United States

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.

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2022 Joint MMM-INTERMAG

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

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.

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

technical paper

The spin current with out-of-plane spin polarization (sigma-z) is favorable for the efficient switching of perpendicular magnetized devices, which is required for high-density memories [1,2]. Recently we observed sigma-z both in non-collinear antiferromagnets Mn3Pt [3] and Mn3SnN [4], as well as in collinear antiferromagnets Mn2Au [5,6] and RuO2 [7] thin films. Strong out-of-plane polarized spin current is generated when the charge current is applied along the magnetic mirror plane of non-collinear antiferromagnet, but tiny when perpendicular. With the aid of strong sigma-z, current induced spin-orbit torque (SOT) switching of adjacent perpendicular ferromagnet is realized without external magnetic field. In Mn2Au films, sigma-z is generated at two spin sublattices with broken spatial symmetry, and the antiparallel antiferromagnetic moments play an important role. The out-of-plane polarized spin current can be controlled by the current- and electric field-induced Néel vector switching. Thus this Néel vector-dependent spin Hal effect is termed as “antiferromagnetic spin Hall effect”, which adds another twist to the atomic-level control of spin currents via the antiferromagnetic spin tructure. RuO2 is a tetragonal itinerant collinear antiferromagnet with nonmagnetic atoms at noncentrosymmetric positions [8]. This particular crystal structure produces anisotropic band structure，enabling RuO2 a efficient spin source due to the spin splitting effect. Spin current generated by spin splitting effect do not meet conventional “cross product relationship”. The spin current flow direction is related to the crystal structure，while the spin polarization direction is related to the Néel vector. Spin splitting effect has more efficient spin-charge convention and more controllable spin polarization. The role of sigma-z for the field-free SOT switching is theoretically analyzed, and different roles of sigma-z and conventional in-plane spin polarization (sigma-y) are presented with different external magnetic field. Our findings would help to use out-of-plane polarization for efficient SOT-MRAM to combine the advantage of SOT and spin-transfer torque.

![](https://assets.underline.io/uploads/markdown_image/1/image/2cd5af1ecc73195bd6fc92b4627ec76c.jpg)

Fig. 1. Schematic of out-of-plane polarized spin current and field-free spin-orbit torque switching.

Out-of-plane spin polarization and antiferromagnetic spin Hall effect

The interplay between electronic transport and the antiferromagnetic order has attracted a surge of interest. Recent studies have shown that a moderate change in the spin orientation of a collinear antiferromagnet may significantly affect the electronic band structure and subsequently manifest itself in transport properties [1]. Among numerous electrical probes to read out such magnetic order, unidirectional magnetoresistance (UMR), where the resistance changes under the reversal of the current direction, can provide rich insights into the transport properties of spin-orbit coupled systems. However, UMR has never been observed in antiferromagnets before, given the absence of intrinsic spin-dependent scattering. Here, we report that a sizable UMR can emerge in an antiferromagnetic system, specifically in a collinear-antiferromagnet/heavy-metal bilayer. The observed UMR in the antiferromagnetic phase of a FeRh/Pt bilayer evolves nonlinearly with increasing magnetic field, persists to large values at high magnetic field and, most notably, exhibits a sign change at a critical field, which is in stark contrast with the UMRs observed in ferromagnetic and non-magnetic systems [2-3]. We attribute this UMR to the strong effective magnetic field due to spin canting in FeRh. Our results can motivate the growing fields of non-centrosymmetric and topological systems, and suggest a route to the development of tunable antiferromagnet-based spintronics devices. This research was primarily supported by the NSF through the University of Illinois at Urbana-Champaign Materials Research Science and Engineering Center DMR-1720633 and was carried out in part in the Materials Research Laboratory Central Research Facilities, University of Illinois. Thin-film growth at Argonne National Laboratory was supported by the U.S. Department of Energy, Office of Science, Materials Science and Engineering Division.

![](https://assets.underline.io/uploads/markdown_image/1/image/756eaf87bcd78eaae92bc5c59ee591d2.jpg)

Fig. 1: UMR in the antiferromagnetic phase of FeRh [110]/Pt (T = 10 K), as a function of field B at various current densities J.

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Fig 2: Generation of a nonlinear charge current transverse to the applied B field (top left), which increases considerably in the presence of canting (bottom right).

Observation of unidirectional magnetoresistance in collinear-antiferromagnet/heavy-metal bilayers

Antiferromagnetic (AF) spintronics received an enormous impulse after the first demonstrations of electrical switching of the AF order [1]. However, a lot of these observations can equally well be explained by non-magnetic, parasitic effects caused by the same electrical current pulses that are intended to manipulate the magnetic state of the AF [2]. While it is possible to distinguish between magnetic and non-magnetic effects using imaging techniques that can resolve the AF order [3], these techniques are usually very complex. Moreover, since they require access to the AF layer, they are not suitable for systems where the AF is buried beneath other layers. Our approach is to distinguish between the magnetic and non-magnetic effects by suppressing the magnetic effects using high magnetic fields. In this contribution, we study the high magnetic field behavior of the electrical switching of thin-film AFs NiO and CoO, using the devices shown in Fig. 1. We perform switching experiments in magnetic fields up to 16 Tesla (Fig. 2). The measurements show that these high magnetic fields indeed suppress the current-induced switching of the AF order, whereas the thermal effects remain unaffected. Hence, this technique allows to irrefutably separate the magnetic and non-magnetic effects. These results are corroborated by a model accounting for the multi-domain character of the AF. Finally, the experiments with CoO yield an unexpected dependence of the magnetic configuration on the direction of the high magnetic fields. This indicates an unexpectedly complex magnetic anisotropy in CoO that depends on the magnetic field strength and orientation, most likely due to unquenched orbital momentum. These results both demonstrate that combining electrical methods with strong magnetic fields can be a valuable tool for AF spintronics, and give invaluable insight into the interplay of spin-Hall magnetoresistance and thermal effects as well as the domain structure and complex anisotropy of thin-film antiferromagnets.

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Fig. 1: Micrograph of the device used for the experiments.

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Fig. 2: Switching amplitude as a function of magnetic field. The lines are calculated with the model; the pie charts represent the modeled domain distribution.

Suppressing Electrical Switching of Antiferromagnets with High Magnetic Fields

The proximity-coupling of a chiral non-collinear antiferromagnet (AFM)1,2 with a singlet superconductor allows spin-unpolarized singlet Cooper pairs to be converted into spin-polarized triplet pairs3,4, thereby enabling non-dissipative, long-range spin correlations3,4. The mechanism of this conversion derives from fictitious magnetic fields that are created by a non-zero Berry phase5 in AFMs with non-collinear atomic-scale spin arrangements1,2. In this talk, I would like to describe our recent achievement of long-ranged lateral Josephson supercurrents through an epitaxial thin film of the triangular chiral AFM Mn3Ge6. The Josephson supercurrents in this chiral AFM decay by approximately 1–2 orders of magnitude slower than would be expected for singlet pair correlations3,4 and their response to an external magnetic field reflects a clear spatial quantum interference. Given the long-range supercurrents present in both single- and mixed-phase Mn3Ge, but absent in a collinear AFM IrMn, our results pave a way for the topological generation of spin-polarized triplet pairs3,4 via Berry phase engineering5 of the chiral AFMs.

Long-range supercurrents through a chiral non-collinear antiferromagnet in lateral Josephson junctions

Antiferromagnets are at the forefront of research in spintronics. Recent results demonstrate their high potential for revolutionizing memory technologies. However, many of the underlying phenomena remain to be explored. Here, we study the domain structure and magnetic reversal of the canted antiferromagnet α-Fe2O3. Using x-ray magnetic linear dichroism (XMLD) measurements, we observe a strongly field-dependent domain structure of α-Fe2O3 (see Fig. 1a). To study the magnetic field control of the Néel order and demagnetization process in more detail, we employ spin Hall magnetoresistance (SMR) measurements in α-Fe2O3/Pt bilayer devices. The angle-dependent SMR shows the characteristic saturated negative SMR signal of antiferromagnets (light red curve in Fig. 1b) in agreement with previous findings1,2. The dark red curve shows the remanent resistance as a function of the angle of the preceding saturating magnetic field. The data show a simple scaling between the saturated SMR signal and the remanent resistance by a factor of 5. This implies that the internal fields driving the demagnetization do not follow the crystal symmetry of α-Fe2O3. Furthermore, the Dzyaloshinskii-Moriya interaction (DMI) induces canting of the two magnetic sublattices giving rise to a ferromagnetic moment at room temperature. The ferromagnetic moment lifts the degeneracy of the sublattices and consequently the orientation of the Néel vector with respect to the applied magnetic field resulting in hysteresis in the SMR signal. The irreversibility upon switching the direction of the magnetic field elucidates the nature and formation of antiferromagnetic as well as ferromagnetic domain walls at low magnetic fields. The insights gained from our work serve as a foundation for further studies of electrical and optical manipulation of the domain structure of canted antiferromagnets.

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Fig. 1: (a) XMLD image of the domain structure of α-Fe2O3 in zero magnetic field (left) and in 250 mT in-plane magnetic field (right). (b) Transverse remanent SMR signal Rrem (dark red) of α-Fe2O3/Pt Hall cross after H has been reduced from a saturated state Rsat (light red) to zero field as a function of angle of the applied magnetic field.

Roles of Destressing and Dzyaloshinskii-Moriya Interaction for Magnetic Reversal in α-Fe2O3

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.

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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.

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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.

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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.

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

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Next from 2022 Joint MMM-INTERMAG

Out-of-plane spin polarization and antiferromagnetic spin Hall effect

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