Nano Research
Nano Res
DOI 10.1007/s12274-015-0864-1
Perpendicular magnetic clusters with configurable
domain structures via dipole-dipole interactions
Weimin Li1,2, Seng Kai Wong2, Tun Seng Herng1, Lee Koon Yap2, Cheow Hin Sim2, Zhengchun Yang1, Yunjie
Chen2, Jianzhong Shi2, Guchang Han2, Junmin Xue1, and Jun Ding1 ()
Nano Res., Just Accepted Manuscript • DOI 10.1007/s12274-015-0864-1
http://www.thenanoresearch.com on July 23, 2015
© Tsinghua University Press 2015
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1
Possible application of perpendicular magnetic clusters with configurable domain structures
via dipole-dipole interactions. Upper: Programmable Logic Device. Lower: Perpendicular
Magnetic Domino.
1
Perpendicular
Magnetic
Clusters
with
Configurable
Domain
Structures
via
Dipole-dipole Interactions
Weimin Li1,2, Seng Kai Wong2, Tun Seng Herng1, Lee Koon Yap2, Cheow Hin Sim2,
Zhengchun Yang1, Yunjie Chen2, Jianzhong Shi2, Guchang Han2,Junmin Xue1, Jun Ding1,*
1
Department of Materials Science and Engineering, National University of Singapore, BLK
EA#03-09, 9 Engineering Drive 1 , 117576, Singapore
2
Data Storage Institute, Agency for Science, Technology and Research (A*STAR), DSI
Building, 5 Engineering Drive 1, 117608, Singapore
Address correspondence to Jun Ding, [email protected]
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
simulation/calculation.
magnetization
Potential
and
application
perpendicular
have
been
anisotropy)
proposed
using
LLG
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
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
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
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
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:
𝐻𝑑𝑖𝑝 =
𝑀𝑠 ∙𝑉𝑏𝑖𝑡
𝑟3
(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 (r3). 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
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 -13.5 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
-14.5 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 S15.
2.4 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
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
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) =𝑓0 exp(−
±
𝐸𝐵
(ℎ)
𝑘𝐵 𝑇
)
(2)
τ is the relaxation time, f0 is attempt frequency (~109 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
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 S1.
4.2 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
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
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 5 10-9 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
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
NRF2012NRF-CRP001-029.
13
by
NRF-CRP9-2011-01
and
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15
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
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
Figure 1
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Figure 2
Figure 3
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Figure 4
Figure 5
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Figure 6
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Figure 7
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Figure 8
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