Chiral nanomagnetic systems and logic

Magnetically coupled nanomagnets have many possible applications including non-volatile memories, logic gates, and sensors. So far, the most effective couplings have been found to occur between the magnetic layers in vertically layered stacks. We have exploited the Dzyaloshinskii-Moriya interaction to control the lateral coupling between out-of-plane and in-plane non-homogeneous magnetic structures, and demonstrate unique phenomena associated with such chirally coupled nanomagnets [1, 2]. Based on this chiral coupling, we have further develop a method of performing all-electric logic operations and cascading with domain-wall racetracks, providing a viable platform for novel logic-in-memory architectures [3, 4].

It is possible to design complex coupled nanomagnetic systems with lateral magnetic coupling such as those used for nanomagnet logic or artificial spin ice. Currently, most laterally coupled nanomagnet systems make use of the dipolar interaction, for which the coupling strength is proportional to the volume of nanomagnet. However, in order to electrically control these systems via spin-orbit torques, the nanomagnets should be extremely thin, which means that the dipolar coupling is very weak. Here, we couple the nanomagnets via the interfacial Dzyaloshinskii-Moriya interaction (iDMI). iDMI can be expressed by an energy term H_DM = - D_ij·(m_i× m_j), which represents the antisymmetric exchange coupling between two neighbouring magnetic moments m_iand m_jinduced by the spin-orbit interaction in a structurally asymmetric environment (Fig. 1a). Since it is an interfacial effect, iDMI-induced coupling is only effective in thin magnetic films. In a homogeneous film, the presence of iDMI results in chiral domain walls and topological non-trivial magnetic textures such as cycloids or skyrmions.

We have patterned regions with in-plane (IP) and out-of-plane (OOP) magnetic anisotropy in a magnetic element using selective oxidation of Pt/Co/Al films (Fig. 1b). In addition to classical non-chiral interactions, the magnetization in the OOP and IP parts of the islands are coupled via iDMI arising from the Pt underlayer. As shown in Fig. 1b, this results in chirally coupled magnetization so that, when the IP region is set to point to the right (→) with an in-plane magnetic field, the OOP regions on the left and right of the IP region point down (⊗) and up (⊙) accordingly, giving either ⊗→ or →⊙ configurations. This agrees with the left-handed chirality generally expected from the negative sign of the iDMI in Pt/Co/AlOx and shown in the schematics in Fig. 1a.

Enlarged view: chiral magnetic systems 1 — *Fig. 1.* Chiral coupling between OOP and IP magnets. (a) Schematics of the coupled magnetization states favored by the DMI in adjacent OOP (red) and IP (blue) regions of a Pt/Co/AlOx trilayer. (b) Scanning electron micrograph (SEM) of coupled OOP-IP elements and its corresponding X-ray photoemission electron microscopy (X-PEEM) image. Red and blue colors in SEM image indicate regions with OOP and IP magnetization, respectively. The bright and dark magnetic contrasts in the OOP regions in PEEM image corresponded to ⊗ and ⊙ magnetization, respectively. (c) Magnetic force microscopy (MFM) images of synthetic skyrmions with 2, 3, 4, and 5 IP rings. (d) Coloured MFM image of an artificial spin system consisting of OOP elements arranged on a square lattice and acting like Ising-like moments coupled via IP spacers. Antiferromagnetic domains are shaded in green and purple. Reproduced from [1].

We have exploited this concept for various purposes in the single-domain regime such as lateral exchange bias, field-free current-induced switching between multistate magnetic configurations, as well as synthetic lateral antiferromagnets, skyrmions (Fig. 1c), and artificial spin ices (Fig. 1d) [1, 5, 6] covering a broad range of length scales. We have also developed this concept for device applications in the combination with mobile domain-walls (DWs) to realize chiral DW injection [7], to bias the DW torques [8] and to create DW logic devices [2, 3]. When passing a chiral DW through a narrow IP region, which acts as a logic inverter, an up|down (⊙|⊗) DW transforms into a ⊗|⊙ DW and vice versa (Fig. 2a). This inverter is equivalent to a NOT gate in Boolean logic with the binary data encoded into the magnetization of the moving domains, i.e. ⊗ =”1” and ⊙ =”0”. With devices based on this logic building block, we have demonstrated a complete set of all-electric logic operations and cascading with DW racetracks (Fig. 2b). The DW inverter can be also geometrically tailored to serve as a current-driven DW diode (Fig. 2c) [9]. The range of applications was also broadened with an investigation of the dynamic properties of polar-vortex oscillators established in chirally systems. Here we have shown that such current-driven oscillators can, as a result of their synchronization (Fig. 2d), serve as a platform for neuro-inspired computation [10]. With this work, we offer an alternative to go beyond the so-called “von Neumann bottleneck”, reducing the energy used and the time needed for the transfer of data between computation and storage units.

Enlarged view: chiral magnetic systems 2 — *Fig 2*. Computation with chirally coupled systems. (a) Schematic showing current-driven domain-wall inversion, which occurs as the domain-wall transfers across the in-plane region (in blue). Reproduced from [2]. (b) Full adder gate. Left: logic circuit symbol for the full adder with input operands of “a =0”, “b =1”, and a carry bit of “c_in =1”. Right: magnetic force microscopy (MFM) image of the full adder magnetic circuit. The bright and dark contrast in the device regions in the MFM image corresponds to up and down magnetization, respectively. Reproduced from [1]. (c) Domain wall diode based on the geometrical asymmetry of the domain wall inverter. Reproduced from [9]. (d) Frequency spectrum of two polar-vortex oscillators (shown in the inset) patterned in an out-of-plane magnetized slab. The mutual synchronization can be used in neuro-inspired computation schemes. Reproduced from [10].

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