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Rewritable artificial magnetic charge ice

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Science  20 May 2016:
Vol. 352, Issue 6288, pp. 962-966
DOI: 10.1126/science.aad8037

From a bar to a charge, magnetically

Artificial spin ices are arrays of nanoscale bar magnets that can mimic the behavior of naturally occurring “frustrated” magnetic materials. Usually the arrays take the form of a square lattice with the bar magnets perpendicular to its sides. Wang et al. “broke up” each bar into a positive and negative magnetic charge. Working backward from an array of these charges, they designed a structure that has bar magnets oriented not only perpendicularly to the sides of the square lattice but also diagonally. Compared to the traditional one, this structure was much more controllable by global and local magnetic fields.

Science, this issue p. 962

Abstract

Artificial ices enable the study of geometrical frustration by design and through direct observation. However, it has proven difficult to achieve tailored long-range ordering of their diverse configurations, limiting both fundamental and applied research directions. We designed an artificial spin structure that produces a magnetic charge ice with tunable long-range ordering of eight different configurations. We also developed a technique to precisely manipulate the local magnetic charge states and demonstrate write-read-erase multifunctionality at room temperature. This globally reconfigurable and locally writable magnetic charge ice could provide a setting for designing magnetic monopole defects, tailoring magnonics, and controlling the properties of other two-dimensional materials.

Artificial ices are structures in which the constituents obey analogs of the “two-in, two-out” Pauling’s ice rule that determines the proton positional ordering in water ice. These structures provide a material-by-design approach to physical properties and functionalities (127). Artificial ice can be created from ferromagnetic islands and connected wires (3, 5), topological components such as superconducting vortices (2426), and nonmagnetic colloidal particles (27). Among them, artificial spin ice is the most investigated system (121) that was first demonstrated in a square lattice of elongated interacting ferromagnetic nanoislands (1). In this case, the ice rule corresponds to two spins pointing inward and two pointing outward at the vertex of a square lattice. Extensive experiments have been conducted using various thermal (68) and magnetization approaches (911) to obtain ordered states of the spin ice. Long-range ordering was realized in the diagonally polarized magnetic state through the magnetization method (11, 14). For the nominal ground state, sizable domains and crystallites were obtained in as-grown samples (11), and larger domains were obtained in samples heated above their Curie temperatures (~500°C for permalloy island arrays) (6). At room temperature, long-range ordering of the ground state has been achieved only in ultrathin (3-nm-thick) samples via thermal relaxation (8). Other spin and charge configurations have only been observed locally and at crystallite boundaries (5, 6). The difficulty in creating tailored multiple ordered states limits the experimental investigation of the spin and magnetic charge dynamics that can emerge from or between the ordered states (6, 1013), especially for a thermally stable (athermal) sample at room temperature. This also hinders the potential applications of artificial ice for data storage, memory, and logic devices (3, 4) or as a medium for reconfigurable magnonics (28).

We designed an artificial spin structure in which we can conveniently obtain multiple long-range orderings of a magnetic charge ice lattice at room temperature. In a typical square spin ice (Fig. 1A), the single-domain magnetic islands are considered to be macro-Ising spins (11). Each macrospin can be replaced with a dumbbell of magnetic charges, one positive and one negative (3, 4, 29) (Fig. 1B). If we break the connections between the pairs of magnetic charges with opposite signs (Fig. 1C), we can design a different pattern of connections (Fig. 1D). Figure 1E shows the resulting artificial spin structure explicitly. The structure consists of a square lattice of plaquettes (labeled M and N) containing ferromagnetic nanoislands with three orientations (horizontal, vertical, and diagonal). The magnetic charge distribution is indicated by the calculated stray field distribution (Fig. 1F), which leads to a magnetic charge ice with the charge ice rule of two negative and two positive charges within each square plaquette.

Fig. 1 Design of magnetic charge ices.

(A) Typical artificial square spin ice in which the length of the magnetic nanoisland equals the separation of the ends of the nearest islands. Each island is an Ising spin (black arrows). The spin configuration of the lowest-energy ground state is shown. (B) Distribution of magnetic charges corresponding to the square spin ice shown in (A). Pairing of the positive (red) and negative (blue) charges is indicated by black dotted lines. (C) Distribution of magnetic charges with charge connections removed. (D) Redesign of the connections of paired charges with positive and negative polarities. (E) Design of the magnetic nanostructure based on (D). The arrows indicate the spin configuration of the ground state and are color coded for the three subsets of islands placed in three different orientations (horizontal, vertical, and diagonal). Two types of plaquettes are marked with M and N. (F) Calculated magnetic stray field associated with the spin configuration of the structure in (A) for islands with dimensions of 300 nm by 80 nm by 25 nm. Arrows indicate the local field directions. Color is encoded by the out-of-plane component of the field (red, out of the plane; blue, into the plane). The red and blue spots represent the positive and negative magnetic charges, respectively. μ0, vacuum permeability; H, magnetic field. (G) Calculated magnetic stray fields of a 2-by-2 square plaquette, highlighted by the red frame in (E), for the eight possible spin- and charge-ordered configurations, separated into three charge types. Dotted lines denote the orientation of the islands containing the pair of magnetic charges (negative charge, blue; positive charge, red). To compare the magnetic simulations with the experimental magnetic force microscopy images, the stray field was calculated at a plane 100 nm above the surface of the sample.

The magnetic charge distribution in Fig. 1F is exactly the same as that of the ground state of a square spin ice structure (fig. S1). However, in contrast to the square spin ice, which has spins on four sides of the square plaquette and all oriented toward the plaquette center or vertex (Fig. 1A), the structure in Fig. 1E places one spin within the plaquette while removing two from the sides, breaking the fourfold symmetry of the square lattice. Moreover, the three spins associated with each plaquette do not meet at a vertex. Our design contains two types of plaquettes, one rotated by 180° from the other (denoted as M and N in Fig. 1E). Each plaquette (M or N) consists of three islands, each with two degrees of freedom coming from spin, resulting in a total multiplicity of eight configurations of magnetic charges. (See figs. S1 and S2 for detailed comparisons of the spin and charge configurations between the standard square spin ice and our design.) The eight ordered charge configurations (Fig. 1G) that we predicted are separated into three groups on the basis of their energies (see the calculated energies in fig. S3): a twofold degenerate type I ground state (I1 and I2), a twofold degenerate excited type II state (II1 and II2), and a fourfold degenerate excited type III state (III1, III2, III3, and III4) (Fig. 1G).

Because of the large energy barrier for the spins, the spin system in Fig. 1E is athermal at room temperature. An external applied magnetic field can be used to overcome the energy barrier. For a given island, the minimal magnetic field required to flip its spin moment varies with the angle between the applied field and the island (fig. S4). This enables separate control of the spin moments of each differently oriented island. In a square spin ice, there are two orientations of the islands, and the spins can only be aligned in diagonal directions by an applied magnetic field, enabling solely the type II phases with long-range ordering (11, 14). Our design (Fig. 1E) provides an additional freedom for aligning the spins: There are three sets of islands oriented in the horizontal, vertical, and diagonal directions. More importantly, for each of the predicted ordered states shown in Fig. 1G, the spin moments of each of the three oriented islands (horizontal, vertical, and diagonal) are all magnetized in the same direction. This enables the creation of long-range ordering for all of the predicted charge configurations by tuning the in-plane external magnetic field angle and amplitude. We calculated the field-angle dependence of the moment-flipping curves for the three sets of islands (fig. S4C) and designed an effective magnetization protocol to realize the various ordered charge states (30).

To experimentally demonstrate the magnetic charge ordering, we fabricated arrays of permalloy (Ni0.8Fe0.2) nanoislands (300 nm long, 80 nm wide, and 25 nm thick) onto a Si/SiO2 substrate (30), according to the design in Fig. 1E. A scanning electron microscopy image of the sample is presented in Fig. 2A. To control and visualize the charge configurations, we used a customized magnetic force microscope (MFM) equipped with a two-dimensional (2D) vector magnet. Figure 3A shows a schematic drawing of our experimental setup. The 2D electromagnetic solenoid magnet provides in-plane magnetic fields in any desired orientation, enabling us to accurately tune the field angle and amplitude.

Fig. 2 Realization of magnetic charge ices.

(A) Scanning electron microscopy image of permalloy (Ni80Fe20) magnetic islands (300 nm long, 80 nm wide, and 25 nm thick). (B to I) Magnetic force microscopy images of the various ordered states corresponding to all of the configurations in Fig. 1G. (B and C) Twofold degenerate type I ground states: I1 (B) and I2(C). (D and E) Twofold degenerate excited type II states: II1 (D) and II2 (E). (F to I) Fourfold degenerate excited type III states: III1 (F), III2 (G), III3 (H), and III4 (I). The lift height of the MFM scanning is 100 nm.

Fig. 3 Rewritable magnetic charge ices.

(A) Sketch of the experimental setup: an MFM equipped with a 2D vector magnet. The 2D solenoid magnet provides magnetic fields in any desired orientation in the sample plane. The vertically magnetized MFM probe generates a stray magnetic field (green arrows) with in-plane components at the tip. (B) Magnetization loop of a single magnetic island, with an illustration of the write, erase, and read functions. Mx, magnetization along the island. (C to G) Magnetic force microscopy images of the patterned magnetic charge ice at the same area of the sample. (C) The initial state is a type I1 state. (D) A square area of a type III3 state was written in the center of (C). (E) A smaller square region of type III3 order was erased back to a type I1 state from (D). (F) A round region of type II2 order was written onto the freshly erased area from (E). (G) “ICE” letters of type III4 states were scribed on a type I background state.

The as-grown (fig. S5) and demagnetized (fig. S6) samples show mixed charge states of all eight charge configurations at both the M and N plaquettes. Results of statistical analysis for the demagnetized samples show that the charge-neutral configurations (type I) are strongly favored and the collective interaction can be enhanced by reducing the charge separation (fig. S6). Using the designed magnetization protocol (fig. S7), we successfully obtained all eight configurations of magnetic charge ordering, as shown by the magnetic force microscopy images in Fig. 2, B to I. Each of these ordered states possesses long-range ordering and can be reproduced over the entire patterned sample area (80 μm by 80 μm). For type I and II ordered states, there is no net charge in each plaquette, and the magnetic charge follows the “two-positive, two-negative” charge ice rule. In the type III ordered states, each plaquette with magnetic charges following the “three-positive (or negative), one-negative (or positive)” charge ice rule has an effective magnetic charge of two, with opposite signs on the M and N plaquettes. This distribution of magnetic charges in the square lattice of the type III state resembles the distribution of electrical charges in ionic compounds, such as Mg2+O2–. Thus, the type III states (Fig. 2, F to I) resemble an ionic crystal with magnetic charges (31), where we can associate M2+N2– with the type III2 and III4 states and M2–N2+ with the type III1 and III3 states. In principle, all of these magnetic charge distributions could also exist in a square spin ice structure (figs. S1E and S2). In fact, our micromagnetic simulation result indicates that the square spin ice and our engineered spin structure not only produce the same magnetic charge arrangements but also have the same excitation energies for the type I, II, and III configurations (fig. S3). However, with the square spin ice arrangement, long-range ordering of type I states has only been realized in a thermally relaxed sample, and that of the type III states has not yet been experimentally realized because of the spin arrangement of the islands.

The reconfigurable ordered magnetic charges can be used, for example, as templates to form other artificial ices, such as superconducting vortex ices (25, 26), by introducing icelike pinning potentials for superconducting vortices. These charges can also be applied to couple with other electronic materials, such as 2D electron gas (32, 33) and graphene (34), by producing reconfigurable periodically distributed field potentials. For applications such as data storage, memory, and logic devices (3, 35, 36), however, local control of the magnetic charge states is desired. Toward this end, we developed a 2D magnetic field–assisted magnetic force microscopy patterning technique, which allows us to conveniently manipulate the local charge configurations.

As illustrated in Fig. 3A, the magnetic tip of an MFM generates an in-plane component of stray magnetic fields near the tip. The interaction of the MFM tip’s stray field, ΔHm, with a single ferromagnetic island can be tuned by adjusting the height of the MFM tip from the sample, which is 100 nm in this experiment. To locally switch the spin states of an island, we apply an in-plane magnetic field Hap slightly below the ferromagnetic island’s spin-moment–flipping field Hf (Fig. 3B). At this field value, the spin states of the entire sample will not be altered because Hap < Hf. When the MFM probe scans over an island, the total magnetic field on that island will change in the range Hap ± ΔHm. We adjust Hap and ΔHm to satisfy the condition Hap < Hf < (Hap + ΔHm) (light blue region in Fig. 3B). In this case, the spin of the underlying island flips when the MFM tip scans over it, providing a “write” function. A subsequent applied magnetic field in the opposite direction with –(Hap + ΔHm) < –Hf < –(Hap – ΔHm) (green region in Fig. 3B) will switch the spin back, implementing the “erase” function (Fig. 3B). When the applied field is zero, the stray field provided by the MFM probe (yellow region in Fig. 3B) is too small to flip any islands, and this works as the “read” mode. Because the value of Hf depends on the angle between the applied field and the island, similar to the global control of the charge ordering, we can locally manipulate the charge states into any desired configuration.

We demonstrate the experimental realization of the write, read, and erase functions in Fig. 3, C to F. We first prepare the entire sample in the type I ground state (Fig. 3C) by applying and zeroing an in-plane magnetic field of 90 mT along the diagonal direction. We then write a square area of type III ordered state in the center (Fig. 3D) and subsequently erase a smaller square region in the central area by switching the type III state back into the type I state (Fig. 3E). Finally, we write a type II state into a small circular area inside the type III square (Fig. 3F). We can also write letters, as presented in Fig. 3G where the word “ICE” is scribed with type III order on a type I background. Such magnetic charge patterning can easily be realized by programming the 2D magnet to turn on or off and to switch the field directions during the magnetic force microscopy scanning, resembling the patterning process applied in electron beam lithography and in optical lithography using a laser pattern generator. See fig. S8 for more patterns of magnetic charge arrays. These rewritable magnetic charge patterns could be transferred to other materials, for example, through magnetolithography (37).

In addition to the aforementioned applications on coupling with superconducting vortices and other electronic systems, this reconfigurable magnetic charge ice can provide a platform to explore phenomena such as the ground state of a frustrated lattice (6). Combined with other control parameters such as the thickness of the islands (11), temperature (6), or oscillating magnetic field (10), our platform provides a versatile system to study and tailor phase transitions and defect formation (fig. S9). For example, the single spin control enabled by our method allows the creation of magnetic defects such as magnetic monopoles and Dirac strings (16, 17, 20) at any desired location. It also provides a direct technique to program magnetic logic circuits (35, 36). Our strategy to decouple the arrangement of spins and magnetic charges should stimulate further creation and exploration of exotic phases of magnetic charges and their phase transitions and should also foster applications. We also note that Fig. 1E is not the only spin arrangement for achieving the same magnetic charge distribution. In fig. S10, we present several other possible designs of the spin and charge arrangements, including the type IV charge-ordered state in which all positive or negative charges are confined within a single plaquette. Furthermore, it is not necessary to keep the length of all ferromagnetic islands the same, as recently reported in Shakti spin ices (18, 19). Our strategy could also be applied to other artificial spin ices to produce artificial structures with controllable magnetic charge orders, which would provide reconfigurable platforms for magnonic investigations, such as programming spin-wave band structures and designing spin-wave transmission channels (5, 28).

Supplementary Materials

www.sciencemag.org/content/352/6288/962/suppl/DC1

Materials and Methods

Figs. S1 to S10

Reference (38)

References and Notes

  1. Supplementary materials are available on Science Online.
Acknowledgments: We thank W. J. Jiang, S. Zhang, W. Zhang, and M. P. Smylie for critical comments. This work was supported by the U.S. Department of Energy (DOE), Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division. Z.-L.X. and J.X. were supported by NSF grant no. DMR-1407175. Use of the Center for Nanoscale Materials, an Office of Science user facility, was supported by the DOE, Office of Science, Office of Basic Energy Sciences, under contract no. DE-AC02-06CH11357.
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