United States

Recently antiferromagnetic materials have been gathering increasing attention from the spintronics community, as detecting and manipulating antiferromagnetic (AFM) order electrically is an important milestone for realizing antiferromagnetic devices. Characterizing the type and amplitude of the spin-orbit torques (SOT) is crucial for understanding and predicting AFM dynamics. One important technique to identify and measure SOTs is to perform harmonic Hall measurements in an AFM/heavy metal (HM) layer.&lt;br/&gt;In this study, we report the full angular dependence of 1&lt;sup&gt;st&lt;/sup&gt; and 2&lt;sup&gt;nd&lt;/sup&gt; harmonic voltage measurements in epitaxial c-axis oriented α-Fe&lt;sub&gt;2&lt;/sub&gt;O&lt;sub&gt;3&lt;/sub&gt;/Pt bilayer heterostructures (Fig. 1a). By modeling the harmonic resistance signals together with known material parameters such as the exchange field, anisotropy and DMI constant (Fig. 1b), we extract the amplitudes of field-like and anti-damping-like spin-orbit torques from field-dependent measurements in XY, XZ and YZ plane scans (Fig. 1a). Our model suggests a small angle tilt of the easy-plane and indicates that the amplitude of the field-like torques are significantly larger than anti-damping-like torques. Additionally, we show that there is an anomalous Hall-effect contribution in out-of-plane scans and that the Oersted fields are negligible compared to field-like torques. Our work provides a straight-forward way of characterization of spin-orbit torques in AFM/HM heterostructures.

![](https://assets.underline.io/uploads/markdown_image/1/image/87a94b08c94b21f9137b16231524bc27.jpg)

a) Transverse measurement configuration showing the Pt Hall cross with 5 µm channel width on AFM α-Fe2O3 layer. An AC current and the transverse voltage is measured with a lock-in amplifier. The thicknesses of α-Fe2O layer and Pt layers are 30 nm and 5 nm respectively. Next to it, geometry of magnetic field scans in the 3 principal planes (XY, XZ and YZ) is shown. b) Model geometry: D represents both the DMI vector and the hard axis direction. n is the Néel vector which lies in the easy plane. B is the external magnetic field. Alternating current is in x-direction and the spin accumulation in the y-direction. The Néel vector is perpendicular to both D and B.

2022 Joint MMM-INTERMAG

Quantifying Spin-Orbit Torques in AFM/HM Heterostructures

The International Conference on Electron, Ion and Photon Beam Technology and Nanofabrication (EIPBN), affectionately known as "3-Beams," is the premier gathering of scientists and engineers who are dedicated to electron, ion and photon lithography, imaging, and analysis; atomically precise fabrication; nanofabrication process technologies and related emerging technologies; and their applications in a broad spectrum of fields. In its 64th meeting, researchers from academia, government laboratories, and industry from around the world meet to present and discuss recent and future trends in these technologies.
 
 
 
[![](https://assets.underline.io/uploads/markdown_image/1/image/4bdf4450aa93073cd684b096b403df2e.png)](https://drive.google.com/file/d/1CPaA3-Yf7_maBxJMUJaUORLF3HGO9CIe/view?usp=sharing) [![](https://assets.underline.io/uploads/markdown_image/1/image/cea8a407085dee5422a2c16738ce27ca.png)](https://eipbn.org/abstracts/2021/)

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EIPBN 2021

Recently antiferromagnetic materials have been gathering increasing attention from the spintronics community, as detecting and manipulating antiferromagnetic (AFM) order electrically is an important milestone for realizing antiferromagnetic devices. Characterizing the type and amplitude of the spin-orbit torques (SOT) is crucial for understanding and predicting AFM dynamics. One important technique to identify and measure SOTs is to perform harmonic Hall measurements in an AFM/heavy metal (HM) layer. In this study, we report the full angular dependence of 1st and 2nd harmonic voltage measurements in epitaxial c-axis oriented α-Fe2O3/Pt bilayer heterostructures (Fig. 1a). By modeling the harmonic resistance signals together with known material parameters such as the exchange field, anisotropy and DMI constant (Fig. 1b), we extract the amplitudes of field-like and anti-damping-like spin-orbit torques from field-dependent measurements in XY, XZ and YZ plane scans (Fig. 1a). Our model suggests a small angle tilt of the easy-plane and indicates that the amplitude of the field-like torques are significantly larger than anti-damping-like torques. Additionally, we show that there is an anomalous Hall-effect contribution in out-of-plane scans and that the Oersted fields are negligible compared to field-like torques. Our work provides a straight-forward way of characterization of spin-orbit torques in AFM/HM heterostructures.

![](https://assets.underline.io/uploads/markdown_image/1/image/87a94b08c94b21f9137b16231524bc27.jpg)

a) Transverse measurement configuration showing the Pt Hall cross with 5 µm channel width on AFM α-Fe2O3 layer. An AC current and the transverse voltage is measured with a lock-in amplifier. The thicknesses of α-Fe2O layer and Pt layers are 30 nm and 5 nm respectively. Next to it, geometry of magnetic field scans in the 3 principal planes (XY, XZ and YZ) is shown. b) Model geometry: D represents both the DMI vector and the hard axis direction. n is the Néel vector which lies in the easy plane. B is the external magnetic field. Alternating current is in x-direction and the spin accumulation in the y-direction. The Néel vector is perpendicular to both D and B.

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.

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

A magnetization m is the well-known hallmark of magnetic order in ferromagnets. A counterpart to m describing the magnetic order in antiferromagnets has conspicuously remained absent in the world of magnetism. We derive a Néel operator τ that describes collinear antiferromagnetic order, in the same way a magnetization m signals ferromagnetic order [1]. While m is even under space inversion and odd under time reversal, τ describes a toroidal moment that is odd under both symmetries. Thus m and τ quantify complementary aspects of magnetic order in solids. Orbital ferromagnetic order can be attributed to dipolar equilibrium currents that give rise to a magnetization. We show that, in the same way, antiferromagnetic order arises from quadrupolar equilibrium currents that generate the toroidal moment τ. Considering an antiferromagnetic diamond structure as an example (Fig. 1), we derive explicit analytical expressions for the Néel operator τ and the effects of AFM order on the itinerant electrons in this system [1]. As an example for the efficacy of our approach, we develop a unified theory for magnetoelectricity in quasi-2D paramagnets, ferromagnets and antiferromagnets. In magnetoelectric media, an electric field can induce a magnetization and a magnetic field can induce a polarization, while the system remains in thermal equilibrium [2,3]. This effect appeals to recent efforts to manipulate magnetic order electrically [4]. It requires that both space-inversion and time-reversal symmetry are broken. We present a comprehensive theory [1] for magnetoelectricity in quasi-2D systems, where antiferromagnetic order and toroidal moments play a central role. We obtain quantitative expressions for the magnetoelectric responses due to electric and magnetic fields that reveal explicitly, for the first time, the inherent duality of these responses required by thermodynamics.

![](https://assets.underline.io/uploads/markdown_image/1/image/fa70f074e078d7f874157bfe833bf03c.jpg)

Figure 1: The antiferromagnetic diamond structure breaks time-reversal symmetry θ and inversion symmetry I (though the joint operation θI remains a good symmetry).

Toroidal moments: hallmarks of collinear antiferromagnetic order

Self-localized spin structures can substantially enrich the scope of the field-free antiferromagnetic spintronics [1]. One of them - the domain wall (DW) is a topological soliton that bridge a connection between two ground states, similar to a link in a Josephson junction (JJ) between two superconductors. JJs are intensively investigated for decades as they promise important advantages for electronics. In particular, JJ-based qubits are already successfully realized and commercialized. We demonstrate that the DW in bi-axial AFM with the easy-axis type of primary anisotropy driven by a spin current is a close analogy of a long Josephson junction (LJJ). Thus, the dynamics of the Neel vector angle inside the DW (Josephson phase Φ) is described by a sine-Gordon type of equation, where applied spin transfer torque (STT) represents a bias current through the junction, anisotropy in a basal plane defines a plasma frequency, and characteristic speed of magnons, defined by nonhomogeneous exchange energy, corresponds to Swihart velocity. In contrast with a conventional LJJ, a DW has additional degrees of freedom, namely the position of its center X and distribution of the current along a DW. We show by micromagnetic simulations, that when the polarization of the STT is parallel to the easy axis of an AFM, the above allows to nucleate and propel a single kink-type Φ soliton [2], which is Bloch line (Fig.1) that corresponds to the Josephson vortex in LJJ, as well as their series. Withal, a weak alternate current excites Φ-type intrawall spin waves, an analog of plasma waves in LJJ, which spectrum has a bandgap, defined by the anisotropy (Fig.2). STT with a perpendicular polarization allows manipulating the X position, particularly to excite the flexural vibrations of the DW with a gapless spectrum [3] (Fig.2). The variety of possible spin transport regimes together with the possibility of DW movement or bending under the action of applied spin current, offers considerable scope for developing novel spintronics devices.

![](https://assets.underline.io/uploads/markdown_image/1/image/ec00686c8da48a4e0f62c64d5949d0c0.jpg)

Generation of the Bloch line, - an anlog of the Josephson vortex.

![](https://assets.underline.io/uploads/markdown_image/1/image/b8a610941c6971f9af5c49d7f985cadd.jpg)

Dispersion law for Φ (red) and X (blue) intrawall modes in easy-axis Cr2O3 antiferromagnet with the presence of in-plane anisotropy.

Spin transport in a long Josephson junction based on an antiferromagnetic domain wall.

The thermal Hall effect, sometimes also called Righi-Leduc effect, appears as transversal heat currents induced by thermal gradients. Magnons, the magnetic excitations in long-ranged ordered systems, transport spin and heat with no charge currents. In this talk I demonstrate that the transversal transport coefficient in a two-dimensional honeycomb antiferromagnet features clear signs of magnetic and topological phase transitions. An external magnetic field drives the system from the antiferromagnetic phase via the noncollinear spin-flop phase into the field-polarized phase. Additionally, topological phase transitions are found in the spin flop phase. Both types of phase transitions manifest themselves in prominent and distinguishing features in the thermal conductivities; depending on the temperature, the conductivity changes by several orders of magnitude, providing a means to identify experimentally these phase transitions.

![](https://assets.underline.io/uploads/markdown_image/1/image/13ae6acc84046eacddf6d5ad89e32051.jpg)

Thermal Hall Effect of Magnons in Collinear Antiferromagnetic Insulators: Signatures of Magnetic and Topological Phase Transitions

The intrinsic anomalous Hall effect (AHE) present in noncollinear Mn3NiN shows boosted values in spite of the vanishing magnetisation and modest spin-orbit coupling present in the material, while the related anomalous Nernst effect (ANE) has been predicted to be an order of magnitude greater than Mn3Sn [1,2]. In addition, recent reports suggest an unconventional component in the spin-to-charge conversion process in the related material Mn3GaN due to the magnetic ordering symmetry [3]. The shared origin of these effects lies in the Berry curvature of the band structure. In this talk I will review our current progress with this system, growth of epitaxial films by pulsed laser deposition on various perovskite substrates and comparison of properties to literature reports. Our recent measurements are taken on Mn3NiN films grown on STO and BTO substrates, and I will discuss their properties in light of the magnetic-order biaxial in-plane strain phase diagram that we have established previously [4]. I will discuss our recent experimental measurement of spectroscopic MOKE, AHE and ANE compared to the theoretical prediction calculated using spin density functional theory (SDFT) and linear response approximation, highlighting where we find strikingly good agreement. These materials are also predicted to host giant piezomagnetism and strong sensitivity of the Berry phase curvature to strain. These different properties do not necessarily add constructively and I will present our current views on this based on the variation of the AHE in films grown on piezoelectrically controlled BTO.

![](https://assets.underline.io/uploads/markdown_image/1/image/c92f36e3b266ca0502d83be0d150abc5.jpg)

Spectroscopic MOKE and other Berry phased boosted properties of ferrimagnetic and antiferromagnetic Mn3NiN

Spectroscopic MOKE and other Berry phased boosted properties of ferrimagnetic and antiferromagnetic Mn3NiN

Antiferromagnets (AFMs) are magnetically ordered materials without a macroscopic magnetization. There is accelerating interest in using them for memory applications, motivated by the possibility for electrically controlling AFM order via spin-orbit torques, and its read-out via magnetoresistive effects [1-2]. Here we show that micrometer-scale bits of the antiferromagnet PtMn, grown on a Ta or Pt heavy metal (HM) layer, can be switched reversibly between different magnetic states by electric currents, with readout through a second harmonic voltage technique [3]. The device exhibits multiple states, which can be set using different current amplitudes and may find application in neuromorphic computing. Micromagnetic simulations suggest that these metastable states consist of vortex and anti-vortex textures that move in response to current. We also demonstrate, using a modified device layout, direct voltage measurements to read out the electrically-induced switching of noncollinear PtMn3. The modified layout and measurement methodology, which was recently demonstrated using the IrMn3/Pt material system [4], is utilized here to distinguish current-induced magnetic and nonmagnetic switching signals in PtMn3/Pt devices. We also realize switching down to 10 µs pulse width, which shows the potential for fast device applications. The effect of temperature and external magnetic field (up to 15 T) are also studied. Our results pave the way towards practical PtMn and PtMn3 antiferromagnetic memories integrated on silicon, and indicate the importance of micromagnetic textures in the static and dynamic behavior of antiferromagnetic devices.

Electrical manipulation of antiferromagnetic order in PtMn and PtMn3 pillars

In antiferromagnetic topological insulator MnBi2Te4, the interplay between topological electrons and magnetization dynamics in the form of spin torques and charge pumping remains an open question. Using the Berry phase theory, we develop a universal formalism to quantify the spin-orbit torques (SOTs) and their reciprocal effects in layered MnBi2Te4, where the symmetry of SOTs exhibits an even-odd layer-number pattern. The dynamical consequences of our finding are demonstrated by the SOT-driven magnetic resonances. In particular, we identify an anomalous exchange (AE) mode in the tri-septuple layer (SL) case, where the magnetic moments from the top and bottom SL rotate with a pi phase difference while those in the middle SL stay static. Unlike the ordinary exchange mode and the acoustic mode, the AE mode does not react to a microwave electromagnetic field. Therefore, the AE resonance can only be excited by the peculiar SOTs we find, providing a unique way to verify the SOTs in MnBi2Te4. Our study lays the theoretical foundation of current-induced spin dynamics in intrinsic antiferromagnetic topological insulators.

![](https://assets.underline.io/uploads/markdown_image/1/image/4045560a7cd6d072b78a10061469d722.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/d50337c92d0bcff8e7d7da23d0825a66.jpg)

Anomalous Exchange Resonance Driven by Spin-Orbit Torques in Intrinsic Antiferromagnetic Topological Insulator

Spin pumping has been an efficient way of spin generation, which converts coherent spin precessions in a magnet into pure spin currents in an adjacent metal. Recently, spin pumping has been demonstrated in easy-axis antiferromagnets (AFs) that operate at the terahertz frequency range, opening the exciting possibility of signal generation and processing at ultrafast speed. However, easy-plane AFs which are experimentally easier to prepare than their easy-axis counterparts, were considered to be bad candidates for spin pumping because the N\'{e}el vector is linearly polarized due to the easy-plane anisotropy, placing a major restriction on the choice of materials for practical applications. Here, using NiO and α-Fe2O3 (hematite) as two archetypal easy-plane AFs, we theoretically challenge this seemingly established conclusion by showing that easy-plane AFs can pump DC spin currents with the help of either the Dzyaloshinskii-Moriya interaction or an applied magnetic field without inducing the spin-flop transition. The magnitude of spin pumping turns out to be as strong as that in easy-axis AFs, which significantly broadens the materials pool for antiferromagnetic spintronics. Furthermore, we find that in the presence of a magnetic field, NiO can function as a sub-terahertz spin-torque oscillator at a highly reduced threshold current density.

![](https://assets.underline.io/uploads/markdown_image/1/image/0487d1f128d8b2c5f538c85b9f9d5307.jpg)

DC output as a function of the applied magnetic field for different values of DM interaction in α-Fe2O3

![](https://assets.underline.io/uploads/markdown_image/1/image/c322020ac034c68f560001032918d42e.jpg)

DC output as a function of the applied magnetic field along the in-plane easy axis direction below the spin-flop transition for different driving frequencies in NiO

Coherent Spin Pumping in Easy-Plane Antiferromagnets

The spin-1/2 of an electron makes it an archetypal two-level system and inspires the description of other two-level systems using an analogous pseudospin. The quantized spin excitations of an ordered antiferromagnet can be viewed as pairs of spin-up and -down magnons and can be characterized by a magnonic pseudospin. The similarity between electronic spin and magnonic pseudospin has triggered the prediction of exciting phenomena like emergent spin-orbit coupling and topological states in antiferromagnetic magnonics. In the last year, first experimental observations of the associated dynamics of antiferromagnetic pseudospin have been reported [1,2]. Based on these findings, we will expand the concept of magnon pseudospin and the description of magnon pseudospin dynamics [3,4] and discuss the influence of dimensionality on the magnon Hanle effect. Additionally, we show our recent experiments demonstrating control of magnon spin transport and pseudospin dynamics in thin films with varying thickness of the antiferromagnetic insulator hematite (α-Fe2O3) utilizing two Pt strips for all-electrical magnon injection and detection [2] . We observe an oscillation in polarity of the magnon spin signal at the detector as a function of the applied magnetic field, which we quantitatively explain in terms of diffusive magnon transport. In particular, we observe a coherent precession of the magnon pseudospin caused by the easy-plane anisotropy and the Dzyaloshinskii-Moriya interaction. Moreover, we find peculiar changes in the magnon spin signal for thicker hematite layers. Our results are paramount in unnlocking the high potential of antiferromagnetic magnonics towards the realization of electronics-inspired phenomena. Financial support from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy - EXC-2111 - 390814868 and project AL2110/2-1, and the Research Council of Norway through its Centers of Excellence funding scheme, project 262633, "QuSpin" is gratefully acknowledged.

Antiferromagnetic Magnon Pseudospin Dynamics and the Magnon Hanle Effect in Hematite Thin Films

Antiferromagnetic materials (AFMs) provide a pathway to overcome the limitations of ferromagnet-based spintronics, enabling fast and high density memory devices, as well as terahertz detectors and sources. This has fueled intensive research on the electrical manipulation of metallic AFMs using interfacial spin-orbit torque (SOT) from a heavy metal (HM) layer [1-4]. However, the threshold current density in HM/AFM bilayers is typically large, thus creating non-magnetic contributions to resistive switching signals, complicating their interpretation. Here, we present a new device structure and measurement protocol based on differential voltage measurements, allowing in situ reference measurements and to systematically separate the switching signals originating in the AFM and HM layers of a HM/AFM heterostructure [5]. The proposed device consists of a double-cross HM structure with six terminals, where the AFM, patterned in a micropillar shape, is placed on one of the two crosses. We successfully use this method in devices formed by Pt and the non-collinear AFM IrMn3. The results provide clear evidence of electrical switching of the AFM order parameter in the IrMn3 pillar by SOT in the range of writing current densities from 36 to 50 MA/cm2 with no appreciable switching signal from the Pt layer. We discuss the role of different switching configurations (180° and 90° writing currents), as well as the role of thermal activation on the switching characteristics. Control experiments in Pt-only double-cross samples without an AFM pillar reveal HM-dominated switching at higher current densities ~60 MA/cm2. We discuss active readout of the switching signals using a differential amplifier, with large peak-to-peak output voltage ~100 mV. The structure allows for reliable electrical measurement of resistive signatures of AFM switching induced by SOT, which will be important not only for the fundamental understanding of current-induced AFM domain dynamics, but also as an electrical readout method for practical applications in memory and computing devices.

![](https://assets.underline.io/uploads/markdown_image/1/image/9f7b7e5713bbb79e6a1b7f3436e814c5.jpg)

Fig. 1. Design of double-cross device for differential voltage measurements and the measured differential voltage for the 180° switching configuration with 20 mA write pulses.

Observation of current-induced switching in non-collinear antiferromagnetic IrMn3 by differential voltage measurements

Antiferromagnetic materials have recently attracted much interest due to a number of advantages including high resonance frequencies up to the terahertz. Further, the possibility to electrically modulate the magnetic properties such as the anisotropy makes them an excellent candidate for energy-efficient devices at ultra-high frequencies. In this study, we theoretically explored one such application in the dynamic manipulation of electromagnetic responses with a broad tunable spectral range. The materials considered were dielectric antiferromagnets with strong magneto-electric or –elastic coupling which can achieve robust control in the perpendicular magnetic anisotropy. The metallic counterparts were not suitable due to the anticipated large loss. A theoretical analysis based on the Landau-Lifshitz equation was used to derive the frequency-dependent permeability and the resonant frequency of the antiferromagnet for different biaxial anisotropy profiles and incident electromagnetic wave polarizations. Numerical calculations based on typical parameters available in the literature (such as NiO) strongly indicated that the resonance frequency modulation as much as 10’s of percent may be possible in the sub-mm wavelength range, along with the corresponding changes in the permeability. Application to specific devices such as a bandpass filter further illustrated the validity of the concept. Funding Acknowledgement This work was supported, in part, by the U.S. Army Research Office (No. W911NF-16-1-0472).

![](https://assets.underline.io/uploads/markdown_image/1/image/6ffd93f402fd8b4c21123e86d0bbb698.jpg)

Fig.1 Schematic of the magnetic-piezoelectric composite. Electric field along out-of-plane direction causes magneto-elastic effects and influences eigen-frequency by modifying in-plane magnetic anisotropy. EM wave is incident along x-axis.


![](https://assets.underline.io/uploads/markdown_image/1/image/e677976b7cbcf549791f319205ea030e.jpg)

Fig.2 Data showing a high electric field tunable AFMR frequency shift with external voltage at 0, -V, and +V=8kV/cm (Not the final results)

Quantifying Spin-Orbit Torques in AFM/HM Heterostructures

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