Method of controlling interactions between artificial spin ice phase adjacent nanomagnets

Abstract

The application discloses a method for controlling the interaction between adjacent nanometer small magnets of artificial spin ice, wherein the interaction between adjacent nanometer small magnets is controlled by adjusting the length of selected nanometer small magnets in an artificial spin ice lattice, the vertex degeneracy and ground state of the artificial spin ice are controlled, and a phase transition from a spin liquid state to a long-range ordered crystal state is directly presented. The application proves that the local interaction of the artificial spin ice has a significant influence on the collective behavior and finally influences the properties of the whole system, and selectively adjusting the length of the nanometer small magnets can be used as a convenient way to adjust the local coupling strength, which enables the application to observe various low-energy states and phase transitions in the completely discrete artificial spin ice.

Description

Technical Field

[0001] This invention belongs to the field of artificial spin ice technology, specifically relating to a method for controlling the interaction between adjacent nanomagnets in artificial spin ice. Background Technology

[0002] Artificial spin ice is an array of dipole-coupled nanomagnets with collective interactions. It allows for the direct study of fascinating collective phenomena from different microscopic states. However, obtaining the ground state experimentally in geometrically frustrated systems is difficult, limiting the research and application of novel properties and functions based on low-energy states.

[0003] The collective properties of artificial spin ice are directly related to the geometric arrangement of their lattice and nanomagnets, and closely related to the competitive interactions between the nanomagnets that form the unit cells, i.e., single domains. The difficulty in obtaining long-range ordered states in kakeme artificial spin ice stems from the high frustration of the three nanomagnets at the vertices, leading to high degeneracy of the ground state. When only nearest-neighbor interactions are considered, the ground state of kakeme artificial spin ice exhibits neither magnetic charge order nor spin order. Long-range interactions of nanomagnets are much weaker than nearest-neighbor interactions; therefore, the properties of artificial spin ice are primarily determined by nearest-neighbor interactions. In recent years, researchers have utilized the micromagnetic properties of the vertices in the honeycomb structure of nanowire networks to achieve long-range ordered spin crystal phases in connected kakeme ice structures, introducing vertex grooves to reduce vertex degeneracy. More recently, researchers have introduced asymmetric microbridges at the vertices, breaking the sixfold symmetry of the vertices in kakeme artificial spin ice. However, these methods are not applicable to artificial spin ice composed of discrete nanomagnets. Summary of the Invention

[0004] The technical problem solved by this invention is to provide a method for controlling the interaction between adjacent nanomagnets by adjusting the length of selected nanomagnets in an artificial spin ice lattice, thereby achieving vertex degeneracy and ground state control of the artificial spin ice.

[0005] Technical Solution: To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0006] A method for controlling the interaction between adjacent nanomagnets in artificial spin ice is proposed. By adjusting the length of selected nanomagnets in the spin ice lattice, the vertex degeneracy and ground state of the artificial spin ice can be controlled, and the phase transition from the spin liquid state to the long-range ordered crystal state of the artificial spin ice can be directly observed.

[0007] Furthermore, by inducing non-equivalent interactions between three nanomagnets at the vertex of the Kagome artificial spin ice, the ground state degeneracy of the Kagome artificial spin ice vertex is reduced from 6 to 2, thereby realizing the long-range ordered spin crystal state of the Kagome artificial spin ice.

[0008] Furthermore, by selectively increasing the length of one of the three nanomagnets at each vertex, while keeping the lengths and lattice constants of the other two nanomagnets β unchanged, the triple rotational symmetry of the vertex is broken, making the interaction between the three nanomagnets at each vertex no longer equal.

[0009] Furthermore, the original six-fold degenerate vertex is divided into two groups of different energies: KI-type and K-II-type configurations. The magnetic interaction energy between the two β nanomagnets in the KI-type vertex is denoted as J1, and the magnetic interaction energy between the α and β nanomagnets in the K-II-type vertex is denoted as J2.

[0010] Furthermore, since each vertex that satisfies the Kagome-Ice rule contains only one frustrated magnet pair, J1 and J2 also represent the energies of the KI and K-II type vertices, respectively; since the extended α nanomagnet endpoints are closer to the vertex center, J1 is lower than J2, resulting in the KI type double degenerate vertex configuration being the ground state.

[0011] Furthermore, when all vertices satisfy the KI-type ground state configuration, a long-range ordered spin crystal state can appear.

[0012] Furthermore, by changing the length Lα of the α nanomagnet, the energy difference between the KI-type and K-II-type vertices can be further adjusted, thereby achieving the adjustment of the effective temperature of the Kagome artificial spin ice by changing the length of the α nanomagnet, and thus achieving the adjustment of physical phase transition in the completely discrete Kagome artificial spin ice.

[0013] Beneficial effects: Compared with the prior art, the present invention has the following advantages:

[0014] This invention discloses a method for controlling the interaction between adjacent nanomagnets in artificial spin ice. It proposes a novel approach to customize the vertex degeneracy and ground state of the kakeme artificial spin ice, directly exhibiting a phase transition from a spin liquid state (SL1) to a long-range ordered spin crystal state (LRO). Unlike the connected structure of kakeme artificial spin ice ground state achieved in the prior art, whose coupling is mainly controlled by short-range exchange interactions, the discrete artificial spin ice of this invention maintains long-range dipole interactions. Attached Figure Description

[0015] Figure 1 This is a schematic diagram of the adjustable cage-like artificial spin ice of the present invention, wherein:

[0016] (a) is a schematic diagram of tunable kagome artificial spin ice with increased length Lα of α small magnet and fixed length Lβ of β nano magnet; (b) is a schematic diagram of dividing the six low-energy vertex configurations that satisfy the kagome spin ice rules into two groups according to energy; (c) is an evolution diagram of vertex energy as a function of La; (d) and (e) are SEM images of kagome artificial spin ice with Lα = 220nm (d) and 420nm (e), respectively; (f) and (g) are MFM images corresponding to (d) and (e), respectively.

[0017] Figure 2 The schematic diagram of the transformation from spin liquid to spin crystal of the present invention, wherein: (a)-(f) are MFM images at Lα of 220nm, 270nm, 320nm, 370nm, 420nm and 440nm respectively; (g)-(l) are spin configuration and vertex distribution diagrams extracted from (a)-(f) respectively; (m)-(r) are corresponding diagrams of magnetic structure factors calculated from the spin configurations of (g)-(l);

[0018] Figure 3 This is a sample design drawing of Kagome artificial spin ice;

[0019] Figure 4 These are SEM images of six samples with different Lα values.

[0020] Figure 5 This is a ground-state example diagram of a novel type of artificial spin ice designed with a cage-like pattern;

[0021] Figure 6 This is the composite ground state diagram of the designed cage-like artificial spin ice. Detailed Implementation

[0022] The present invention will be further illustrated below with reference to specific embodiments. These embodiments are implemented based on the technical solutions of the present invention, and it should be understood that these embodiments are only used to illustrate the present invention and are not intended to limit the scope of the present invention.

[0023] The method of the present invention for controlling the interaction between adjacent nanomagnets in artificial spin ice controls the interaction between adjacent nanomagnets by adjusting the length of selected nanomagnets in the artificial spin ice lattice, thereby achieving control over the vertex degeneracy and ground state of the artificial spin ice and directly exhibiting a phase transition from a spin liquid state to a long-range ordered spin crystal state.

[0024] In square artificial spin ice, the six vertex configurations that satisfy the spin ice rule are divided into two categories based on energy. The lowest energy configuration is doubly degenerate, leading to a long-range ordered ground state. In square artificial spin ice, the low degeneracy of the nanomagnets is caused by the non-equivalent interactions between the nanomagnets at each vertex. Based on this concept, this invention proposes a method to reduce the ground state degeneracy of the Kagome artificial spin ice vertex from 6 to 2 by inducing non-equivalent interactions between three nanomagnets at one vertex, thereby achieving a long-range ordered spin crystal state in Kagome artificial spin ice.

[0025] like Figure 1 As shown in Figure a, in the three nanomagnets at each vertex, the present invention selectively increases the length of one of the nanomagnets (α), while keeping the lengths and lattice constants of the other two nanomagnets (β) unchanged (see Figure a). Figure 3 (Detailed arrangement of α and β nanomagnets in the lattice). This breaks the triple rotational symmetry at the vertices. The interactions between the three nanomagnets at each vertex are no longer equal.

[0026] like Figure 1 As shown in (b), the original six-fold degenerate vertex is divided into two groups of different energies: KI-type and K-II-type configurations. In this invention, the magnetic interaction energy between the two β nanomagnets in the KI-type vertex is denoted as J1, and the magnetic interaction energy between the α and β nanomagnets in the K-II-type vertex is denoted as J2. Figure 1 (b) Since each vertex satisfying the Kagome-Ice rule contains only one frustrated magnet pair, J1 and J2 also represent the energies of the KI and K-II type vertices, respectively. Because the extended α-nano magnet endpoints are closer to the vertex center, J1 is lower than J2, resulting in the KI type doubly degenerate vertex configuration being the ground state. Figure 1 As shown in (a), a long-range ordered spin crystal state appears when all vertices satisfy the KI-type ground state configuration. This invention can further adjust the energy difference between KI-type and K-II-type vertices by changing the length (Lα) of the α nanomagnet.

[0027] Figure 1 (c) The variation of vertex energy with Lα for KI and K-II type vertices obtained using Mumax3 micromagnetic simulation is presented. The results show that J2 increases with increasing Lα, while J1 remains constant. Therefore, the energy difference J2-J1 between KI type and K-II type vertices increases with increasing Lα. Thus, changing the length of the α nanomagnet allows this invention to regulate its effective temperature, similar to adjusting the vertex slots in a connected honeycomb structure. This enables the invention to regulate physical phase transitions in completely discrete cage-like artificial spin ice.

[0028] To experimentally verify this method of the present invention, permalloy nanomagnets were used to prepare kake-mesh artificial spin ice. The specific details of the fabrication process and parameters of the kake-mesh artificial spin ice sample are as follows:

[0029] S1: Sample Preparation

[0030] A series of nanomagnet arrays were fabricated on a silicon substrate with a 200 nm silicon nitride layer. A double layer of electron beam adhesive, consisting of PMMA 495 (100 nm) and PMMA 950 (80 nm), was coated on the substrate. The nanomagnet arrays were then exposed using electron beam lithography, followed by electron beam evaporation to... A 15 nm thick permalloy (Ni0.8Fe0.2) was deposited at a deposition rate of / s. To prevent oxidation of the permalloy, a 3 nm thick aluminum capping layer was deposited on top. Each array measures 100 μm × 100 μm and contains approximately 8104 nanomagnets. Samples are shown below. Figure 3 As shown, the dashed box in the lower left corner represents the basic repeating unit of the sample design. The adjustable-length α magnet is highlighted with a black line.

[0031] And set the Lα values ​​of the α nanomagnets (220nm, 270nm, 320nm, 370nm, 420nm, and 440nm), such as Figure 4 The image shows SEM images of six samples with different Lα values. The scale bar is 500 nm. The length (Lβ) of the β-magnet is fixed at 220 nm, and the lattice constant a = 640 nm. Figure 1 (a)). The width and thickness of all nanomagnets are 80 nm and 15 nm, respectively.

[0032] S2: Sample demagnetization

[0033] The sample was mounted on a motor rotating at 2000 rpm. An oscillating in-plane magnetic field (a sine wave with a period of 40 s) was applied to the test sample. The amplitude of the oscillating magnetic field slowly decreased from 1000 Gs (far exceeding the saturation magnetic field of the nanomagnets of this invention) to 0 over 72 hours.

[0034] A demagnetization procedure lasting 72 hours was performed to obtain a low-energy state for the system. Figure 1 (d) and (e) are scanning electron microscope (SEM) images of the samples at Lα = 220 nm and 420 nm, respectively. The corresponding magnetic force microscope (MFM) images are shown in [the images]. Figure 1 (f) and Figure 1 In (g), this allows the invention to determine the configuration of the magnetic moment (or spin) (see...). Figure 1 (f) and Figure 1(The arrow in (g)). The results show that all vertices in all measured samples satisfy the Kagome ice rule (two in / one out or two out / one in). This indicates that the demagnetization procedure of the present invention successfully brought the samples into a low-energy ice rule state. Traditional (Lα=Lβ) Kagome artificial spin ice ( Figure 1 (d) shows a disordered spin and magnetic charge configuration. Figure 1 (f)) is consistent with the state of the frozen spin liquid SL1. When Lα > Lβ, it has perfect spin and magnetic charge order ( Figure 1 (g)) successfully realized the ground state of a long-range ordered spin crystal.

[0035] Figure 2 In (a)-2(f), as the Lα value increases, the MFM images of the samples show a transition from the SL1 phase to a long-range ordered spin crystal phase. Figure 2 The vertex distribution diagram corresponding to (g)-2(l) shows that the crystalline domain increases with increasing Lα. When Lα = 220 nm (conventional kagome artificial spin ice), KI and K-II type vertices degenerate, resulting in disordered distributions of KI and K-II type vertices, at 33.75% and 66.25%, respectively. This is consistent with the overall 1 / 3 and 2 / 3 configurations (or randomness) of KI and K-II type vertices, consistent with the expectations of spin liquids, and demonstrates that the demagnetization process of this invention effectively brings the system to an effective thermal equilibrium state. When Lα > 220 nm, K-II type vertices enter the excited state. With increasing Lα, the energy difference between KI type vertices and K-II type vertices increases ( Figure 1 (c)). For example Figure 2 As shown in (g)-2(l), the ordered regions of KI-type vertices appear and increase with increasing Lα. For samples with larger Lα, such as 420 nm ( Figure 2 (k)), 92.6% of the vertices are in the KI type ground state, and the domain walls (dark gray) composed of excited state K-II type vertices are clearly visible.

[0036] S3: Micromagnetic Simulation

[0037] Micromagnetic simulations were performed using Mumax3, with the permalloy material having an exchange constant of 1.3 × 10⁻⁶. -11 J / m, saturation magnetization is 8.6×10 5 A / m, Gilbert damping is 0.01. Mesh size is 2×2×2nm. 3This invention considers a pair of adjacent nanomagnets. The ground state is a "one-in, one-out" or "end-to-end" configuration, while the frustrated high-energy configuration is a "simultaneous in" or "simultaneous out" configuration. This invention extracts the energies of the ground state configuration and the frustrated high-energy configuration from micromagnetic simulations. The interaction energy (J1 or J2) of the pair of small magnets is obtained by subtracting the ground state energy from the frustrated high energy. In this case, the ground state energy of a pair of adjacent small magnets is zero.

[0038] S4: Further elucidation of spin order using the magnetic spin structure factor

[0039] The magnetic spin structure factor diagram is shown below. Figure 2 As shown in (m)-2(r), where Figures (a)-(f) are MFM images with a scale bar of 2 μm; Figures (g)-(1) are the spin configurations and vertex distributions extracted from (a)-(f), with KI and K-II vertices represented in light and dark gray, respectively. Figures (m)-(r) are the corresponding graphs of magnetic structure factors calculated based on the spin configurations in (g)-(1).

[0040] For conventional cage-like artificial spin ice (Lα = 220 nm), the magnetic spin structure factor plot shows a structured dispersion mode. Figure 2 (m)), which is consistent with the previous results for the SL1 phase. With the gradual increase of Lα, the appearance and enhancement of the Bragg peak can be clearly observed in this invention. Figure 2 (n)-2(r)). This further demonstrates the transition from spin liquid to long-range ordered spin crystal.

[0041] Figure 5 These are novel ground-state examples of improved Kagome artificial spin ice. (a) is a magnetic antiferroic tape-like ground state with light gray and dark gray spins pointing to the right and left, respectively. (b) is a polarized ground state with the spin generally upward. Although this spin structure can also be realized in standard Kagome artificial spin ice using a polarized external magnetic field, it is an excited state of metastable conditions, while the spin structure shown in this invention is in the lowest-energy ground state. In (a) and (b), all vertices satisfy the KI-type configuration. (c) and (d) are spin structure factor diagrams for (a) and (b), respectively. (e) and (f) represent the magnetic charge ordering of (a) and (b).

[0042] Figure 6 This is the composite ground state of artificial spin ice in a kakeme lattice. The top image shows the ground state spin and charge configurations of the spin liquid state and the spin crystal state on the left and right sides, respectively, within the same kakeme lattice. Gray and white represent the two phases of magnetic charge. The bottom image is an enlarged view of the arrangement of nanomagnets within the rectangular frame of the top image.

[0043] This invention demonstrates that local interactions in artificial spin ice significantly influence their collective behavior and ultimately affect the properties of the entire system. Selectively adjusting the length of nanomagnets provides a convenient way to tune local coupling strength, enabling the observation of various low-energy states and phase transitions in completely discrete artificial spin ice. This invention also demonstrates that the crystallization of cage-like spin ice with reduced vertex degeneracy is dominated only by nearest-neighbor interactions. This method can be used to manipulate frustration in artificial spin ice to obtain more exotic ground-state phases (see...). Figure 5 This will also enable the present invention to achieve new magnetic structures; for example, novel composite states can be designed to allow different low-energy states to coexist in the same sample, such as... Figure 6 This invention describes a coexistence of spin liquids and spin crystals in a mixed state. This allows the study of phase transitions between these novel low-energy states. Furthermore, the invention can be applied to various spin dynamics systems under thermal annealing experiments or magnetic field reversal. Additionally, the method is applicable to other types of artificial spin ice, providing new opportunities to explore more exotic collective phenomena, such as novel phases and phase transitions. It can also be combined with other structural modification strategies, such as lattice transformations, to design novel artificial spin ice with tunable degeneracy. Moreover, the method preserves the dipole coupling between unconnected nanomagnets, which can lead to different spin dynamic properties and applications compared to connected systems. Finally, the Bragg peak splitting caused by interdomain spin scattering can provide another approach to studying domain / domain wall formation in artificial spin ice.

[0044] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for controlling the interaction between adjacent nanomagnets in artificial spin ice, characterized in that: By adjusting the length of selected nanomagnets in the spin ice lattice, the vertex degeneracy and ground state of the artificial spin ice can be controlled, and a phase transition from the spin liquid state to the long-range ordered crystal state can be directly observed. In square artificial spin ice, the low degeneracy of the nanomagnets is caused by the non-equivalent interaction between the nanomagnets at each vertex. In the Kagome artificial spin ice, by inducing the non-equivalent interaction between the three nanomagnets at the vertex, the ground state degeneracy of the Kagome artificial spin ice vertex is reduced from 6 to 2, thereby realizing the long-range ordered spin crystal state of the Kagome artificial spin ice. By selectively increasing the length of one of the three nanomagnets at each vertex, while keeping the lengths and lattice constants of the other two nanomagnets β unchanged, the triple rotational symmetry of the vertex is broken, making the interaction between the three nanomagnets at each vertex no longer equal.

2. The method for controlling the interaction between adjacent nanomagnets in artificial spin ice according to claim 1, characterized in that: The original six-fold degenerate vertices are divided into two groups of different energies: KI-type and K-II-type configurations. The magnetic interaction energy between the two β nanomagnets in the KI-type vertex is denoted as J1, and the magnetic interaction energy between the α and β nanomagnets in the K-II-type vertex is denoted as J2.

3. The method for controlling the interaction between adjacent nanomagnets in artificial spin ice according to claim 2, characterized in that: Since each vertex that satisfies the Kagome-Ice rule contains only one frustrated magnet pair, J1 and J2 also represent the energies of the KI and K-II type vertices, respectively. Because the extended α nanomagnet endpoints are closer to the vertex center, J1 is lower than J2, resulting in the KI type double degenerate vertex configuration being the ground state.

4. The method for controlling the interaction between adjacent nanomagnets in artificial spin ice according to claim 3, characterized in that: When all vertices satisfy the KI-type ground state configuration, a long-range ordered spin crystal state can appear.

5. The method for controlling the interaction between adjacent nanomagnets in artificial spin ice according to claim 4, characterized in that: By changing the length Lα of the α nanomagnet, the energy difference between the KI-type and K-II-type vertices can be further adjusted, thereby achieving the adjustment of the effective temperature of the Kagome artificial spin ice by changing the length of the α nanomagnet, and thus achieving the adjustment of physical phase transition in the completely discrete Kagome artificial spin ice.

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