Perpendicular magnetic clusters with configurable domain structures via dipole-dipole interactions

Transcription

1 Nano Research DOI /s Nano Res 1 Perpendicular magnetic clusters with configurable domain structures via dipole-dipole interactions Weimin Li 1,2, Seng Kai Wong 2, Tun Seng Herng 1, Lee Koon Yap 2, Cheow Hin Sim 2, Zhengchun Yang 1, Yunjie Chen 2, Jianzhong Shi 2, Guchang Han 2, Junmin Xue 1, and Jun Ding 1 ( ) Nano Res., Just Accepted Manuscript DOI /s on July 23, 2015 Tsinghua University Press 2015 Just Accepted This is a Just Accepted manuscript, which has been examined by the peer-review process and has been accepted for publication. A Just Accepted manuscript is published online shortly after its acceptance, which is prior to technical editing and formatting and author proofing. Tsinghua University Press (TUP) provides Just Accepted as an optional and free service which allows authors to make their results available to the research community as soon as possible after acceptance. After a manuscript has been technically edited and formatted, it will be removed from the Just Accepted Web site and published as an ASAP article. Please note that technical editing may introduce minor changes to the manuscript text and/or graphics which may affect the content, and all legal disclaimers that apply to the journal pertain. In no event shall TUP be held responsible for errors or consequences arising from the use of any information contained in these Just Accepted manuscripts. To cite this manuscript please use its Digital Object Identifier (DOI ), which is identical for all formats of publication.

2 Possible application of perpendicular magnetic clusters with configurable domain structures via dipole-dipole interactions. Upper: Programmable Logic Device. Lower: Perpendicular Magnetic Domino. 1

3 Perpendicular Magnetic Clusters with Configurable Domain Structures via Dipole-dipole Interactions Weimin Li 1,2, Seng Kai Wong 2, Tun Seng Herng 1, Lee Koon Yap 2, Cheow Hin Sim 2, Zhengchun Yang 1, Yunjie Chen 2, Jianzhong Shi 2, Guchang Han 2,Junmin Xue 1, Jun Ding 1, * 1 Department of Materials Science and Engineering, National University of Singapore, BLK EA#03-09, 9 Engineering Drive 1, , Singapore 2 Data Storage Institute, Agency for Science, Technology and Research (A*STAR), DSI Building, 5 Engineering Drive 1, , Singapore Address correspondence to Jun Ding, msedingj@nus.edu.sg Abstract The study of magnetic single domain islands based on in-plane anisotropy (usually, shape anisotropy) and their dipole-dipole interactions have been investigated extensively in recent year, driven by potential applications in magnetic recording, spintronics, magneto-biology, etc. Here, we propose a concept of out-of-plane magnetic clusters with configurable domain structure (multi-flux states) via dipole-dipole interactions. Their flux stages can be switched through an external magnetic field. The concept has been successfully demonstrated by patterned [Co/Pd] islands. [Co/Pd] multilayer shows a large perpendicular anisotropy, a well physical separation and uniform intrinsic proprieties after being patterned into individual islands by electron beam lithography. A three-island cluster with six stable flux states has been realized by optimizing island size, thickness, gap, anisotropy, saturation magnetization, etc. Based on Co/Pd multi-layers, we have optimized island structure by tuning magnetic properties (saturation magnetization and perpendicular anisotropy) using LLG simulation/calculation. Potential application have been proposed including a flexi-programmable logic device with the AND, OR, NAND or NOR functionalities and a magnetic domino, which can propagate the magnetic current as far as 1 um down from the surface via vertical dipole-dipole interactions. Keywords perpendicular anisotropy, dipole-dipole interaction, multi-states magnetic recording, logic device, magnetic domino. 2

4 Introduction Recently, various artificial 2D magnetic domains, well known as spin ice has been captured the attentions of scientific community, owing to its unusual magnetic and quantum properties [1-2]. Using the lithographically techniques, geometrically dipole-dipole interactions [3-4] in various spin ice structures such as square [5], hexagonal [6], triangular [7-8], brickwork [9] have been fabricated and investigated theoretically and experimentally based on magnetic in-plane anisotropy (shape anisotropy). Some magnetic nanostructures with in-plane anisotropy have shown great potential for magnetic logic-devices [10-12]. Planar magnetic quantum-dot cellar automata (MQCA) as a logic device formed at least one chain of magnetic islands with in-plane anisotropy is widely investigated for digital computation [11-13]. Another proposed application of these configurable magnetic domain structures is nanomagnet logic (NML) [14] elements which are reconfigurable at run-time. Today, magnetic media of perpendicular anisotropy (or out-of-plane anisotropy) are widely used in magnetic data storage. Bit-patterned media based on closely-packed perpendicular islands have shown their great potential as the next generation high-density magnetic information storage [15]. It is interesting to use perpendicular magnetic clusters for configurable magnetic domains for various applications. In this work, we makes use of commonly used bit patterned media structure, [Co/Pd] multilayer [16-17] with a preferred axis perpendicular to the film plane (out-of-plane anisotropy) as our magnetic cluster materials. It is worthwhile to highlight that the beauty of this [Co/Pd] structure is its uniform and therefore small switching fields distribution (a well uniformity in switching fields after patterned into individual islands) that is favorable for a higher storage density in media recording applications. The switching field of individual island as well as dipole-dipole interaction between neighboring islands have been investigated by varying islands sizes and gaps using micromagnetic simulation. Six stable flux states in a three-island cluster are observed by Magnetic Force Microscope (MFM) at different external field. We have utilized the dipole-dipole interaction characteristic of magnetic islands to design a non-volatile and programmable logic device with AND, OR, NAND or NOR functionalities. Besides, a vertical "magnetic domino" via ferromagnetic coupling which can propagate magnetic current as far as 1 μm has been realized by micromagnetic simulation. In supporting information, we have demonstrated that a multi-state bit-pattern medium may be developed based on dipole-dipole interactions, which allows some enhancement of recording density with the same head pole and servo system. Besides, a three input majority gate computational 3

5 paradigm based on both ferromagnetic and antiferromagnetic coupling has been realized by micromagnetic simulation. These works lay an important milestone for future data storage and logic device applications. 1. Concept of "configurable magnetic clusters with perpendicular anisotropy via dipole-dipole interactions" A magnetized element (here island with perpendicular anisotropy) may be treated as a dipole (as shown in Fig. S3). If a dipole marked as "A" is placed in presence of reversal fields, it may switch at Hc as the intrinsic coercivity (Figure S3(a)). If a dipole "B" is placed closely with dipole "A", the switching field of dipole "A" decreases to Hc-Hdip for parallel configuration (Figure S3(b)), increases to Hc+Hdip for antiparallel configuration (Figure S3(c)). Based on the concept, we can propose perpendicular magnetic clusters with configurable domain structures via dipole-dipole interactions. A configurable two-island cluster may consist of two islands with different intrinsic switching fields Hc0,1 and Hc0,2 (Hc0,1<Hc0,2), as shown in Figure 1(a) and Figure 1(b). When a reversal field (negative field) is applied on the two-island cluster after saturation (by positive field), island 1 is expected to switch first due to low Hc0,1. It is noted that switching energy barrier will be reduced when the neighboring islands have the same magnetization spin direction, resulting switching field decrement of islands 1 (Hc1=Hc0,1-Hdip). After switching of island 1, island 1 and island 2 have opposite spin direction. The switching energy barrier of island 2 will increase. In this case, the switching field of island 2 can be written as Hc2=Hc0,2+Hdip. The difference in switching fields between island 1 and island 2 in the two-island cluster system is defined as ΔH, ΔH=Hc2-Hc1=(Hc0,2-Hc0,1)+2Hdip. The value of ΔH is a key parameter in differentiation of the two magnetic flux states. Based on the previous model, we can extend to three-island cluster with two cases: 1. same intrinsic switching fields (Hc0,1=Hc0,2=Hc0,3), as shown in Figure 2(a); 2. Different intrinsic switching fields (Hc0,1<Hc0,2<Hc0,3), as shown in Figure 2(b). Figure 2 (a) schemes the dipole-dipole interactions in a three-island cluster and their controllable magnetic states. For easy understanding, we number the islands from left to right according to the position, e. g. island 1, island 2, etc. Once a reversal field is applied on the cluster till saturation, island 2 is expected to switch first due to minimum switching energy barrier. With further increasing of the reversal field, theoretically, island 1 and island 3 will switch at the same time due to equally dipole-dipole interaction. Four-flux states can be observed. 4

6 When the intrinsic switching fields of three islands are various, more flux states could be obtained. Switching field of a single island increases with decreasing island size, as confirmed by both experimental and micromagnetic simulation (discussed in the following text). We design a cluster consisting of three islands with different intrinsic switching field (Hc0,1>Hc0,2>Hc0,3) by the way of three different island size (island 1<island 2<island 3). Under an application of reversal field, island 2 switches first due to strong dipole-dipole interactions with an influence of two neighboring islands. With a further increasing of reversal field, switching energy barrier between island 1 and island 3 is not the same due to the different coupling. Although island 1 and island 3 feel the same dipole-dipole interaction from island 2, island 3 switches earlier than island 1 due to smaller intrinsic switching field (Hc0,1>Hc0,3). Six-flux states may be observed (Figure 2(b)). In additional to the three-island cluster model, we have designed various cluster structures such as five-island cluster and nano maze (Figure S4-S6), etc. A cluster with six-flux states and ten-flux states are demonstrated in five-island cluster with uniform islands and non-uniform islands, respectively. An eighteen-flux states nano maze via both dipole-dipole interaction and size effect is also obtained through simulation (Figure S6). 2. Demonstration of "configurable magnetic clusters via dipole-dipole interactions" by [Co/Pd] islands In order to realize the concept of "configurable magnetic clusters via dipole-dipole interactions" illustrated in previous models, [Co/Pd] multilayers, which show a well physical separation and uniform intrinsic proprieties (narrow intrinsic switching field distribution, Figure S7-S10) after patterned into individual islands are used for experimental demonstration. 2.1 [Co/Pd] single domain island size The island size in multi-island cluster is a crucial point and it must be big enough to fulfill the thermal stability criterion (calculated as 5 nm for this [Co/Pd] sample with effective thickness of 12 nm). Additionally, the island size must be of single domain particle size (as the upper size limit). Simulation result (Figure S11) indicates the single domain state is energetically stable below 600 nm. This result agrees with our MFM observation and fulfills the scope of this work. Coercivity of a single island as a function of island size (up to 5000 nm) is also investigated by simulation (Figure 3). The measured coercivity at different island 5

7 size by MFM observations is indicated by red dot. Apparently, coercivity increases with island size when the size less than 20 nm, which is attributed to superparamagnetic effects. For the island size of 20 nm to 600 nm, the coercivity decreases with an increase of island size is mostly due to the change in magnetization reversal modes. Beyond the island size of 600 nm, the coercivity becomes insensitive to the islands size and reaches stable value of ~11 koe. 2.2 Maximum dipole-dipole interactions in three-island [Co/Pd] cluster In order to get distinct multi-states in configurable three-island [Co/Pd] cluster, a large dipole-dipole interaction between neighboring islands is desired. Dipole-dipole interaction is strongly influenced by the dimension of islands, including island size, thickness and gap. It can be represented by the simplified following formula for a homogenous spherical dot island: H dip = M s V bit r 3 (1) where Vbit is the volume of the island and r is center-to-center distance (size+gap) between two neighboring islands. As shown in Equation (1), dipole field decays quickly with the separation r (r 3 ). Only the nearest neighbors and next nearest neighbors play the dominant contribution to the dipole field of a particular island. As described in previously, our Co/Pd multi-layer islands have a thickness of 12 nm, and a magnetization of 600 emu/cc based on our available sputtering and e-beam lithography systems. In this circumstance, ΔH is only influenced by island size & gap. Absolute value of ΔH as a function of island dimension, including island size and gap in a three-island [Co/Pd] cluster with thickness of 12 nm is plotted in Figure 4(b). ΔH is defined as difference in reversal fields (normal to film surface) between first (Hc2) and last (Hc1 or Hc3, Hc1 = Hc3) switched island. It shows ΔH increases with the decreases of island gap, down to 5 nm (Figure S14). Nevertheless, the best achievable uniform gap size is ~12 nm based on our experiment data, owing to the limited resolution of our electron beam lithography system. The maximum ΔH (~1 koe) is obtained at island size of ~90 nm. 2.3 Demonstration of a three-island [Co/Pd] cluster with uniform islands Using the optimized parameters for [Co/Pd] islands (island size of 90 nm, gap of 12 nm, thickness of 12 nm and film saturation magnetization of 600 emu/cc), we have fabricated [Co/Pd] clusters to demonstrate "configurable magnetic cluster via dipole-dipole interactions". 6

8 Dipole-dipole interaction of clusters consisting of three closely arranged [Co/Pd] islands is investigated systematically by experiments. Reversal process for a three-island cluster with uniform island size of 90 nm and gap of 12 nm in the presence of external out-of-plane magnetic field are observed by MFM (Figure 5(a)). All remanent states were captured after saturating the sample followed by applying different reversal fields. As discussed in Figure 2(a), when three uniform islands are placed closely with each other, their switching energy barriers influence with each other. Figure 5(a) shows island 2 switches at koe after saturating the sample at 15 koe. The first reversal of island 2 is due to positive dipole-dipole interaction (same magnetization spin direction) with two neighboring islands. When the negative field increases, island 1 and island 3 are expected to switch at the same time due to their equivalent sites. However, it is interested to have observed sequential switching between island 1 and island 3 in our experiment. Two possible remanent states at reversal field of koe are observed with equal probability from statistical data analysis, as type A and type B shown in Figure 5(a). The earlier switched island will switch back earlier than the other one in presence of opposite reversal field. As we mentioned above, magnetic islands in our sample is not absolutely uniform, as indicated in deviations of intrinsic properties (intrinsic switching field distribution [16-19] reported in our previous paper). Therefore, for island 1 and island 3, which one switches earlier than the other, is determined by their intrinsic properties (defects, shape, size, etc). As long as the second island finished switching, it poses an extra field and therefore holds on the reversal of the last-switched island. The switching field of the last-switched island is -15 koe from MFM observations. Six-flux states are found in Figure 5(a). Sequential and individual switching in five-island cluster with uniform islands is also observed similarly as three-island cluster with uniform islands due to the same dipole-to-dipole interaction rule. Ten-flux states are found as shown in Figure S Demonstration of a three-island [Co/Pd] cluster with non-uniform islands In order to avoid this uncertainty of switching sequence between island 1 and island 3 in Figure 5(a), we designed a three-island cluster with different sizes (island 1 ~60 nm, island 2 ~80 nm and island 3 ~90 nm) (Figure 5(b)). Island 2 switches first due to strong dipole-dipole interaction with two neighboring islands. Next is island 3 and followed by island 1. This observation agrees well with our model in Figure 2(b) and results in Figure 3 that larger island has lower switching field and it will switch earlier than smaller one. Sequential and individual switching in five-island cluster with non-uniform islands is also observed. 7

9 ΔH is equal to 1.5 koe for three-island cluster with uniform islands, and 2.5 koe for three-island cluster with non-uniform islands. The value of ΔH is much larger than intrinsic SFD (0.9 koe [16-19] reported in our previous paper). It indicates that the multi-states of three-island cluster are caused by dipole-dipole interaction rather than intrinsic switching field distribution. 3. Optimization of "configurable magnetic clusters via dipole-dipole interactions" for potential applications In potential spintronics device for logic, memory applications, a high value of ΔH/Hc is more desired than a high value of ΔH. Based on Equation 1, ΔH is dependent on several parameters, such as saturation magnetization (Ms), island dimension (including thickness & size) and gap. Hc is related to anisotropy constant Ku. In this work, we have studied how to optimize island cluster structure in terms of magnetization, magnetic anisotropy, island size, thickness and gapthrough LLG calculation. 3.1 Saturation magnetization (Ms) and island thickness As shown in Equation 1, island gap should be kept as small as possible. Based on today s lithography technology (for example e-beam), it is difficult to reduce a gap smaller than 10 nm. We have kept gap to be 10 nm for the following study. When island size and gap are kept in 90 nm and 10 nm, respectively, the relationship between ΔH, saturation magnetization (Ms) and thickness of three-island cluster is investigated by micromagnetic simulation (Figure 6(a)). Also shown in Equation 1, an increase of saturation magnetization (Ms) and/or island volume (here thickness, as island size is kept as a constant of 90 nm) can increase ΔH. Figure 6(a) confirms that large island thickness and high saturation magnetization are desired for high value of ΔH. A too large thickness may affect epitaxial layer structure, and result in reduction of magnetic anisotropy. 20 nm may be a reasonable value for thickness. As for saturation magnetization, the highest achievable value is 1300 emu/cc (for pure Co). Increased magnetization has been reported for Co/Pd via changing thickness of Pd layer while perpendicular magnetic anisotropy can be kept [20]. A saturation magnetization of 1000 emu/cc would be a reasonable value for our optimization. As shown in Figure 6(a), a thick layer (~20 nm) with large saturation magnetization (Ms~1000 emu/cc) may have a large value of ΔH (~1.8 koe). 3.2 Island size 8

10 Figure 6(b) shows ΔH of a three-island cluster (with optimized parameters from Figure 6(a) that island thickness of 20nm, island gap of 10nm and saturation magnetization (Ms) of 1000 emu/cc) as a function of island size. ΔH increases with increasing of island size. When island size reaches 100 nm, ΔH is insensitive to island size. A cluster with island size as smaller as 20 nm is enough to induce high dipole-dipole interaction. As smaller island size is desired for spintronics devices for logic, memory and other applications, we may select 20 nm as the optimized island size. 3.3 Anisotropy constant A low Hc is preferred in magnetic logic device. Since the value of Hc is related to anisotropy constant Ku, we investigated the coercivity of single island as a function of anisotropy constant Ku by simulation (Figure 6(c)). Coercivity lineally increases with increasing of Ku for Ku larger than 100 kerg/cc. When Ku is smaller than 100 kerg/cc, magnetic energy (KuV) is getting close to thermal energy (kbt). Coercivity decreases to zero when thermal energy is comparable to anisotropy energy. Thermal stability of a coherent non-interacting particle can be analyzed by simple coherent non-interacting rate equation model [21-22]: τ ± 1 (h) =f 0 exp ( E B ± (h) k B T ) (2) τ is the relaxation time, f0 is attempt frequency (~10 9 Hz), EB is the energy barrier, kb is Boltzmann constant, T is temperature (~300K). When τ equals to 10 years, KuV =40kBT, Ku is calculated to ~200 kerg/cc. Therefore, when Ku is larger than 200 kerg/cc, island with saturation magnetization (Ms) of 1000 emu/cc, size of 20 nm, gap of 10 nm, thickness of 20 nm is assumed to have stable thermal stability. Coercivity as a function of island size for a single island with different anisotropy is simulated in supporting information (Figure S16). In a magnetic cluster, the switching field of an island is influenced by the neighboring islands. Both dipole-dipole interaction and demagnetized field make contribution to switching field. Based on the geometry of island size of 20 nm, gap of 10 nm and saturation magnetization (Ms) of 1000 emu/cc, the dipole-dipole interactions can generate a relatively large ΔH (~1.8 koe). A dipole field of -900Oe might switch the island, as it exceeds the coercovity (or anisotropy field), as shown in Fig. S16. Therefore, a higher magnetic anisotropy needs to be selected particularly for magnetic logic device applications. A much higher magnetic anisotropy of approximately 1000 kerg/cc is required instead of 200 kerg/cc, in order to keep an energy barrier 200 erg/cc. 9

11 In summary, uniform islands of size of 20 nm, thickness of 20 nm, gap of 10 nm,, saturation magnetization (Ms) of 1000 emu/cc and anisotropy constant (Ku) of 1000 kerg/cc were used for the simulation/calculation for applications of magnetic logic device and magnetic domino, as described below. 4. Potential practical applications 4.1 Programmable Logic Device A configurable logic device consisting of three uniform exchange-coupled islands and a metallic layer structure is proposed (Figure 7(a)). Three magnetic islands are connected by the non-magnetic metallic layer to ensure the magnetizations of the three magnetic islands can be switched independently. The switching of the magnetic islands is controlled by a combination of three independent input currents (IA, IB, IC) with magnetic fields. The spin polarization change between island 2 and island 3 under external electrical stimulus can be detected by variation in resistance of these two islands, readout as output of logic device. The lower resistances state due to parallel alignment of island 2 and island 3 corresponds to logical 1, while higher resistances state caused by antiparallel alignment of island 2 and island 3 is read as logical 0. The logic device operation can be triggered by key two steps. First, ones need to initialize the logic devices into AND, OR, NAND, or NOR operation by inputting the initial current (line A), denoted as the initial setting process. For initializing a device operation, a current with a magnetic field that is sufficient to rotate magnetic islands into preference pattern is required (Figure 7(b)). Once the logic gate is operated in the selected logic mode, the users can input the signal via B and C line, named as the logic operation process. Since the direction of the magnetization is maintained when the current is turned off, the information is non-volatile and can be read out repeatedly by measurement the resistance of the island 2 and island 3. Logic operations for four functional gates are summarized in Application S Perpendicular Magnetic Domino Another key practical application of our configurable magnetic islands is "magnetic domino" (one chain of magnetic dots coupled only to nearest neighbors (Figure S2(a)), which can propagate the "magnetic current" in a long distance via vertical dipole-dipole interactions. In our proposal, the driving force for magnetic domino is a magnetic nano-bar (Figure S17). It indicates that a magnetic nano-bar (with diameter of 50nm and length of 100nm) in the distance of 50nm can only result in the switching of the top dot in magnetic domino. The 10

12 information propagates along the magnetic domino entirely via magnetic dipole-dipole interactions. Figure 8(a) illustrates the proposed fabrication process of magnetic domino with length of 500nm in total. Magnetic multilayers can be deposited by dc magnetron sputtering system. Non-magnetic layer (1nm) between two magnetic layer (50nm) are used to isolate the neighboring vertical islands. Anisotropy constant (Ku) and saturation magnetization (Ms) of different magnetic layers used in micromagnetic simulation are also indicated in the Figure 8(a). Material with large Ku and Ms in the top layer is desired to generate large out-of-plane reversal fields at the initial propagation of the magnetic domino. The magnetic domino is saturated by an opposite external field followed by in presence of a magnetic nano-bar. After removing the magnetic nano-bar, the propagation process of magnetic domino is captured by LLG micromagnetic simulator at the same time interval. It indicates that the magnetization spreads from one dot to another from the top down. Simulation result shows that the magnetic current can spread as far as 1 μm (not shown here) via vertical dipole-dipole interactions. It shows a prominent application in future logic device. In addition, multi-states bit pattered medium consisting of closely arranged magnetic islands to achieve ultra-high magnetic recording density and a three input MQCA device based on both ferromagnetic and antiferromagnetic coupling are demonstrated in Application S2 and S3, respectively. 5. Conclusion In conclusion, perpendicular magnetic clusters with configurable domain structures via dipole-dipole interactions are demonstrated. The [Co/Pd] cluster with a strong out-of-plane anisotropy shows a well defined physical gap and uniform intrinsic properties. Maximum dipole-dipole interaction in [Co/Pd] three-island cluster is obtained by varying island size and gap using micromagnetic simulation. Six stable magnetic states in three-island [Co/Pd] cluster are observed by MFM after saturating the sample followed by applying different reversal fields. In order to make use of dipole-dipole interaction to generate distinct multi-states in a cluster for potential memory or logic applications, optimized material parameters other than our demonstrated [Co/Pd] are proposed by micromagnetic simulation. A cluster consisting of three uniform islands (with island size of 20 nm, gap of 10 nm, thickness of 20 nm, saturation magnetization (Ms) of 1000 emu/cc and Ku of 1000 kerg/cc) is assumed to have sufficient dipole-dipole interaction leading to distinguish flux states and stable thermal stability. 11

13 Several potential applications of configurable domain structures via dipole-dipole interactions have been proposed. One is a simple and configurable logic device consisting of three exchange-coupled islands and a metallic layer. Three independent input current lines are sufficient to provide four functionalities: AND, OR, NAND and NOR gates. The other potential application is magnetic domino which can propagate the magnetic current as far as 1 μm away via vertical dipole-dipole interaction. Experimental Section Sample preparation. [Co3/Pd8]10 multilayer for this study is prepared using a dc magnetron sputtering machine on a thermally oxidized Si substrate. The number following the symbols is the respective layer thickness in angstrom and the subscript refers to the number of repetitions. The film are deposited on [Ta50/Cu50/Pd30] to induce proper crystallographic growth of the Co layer and capped with [Pd30/Ta50] for protection. The base pressure is Torr while the Ar working pressure during sputtering is 1.5 mtorr. The patterned dots are generated using high resolution electron beam lithography (Eli onix ELS 7000 EBL) by first coating the film with hydrogen silsesquioxane (HSQ) photoresist. Ar + ion-milling is carried out at angle of 3ºoff normal incidence to the sample to form discrete magnetic islands (Figure S7). Milling is stopped as soon as isolated magnetic islands are identified. In total, approximately 30 nm of material that included the [Co/Pd] (~12nm) magnetic layer is milled to ensure sufficient isolation between islands (Figure S10). Experimental measurement. The physical structure of the patterned islands is investigated in Scanning Electron Microscope (SEM, Zeiss Supra 40) to obtain plane views. Magnetic remanent states are characterized by MFM using a Digital Instruments Dimension 3000 Scanning Probe Microscope (SPM) with high resolution MFM tips. Saturation magnetization and coercivity of the continuous film before patterning are measured by Vibrating Sample Magnetometer (VSM) and Superconducting Quantum Interference Device system (SQUIDs). The ex situ out-of-plane magnetic field before MFM measurements are implemented by VSM. Micromagnetic simulation. A Landau-Liftshitz-Gilbert (LLG) simulator is used for micromagnetic simulation of nanomagnets. This simulator is based on an energy minimization procedure that searches the 12

14 grid point by point and a parallel (Fourier space) implementation of general LLG equation solves. The energy terms in this simulation include the exchange coupling (Ex), uniaxial anisotropy (Ek), stray field (or demagnetization including dipolar interactions) (Ed) and external field (Ez) contributions. 3D complex Fast Fourier Transform (FFT) method (that is, parallel solution in time) is used to compute the solution to the LLG equations. In this work, all the parameters of [Co/Pd] island in simulation including saturation magnetization of 600 emu/cc, anisotropy constant of 580 kerg/cc, island size of 90 nm, island-to-island gap of 12 nm, etc., are obtained from our experimental measurements. An exchange stiffness of 10-6 erg/cm is used based on references [23-25]. The size of the finite element mesh is 5 nm which is well below the exchange length of 8.5 nm for [Co/Pd] multilayer [16]. Acknowledgements This research work was financially supported by NRF-CRP and NRF2012NRF-CRP

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17 Figure Captions Figure 1. A schematic of origins of dipole-dipole interactions in a two-island cluster system with different islands (with different switching fields). Hc0,1 and Hc0,2 are switching fields of single island 1 (d) and island 2 (e) without considering dipole-dipole interactions. Hc0,1 is smaller than Hc0,2 (g). When island 1 and island 2 are placed closely with other, their switching field could vary due to increased or decreased energy barrier (c). When a reversal field (negative field) is applied on the two-island cluster after saturation at the same magnetization direction (by positive field), island 1 is expected to switch first at (Hc0,1-Hdip) due to smaller energy barrier and dipole-dipole interaction. After switching of island 1, two neighboring islands have the opposite spin direction. Switching energy of island 2 increases due to dipole-dipole interaction, therefore, island 2 switch at (Hc0,2+Hdip) (f). Hc1 and Hc2 are switching fields of island 1 and island 2 after considering dipole-dipole interactions. Figure 2. Model of a three-island cluster with uniform (a) and non-uniform (b) islands. Upper, a schematic of switching energy barrier and magnetic states of a three-island cluster. Lower, a hysteresis loop and corresponding magnetic states of a three-island cluster. Figure 3. Single [Co/Pd] island with thickness of 12 nm. (a) MFM images of single [Co/Pd] island with thickness of 12 nm and island size of 3 μm with up (left image) and down (right image) magnetization directions. (b) Simulation result of coercivity (switching field) of [Co/Pd] island as a function of island size by LLG simulator. Red dot is the measured coercivity by MFM observation. Insert: enlarged curve when island size is smaller than 100 nm. Figure 4. Simulation of dipole-dipole interactions in three-island [Co/Pd] cluster. (a) Illustration of reversal process and corresponding switching fields for three-island cluster in the presence of an external magnetic field perpendicular to film surface. (b) Simulation result of ΔH of three-island [Co/Pd] cluster with thickness of 12 nm as a function of island dimension, including island size and gap. H is defined as difference in reversal fields between first (Hc2) and last (Hc1 or Hc3, Hc1 = Hc3) switching island. Figure 5. Demonstration of a three-island [Co/Pd] cluster with uniform islands (a) and non-uniform islands (b). Upper, SEM images of a three-island cluster (with island size of 90 16

18 nm and gap of 12 nm). Lower, MFM images of a three-island cluster at different magnetic reversal fields perpendicular to film plane. Figure 6. (a) Simulation results of ΔH in a three-island cluster as a function of island thickness and saturation magnetization (Ms). Cluster has uniform island size of 90 nm and gap of 10nm. (b) Simulation results of ΔH as a function of island size. (c) Simulation result of coercivity as a function of anisotropy constant Ku. Figure 7. Programmable Logic Device. (a) a schematic of a non-volatile and programmable logic device based on three-island cluster with uniform island size. One can control the functionality of logic device (AND, OR, NAND, or NOR operation) by manipulating its spin polarization information (up or down) of the islands via a strong dipole-dipole interaction between their neighboring islands through external current with multi-level magnetic fields. Once this structure is employed as a programmable logic device, the operation has to proceed in two steps: "initial setting" by input current A and "logic operation" by combination of input currents B and C. The spin polarization change between island 2 and island 3 can be detected by variation in resistance of these two islands, readout as the output of logic device. (b) initial setting shown in a hysteresis loop of a three-island cluster with uniform island size of 20nm, gap of 10nm, thickness of 20nm, Ku of 1000 kerg/cc and Ms of 1000 emu/cc. Figure 8. Perpendicular Magnetic Domino. (a) a schematic of proposed fabrication process of magnetic domino by E-beam lithography. The magnetic domino is saturated by an external magnetic field before being in presence of a reversal field generated by a magnetic bar. (b) simulated reversal process of magnetic domino captured by LLG micromagnetic simulator. 17

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