An artificial antiferromagnetic structure and storage element
By regulating the interface DM interaction in the artificial antiferromagnetic structure, a deterministic magnetization flip with a controllable spin orbit moment under low applied magnetic field or no applied magnetic field is achieved, solving the problem of dependence on high-intensity auxiliary magnetic fields in traditional methods and enhancing the application potential of spintronic devices.
Patent Information
- Application Number
- CN202110779625.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2021-07-09
- Publication Date
- 2025-03-11
- Estimated Expiration
- 2041-07-09
AI Technical Summary
In a vertically anisotropic artificial antiferromagnetic structure with strong antiferromagnetic coupling, achieving deterministic magnetization flips caused by spin orbit moment requires an auxiliary magnetic field up to 2000 Oe to 10000 Oe, limiting its application in spin electronic devices.
By stacking the first metal layer, artificially synthesized antiferromagnetic layer and second metal layer in sequence, the interface DM interactions of different interfaces are used to form a stable chiral Néel magnetic domain wall, and by regulating the thickness and material of the first metal layer and the second metal layer, the size and direction of the interface DM interaction are different, thereby achieving magnetization flip under a small auxiliary magnetic field or even a zero magnetic field.
The deterministic magnetization flip of the spin orbit moment controllable under low applied magnetic fields or even no applied magnetic fields is achieved, and the dependence on high-intensity auxiliary magnetic fields in traditional methods is overcome, and the application potential of artificial antiferromagnetic structures in spintronic devices is enhanced.
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Abstract
Description
Technical Field
[0001] The invention relates to the fields of information technology and spin electronics, and in particular to an artificial antiferromagnetic structure and a storage element. Background Art
[0002] Artificial antiferromagnetic structure refers to two magnetic layers that generate interlayer exchange coupling through the middle non-magnetic layer, and under the action of interlayer exchange coupling, the magnetic moments of the ferromagnetic layers are arranged in antiparallel. Due to the strong antiferromagnetic interlayer exchange coupling, artificial antiferromagnetic structure has the advantages of small stray magnetic field and insensitivity to external magnetic field disturbance. It is widely used as a pinning layer in spin valve structure or magnetic tunnel junction, which greatly promotes the development of giant magnetoresistance and tunnel magnetoresistance devices. In recent years, with the discovery of novel physical phenomena such as magnetization reversal caused by spin-orbit moment, fast domain wall movement, artificial spin ice, etc. in artificial antiferromagnetic structure, people realize that artificial antiferromagnetic structure can not only be used as auxiliary functional layer of spin electronic devices, but also can become the carrier of new non-volatile storage and spin logic devices. In particular, perpendicular anisotropic artificial antiferromagnetic structure with strong antiferromagnetic coupling has broad application prospects in high-density information storage and terahertz fields because of its high thermal stability, fast spin dynamics and efficient magnetization reversal caused by spin-orbit moment. However, in order to achieve deterministic magnetization reversal caused by spin-orbit moment in a perpendicular anisotropic artificial antiferromagnetic structure with strong antiferromagnetic coupling, an auxiliary magnetic field of up to 2000Oe to 10000Oe must be applied along the direction of current, which becomes a bottleneck in the application of strong antiferromagnetic coupling perpendicular anisotropic artificial antiferromagnetic structure in spin electronics devices.
[0003] Therefore, how to achieve controllable deterministic magnetization reversal of spin-orbit torque with low external magnetic field or no external magnetic field becomes a technical problem that needs to be solved urgently. Summary of the invention
[0004] In order to solve the technical problem of how to achieve controllable deterministic magnetization reversal of spin-orbit torque in a low external magnetic field or without an external magnetic field as described in the above background technology, the present invention provides an artificial antiferromagnetic structure and a storage element to achieve controllable deterministic magnetization reversal of spin-orbit torque in a low external magnetic field or even without an external magnetic field.
[0005] According to the first aspect, an embodiment of the present application provides an artificial antiferromagnetic structure, comprising: a first metal layer, an artificial antiferromagnetic layer, and a second metal layer stacked in sequence, wherein there is a first interface DM interaction between the first metal layer and the artificial antiferromagnetic layer, and there is a second interface DM interaction between the second metal layer and the artificial antiferromagnetic layer, and the first interface DM interaction is different from the second interface DM interaction.
[0006] Optionally, the first metal layer and the second metal layer have different materials and / or thicknesses.
[0007] Optionally, the artificial antiferromagnetic structure further includes: a buffer layer stacked on a side of the first metal layer away from the artificial antiferromagnetic layer; and a thickness of the first metal layer is greater than a thickness of the second metal layer.
[0008] Optionally, the first interface DM interaction is greater than the second interface DM interaction.
[0009] Optionally, the first metal layer includes any one of Ta, Pt, Ir, W, Mo, Pd, Au, CoPt, FePt, IrMn, and PtMn.
[0010] Optionally, the first metal layer has a thickness of 1-10 nm.
[0011] Optionally, the second metal layer includes one or more of Ru, Ta, Pt, W, Ti, Mo, Pd, Au, Cr, Cu, and Hf.
[0012] Optionally, the second metal layer comprises a composite layer of at least two metal layers, wherein the magnitude of the second interface DM interaction is regulated by changing the relative thickness and sequence of the metal layers in the composite layer.
[0013] Optionally, the artificial antiferromagnetic layer includes: a first ferromagnetic layer, a non-ferromagnetic layer, and a second ferromagnetic layer stacked in sequence, wherein the first ferromagnetic layer and the second ferromagnetic layer form an antiferromagnetic coupling through the non-ferromagnetic layer, the magnetic moments in the first ferromagnetic layer and the second ferromagnetic layer are arranged antiparallel, and the first ferromagnetic layer and the second ferromagnetic layer are ferromagnetic materials with perpendicular magnetic anisotropy.
[0014] According to the second aspect, this embodiment provides a storage element, comprising the artificial antiferromagnetic structure as described in any one of the first aspects above.
[0015] The embodiment of the present application comprises a first metal layer, an artificial antiferromagnetic layer, and a second metal layer stacked in sequence, wherein a first interface DM interaction exists between the first metal layer and the artificial antiferromagnetic layer, a second interface DM interaction exists between the second metal layer and the artificial antiferromagnetic layer, and the first interface DM interaction is different from the second interface DM interaction. The strong interface DM interaction enables the artificial antiferromagnetic layer to form a stable chiral Néel magnetic domain wall. When there is a difference in the magnitude and / or direction of the first interface DM interaction and the second interface DM interaction, the passage of current under a very small auxiliary magnetic field or even a zero magnetic field can make the movement speed of the up-to-down and down-to-up magnetic domain walls in the chiral Néel magnetic domain wall significantly different, thereby obtaining a deterministic magnetization reversal caused by the spin-orbit moment.
[0016] Furthermore, by regulating the thickness and / or material of the first metal layer and / or the second metal layer, the magnitude and / or direction of the first interface DM interaction and the second interface DM interaction are different, so that the movement speed of the up-to-down and down-to-up magnetic domain walls in the artificial antiferromagnetic layer is significantly different.
[0017] Furthermore, the artificial antiferromagnetic layer is a first ferromagnetic layer, a non-ferromagnetic layer and a first ferromagnetic layer stacked in sequence, wherein the antiferromagnetic coupling is formed through the non-ferromagnetic layer, and the magnetic moments in the first ferromagnetic layer and the first ferromagnetic layer are arranged in antiparallel, and can be magnetized as a whole under the action of an external magnetic field or a spin-orbit moment. Therefore, when the DM interactions of the upper and lower interfaces of the artificial antiferromagnetic layer are different, the movement speeds of the up-to-down and down-to-up magnetic domain walls in the artificial antiferromagnetic layer are different, and a very small auxiliary magnetic field is applied along the direction of the current, and the spin-orbit moment effect generated by the current can be used to flip the magnetic moment direction of the perpendicular magnetization magnetic layer as a whole.
[0018] Furthermore, the first ferromagnetic layer and the first ferromagnetic layer are ferromagnetic materials with perpendicular magnetic anisotropy. To ensure the perpendicular anisotropy of the grown material, the ferromagnetic layer needs to be grown on a thicker metal layer. Therefore, the stacked structure is that a thicker first metal layer is grown on the buffer layer, and the first ferromagnetic layer, the non-ferromagnetic layer and the first ferromagnetic layer in the artificial antiferromagnetic layer are grown in sequence on the first metal layer, wherein a second metal layer with a thickness less than the first metal layer is grown on the first ferromagnetic layer, which ensures that the ferromagnetic layer has good perpendicular anisotropy and that there is a large difference in the DM interaction between the upper and lower interfaces of the artificial antiferromagnetic layer. The spin-orbit moment is controllable and deterministic magnetization reversal is achieved with a low external magnetic field or even without an external magnetic field. BRIEF DESCRIPTION OF THE DRAWINGS
[0019] The drawings described herein are used to provide a further understanding of the present invention and constitute a part of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:
[0020] Figure 1 is a schematic structural diagram of an artificial antiferromagnetic structure according to an embodiment of the present invention;
[0021] Figure 2 A schematic structural diagram of another artificial antiferromagnetic structure according to an embodiment of the present invention;
[0022] Figure 3 The normalized magnetic properties and Hall resistance curves of the artificial antiferromagnetic structure of an embodiment of the present invention;
[0023] Figure 4 This is a curve showing the relationship between Hall resistance and current when an auxiliary magnetic field is applied to the artificial antiferromagnetic structure of an embodiment of the present invention. DETAILED DESCRIPTION
[0024] In order to have a clearer understanding of the technical features, purposes and effects of the present invention, the specific embodiments of the present invention are now described with reference to the accompanying drawings. In the drawings, the same reference numerals represent components with the same structure or similar structures but the same functions.
[0025] In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention may also be implemented in other ways different from those described herein. Therefore, the protection scope of the present invention is not limited to the specific embodiments disclosed below.
[0026] The present application embodiment provides an artificial antiferromagnetic structure, such as Figure 1 As shown, it may include:
[0027] A first metal layer 10, an artificial antiferromagnetic layer 20, and a second metal layer 30 are sequentially stacked, wherein a first interface DM interaction exists between the first metal layer 10 and the artificial antiferromagnetic layer 20, and a second interface DM interaction exists between the second metal layer 30 and the artificial antiferromagnetic layer 20, and the first interface DM interaction is different from the second interface DM interaction. Exemplarily, the artificial antiferromagnetic layer, the first metal layer 10, and the second metal layer 30 form a sandwich structure, and generally, DM interaction exists at the interface between a magnet having non-centrosymmetry and a ferromagnet and a metal, therefore, a first interface DM interaction exists at the interface between the artificial antiferromagnetic layer and the first metal layer 10, and a second interface DM interaction exists at the interface between the artificial antiferromagnetic layer and the second metal layer 30, and a strong interface DM interaction enables the artificial antiferromagnetic layer 20 to form a stable chiral Néel domain wall. When there is a difference in the magnitude and / or direction of the first interface DM interaction and the second interface DM interaction, the movement speeds of the up-to-down and down-to-up magnetic domain walls in the chiral Néel magnetic domain wall can be significantly different by passing an electric current under a very small auxiliary magnetic field or even a zero magnetic field, thereby obtaining a deterministic magnetization reversal caused by the spin-orbit moment.
[0028] As an exemplary embodiment, the first metal layer 10 and the second metal layer 30 have different materials and / or thicknesses. By regulating the thickness and / or material of the first metal layer 10 and / or the second metal layer 30, the magnitude and / or direction of the first interface DM interaction and the second interface DM interaction are different, so that the movement speeds of the up-to-down and down-to-up magnetic domain walls in the artificial synthetic antiferromagnetic layer 20 are different. For example, the first metal layer 10 can be a thicker metal layer, such as 1-10nm, and the second metal layer 30 can be a thinner metal layer or a composite layer of at least two metal layers, such as 1-3nm. Since the thickness and / or material of the first metal layer 10 and the second metal layer 30 are different, and the interfaces of the artificial antiferromagnetic layer 20 adjacent to the first metal layer 10 and the second metal layer 30 are the same, the first interface DM interaction and the second interface DM interaction are different, which causes the difference in the movement speed of the chiral Néel magnetic domain wall in the artificial antiferromagnetic structure. The movement speed of the up-to-down and down-to-up magnetic domain walls in the chiral Néel magnetic domain wall can be significantly different under a very small auxiliary magnetic field or even a zero magnetic field.
[0029] As an exemplary embodiment, Figure 2As shown, the artificial antiferromagnetic layer 20 includes: a first ferromagnetic layer 21, a non-ferromagnetic layer 22, and a second ferromagnetic layer 23 stacked in sequence, wherein the first ferromagnetic layer 21 and the second ferromagnetic layer 23 form an antiferromagnetic coupling through the non-ferromagnetic layer 22, the magnetic moments in the first ferromagnetic layer 21 and the second ferromagnetic layer 23 are arranged in antiparallel, and the first ferromagnetic layer 21 and the second ferromagnetic layer 23 are ferromagnetic materials with perpendicular magnetic anisotropy. Exemplarily, the ferromagnetic layer can be a ferromagnetic material with perpendicular magnetic anisotropy such as Co, Fe, Ni, CoFe, CoFeB, CoNi, CoPt, CoTb, FePt, etc., and the thickness of the ferromagnetic layer is 0.5-10nm; the manufacturing materials and thickness of the first ferromagnetic layer 21 and the second ferromagnetic layer 23 can be the same or different. The non-ferromagnetic layer 22 can be one of Ta, Ru, Pt, Ti, W, Cr, Cu, Hf, Mo, Pd, and Au, and the thickness is 0.3-3nm. As Figure 2 As shown, the second metal layer 30 includes at least two metal composite layers, including a first composite layer 31 and a second composite layer 32 stacked in sequence, wherein the size of the second interface DM interaction can be regulated by changing the relative thickness and growth order between the first composite layer 31 and the second composite layer 32.
[0030] The following description is made by taking the first ferromagnetic layer 21 and the second ferromagnetic layer 23 as Co / Pt / Co, the non-ferromagnetic layer 22 as Ru, the first metal layer 10 as Pt, and the second metal layer 30 as a Pt / Ta composite layer as an example:
[0031] In order to ensure the perpendicular anisotropy of the ferromagnetic layer, the ferromagnetic layer needs to be grown on a thicker metal layer. As an exemplary embodiment, the artificial antiferromagnetic structure also includes: a substrate and a buffer layer 40 grown on the substrate. In this embodiment, the buffer layer 40 can be a metal such as Ta, Cr, Ru, Ti, Al, etc. A first metal layer 10 with a relatively thick thickness is grown on the buffer layer 40, for example, 1-10nm of Pt is grown. In this embodiment, 5nm can be taken as an example. The first ferromagnetic layer 21, the non-ferromagnetic layer 22 and the second ferromagnetic layer 23 of the artificial synthetic antiferromagnetic layer 20 are grown in sequence on the first metal layer 10, wherein the second metal layer 30 is grown on the second ferromagnetic layer 23, for example, 1nm of Pt and 2nm of Ta are grown in sequence. As an exemplary embodiment, each film layer in the artificial synthetic antiferromagnetic layer 20 can be sputtered and grown at room temperature using a magnetron sputtering instrument. Exemplarily, the background vacuum of the magnetron sputtering instrument is better than 1×10 -8 torr, the sputtering gas is Ar, and the metal target can be sputtered by DC sputtering to grow each film layer.
[0032] Exemplarily, both the first metal layer 10 and the second metal layer 30 will generate spin currents, and the spin current of the first metal layer 10 acts on the lower ferromagnetic layer of the artificial antiferromagnetic layer 20, namely the first ferromagnetic layer 21, and the spin current of the second metal layer 30 acts on the upper ferromagnetic layer of the artificial antiferromagnetic layer 20, namely the second ferromagnetic layer 23. Since the thickness of the first metal layer 10 is relatively thick, the spin current in the first metal layer 10 serves as the main source of the spin current of the artificial antiferromagnetic layer 20.
[0033] For example, the first ferromagnetic layer 21 and the second ferromagnetic layer 23 have significant perpendicular magnetic anisotropy, and the two ferromagnetic layers are coupled together through the middle non-ferromagnetic layer 22, the artificial antiferromagnetic structure magnetically cancels out, the stray magnetic field is very small, and will not interfere with neighboring magnetic units; the anomalous Hall effect is not canceled out. Figure 3 When the external magnetic field is perpendicular to the film surface, the normalized magnetic properties (M) and Hall resistance (R) of the artificial antiferromagnetic structure are measured. H ) curve, and shows the arrangement direction of the magnetic moments of the two magnetic layers under different magnetic fields ( Figure 3 The directions of the magnetic moments of the two magnetic layers are shown by arrows. Figure 3 It can be seen that the artificial antiferromagnetic structure has significant perpendicular magnetic anisotropy, strong antiferromagnetic coupling between the two magnetic layers, and the interlayer coupling field is as high as 7500Oe; within the range of ±7500Oe, the magnetic properties of the artificial antiferromagnetic samples studied are canceled, while the anomalous Hall resistance is not canceled. Due to the existence of strong antiferromagnetic coupling, the magnetic moments in the upper and lower magnetic layers are arranged antiparallel. Therefore, the two magnetic layers can undergo magnetization reversal as a whole, that is, the magnetic moments in the upper and lower magnetic layers are reversed at the same time, and the magnetic moments after the reversal are still arranged antiparallel.
[0034] Exemplarily, when the first metal layer 10 is a Pt layer with a thickness of more than 5nm and the first ferromagnetic layer 21 is a Co / Pt / Co layer, the effective field of the first interface DM interaction is measured to be 1300Oe by experiments, and when the thickness of the second metal layer 30 is less than the first metal layer 10, or a composite layer Pt / Ta composite layer is used, the interface DM interaction between the second metal layer 30 and the second ferromagnetic layer 23 can be effectively reduced, so that the second interface DM interaction is smaller than the first interface interaction, and by changing the material and the thickness of the material in the second metal layer 30, for example, changing the relative thickness and / or sequence of Pt and Ta, the magnitude of the second interface DM interaction can be further adjusted. Exemplarily, when the thickness of Pt is 1nm and the thickness of Ta is 2nm, the effective field of the second interface DM interaction between the second ferromagnetic layer 23, i.e., the Co / Pt / Co layer, and the second metal layer 30, i.e., the Pt / Ta layer, is about 650Oe. Therefore, the first interface DM interaction and the second interface DM interaction will have a large difference when the thickness of the first metal layer 10 and the second metal layer 30 are different and / or the material is different or the material growth sequence is different. Therefore, by adjusting the material and / or thickness of the first metal layer 10 and the second metal layer 30 , the interfacial DM interaction between the artificial antiferromagnetic layer and the two metal layers can be adjusted to have significant differences.
[0035] The interface between the first metal layer 10 and the first ferromagnetic layer 21 is the interface between the Pt layer and the Co / Pt / Co layer, where there is a strong DMI interaction, resulting in the formation of a stable chiral Néel domain wall in the magnetic domains in the Co / Pt / Co layer. For example, a left-handed Néel domain wall can be formed in the Co / Pt / Co layer. Figure 4 FIG. 4 shows a curve showing the relationship between the Hall resistance and the current when different auxiliary magnetic fields are applied along the current direction to an exemplary artificial antiferromagnetic structure. Figure 4 It can be seen that when there is a significant difference in the interfacial DM interaction between the artificial antiferromagnetic layer and the two metal layers, only an auxiliary magnetic field of ±40Oe is required to obtain a significant spin-orbit moment-induced magnetization reversal. When the auxiliary magnetic field is positive, the change of the Hall resistance with the current will change from counterclockwise (Hx<2400Oe) to clockwise (Hx>2400Oe).
[0036] When the magnetic domain wall in the artificial antiferromagnetic structure is a left-handed Néel wall, when the magnetic domain wall in the first ferromagnetic layer 21 is ↑←↓, due to the strong antiferromagnetic coupling, the corresponding magnetic domain wall in the second ferromagnetic layer 23 is ↓→↑. This antiferromagnetically coupled magnetic domain wall can be called the first magnetic domain wall. Similarly, when the magnetic domain wall in the first ferromagnetic layer 21 is ↓→↑, the corresponding magnetic domain wall in the second ferromagnetic layer 23 is ↑←↓, and this antiferromagnetically coupled magnetic domain wall can be called the second magnetic domain wall. When the auxiliary magnetic field is 0 < Hx < 2400 Oe, the moving speed of the first magnetic domain wall is greater than that of the second magnetic domain wall, resulting in a counterclockwise magnetization reversal. When the auxiliary magnetic field is greater than Hx > 2400 Oe, the moving speed of the second magnetic domain wall is greater than that of the first magnetic domain wall, resulting in a clockwise magnetization reversal. When the applied auxiliary magnetic field is reversed, when Hx < -2400 Oe correspondingly, the speed of the first magnetic domain wall is greater than that of the second magnetic domain wall, resulting in a counterclockwise magnetization reversal, and when -2400 Oe < Hx < 0, the speed of the second magnetic domain wall is greater than that of the first magnetic domain wall, resulting in a clockwise magnetization reversal.
[0037] The embodiment of the present invention also provides a storage element based on the artificial synthetic antiferromagnetic layer described in the above embodiment. Through the artificial synthetic antiferromagnetic structure described in the above embodiment, a deterministic magnetization reversal caused by the spin-orbit torque can be achieved without applying an auxiliary magnetic field.
[0038] So far, the technical solutions of the present disclosure have been described in combination with multiple previous embodiments. However, it is easy for those skilled in the art to understand that the protection scope of the present disclosure is not limited to these specific embodiments. Without departing from the technical principle of the present disclosure, those skilled in the art can split and combine the technical solutions in the above-mentioned various embodiments, and can also make equivalent changes or replacements to the relevant technical features. Any changes, equivalent replacements, improvements, etc. made within the technical concept and / or technical principle of the present disclosure will fall within the protection scope of the present disclosure.
[0039] Each embodiment in this specification is described in a progressive manner. The same or similar parts between the embodiments can be referred to each other, and each embodiment focuses on the differences from other embodiments. In particular, for the system embodiment, since it is basically similar to the method embodiment, the description is relatively simple, and the relevant parts can be referred to the partial description of the method embodiment.
[0040] The above are only the embodiments of the present invention and are not used to limit the present invention. For those skilled in the art, the present invention can have various changes and modifications. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the scope of the claims of the present invention.
Claims
1. An artificial antiferromagnetic structure, characterized in that: include: A first metal layer, an artificial antiferromagnetic layer, and a second metal layer are stacked in sequence, wherein the first metal layer and the second metal layer are made of different materials and / or have different thicknesses; The artificial synthetic antiferromagnetic layer comprises: a first ferromagnetic layer, a non-ferromagnetic layer and a second ferromagnetic layer stacked in sequence, wherein the first ferromagnetic layer and the second ferromagnetic layer form an antiferromagnetic coupling through the non-ferromagnetic layer, the magnetic moments in the first ferromagnetic layer and the second ferromagnetic layer are arranged in antiparallel, and the first ferromagnetic layer and the second ferromagnetic layer are ferromagnetic materials with perpendicular magnetic anisotropy; There is a first interface DM interaction between the first metal layer and the artificial antiferromagnetic layer, and there is a second interface DM interaction between the second metal layer and the artificial antiferromagnetic layer. The first interfacial DM interaction is different from the second interfacial DM interaction; The second metal layer includes a composite layer of at least two metal layers, wherein the magnitude of the second interface DM interaction is regulated by changing the relative thickness and sequence of the metal layers in the composite layer.
2. The artificial antiferromagnetic structure according to claim 1, characterized in that: Also includes: A buffer layer, stacked on a side of the first metal layer away from the artificial antiferromagnetic layer; The thickness of the first metal layer is greater than the thickness of the second metal layer.
3. The artificial antiferromagnetic structure according to claim 1, characterized in that: The first interface DM interaction is greater than the second interface DM interaction.
4. The artificial antiferromagnetic structure according to claim 1, characterized in that: The first metal layer includes any one of Ta, Pt, Ir, W, Mo, Pd, Au, CoPt, FePt, IrMn, and PtMn.
5. The artificial antiferromagnetic structure according to any one of claims 1 to 4, characterized in that: The thickness of the first metal layer is 1-10 nm.
6. The artificial antiferromagnetic structure according to claim 1, characterized in that: The second metal layer includes one or more of Ru, Ta, Pt, W, Ti, Mo, Pd, Au, Cr, Cu, and Hf.
7. A storage element, characterized in that: Comprising the artificial antiferromagnetic structure as described in any one of claims 1-6.
Citation Information
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