities. Dotted white lines are drawn as guide to the eyes .98 Figure 6.6 MFM images of a ring network of the hexagons with s = 200 nm at remanance after a magnetic field was applied. White (black) curved dotted arrows represent the CW (CCW) chiralities 99 ix along the nanowire, and/or (b) difference in current density along the nanowire due to structural variation, like the notch structure. Besides domain wall propagation and transformation during the injection of current pulses, it is striking to note that the vortex core of the hexagon oscillates off-centre along the x-direction when a sequence of current pulses of increasing amplitude were injected along the nanowire [Figs. 6.12(d)-(g)]. Such an occurrence of vortex core displacement was observed in a circular disk when a current pulse was injected through the disk [6], which was attributed to the fabrication defects in the disk. Unlike ref. [6], the pulsed current did not flow symmetrically through the central axis of the hexagon in our case. It appears that as the spin-polarised electrons flow along the nanowire, the domain wall moves due to spin-transfer torque from the spin electrons at the critical current. This causes changes in the domain configuration at the intersection of the hexagon and nanowire, which drags the vortex core off-centre in order to create a new equilibrium state. With another current-pulse of larger amplitude, the domains propagate further, forming a new domain configuration in the region. At the same time, to counter the formation of a new domain, the vortex core displaces in opposite direction. It was found that the vortex core is centred on the hexagon only when the domain configuration at the hexagon-wire intersection attains the lowest energy state. 6.5.2 Hexagons in a ring network with a notched nanowire The equipment set-up for the hexagons in a ring network with a notched nanowire is the same as previous section. The ring network under study has an inter-element spacing of about 100 nm [Fig. 6.14]. In this set of experiments, mA current pulses were sequentially injected into the nanowire as shown in Fig. 6.15. 110 The MFM image of hexagons in a ring network with a nanowire at the remanence state is shown in Fig. 6.13(a). Upon the initial injection of a 3.0 mA current pulse, a transverse wall formed near the notched region [Fig. 6.13(b)]. It remained around the notched region even after a few pulses were injected. It appears that both the notch and the hexagon-nanowire intersection act as a potential barrier for the transverse wall, which is not able to propagate at a current density of ~2.5 x 107 A/cm2. Figure 6.14 Schematic of the current-pulse experiment for ferromagnetic hexagons in a ring network adjacent to a notched nanowire structure. 111 eî Figure 6.15 MFM images of the ferromagnetic hexagons in a ring network adjacent to a nanowire with a notch: (a) remanent state prior to current injection, and [(b)-(h)] magnetic states after subsequent injections of pulsed current of constant amplitude of mA. Dotted white lines are drawn as guide to the eyes. 112 Strikingly, after the eleventh pulse, the transverse wall on the left-hand-side of the notch is not observed [Fig. 6.14(g)]. Repeated current pulses have resulted in electromigration which caused roughening of the nanowire. This phenomenon was also observed earlier in the notched nanowire with a single hexagon. Electron-migration appears to have caused a change in the geometry of the nanowire, resulting in the segregation of domains along the affected edges of the nanowire by shape anisotropy. Therefore, although domain wall propagation through the potential barrier of the hexagonnanowire intersection was not possible even at a relatively high current density of ~2.5 x 107 A/cm2, successive current-pulse injection will deform the domain formation due to electron-migration effect on the nanowire. 6.5.3 Hexagons in a ring network with a nanowire Unlike the earlier sample, the nanowire in contact with one of the six hexagons in a ring network does not have a notched structure. Here, a 3.2 mA current pulse was injected into the nanowire as shown in Fig. 6.16(a). As observed from the MFM image, the pulse injection did cause any domain transformation in the nanowire with the hexagon. However, upon injection of a 3.3 mA current pulse (~2.75 x 107 A/cm2), magnetisation reversal of the nanowire and chirality transformation from CW to CCW in the attached hexagon was observed [see Fig. 6.16(b)]. This can be attributed to the spin-transfer torque effect, which resulted in the domain wall motion. However, the chirality of the neighbouring hexagons remained unchanged at the inter-element spacing of 100 nm. It appears that the chirality reversal of an individual hexagon by spin-transfer torque effect could take place when the inter-element spacing becomes negligible like the case of the combined hexagon-nanowire structure. 113 eî Figure 6.16 MFM images of the ferromagnetic hexagons in a ring network adjacent to a nanowire without a notch, after a current pulse injection of (a) 3.2 mA, (b) 3.3 mA , and (c) -3.3 mA, respectively. Dotted white lines are drawn as guide to the eyes. In an attempt to reverse the magnetisation of the nanowire and the adjacent hexagon, a pulse of similar current density was applied in the opposite direction as shown in Fig. 6.16(c). Although there is no significant change to the magnetisation state around the hexagon-nanowire region, a vortex wall with CW chirality was developed along the right-hand-side of the nanowire. Therefore, we have observed that the magnetisation in the hexagon-nanowire structure can be altered by current-induced domain wall motion. 114 6.6 Voltage-Pulse Injection Perpendicular to Ferromagnetic Structures In addition to a lateral current pulse, we have also investigated the effect of a voltage pulse applied into a NiFe square element “vertically” by using a nanoprobe and characterised the magnetic configuration by SEMPA. A nanoprobe was placed in contact with the centre of a square element [Fig. 6.17(a)]. A voltage pulse of 0.3 V with a pulse width of µs was applied to the centre of two different squares, and µm in length, respectively. Comparing with the SEMPA image captured [Fig. 6.17(b)] before and after the injection of the voltage pulse, the vortex centres in the respective squares have shifted from the centre after the injection, as shown in Fig. 6.17(c). Such changes to the magnetic domains could be due to (i) the spin-transfer torque effect [7] and / or (ii) the Oersted field generated around the nanoprobe during the perpendicularly voltage-pulse injection. Due to the low quality of the SEMPA signal and time constraints, we did not conduct a systematic study on the effect of voltage-pulse injection. Nevertheless, this technique presents a potential method to directly reverse the vortex chirality using a confined current injected perpendicular to the plane of the magnetic layer with a probe contact. 115 Figure 6.17 (a) SEM image of a nanoprobe in contact with a NiFe square structure at title angle. SEMPA images of square structures: (b) before and (c) after a voltage-pulse of 0.3 V was injected. 116 6.7 Summary A systematic study on the magnetic properties and the influence of a nanowire in contact with both a single hexagon and hexagons in a ring network was carried out. MFM studies in combination with micromagnetic simulation has shown that the modulation in width of the wire by the attachment of a hexagon can induce domain wall formation in the nanowire. The magnetic-field induced experimental results indicate that the chirality reversal of a hexagon occurs at different magnetic field strengths with the attachment of a single nanowire with and without notch. However, the reversal of the chiralities in the ring network with two separate nanowires behaved differently, which was attributed to the modification of the total magnetic energy of the system. Although the propagation of the domain in the nanowire does not affect the spin configuration of the ring network, the hexagons in the ring network proved to be robust against the domain configuration in adjacent nanowires. The current-pulse induced domain-wall experiment on the hexagon with a nanowire suggests a possibility of magnetisation reversal. The results indicate that the composite hexagon-nanowire structure has the potential to be a building block for magnetic logic devices. 117 Chapter References [1] R. McMichael and M. Donahue, http://math.nist.gov/oommf. [2] K. Shigeto, T. Shinjo, and T. Ono, Appl. Phys. Lett. 75, 2815 (1999). [3] J. C. Slonczewski, J. Magn. Magn. Mat. 159, L1 (1996). [4] J. C. Slonczewski, J. Magn. Magn. Mat. 195, L261 (1999). [5] L. Berger, Phys. Rev. B 54, 9353 (1996). [6] L. Heyne, M. Kläui, D. Backes, et al., Phys. Rev. Lett. 100, 066603 (2008). [7] D. D. Sheka, Y. Gaididei, and F. G. Mertens, Appl. Phys. Lett. 91, 082509 (2007). 118 Chapter 7. CONCLUSIONS AND RECOMMENDATIONS 7.1 Conclusions In this course of study, a comprehensive investigation of the regular hexagonal shaped ferromagnetic elements has been performed. The interest in these structures is due to their moderate stray field and reasonably high symmetry, which enable the possible application of these elements in logic devices. NiFe elements of different arrangements and inter-element spacings were prepared by EBL, sputtering and lift-off processes. Their magnetic properties were characterised by SEMPA and MFM, and compared with micromagnetic modelling. The main contributions and some important results are summarised as follows: (1) An integrated UHV characterisation system was set up which allows for direct imaging of the spin configuration of ferromagnetic elements as well as in-situ nanofabrication and modification of their physical structures. In addition, the integrated system is also equipped with four nanoprobes which makes it possible study electrical transport measurements and perform current-driven domain wall motion measurements in the same setup. (2) Instead of using samples of pre-determined thicknesses, thickness reduction study by successive in-situ FIB trimming of an array of 10 × hexagons with diagonal lengths of µm and an inter-element spacing of 200 nm has been conducted together with SEMPA imaging. The advantage of this approach is that process fluctuation is minimised while investigating the thickness effect. 119 The results suggest that the vortex state in hexagons remains stable over a wide thickness range. (3) A one-to-one correlation between SEMPA and MFM images of vortices has been established through comparison with simulated images. This makes it possible to study the effect of inter-element spacing and symmetry on the relative chirality of vortices in hexagonal elements. (4) By making use of the moderate stray field and well-defined symmetry of hexagons, which is lacking in vortices formed in circular elements, we have shown that it is possible to control the relative chirality of vortices in a ring network of hexagonal elements when the inter-element spacing is kept small. The reversible chirality configuration by an applied field at different angles demonstrates the robustness of such a configuration. However, this alternating chirality distribution disappears in rings with either large inter-element spacing, additional / removed elements, or in linear chains. The results imply that, in addition to the strength, the symmetry of the stray field also plays an important role in determining the relative chirality of individual hexagons. The robustness of such configuration makes the ring network a promising building block for more complex structures with controlled chirality configuration. (5) A systematic study of composite structures consisting of hexagons and a nanowire was also carried out by both magnetic-field and current-pulse induced domain wall motion measurements. Although a notched nanowire has been demonstrated to behave as a domain wall barrier for chirality reversal of the adjacent hexagon in contrast to one without a notch, the hexagons were found to 120 switch concurrently when both types of nanowires were used in the same ring network. This is probably due to the robust nature of the spin configuration in the ring network of hexagons. The current-pulse induced domain-wall motion experiment on the hexagon with a nanowire suggests a possibility of magnetisation reversal via the spin-transfer torque effect. These results indicate that the hexagon with a nanowire is useful as a building block for potential magnetic logic devices. 7.2 Recommendations for future work Several novel findings on hexagonal ferromagnetic elements have been reported in this thesis. There are numerous promising avenues which can be further explored in the area of hexagonal elements. The following are some recommendations for future work: (1) Size-effect of a hexagon on a nanowire This study, [see Fig. 7.1(a)], will provide an understanding of the size-effect of the adjacent hexagon on the critical current required for vortex core displacement as well as the reversal of the chirality. Moreover, a systematic thickness variation study on the composite hexagon-nanowire can also be explored. (2) Current-pulse induced domain-wall motion study in a nanowire adjacent to multiple hexagons Due to the generation and propagation of domain walls as current is injected past the first hexagon, it is possible to realise a “domino” effect on successive hexagons attached to the wire [Fig. 7.1(b)]. When the first vortex core gets displaced by a current pulse, the neighbouring vortex cores may be affected by the domain walls 121 generated by the first hexagon as it propagates down the wire. Instead of having magnetic-field induced switching, it will be interesting to study how current pulses will drive the domain walls in the nanowire, which may alter the chirality of the elements appended to the wire. Consequently, the spin configurations of the adjacent hexagons may be altered, realising a possible logic circuit. Figure 7.1 Proposed schemes to study the effect of current driven domain wall motion using two nanoprobes for (a) a single hexagon-nanowire with systematic size reduction of the hexagon, and (b) different placement of hexagons along the nanowire. 122 (3) Current-pulse injection perpendicular to ferromagnetic structures As an extension to the work described in Chapter 6.6, further studies can be done to determine the feasibility of switching the vortex chirality of a ferromagnetic element by directly injecting a confined current perpendicular to the plane of the element with a probe contact. This has the potential to realise a bit patterned storage medium in which the chirality of the vortices could be accessed and written by single or multiple probe(s). The above recommendations may be characterised by using the integrated UHV characterisation system which is capable of in-situ current driven magnetisation switching of ferromagnetic elements by the nanoprobe system, and magnetic imaging by SEMPA system, respectively. Alternatively, the above mentioned experiments (suggestions and 2) can also be performed by a customised MFM technique. 123 LIST OF PUBLICATIONS Journal papers: 1. S. Y. H. Lua, S. S. Kushvaha, Y. H. Wu, K. L. Teo, and T. C. Chong, “Spin configuration of hexagonal shaped ferromagnetic elements in different arrangement”, Journal of Applied Physics (2009) (Accepted for publication). 2. S. Y. H. Lua, S. S. Kushvaha, Y. H. Wu, K. L. Teo, and T. C. Chong, “Effect of insitu FIB trimming on the spin configurations of Hexagonal Shaped Ferromagnetic Elements imaged by SEMPA”, IEEE Transactions on Magnetics 44, 3229 (2008). 3. S. Y. H. Lua, S. S. Kushvaha, Y. H. Wu, K. L. Teo, and T. C. Chong, “Chirality control and switching of vortices formed in hexagonal shaped ferromagnetic elements”, Applied Physics Letters 93, 122504 (2008). Others: 1. S. Y. H. Lua, Y. H. Wu, K. L. Teo, and T. C. Chong, “Effect of an Exchange Tab on the Magnetisation Switching process of Magnetic Nanowires”, Journal of Physics D: Applied Physics 40, 3011 (2007). 124 Conferences: 1. S. Y. H. Lua, S. S. Kushvaha, Y. H. Wu, K. L. Teo, and T. C. Chong, “Spin configuration of hexagonal shaped ferromagnetic elements in a ring network”, presented at 53rd Magnetism and Magnetic Materials Conference, Austin, Texas, U.S.A., 10 – 14 November 2008. 2. S. Y. H. Lua, S. S. Kushvaha, Y. H. Wu, K. L. Teo, and T. C. Chong, “Effect of insitu FIB trimming on the spin configurations of Hexagonal Shaped Ferromagnetic Elements”, presented at IEEE International Magnetics Conference (INTERMAG), Madrid, Spain, – May 2008. Others: 1. S. Y. H. Lua, Y. H. Wu, K. L. Teo, and T. C. Chong, “Transport Study of Domain Walls Induced by an Exchange Tab in Magnetic Nanowires”, presented at Materials Research Society Fall 2006 Meeting, Boston, U.S.A., 27 November - December 2006. 125 [...]... study of ferromagnetic structures In addition to steady state spin configurations, much effort has also been devoted to the study of vortex switching dynamics Ferromagnetic resonance [75], [76], [77] and Brillouin light scattering techniques [77], [78], [79] have been employed in the study of the spectral and spatial components of the spin wave modes in the ferromagnetic structures The topography of. .. follows: a) To study the spin configuration of hexagonal ferromagnetic elements using both micromagnetic modelling and magnetic imaging; b) To study the magnetostatic interaction of hexagonal elements in different arrangements by focusing on not only the effects of inter-element spacing but also the role of stray field symmetry in determining the chirality of vortices; c) To explore the possibility of using... of the array of hexagonal elements with different inter-element spacings In addition, the effect of thickness reduction by in-situ FIB will be studied A model will be used to illustrate the formation of different chirality configurations formed in the array Chapter 5 investigates the magnetostatic interaction of various types of arrangements of the hexagonal elements Moreover, a method to control of. .. twisting of the spins leads to a configuration where the magnetisation points along the out -of- plane direction, at a cost of magnetostatic energy The balance between these two contributions determines the size of the vortex core, which is of the order of the exchange length of the material [16]-[18] When the magnetisation is curling along a circumference, as in circular dots, the divergence of the magnetisation... magnetic field and spin polarised current to switch the chirality of magnetic vortices in hexagonal elements In addition to the study of hexagonal elements, another distinct part of this thesis work is to set up a unique characterisation system which allows for both magnetic imaging experiment and modification of magnetic elements to be carried out in a same setup The integrated system consists of a scanning... Fig 1.7] However, so far, only the magnetic properties of large 10 arrays have been studied The studies of the spin configuration and potential applications of these devices are still lacking Figure 1.8 (a) SEM images of pentagon arrays in different sizes, 500 nm and 100 nm, respectively [After R P Cowburn, 2000, Ref 1] (b) SEM image of an array of elongated hexagons, 1 mm long and 500 nm wide with... chirality configuration as well as switching of chirality by using a magnetic field of appropriate strength and direction will be discussed Chapter 6 discusses the magnetostatic interaction of the hexagons arranged in ring network with an adjacent nanowire Field-induced switching of the composite ferromagnetic structures will be discussed Moreover, current driven domain wall motion in the above-mentioned structures. .. micrograph of a ring network of NiFe hexagons with diagonal lengths of 2 m and s = 200 nm, in contact with a wire of 400 nm width (b) – (g) MFM images of the hexagons after a magnetic field was applied White (black) curved dotted arrows represent the CW (CCW) chiralities Dotted white lines are drawn as guide to the eyes 100 Figure 6.8 (a) A scanning electron micrograph of a ring network of NiFe hexagons... stray field of the circular disk is weak, so the magnetostatic interaction among the circular disk will be small when they are arranged in large arrays The very small outof-plane (vortex core) component of the magnetisation has been observed experimentally [19], [20] The first step to the realisation of real application of vortex structure is to achieve perfect controllability of its sense of rotation,... 6.14 Schematic of the current-pulse experiment for ferromagnetic hexagons in a ring network adjacent to a notched nanowire structure 111 Figure 6.15 MFM images of the ferromagnetic hexagons in a ring network adjacent to a nanowire with a notch: (a) remanent state prior to current injection, and [(b)-(h)] magnetic states after subsequent injections of pulsed current of constant amplitude of 3 mA Dotted . Study of Spin Configuration of Hexagonal Shaped Ferromagnetic Structures LUA YAN HWEE, SUNNY (B. Eng (Hons.), NUS) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY. University of Singapore 2008 i ABSTRACT This thesis work consists of two distinct parts: the set-up of a unique characterisation system and the study of spin configurations in hexagonal ferromagnetic. sketch of the spin orientations of a Neél wall in a uniaxial material. 25 Figure 2.3 Schematic of spin orientation of a (a) transverse and (b) vortex head-to- head domain wall in a soft ferromagnetic