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Antiferromagnets (AFs) are promising candidates for next generation spintronic devices. Hematite (α-Fe&lt;sub&gt;2&lt;/sub&gt;O&lt;sub&gt;3&lt;/sub&gt;), an easy-plane AF insulator with triaxial anisotropy, is one of the materials at the forefront of this effort, spurring discoveries of magnon-mediated long-distance spin transport and unambiguous control of the AF order by electrical current [1]. Contrary to ferromagnets, where domain structure is governed by long-range demagnetizing fields, the domain structure in AFs is controlled by destressing fields of magnetoelastic origin [2]. The electrical control of domains has been studied in AFs with an adjacent heavy metal as a source of interfacial anti-damping-like spin-orbit torque (SOT). But, AF switching has been shown to at least partially result from thermo-magnetoelastic torques, generated by current-induced temperature gradients [3,4]. The competition of a thermo-magnetoelastic torque and SOT complicates the fundamental understanding of the origin of domain re-distribution. In our work, we develop a method for discerning the two effects by heating a Pt device on α-Fe&lt;sub&gt;2&lt;/sub&gt;O&lt;sub&gt;3&lt;/sub&gt; independently of the applied current. Implementing a combination of angle-dependent spin-Hall magnetoresistance (SMR) and current pulsing, we probe, respectively, the full and partial re-orientation of AF domains in epitaxial α-Fe&lt;sub&gt;2&lt;/sub&gt;O&lt;sub&gt;3&lt;/sub&gt;/Pt bilayers. We find that the origin of the current-induced switching signal, which results from domain re-orientation, is primarily of SOT origin in α-Fe&lt;sub&gt;2&lt;/sub&gt;O&lt;sub&gt;3&lt;/sub&gt;. The remanent switching amplitude (~5% of the expected signal amplitude) and a temperature-dependent study of key switching signatures reveals the existence of pinning barriers to domain wall motion. This study advances the understanding of current-induced effects in AF materials with low anisotropy and high magnetostriction, where magnetoelastic effects are thought to dominate.

**References:**

[1] Y. Cheng, S. Yu, M. Zhu, J. Hwang, and F. Yang, Phys. Rev. Lett. 124, 027202 (2020).&lt;br/&gt;[2] J. Fischer, O. Gomonay, R. Schlitz, K. Ganzhorn, N. Vlietstra, M. Althammer, H. Huebl, M. Opel, R. Gross, S. T. B. Goennenwein, and S. Geprägs, Phys. Rev. B 97, 014417 (2018).&lt;br/&gt;[3] H. Meer, F. Schreiber, C. Schmitt, R. Ramos, E. Saitoh, O. Gomonay, J. Sinova, L. Baldrati, and M. Kläui, Nano Lett. acs.nanolett.0c03367 (2020).&lt;br/&gt;[4] L. Baldrati, C. Schmitt, O. Gomonay, R. Lebrun, R. Ramos, E. Saitoh, J. Sinova, and M. Kläui, Phys. Rev. Lett. 125, 077201 (2020).

**Images:**





INTERMAG 2021

 Mechanism of Current-induced Magnetotransport in Epitaxial Antiferromagnetic α-Fe2O3

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Antiferromagnets (AFs) are promising candidates for next generation spintronic devices. Hematite (α-Fe2O3), an easy-plane AF insulator with triaxial anisotropy, is one of the materials at the forefront of this effort, spurring discoveries of magnon-mediated long-distance spin transport and unambiguous control of the AF order by electrical current [1]. Contrary to ferromagnets, where domain structure is governed by long-range demagnetizing fields, the domain structure in AFs is controlled by destressing fields of magnetoelastic origin [2]. The electrical control of domains has been studied in AFs with an adjacent heavy metal as a source of interfacial anti-damping-like spin-orbit torque (SOT). But, AF switching has been shown to at least partially result from thermo-magnetoelastic torques, generated by current-induced temperature gradients [3,4]. The competition of a thermo-magnetoelastic torque and SOT complicates the fundamental understanding of the origin of domain re-distribution. In our work, we develop a method for discerning the two effects by heating a Pt device on α-Fe2O3 independently of the applied current. Implementing a combination of angle-dependent spin-Hall magnetoresistance (SMR) and current pulsing, we probe, respectively, the full and partial re-orientation of AF domains in epitaxial α-Fe2O3/Pt bilayers. We find that the origin of the current-induced switching signal, which results from domain re-orientation, is primarily of SOT origin in α-Fe2O3. The remanent switching amplitude (~5% of the expected signal amplitude) and a temperature-dependent study of key switching signatures reveals the existence of pinning barriers to domain wall motion. This study advances the understanding of current-induced effects in AF materials with low anisotropy and high magnetostriction, where magnetoelastic effects are thought to dominate.

**References:**

[1] Y. Cheng, S. Yu, M. Zhu, J. Hwang, and F. Yang, Phys. Rev. Lett. 124, 027202 (2020). [2] J. Fischer, O. Gomonay, R. Schlitz, K. Ganzhorn, N. Vlietstra, M. Althammer, H. Huebl, M. Opel, R. Gross, S. T. B. Goennenwein, and S. Geprägs, Phys. Rev. B 97, 014417 (2018). [3] H. Meer, F. Schreiber, C. Schmitt, R. Ramos, E. Saitoh, O. Gomonay, J. Sinova, L. Baldrati, and M. Kläui, Nano Lett. acs.nanolett.0c03367 (2020). [4] L. Baldrati, C. Schmitt, O. Gomonay, R. Lebrun, R. Ramos, E. Saitoh, J. Sinova, and M. Kläui, Phys. Rev. Lett. 125, 077201 (2020).

**Images:**

technical paper

Antiferromagnets (AF) have many potential applications in spintronics such as data storage or long-range spin transport devices. The control of spins in AF by electrical current is proven to be possible by different mechanisms [1,2] but it remains challenging to verify experimentally [3]. Such detection can be unambiguously performed with the use of magnetic imaging techniques [4]. However, they are typically sensitive to the topmost layer and cannot be applied in more complex structures where the AF is buried far from the top interface. To mitigate this problem, we present a study of electrical signals in switching experiment in various temperatures for CoO. Basing on this temperature dependence of electrical data for AF CoO thin film we extract patterns that do not follow the trend expected for thermal effects but are probably fingerprints of magnetic changes. In characterization experiments for CoO, magnetoresistance studies for CoO reveal clear spin-flop transitions and pronounced antiferromagnetic hysteresis loops due to strong in-plane anisotropy. Magnetoresistance shows abrupt changes in Rxy around 7 T (240K) when the magnetic field is aligned along [110] axes (easy axes). They can be attributed to spin-flop transitions observed by means of Spin Hall Magnetoresistance. This behavior is hysteretic and absent when the field is aligned along [100] directions (hard axes) or in T = 304 K (above Néel temperature TN). It confirms the presence of biaxial anisotropy in CoO and easy axes along [110] in agreement with literature [5]. Hysteresis loops in Rxy when the magnetic field is rotated with respect to crystalline axes are observed up to the highest tested magnetic fields due to the strong in-plane anisotropy. In the actual switching experiments of CoO (Fig. 1), the temperature dependence of the transverse resistance Rxy variations after current pulses applied in alternating directions in a CoO | Pt device is examined. Resistivity variations due to thermal effects (such as asymmetric heating) increase with increasing temperature or current pulse amplitude and persist above TN of CoO. However, at lower current magnitudes we find a pattern that decreases with increasing temperature and vanishes above TN suggesting its magnetic origin (Fig. 2). In conclusion, we demonstrate that manipulation of temperature may help to gain more insight into the nature of electrical signals variations in experiments with antiferromagnets. These presented experimental findings can be important for current research acitivities towards using antiferromagnets in real spintronic devices.

**References:**

[1] P. Wadley, B. Howells, J. Zelezny et al., Science, 351, 587 (2016). [2] L. Baldrati, O. Gomonay, A. Ross et al., Phys. Rev. Lett., 123, 177201 (2019). [3] C. C. Chiang, S. Y. Huang, D. Qu, et al., Phys. Rev. Lett., 123, 227203 (2019). [4] M. J. Grzybowski, P. Wadley, K. W. Edmonds et al., Phys. Rev. Lett., 118, 057701 (2017). [5] L. Baldrati, C. Schmitt, O. Gomonay et al., Phys. Rev. Lett., 125, 077201 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/dc1c0c50382cc7fa878e0b12ff757dcd.jpg)
Fig. 1 The switching experiment for CoO (5 nm) | Pt (5 nm) thin films device where the transverse resisitivity Rxy is measured after each pulse of high current (the direction of the pulsing current is changed to perpendicular one after each 5 pulses). Interestingly, above TN the pattern visible in 240K is not present.

![](https://assets.underline.io/uploads/markdown_image/1/image/151b408e9acc0384e83f5b04392a240d.jpg)
Fig. 2 The magnitude of Rxy variations after pulsing in orthogonal directions in CoO for 24 mA current diminishes with increasing temperature and is practically invisible in room temperature (above TN). This trend is different for higher currents where Rxy variations increases with T as expected for thermal effects.

 Switching experiment of antiferromagnetic CoO in different temperatures

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 are such 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. An experimental observation of the associated dynamics of antiferromagnetic pseudospin, however, has eluded experiments thus far. As a first step we will introduce the concept of magnon pseudospin and the description of magnon pseudospin dynamics, as well as briefly discuss similarities to electron spin transport [1]. In the second part, we show our recent experiments demonstrating control of magnon spin transport and pseudospin dynamics in a 15 nm thin film of the antiferromagnetic insulator hematite (α-Fe2O3) utilizing two Pt strips for all-electrical magnon injection and detection [2] (c.f. Fig. 1 (a)). We observe an oscillation in polarity of the magnon spin signal at the detector as a function of the externally applied magnetic field (see Fig. 1 (b)), 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. This observation can be viewed as the magnonic analogue of the electronic Hanle effect and the Datta-Das transistor, unlocking 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.

**References:**

[1] A. Kamra et al., Physical Review B 102, 174445 (2020) [2] T. Wimmer et al., Physical Review Letters 125, 247204 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/ec8627bd4d1b243e84613268af7a73af.jpg)
Fig. 1: (a) Sketch of the device geometry, the electrical wiring, and the coordinate system. The canting of the magnetic sublattices m1 and m2 and the corresponding net moment mnet as well as the Néel order parameter n are illustrated. Upon applying a charge current Iinj to the injector, a spin current Is with spin polarization s is generated via the SHE and injected into the hematite (α-Fe2O3) with thickness t = 15 nm. The emerging antiferromagnetic magnon current is then detected via the inverse SHE induced current at the detector by measuring the electrical voltage drop Veldet. (b) Magnon transport signal Veldet as a function of the external magnetic field magnitude. The signal oscillates between positive and negative values. The qualitative behaviour is very similar to the electronic Hanle effect.

 Observation of Antiferromagnetic Magnon Pseudospin Dynamics and the Magnon Hanle effect



Antiferromagnets (AFMs) have the potential to push spintronic devices from the static or gigahertz frequency range to the terahertz (THz) range for the sake of the high-speed processing. However, the insensitivity of AFMs to magnetic fields also makes it hard to manipulate spin currents. While the ultrafast generation of the spin current in ferromagnet/heavy metal (FM/HM) structures has received a lot of attention in recent years, it is still unknown as to whether a similar scenario can be observed in an AFM/HM system. Here we show the optical generation of ultrafast spin current in an AFM/HM heterostructure at zero external magnetic field and at room temperature by detecting the associated THz emission [1]. We believe this is a common phenomenon in antiferromagnets with strong nonlinear optical effects. Our results open an avenue of fundamental research into antiferromagnetism and a route to AFM spintronic devices.

**References:**

[1] H. Qiu, et al., Nature Physics (https://doi.org/10.1038/s41567-020-01061-7).

**Images:**





 Ultrafast Spin Current Generated from an Antiferromagnet INVITED

Introduction: Compensated ferrimagnets possess two or more inequivalent, antiferromagnetically-coupled sublattices such that the net magnetization is zero. The detailed compensation conditions can be typically tuned by varying the temperature, chemical composition or strain. These materials do not only possess the advantages of an antiferromagnet, i.e. faster switching, higher storage density and being immune to external field perturbation, but also, they are compatible with the commonly employed reading and writing schemes for conventional ferromagnets. A prototypal compensated ferrimagnet is Mn2RuxGa which was first identified as a half metallic compensated ferrimagnet in 2014 [1]. Mn2RuxGa crystallizes in the inverse Heusler structure (Space group No. 216), where Mn atoms occupy 4a and 4c sites of distinct chemical environment. Compensation is achieved when the moments from the two antiferromagnetically coupled Mn sites cancel each other. Ru of composition x then act as a knob for tuning the compensation temperature Tcomp. Previous works have demonstrated high spin polarization [1], large anomalous Hall effect (AHE) [2], finite tunnel magnetoresistance [3], efficient spin-orbit torque switching [4] and all-optical toggle switching [5] in nearly compensated Mn2RuxGa. Here we unveil the potential of exploiting Mn2RuxGa with perpendicular magnetic anisotropy for spontaneous thermoelectric generation at room temperature via anomalous Nernst effect (ANE) with no stray field coupling to the surrounding. Experimental Methods and Results: Epitaxial Mn2RuxGa (001) films with thicknesses ~ 27 nm and x ranging from 0.26 to 0.73 were grown on MgO (001) substrates at a substrate temperature of ~350oC by magnetron co-sputtering Mn2Ga and Ru targets. The unit cell of Mn2RuxGa makes a 45-degree rotation with respect to that of MgO such that the in-plane epitaxial relationship is MgO [100] // Mn2RuxGa [110]. The substrate induced in-plane biaxial compressive strain leads to ~1% of the tetragonal distortion along the out-of-plane c-axis, which defines the easy axis of the magnetization. Millimeter-scale Hall bar devices were fabricated for characterizing the transport and thermoelectric response of Mn2RuxGa films with varying x. An electrical current or a heat current was applied along the long axis of the Hall bar, along the [110] axis of Mn2RuxGa. The in-plane temperature gradient was monitored by measuring the resistance change of two on-chip Pt wires. Vibrating sample magnetometry at room temperature shows that adding Ru from x = 0.26 to x = 0.60 reduces monotonically the saturation magnetization Ms from ~90 kA/m to below 5 kA/m, followed by a slight upturn of MS upon further increasing x to 0.73. This reflects the magnetic compensation of Mn2RuxGa is achieved at room temperature for x ~ 0.6. We also found that the AHE signal for films with x = 0.51 and x = 0.73 are of opposite sign whereas for x = 0.60 the coercivity diverges, which corroborates this interpretation. Concerning the thermoelectric properties of Mn2RuxGa at room temperature, both the Seebeck coefficient Sxx and the anomalous Nernst coefficient Sxy change sign across the compensation. |Sxx| for all the samples are relatively small (&lt;1 μV/K) whereas their transverse counterpart |Sxy| are around 0.3 μV/K, which is comparable to many 3d ferromagnets but with orders of magnitude smaller Ms for Mn2RuxGa. The small |Sxx| also leads to relatively large anomalous Nernst angle |Sxy/Sxx| of the order of 0.5. Sxy can be expressed as Sxy = ρxxαxy + Sxxρxy/ρxx where αxy denotes the transverse thermoelectric conductivity. We found the second term, referring to the collective contribution of AHE and Seebeck effect, is negligible. ANE in Mn2RuxGa is therefore governed by the first term, i.e. the direct conversion from a thermal gradient to a transverse charge current. We obtain αxy = +0.12 A/(K●m) for x = 0.26 which reduces to αxy = +0.07 A/(K●m) and αxy = -0.07 A/(K●m) for x = 0.51 and x = 0.73, respectively. αxy reverses its sign across the compensation suggesting that it depends on the magnetization direction of a Mn sublattice and not on the net moment, in analogy with ρxy of AHE. Finally, it is worth noting that |αxy| and |Sxy| of Mn2RuxGa near the compensation are comparable to those of the chiral antiferromagnetic Mn3Sn [6] with an additional advantage of high tunability. We expect further enhancement of the thermoelectric performance of compensated Heusler compounds by improving the chemical ordering and/or by tuning the Fermi level via substitutional alloying [7]. This work was partly supported by JSPS KAKENHI (No. JP20K15156, JP20K05296).

**References:**

[1] H. Kurt et al., Phys. Rev. Lett. 112, 027201 (2014) [2] N. Thiyagarajah et al., Appl. Phys. Lett. 106, 122402 (2015) [3] K. Borisov et al., Appl. Phys. Lett. 108, 192407 (2016) [4] J. Finley et al., Adv. Mater. 31, 1805361 (2019) [5] C. Banerjee et al., Nat. Commun. 11, 4444 (2020) [6] M. Ikhlas et al., Nat. Phys. 13, 1085 (2017) [7] Y. Sakuraba et al., Phys. Rev. B 101, 134407 (2020)

**Images:**

 Anomalous Nernst effect in compensated ferrimagnetic Mn2RuxGa

Antiferromagnetic spintronics is on the rise as it could provide advantages over ferromagnetic-based conventional spintronics in terms of scalability, reliability and speed, opening the route to extend the working frequency of memory and logic devices from the current GHz range up to THz [1]. The electrical read-out of the magnetic state in antiferromagnetic materials, however, presents additional challenges due to the lack of a net magnetization which prevents the use of the typical detection schemes employed for ferromagnets. The possibility to access the magnetic configuration state in antiferromagnets by electrical methods would then provide a versatile characterization tool and is fundamental for the development of spintronic devices. At variance with ferromagnets, only few antiferromagnetic conductors have been demonstrated to show anisotropic magnetoresistance [2,3] allowing for a direct electric detection of the magnetic configuration by resistive measurements. In IrMn, the most widely used metallic antiferromagnet in applications, a small anisotropic magnetoresistance [4] has been demonstrated, whereas tunneling anisotropic magnetoresistance has been used to infer its magnetic state [5]. Here we follow a different approach exploiting interfacial effects between the antiferromagnet and a suitable neighboring metal layer. This approach, already employed for the insulating antiferromagnet Cr2O3 [6,7], underlines the critical role of interfaces in the determination of the transport properties related to the antiferromagnetic state. In this contribution we report the electrical detection of the antiferromagnetic state of IrMn through anomalous Hall measurements in Ta/IrMn heterostructures, grown by DC magnetron sputtering on a SiO2/Si substrate. The magnetic state is set in the antiferromagnet through out-of-plane field cooling and detected electrically by transverse resistance measurements in Hall bar structures, without the need of any ferromagnetic layer. An offset compensation system has been used to isolate the transverse resistance from spurious contributions (longitudinal resistance and magnetoresistance) [8]. The signal goes to zero at the Néel temperature of the antiferromagnet (TN), above which the system becomes paramagnetic. TN is found out to be 110 K for our 4 nm thick IrMn film, smaller than in the bulk (650 K) because of the finite thickness. The amplitude of the signal increases with the magnetic field applied during the cooling (whereas the value of TN is not affected) and is enhanced by the proximal interface with the Ta layer. We ascribe this enhancement to spin Hall magnetoresistance at room temperature and above, and to magnetic proximity which is the leading term at lower temperatures. From the temperature dependence of the effect and the comparison between Ta/IrMn and Ru/IrMn interfaces, we propose an explanation of such readout based on the simultaneous occurrence of spin-Hall magnetoresistance and magnetic proximity effect in Ta. These findings highlight how interface effects could be generally employed for the investigation of antiferromagnetic materials as well as for the electrical readout of the antiferromagnetic state.

**References:**

[1] T. Jungwirth, J. Sinova, A. Manchon et al, Nat. Phys, Vol. 14, p. 200 (2018) [2] S.Y. Bodnar, L. Smejkal, I. Turek et al, Nat. Commun., Vol. 9, p. 348 (2018) [3] P. Wadley, B. Howells, J. Zelezný et al, Science, Vol. 351, p. 587 (2016) [4] T. Kosub, M. Kopte, F. Radu et al, Phys. Rev. Lett., Vol. 115, p. 097201 (2015) [5] D. Petti, E. Albisetti, H. Reichlová et al, Appl. Phys. Lett., Vol. 102, p. 192404 (2013) [6] J.M. Taylor, E. Lesne, A. Markou et al, Appl. Phys. Lett., Vol. 115, p. 062403 (2019) [7] M. Asa, C. Autieri, R. Pazzocco, et al., Phys. Rev. Research, vol. 2, p. 043394 (2020) [8] M. Asa, C. Rinaldi, R. Pazzocco, et al., J. Appl. Phys., Vol. 128, p. 053904 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/32c3006792ed14c06dba33f4b5099a58.jpg)
(a) Transverse resistance (RXY) in Ta (2 nm)/IrMn (4 nm) /Ta (2 nm) Hall cross at remanence resulting from different field cooling processes. In the inset a sketch of the sample is reported. (b) Anomalous Hall resistance difference (ΔRXY) at remanence between states set with upward (+Bset) and downward (-Bset) field cooling. The value of Bset is reported beside each curve. The inset reports the value of ΔRXY at 10 K as function of the absolute value of the writing field Bset. The red line is a guide for the eye.

 Electrical Readout of the Antiferromagnetic State of IrMn through Anomalous Hall Effect

Recently, manipulation of antiferromagnetic (AFM) order has been gaining the attention of the spintronics community. Magnetic switching of AFM spin axis has been reported in thin films based on electronic transport methods, which provide only spatially averaged information on AFM states. Other techniques, such as x-ray magnetic linear dichroism (XMLD), can provide local information on AFM domains. In this study, we report direct observation of spin reorientation in response to current pulses in (0001) α-Fe2O3/Pt heterostructures. Our experiment combines the application of current pulses and spatially resolved photoemission electron microscopy (PEEM) with XMLD to detect AFM contrast. Pulses were applied in two different configurations A and B (Fig. 1a), and XMLD images were interleaved with current pulse sequences to reveal changes in the AFM domains in the center of the cross (Fig. 1c). Our polarization dependent analysis reveals that the Néel vector of our α-Fe2O3 films have an out-of-plane component in their equilibrium state, contrary to what previous work indicate. Finally, we show clear evidence of AFM domains reorientation outside of the current path, which leads us to the conclusion that spin-orbit torque may not be the only driven effect in the electrical switching process.

**References:**

E. Cogulu, N. Statuto and A. D. Kent, “X-ray Magnetic Linear Dichroism Studies of Electrical Switching of Antiferromagnetic Order in α-Fe2O3 Epitaxial Films” (2020), arXiv:2012.04127 [cond-mat.mes-hall].

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/2634b4eabc849ecf23e77da37868ea40.jpg)
FIG1. (a) PEEM image of the 6-legged Hall cross with schematic representation of the circuit. Dark regions correspond to α-Fe2O3 (30 nm thickness) and bright region correspond to Pt (2 nm thickness). The Pt leads are aligned with the 3 easy axes of Fe2O3. Plus and minus signs represent the connections to the two pulse generator outputs, where the minus sign indicates a connection to ground. (b) Resistance data showing switching between two states after sequential current pulses applied along both current paths showed at panel a. (c) XMLD-PEEM images (4 μm field of view) before and after a 4 mA current pulse along the pulse A & B configurations.

 X-Ray Magnetic Linear Dichroism Studies of Electrical Switching of Antiferromagnetic Order in α-Fe2O3 Epitaxial Films

Antiferromagnets have always been overshadowed by ferromagnets in real-life applications based on magnetism or spintronics. This is primarily due to that antiferromagnet order parameters, in contrast to the ferromagnetic magnetization, are only weakly coupled to magnetic fields, and are hence difficult, in conventional view, to be manipulated. I will discuss several recent theoretical and experimental developments that counter this conventional wisdom, in a class of antiferromagnets that have stable noncollinear magnetic order. I will first explain a theory for the time-reversal-symmetry-breaking counterparts of the conventional SHE and ISHE in the noncollinear antiferromagnet Mn3Sn, which are named as the magnetic spin Hall effect (MSHE) and the magnetic inverse spin Hall effect (MISHE), respectively [1]. I will then discuss the concept of spin density polarization, and how to use it to describe spin-Hall effects in a magnetic insulator as bulk effects, without using the spin current language [2]. I will finally present an exploration on the nontrivial orbital coupling between chiral antiferromagnets and external magnetic fields [3,4], and the potential detection of the elusive itinerant orbital magnetization by magnetic neutron scattering.

**References:**

[1] M. Kimata, H. Chen, et al. Nature 565, 627 (2019). [2] H. Chen, Q. Niu, and A. H. MacDonald, arXiv:1803.01294 [3] H. Chen et al., PRB 101, 104418 (2020). [4] X. Li, A. H. MacDonald, and H. Chen, arXiv:1902.10650

**Images:**

 New aspects of magnetoelectric responses in chiral antiferromagnets INVITED

Suppression of superconductivity due to proximity effects between a superconductor and a ferromagnet can be partially lifted when different directions of the short-range exchange field are sampled simultaneously by a Cooper pair. Partial recovery of the superconducting critical temperature, ΔTC, is therefore expected when the ferromagnet is set in a multi-domain state compared to a single domain state [1-3]. Here, we discuss series of experimental results for ferromagnet(Pt/Co)/spacer(IrMn)/superconductor(NbN) heterostructures [4]. By tuning the various parameters into play, e.g. superconducting coherence length-to-thicknesses ratio, and domain sizes, we obtained a recovery of the superconducting critical temperature ΔTC/TC as large as 10% (Fig. 1(a,b)). Such a large scale of ΔTC/TC opened the pathway for novel investigations. In particular, from the spacer thickness-dependence of ΔTC/TC, characteristic length for Cooper pair penetration (ξIrMn ~ 6.7 nm) (Fig. 1(c)) was deduced in the IrMn antiferromagnet [4]. It is a crucial information for electronic transport, which are currently difficult to access experimentally for antiferromagnets [5].

**References:**

[1] A. I. Buzdin, Rev. Mod. Phys. 77, 935 (2005). [2] M. Houzet and A. I. Buzdin, Phy. Rev. B 74, 214507 (2006). [3] L. Y. Zhu, T. Y. Chen, and C. L. Chien, Phys. Rev. Lett. 101, 017004 (2008). [4] R. L. Seeger et al, in preparation. [5] V. Baltz et al, Rev. Mod. Phys. 90, 015005 (2018).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/66aa596907df1b7ec86357b5f66e2675.jpg)
Fig. 1 (a) Schematics of the saturated (circle) and demagnetized (square) states in a (Pt/Co)n/IrMn/NbN stack. Those states are accessed by performing two procedures involving field-cycling and cooling. (b) Representative data showing the temperature (T)-dependence of the stack’s resistance (R) for the two states represented in (a). ΔTC represents the difference in superconducting critical temperature of the NbN layer between the saturated and demagnetized states of the (Pt/Co) ferromagnet: ΔTC = ΔTC,demag - ΔTC,sat. (c) Spacer thickness dependence of ΔTC/TC, for the case of the IrMn antiferromagnetic (AF) spacer. The line is a fit to the data.

 Penetration depth of Cooper pairs in the IrMn antiferromagnet

Room temperature skyrmions have been the focus of research for development of skyrmionic devices based on thin film multilayers (MLs) with perpendicular anisotropy (PMA) and interfacial Dzyaloshinskii-Moriya interaction (iDMI)1. The skyrmion spin texture is governed by several competing energies: iDMI, exchange energy, anisotropy energy, and magnetostatic energy. It has been shown that the skyrmion wall type and chirality determine the strength of the stray field above and below the thin film structure2. Moreover, knowing the type and strength of the interlayer coupling is a prerequisite for designing future skyrmionic devices3. Recent studies4 showed that the spin texture of the skyrmion in each ferromagnetic (F) layer depends on its position within the ferromagnet/heavy metal ML. The dependence of the skyrmion wall on the vertical position inside the multilayer was attributed to the minimization of the total energy, which included the formation of a flux-closure structure to reduce the magnetostatic energy. However, the existence of even a weak Ruderman–Kittel–Kasuya–Yosida (RKKY) interlayer exchange could significantly alter this scenario by dominating magnetostatic energy contributions. Neglecting the RKKY exchange in modelling work stems from the fact that it has not been thoroughly studied in structures supporting skyrmion formation. Therefore, it is important to investigate the role of RKKY coupling in such multilayered structures in combination with the other energies present in these systems. Here, we report on multilayered systems that allow the assessment of interlayer RKKY interaction relevant for systems with iDMI, thus providing the required input for the design of multilayer systems with well-defined uniform skyrmion spin textures throughout the multilayer system. Note that a similar concept has been already used to measure RKKY interactions5, but for systems with a magnetic in-plane anisotropy without iDMI. Also, because the coercivity of the pinned layer was very small, only antiferromagnetic (AF) exchange coupling could be measured. Here we are interested in systems with PMA with iDMI supporting skyrmions, with ferromagnetic layers that can be coupled either by ferromagnetic or antiferromagnetic RKKY exchange. To assess RKKY interactions in such systems, a rare-earth ferrimagnet based multilayered system is proposed. The magnetically hard rare-earth amorphous ferrimagnet consisting of a TbxFe1-x alloy is exchange-coupled to a thin Co layer. The magnetization of the latter remains pinned up to reasonably high fields by the magnetically hard ferrimagnet layer. This bi-layer system is then separated from a “free” magnetic layer by an interlayer consisting of the typical noble metal used in systems with iDMI. In the simplest case the “free” layer is a 1.5nm-thick Co layer deposited on a Pt substrate to obtain PMA. The net magnetic moment of the rare-earth based ferrimagnet layer is governed by the composition of rare-earth and transition metal (TbxFe1-x with 15 &lt; x &lt; 30), such that either the magnetic moment of the rare-earth or transition metal element aligns parallel to the direction of an applied test-field Hex. Consequently, the adjacent Co layer aligns antiparallel or parallel to Hex, which permits the measurement of a ferromagnetic or antiferromagnetic RKKY exchange coupling, respectively, occurring between the “pinned” and “free” Co layers through the interlayer. The RKKY coupling energy density can be obtained from magnetometry using E=Mfree layer.t.Hex. The situation however becomes more challenging if the “free” Co layer has asymmetric interfaces, hence the material at the top (e.g. Ir) is different from that at the bottom (Pt). In such a case the remanence of the “free” layer is suppressed by the formation of skyrmions or chiral domains arising from the net DMI generated by the asymmetric interfaces. To overcome this problem, we designed the free layer as a multilayer system with symmetric interfaces suppressing the net DMI. The proposed multilayer design permits to reliably measure the RKKY interactions occurring in all typical magnetic multilayer systems exhibiting iDMI, which provides the so-far missing input for micromagnetic simulations of such systems relevant for the design of future skyrmionic devices.

**References:**

1. M. Bacani, M. A. Marioni, J. Schwenk, H. J. Hug, Scientific Reports 9, 3114 (2019). 2. M. A. Marioni, M. Penedo, M. Bacani, J. Schwenk, H. J. Hug, Nano Letters 18, 4, 2263-2267 (2018). 3. D. Suess, C. Vogler, F. Bruckner, P. Heistracher, C. Abert, Aip Advances 8, 11 (2018). 4. W. Legrand, J. Y. Chauleau, D. Maccariello, N. Reyren, S. Collin, K. Bouzehouane, N. Jaouen, V. Cros, A. Fert, Science Advances 4, 7 (2018). 5. S. S. P. Parkin, Physical Review Letters 67 (25), 3598-3601 (1991).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/080ec7629d5cbd156a14f958d9f4fde5.jpg)

 The effect of RKKY exchange coupling through heavy metal interlayers on future skyrmionic devices

Antiferromagnetic (AFM) spintronics is an emerging subject where one tries to exploit the indispensable properties of AFMs for spintronics such as negligible stray fields and terahertz resonance frequencies. Unfavorably, small electric, and magnetic responses make it difficult to write and read the information in AFM spintronic devices. Thus, from the applied perspective, it is crucial to search the AFM materials having manipulable AFM order. Mn3Ge and Mn3Sn are novel functional AFMs that exhibit magnetic responses comparable to FMs1,2. The magnetic states characterized by magnetic cluster octupoles (MCOs) are tunable under a small external magnetic field. Thus, data writing and reading can be realized by inductively using a recording head, likewise FMs. A recent numerical simulation predicts an antiferromagnetic domain wall (AFDW) velocity up to 2 km/s without a walker break down3. A pulse current could drive such AFDW under the threshold current density of 109 A/m2, two or three orders of magnitude smaller than in FMs4. Thus, it could open a new avenue for racetrack memory applications to overcome the shortcomings of low velocity and high energy consumption of ferromagnetic domain walls. Besides, the multistate of MCOs could generate multilevel magnetic responses rather than conventional two-level memory responses. It may provide a new idea for three-dimensional memory without vertical multilayer architecture. Therefore, the understanding of AFDW structure and dynamics in Mn3Sn and Mn3Ge is indispensable for the memory application. We put our focus on Mn3Ge in this study because it has the native advantages of strong chemical stability in air and robustly retaining the MCO structure down to 0.3 K over the Mn3Sn. We grew Mn3Ge single crystal using the bismuth flux method5. The obtained single crystal sample is a perfect hexagonal column, reflecting the hexagonal crystal structure. We performed polar and longitudinal MOKE measurements at room temperature. Figure 1a shows a polar hysteresis loop measured by laser scanning MOKE microscope. The positive and negative signs of the MOKE signal correspond respectively to oppositely aligned MCOs with the order parameters of α±, as shown in the inset of Fig 1a. Figure 1(b) shows the angular dependence of longitudinal MOKE measurement at room temperature. The intensity of decreased from 5.6 mdeg to 0 deg with increasing from 0° to 90°. Domain observation was furtherly performed by using high-resolution CCD MOKE microscope. Firstly, a magnetic field, up to -100 Oe downwards, which is larger than the saturation field according to the MOKE hysteresis loop in Fig. 1b, was applied to reset the magnetization in the crystal. We subtracted the image background at this state; then, we captured MCO domain images continuously while sweeping the magnetic field from -20 Oe down to 30 Oe with a sweep rate of 2.5 Oe/s, as shown in Fig. 2a. The exposure time of the CCD camera was 50 ms. Firstly, the droplet of the tilted MCO domain appears at 2 Oe. Here, the gray at -100 Oe and the white areas at 25 Oe represent the oppositely polarized MCO domains. The droplet occurs at the surface center due to the nearly zero magnetization in Mn3Ge. Noticeably, the color contrast gradually changes from gray to white within a narrow magnetic field range of about 2 Oe. As the grayscale in the CCD camera is proportional to the out-of-plane component of MCO moment Mz. We can obtain the tilting angle φ of the MCO moment where cosφ = Mz/M, as shown in Fig. 2b. In this way, we can understand how the magnetic octupole evolves during the domain nucleation process. The six-fold symmetry in the kagome plane may offer the possibility of a multilevel MCO memory application. The droplet of the switched domain emerges in the magnetic field range from H1 = 1.875 Oe to H2 = 3 Oe, as shown in Fig. 2c. The decrease in magnetic potential energy compensates for the energy consumed by AFDW. Thus, we have: -μ0(MH2-MH1)×ΔV-σ×ΔS=0 where M and, σ denote the MCO moment (7 mµB/Mn) and the 180° AFDW energy density, respectively. ΔV is the volume of the switched MCO domain, and ΔS is the area of nucleated AFDW. We estimated the and by assuming the hemi-ellipsoidal MCO domain beneath the surface, as illustrated in Fig. 2c. The obtained σ is 0.0198 erg/cm2. In conclusion, we have obtained the large MOKE signal, including the polar and longitudinal MOKE. The sizeable MOKE signals enable us visualize the MCO domain optically. Thereby, we systematically studied MCO domain evolution and estimated the AFDW propagation in a single crystal Mn3Ge. Our work provides important insights for the study on the exploitation of the AFDW based memory devices.

**References:**

1. S. Nakatsuji, N. Kiyohara & T. Higo. Nature 527, 212–215 (2015). 2. N. Kiyohara, T. Tomita & S. Nakatsuji. Phys. Rev. Appl. 5, 064009 (2016). 3. T. Nomoto & R. Arita. Phys. Rev. Res. 2, 012045 (2020). 4. S. Sugimoto, Y. Nakatani, Y. Yamane, et al. Commun. Phys. 3, 1–9 (2020). 5. M. Wu, H. Isshiki, T. Chen, et al. Appl. Phys. Lett. 116, 132408 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/cd8a08de8aef0c12c36660d4e468c523.jpg)
Fig.1 Polar and longitudinal MOKE signals in Mn3Ge (a) Field dependence of the polar MOKE. (b) Field dependence of θK under the longitudinal set-up at various values of φ.

![](https://assets.underline.io/uploads/markdown_image/1/image/9ae171773e98317d0425224240aed82b.jpg)
Fig.2 MCO domain evolution on Mn3Ge surface observed by CCD MOKE microscope. a, MCO domain evolution process under the sweeping magnetic field. b, Tilting angle φ of the MCO moment with respect to the magnetic field during the MCO domain nucleation process. c, The left image shows first droplet of nucleated MCO domains and the right image is the schematic diagram of hemi-ellipsoidal MCO domain shape beneath the surface.

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