Recently, 5d and 4d oxides and halides with honeycomb lattice structures are of great interest [1-2] for exhibiting an interplay between an isotropic Heisenberg-type exchange interaction (J) and an anisotropic Kitaev-type exchange interaction (K), see Fig. 1a. We predict that such an interplay can lead to topological edge states with chiral conduction when the anisotropic interaction is at least twice the strength of the isotropic interaction (i.e. K ≥ 2J), see Figs. 1b-c. We show that these interactions give rise to new types of antiferromagnetic orders, which determine the chirality of the edge atomic chain. We show calculations for sodium iridate and alpha-ruthenium chloride, both known to exhibit a zigzag antiferromagnetic order at low temperatures, and discuss the chiral edge conduction in the context of the relative strength between J and K. The edge conduction in the presence of a zigzag antiferromagnetic order will be manifested as a quantized Hall conductance when the number of zigzag atomic chains is odd (see Fig. 1b) since both edges will have the same magnetic orders. On the other hand, the Hall conductance will be zero when the number of zigzag atomic chains is even (see Fig. 1c) since the edges will have opposite magnetic orders. These signatures of the exchange interaction induced chiral edge conductions in odd and even numbers of two-dimensional atomic chains are similar to the well-known signatures of a quantum anomalous Hall insulator and an axion insulator states typically observed in a three-dimensional magnetic topological insulator [3-4], respectively. We further use a widely used model for two-dimensional topological materials to analyze the underlying mechanisms of the predicted phenomena.

![](https://assets.underline.io/uploads/markdown_image/1/image/b67aecaae65e534de04962906894efe1.jpg)

(a) Honeycomb lattice with isotropic (J) and anisotropic (K) exchange interactions. Hall conductance Gxy = Vx / Iy is calculated when the number of zigzag atomic chains is (b) odd and (c) even, as a function of K / J.

Chiral edge conduction induced by large anisotropic exchange interactions.

Rare earth-transition metal (RETM)-based ferrimagnets are known to exhibit strong bulk perpendicular magnetic anisotropy and bulk Dzyaloshinskii-Moriya interaction [1]. These properties make RETM ferrimagnets a model system to study exciting magnetic phenomena such as magnetic skyrmion [2,3], chiral domain wall [3], all-optical switching [4], spin-orbit torque switching [5] and canted magnetic moments. Here, we demonstrate a field-free spin-orbit torque-driven multistate switching of a nearly compensated GdCo ferrimagnet sandwiched between Ta and Pt. We show that our GdCo film exhibits a strong canting of magnetic moments, and the canted moments can be deterministically switched among three stable states using a current-driven spin-orbit torque, even in the absence of a magnetic field. We further show that the three states persist in the presence of an in-plane magnetic field and the levels of the three states can be tuned with the magnitude of the magnetic field. We consider various possible origins of the canting, including concentration gradient, Dzyaloshinskii - Moriya interaction, and balanced pair-correlations of unlike atoms versus like atoms in the growth direction, and discuss various methods to differentiate among these mechanisms. Furthermore, we discuss the possibility of domain formations to explain the observed multistate. Our results provide a new perspective to study the competing magnetic interaction in RETM-based ferrimagnetic alloys at the near-compensation point, and enable a new pathway to achieve multistate spin-orbit torque devices.

![](https://assets.underline.io/uploads/markdown_image/1/image/df0a749c720a6befff1af56d0b3f65bb.jpg)

Multistate switching of canted GdCo moments via spin-orbit torque with zero in-plane symmetry breaking field.


Field-free Spin-orbit Torque-driven Multistate Switching of Canted GdCo Moments

Spin-transfer torque (STT) based magnetoresistive random-access memory (MRAM) is of great current interest for embedded applications, due to its high speed, high endurance, and long retention time. However, state-of-the-art STT MRAM requires a large switching current that leads to reliability issues, high write energy, and limits the density scaling. In this talk, we will show that a conventional current-controlled MTJ can be changed to a voltage-controlled device if we replace the thin oxide barrier with a resonant tunneling barrier. Such a simple modification will combine two established quantum phenomena: interlayer exchange coupling and resonant tunneling within the scaled magnetic structure to enable a resonant-exchange controlled (REC) magnetization switching [1]. REC-driven magnetization switching can substantially lower the write energy, decouple the energy and speed of operations, eliminate the reliability issues, and enable denser MRAM technologies. A voltage-controlled MTJ has a high baseline resistance, which may cause compatibility issues with standard CMOS. We will discuss a magnetic gain cell structure that consists of a REC MTJ and two transistors for a large separation in the output current for the two memory states while retaining the low power advantages of a voltage-controlled write mechanism [2]. We analyze the REC MTJ using quantum-transport simulations on a CoFeB/MgO/Ru/MgO/CoFeB structure and combine the results with an empirical SPICE model to analyze the magnetic gain cell using 45 nm CMOS models in HSPICE. Our simulation results suggest approximately 103 times change in the read current in the gain cell between the two magnetic states. The expected energy and delay are 29.5 fJ/bit and 1.6 ns respectively for a write operation and 7.6 ~ 39 fJ/bit and 0.6 ~ 1 ns respectively for a read operation, thus promising for low energy, fast, and high-density REC MRAM technology.

![](https://assets.underline.io/uploads/markdown_image/1/image/8f55c819fa0feacf6498620a60124061.jpg)

A magnetic gain-cell structure for efficient voltage-controlled MRAM

The discovery of helicity-independent all-optical switching1 as well as ps current-pulse driven magnetization reversal2 of a ferrimagnetic GdFeCo led to a significant development towards ultrafast magnetization reversal of a magnetic tunnel junction (MTJ) based memory element. Ultrafast switching of Co/Pt multilayers coupled with a GdFeCo has been observed within ~ 7 ps which occurs due to RKKY exchange coupling3. However, GdFeCo isn’t a desirable choice for a MTJ as it does not hold PMA for a patterned dot with a diameter less than a mm4. On the other hand, CoGd ferrimagnet can maintain its PMA down to 200 nm diameter4. In this work, we have experimentally observed the all-optical time-resolved magnetization dynamics of a “CoGd/Pt spacer (1 to 4 nm)/ [Co/Pt] multilayers” heterostructure. The magnetization of CoGd is reversed after 1.5 ps. The Co/Pt multilayer which has slightly higher demagnetization rate, stays demagnetized as the electron temperature reaches its Currie temperature before getting switched ~ 3 ps due to enough angular-momentum transfer from the CoGd sublattice as shown in Fig. 1(a). We rule out the possibility of Co/Pt swithcing triggered by non-local spin current generated from CoGd as Co/Pt switched for both ferromagnetic and anti-ferromagnetic coupling. We performed analytical calculation to simulate the time-resolved dynamics as shown in Fig. 1(b) using an extended microscopic three temperature model (M3TM) proposed by Beans et al5. Considering inter-sublattice, intra-sublattice and indirect RKKY exchange scatterings, we explain the magnetization reversal dynamics of different magnetic components of ferromagnetically and antiferromagnetically coupled as well as decoupled ferromagnet-ferrimagnet heterostructures. We demonstrate that irrespective of the nature of RKKY coupling, ultrafast switching of the Co/Pt multilayers can be achieved, and its switching time strongly depends on the RKKY interaction strength. This work experimentally as well as theoretically establishes the mechanism of all-optical switching in such magnetic heterostructures.

![](https://assets.underline.io/uploads/markdown_image/1/image/17766eb2037f4c3871163c64928d3c26.jpg)

(a) Experimental and (b) theoretical time-resolved magnetization dynamics of a ferromagnetically ([Co/Pt]3/Co/Pt 1 nm/CoGd/cap) coupled stacks.

RKKY exchange coupling mediated ultrafast all-optical switching of a ferromagnet

**Session chairs:** Amilcar Bedoya Pinto, Max Planck Institute of Microstructure Physics and Aurelian Rotaru, Stefan cel Mare University


AOC - Fundamental Properties and Cooperative Phenomena III

technical paper

The 15th Joint MMM-INTERMAG Conference (2022 Joint) is sponsored jointly by AIP Publishing and the IEEE Magnetics Society. Members of the international scientific and engineering communities interested in recent developments in fundamental and applied magnetism are invited to attend and contribute to the technical sessions. The technical program will include invited and contributed papers in oral and poster sessions, invited symposia, a plenary session, and an evening session, with about 1500 presentations overall. This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

The 2022 Joint Conference will offer both in-person and prerecorded on-demand content.

For tickets to the event, please register at the following link: https://magnetism.org/register

Please register for the Joint MMM-Intermag conference to join the event.

2022 Joint MMM-INTERMAG

This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

**Session chair:** Jun'ichi Ieda, Japan Atomic Energy Agency



GOH - Spin Dynamics

**Session chair:** Minori Goto, Osaka University



GOM - Voltage-controlled Magnetic Anisotropy and Switching

**Session chair:** Gregory Malinowski, Institut Jean Lamour, Université de Lorraine



Sayeef Salahuddin

4

3

Presentations

Chiral edge conduction induced by large anisotropic exchange interactions.

Field-free Spin-orbit Torque-driven Multistate Switching of Canted GdCo Moments

A magnetic gain-cell structure for efficient voltage-controlled MRAM

RKKY exchange coupling mediated ultrafast all-optical switching of a ferromagnet

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