France



Antiferromagnets (AFMs) exhibit features, such as low magnetic susceptibility, robustness against external fields and lack of stray fields, that are favorable for the building blocks of spintronic devices [1]. This opens the way for a number of potential applications including storage with picosecond switching [2], THz oscillators [3], racetrack memory based on magnetic solitons such as domain walls (DWs) [4] or skyrmions [5].&lt;br/&gt;AFM materials can be characterized by an easy-plane anisotropy which promotes the formation of vortices as well as spiral phases [6]. Vortices have been discussed theoretically in infinite films [7] and observed experimentally by imprinting techniques [8], but they have received less attention than other magnetic solitons. On the other hand, two spiral phases can be obtained statically in an easy-plane AFM with Dzyaloshinksii-Moriya interaction (DMI). For weak DMI constant, &lt;i&gt;λ&lt;/i&gt; &amp;lt; &lt;i&gt;λ&lt;/i&gt;&lt;sub&gt;NF&lt;/sub&gt;, the Néel state is the ground state. For &lt;i&gt;λ&lt;/i&gt; = &lt;i&gt;λ&lt;/i&gt;&lt;sub&gt;NF&lt;/sub&gt;, an intermediate phase is obtained in the form of a nonflat spiral. This spiral presents a continuous rotation of the Néel vector n in the &lt;i&gt;x-z&lt;/i&gt; plane, while its &lt;i&gt;y&lt;/i&gt;-component oscillates around a nonzero value. At &lt;i&gt;λ&lt;/i&gt; &amp;gt; &lt;i&gt;λ&lt;/i&gt;&lt;sub&gt;F&lt;/sub&gt;, a flat spiral is obtained with n fully rotating on the &lt;i&gt;x-z&lt;/i&gt; plane.&lt;br/&gt;In this work, we theoretically study vortices in easy- plane AFMs with an interfacial DMI. We consider a stripe geometry, infinite long in the &lt;i&gt;x&lt;/i&gt;-direction and confined in the &lt;i&gt;y&lt;/i&gt;-direction, as this is the most suitable for applications involving shifting of magnetic information, while it will also give rise to interesting effects on the magnetic structure. We firstly calculate the magnetic ground state, which we find to be uniform (&lt;i&gt;y&lt;/i&gt;-direction) and perpendicular to the boundaries. Then we numerically study the stabilization of a single vortex. We observe that this vortex is Néel close to its core and it gradually becomes Bloch as we go away from the core thus exhibiting a hybrid character. For this reason, we refer to it as &lt;i&gt;hybrid vortex&lt;/i&gt;. The Néel chirality is a consequence of the interfacial DMI, while the Bloch character is due to the boundary conditions which force the Néel vector to be oriented primarily along the &lt;i&gt;y&lt;/i&gt;-axis in the far field. The increase of &lt;i&gt;λ&lt;/i&gt; leads an increase of the vortex core width and a faster rotation of the Néel vector towards the &lt;i&gt;y&lt;/i&gt;-axis. We further analyze the hybrid vortex dynamics by propagating it along the &lt;i&gt;x&lt;/i&gt;-direction at a velocity &lt;i&gt;v&lt;/i&gt;. Figure 1(a) depicts that a propagating vortex is contracted along the &lt;i&gt;x&lt;/i&gt;-direction, similarly to DWs [4] and it is elongated along the &lt;i&gt;y&lt;/i&gt;-direction, similartly to skyrmions [5]. Figure 2(b) shows the width &lt;i&gt;L&lt;/i&gt;&lt;sub&gt;x&lt;/sub&gt; of the propagating vortex in the &lt;i&gt;x&lt;/i&gt;-axis as a function of velocity for various values of &lt;i&gt;λ&lt;/i&gt;. We define the width of the vortex core as the distance between the positions where the &lt;i&gt;z&lt;/i&gt;-component is 0.5. The width &lt;i&gt;L&lt;/i&gt;&lt;sub&gt;x&lt;/sub&gt;, in the direction of propagation, closely follows the law of Lorentz-type contraction &lt;i&gt;L&lt;/i&gt;&lt;sub&gt;x&lt;/sub&gt; = 1/√(1 − &lt;i&gt;v&lt;/i&gt;&lt;sup&gt;2&lt;/sup&gt;) (red solid line) despite that the model is not Lorentz invariant. For each &lt;i&gt;λ&lt;/i&gt;, the vortex achieves a maximum velocity. Therefore, there is a minimum achievable vortex width which decreases with decreasing &lt;i&gt;λ&lt;/i&gt;. When the velocity exceeds the maximum value, the hybrid vortex becomes unstable to periodic configurations, thus giving rise successively to a nonflat spiral at a critical velocity &lt;i&gt;v&lt;/i&gt;&lt;sub&gt;NF&lt;/sub&gt;, a vortex chain and a flat spiral at a critical velocity &lt;i&gt;v&lt;/i&gt;&lt;sub&gt;F&lt;/sub&gt;. We wish to stress that these are dynamical phase transitions, in contrast to the previously-mentioned static transitions. While the spiral phases are anticipated by a study of the 1D model [8], the vortex chain is a feature of the stripe geometry. In addition, no vortex lattice has been found in this system in an infinite film [8]. A theoretical explanation for the dynamical behavior is obtained and it leads to the general result that the velocity of localized excitations in chiral magnets cannot reach the spin wave velocity. Our results provide an understanding of the statics and dynamics of vortices in chiral AFMs and could be useful for the design of antiferromagnetic devices based on magnetic solitons.&lt;br/&gt;&lt;br/&gt;This work was supported by the project “ThunderSKY,” funded by the Hellenic Foundation for Research and Innovation (HFRI) and the General Secretariat for Research and Technology (GSRT), under grant agreement No. 871.

**References:**

[1] V. Baltz et al. Rev. Mod. Phys. 90, 015005 (2018).&lt;br/&gt;[2] V. Lopez-Dominguez et al. Phys. Rev. Appl. 11, 024019 (2019).&lt;br/&gt;[3] R. Khymyn et al. Sci. Rep. 7, 43705 (2017); V. Puliafito et al., Phys. Rev. B 99, 024405 (2019).&lt;br/&gt;[4] T. Shiino et al., Phys. Rev. Lett. 117, 087203 (2016); L. Sánchez-Tejerina et al. Phys. Rev. B 101, 014433 (2020).&lt;br/&gt;[5] A. Salimath et al. Phys. Rev. B 101, 024429 (2020); S. Komineas et al., SciPost Phys. 8, 086 (2020).&lt;br/&gt;[6] J. Chovan et al. Phys. Rev. B 65, 064433 (2002).&lt;br/&gt;[7] S. Komineas and N. Papanicolaou, Nonlinearity 11, 265 (1998).&lt;br/&gt;[8] J. Wu et al., Nat. Phys. 7, 303 (2011); F. P. Chmiel et al., Nat. Mater. 17, 581 (2018).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/5de67f9945e19420ef3d918a0e67991e.jpg)
Figure 1: (a) Vector plot for &lt;i&gt;λ&lt;/i&gt; = 0.4 for the propagating hybrid vortex with velocity &lt;i&gt;v&lt;/i&gt; = 0.60.  (b) Vortex core width &lt;i&gt;L&lt;/i&gt;&lt;sub&gt;x&lt;/sub&gt; in the direction of propagation for a propagating hybrid vortex as a function of velocity &lt;i&gt;v&lt;/i&gt;, for various values of &lt;i&gt;λ&lt;/i&gt;, normalized to the width of a static vortex. The red solid line shows the expected result for Lorentz-type contraction. The dashed lines mark the maximum obtained velocities for the respective &lt;i&gt;λ&lt;/i&gt; values.



INTERMAG 2021

 Theoretical study of hybrid vortex and dynamical phase transitions in an antiferromagnetic nanostripe

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Antiferromagnets (AFMs) exhibit features, such as low magnetic susceptibility, robustness against external fields and lack of stray fields, that are favorable for the building blocks of spintronic devices [1]. This opens the way for a number of potential applications including storage with picosecond switching [2], THz oscillators [3], racetrack memory based on magnetic solitons such as domain walls (DWs) [4] or skyrmions [5]. AFM materials can be characterized by an easy-plane anisotropy which promotes the formation of vortices as well as spiral phases [6]. Vortices have been discussed theoretically in infinite films [7] and observed experimentally by imprinting techniques [8], but they have received less attention than other magnetic solitons. On the other hand, two spiral phases can be obtained statically in an easy-plane AFM with Dzyaloshinksii-Moriya interaction (DMI). For weak DMI constant, λ &lt; λNF, the Néel state is the ground state. For λ = λNF, an intermediate phase is obtained in the form of a nonflat spiral. This spiral presents a continuous rotation of the Néel vector n in the x-z plane, while its y-component oscillates around a nonzero value. At λ &gt; λF, a flat spiral is obtained with n fully rotating on the x-z plane. In this work, we theoretically study vortices in easy- plane AFMs with an interfacial DMI. We consider a stripe geometry, infinite long in the x-direction and confined in the y-direction, as this is the most suitable for applications involving shifting of magnetic information, while it will also give rise to interesting effects on the magnetic structure. We firstly calculate the magnetic ground state, which we find to be uniform (y-direction) and perpendicular to the boundaries. Then we numerically study the stabilization of a single vortex. We observe that this vortex is Néel close to its core and it gradually becomes Bloch as we go away from the core thus exhibiting a hybrid character. For this reason, we refer to it as hybrid vortex. The Néel chirality is a consequence of the interfacial DMI, while the Bloch character is due to the boundary conditions which force the Néel vector to be oriented primarily along the y-axis in the far field. The increase of λ leads an increase of the vortex core width and a faster rotation of the Néel vector towards the y-axis. We further analyze the hybrid vortex dynamics by propagating it along the x-direction at a velocity v. Figure 1(a) depicts that a propagating vortex is contracted along the x-direction, similarly to DWs [4] and it is elongated along the y-direction, similartly to skyrmions [5]. Figure 2(b) shows the width Lx of the propagating vortex in the x-axis as a function of velocity for various values of λ. We define the width of the vortex core as the distance between the positions where the z-component is 0.5. The width Lx, in the direction of propagation, closely follows the law of Lorentz-type contraction Lx = 1/√(1 − v2) (red solid line) despite that the model is not Lorentz invariant. For each λ, the vortex achieves a maximum velocity. Therefore, there is a minimum achievable vortex width which decreases with decreasing λ. When the velocity exceeds the maximum value, the hybrid vortex becomes unstable to periodic configurations, thus giving rise successively to a nonflat spiral at a critical velocity vNF, a vortex chain and a flat spiral at a critical velocity vF. We wish to stress that these are dynamical phase transitions, in contrast to the previously-mentioned static transitions. While the spiral phases are anticipated by a study of the 1D model [8], the vortex chain is a feature of the stripe geometry. In addition, no vortex lattice has been found in this system in an infinite film [8]. A theoretical explanation for the dynamical behavior is obtained and it leads to the general result that the velocity of localized excitations in chiral magnets cannot reach the spin wave velocity. Our results provide an understanding of the statics and dynamics of vortices in chiral AFMs and could be useful for the design of antiferromagnetic devices based on magnetic solitons. This work was supported by the project “ThunderSKY,” funded by the Hellenic Foundation for Research and Innovation (HFRI) and the General Secretariat for Research and Technology (GSRT), under grant agreement No. 871.

**References:**

[1] V. Baltz et al. Rev. Mod. Phys. 90, 015005 (2018). [2] V. Lopez-Dominguez et al. Phys. Rev. Appl. 11, 024019 (2019). [3] R. Khymyn et al. Sci. Rep. 7, 43705 (2017); V. Puliafito et al., Phys. Rev. B 99, 024405 (2019). [4] T. Shiino et al., Phys. Rev. Lett. 117, 087203 (2016); L. Sánchez-Tejerina et al. Phys. Rev. B 101, 014433 (2020). [5] A. Salimath et al. Phys. Rev. B 101, 024429 (2020); S. Komineas et al., SciPost Phys. 8, 086 (2020). [6] J. Chovan et al. Phys. Rev. B 65, 064433 (2002). [7] S. Komineas and N. Papanicolaou, Nonlinearity 11, 265 (1998). [8] J. Wu et al., Nat. Phys. 7, 303 (2011); F. P. Chmiel et al., Nat. Mater. 17, 581 (2018).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/5de67f9945e19420ef3d918a0e67991e.jpg)
Figure 1: (a) Vector plot for λ = 0.4 for the propagating hybrid vortex with velocity v = 0.60. (b) Vortex core width Lx in the direction of propagation for a propagating hybrid vortex as a function of velocity v, for various values of λ, normalized to the width of a static vortex. The red solid line shows the expected result for Lorentz-type contraction. The dashed lines mark the maximum obtained velocities for the respective λ values.

technical paper

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:**

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

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.

 Observation of the magnetic cluster octupole domain evolution in antiferromagnet Mn3Ge

Magnetic layers interfaced with materials with strong spin-orbit coupling (SOC) (such as Pt, Ta) manifest several fascinating phenomena when the inversion symmetry is broken1. One direct consequence of SOC is the interplay between charge and spin transport via spin Hall effect (SHE) in heavy metals, which leads to non-equilibrium spin accumulation at the surfaces2. Another mechanism, the Rashba effect, arises when the electrical carriers move in an interfacial electric field and experience the resultant magnetic field that couples with their spins3. Both mechanisms give rise to spin-orbit torques (SOTs) in the magnetic layer, with damping-like and field-like components4. The SOTs are an efficient way to manipulate chiral magnetic textures, such as Néel domain walls (DWs)5,6 and skyrmions, whose chirality is induced by another product of SOC, the Dzyaloshinskii-Moriya interaction (DMI)7. However, up to now, the SOC was mainly studied in 3d-transition-metals (TM) (Co, Ni, Fe)/5d-heavy-metal (Pt). Very recently, interfacial DMI has been observed in TmIG/Pt and TbIG/Pt garnets thin films grown on Gd3Ga5O12 (GGG) substrates, which was attributed to the orbital moment in rare-earth (RE) material8. On the other hand, experiments on [Co/Tb]n multilayers did not show any SOT contribution from the RE9. The underlying origin of SOC and role of RE (specially Gd, which has no atomic orbital momentum) on SOC in ferrimagnets hence remain to be understood and need to be addressed by sophisticated experimental evidence. Here, we demonstrate that the effects of SOC can be obtained without any need of additional nonmagnetic heavy metal in a single layer GdFeCo ferrimagnet (RE-TM alloy). For this study, a Si/SiOx(100nm)//GdFeCo(5nm)/Al(5nm) film was grown by co-evaporation in ultra-high vacuum with a controlled stoichiometry. The ferrimagnet is composed of two sub-lattices of Gd (RE) and FeCo (TM) which are coupled antiferromagnetically. At the magnetic compensation temperature, TM ≈ 275K for this sample, the net magnetization vanishes (MS) and the anisotropy and the coercive fields diverge. To investigate the existence of SOC inside the ferrimagnetic layer, first we quantify the two components of current-induced effective fields, damping-like (HDL) and field-like (HFL) by using second harmonic Hall voltage measurement technique. The temperature dependence of HDL and HFL per current density in GdFeCo layer are shown in Figure 1(a) and 1(b). Both HDL/J and HFL/J diverge at , showing the expected scaling with 1/MS. Another phenomenon induced by SOC is the DMI, which favours chiral magnetic textures. In the single layer GdFeCo ferrimagnet, we observed chiral Néel domain wall structures of width (Δ) = 20 ± 10 nm, using photoemission electron microscopy combined with X-ray magnetic circular dichroism (XMCD-PEEM) as shown in Figure 2(a), which further indicate the presence of internal DMI or SOC in GdFeCo. The DMI is quantified using Brillouin light scattering (BLS) technique in Damon-Eshbach geometry and the DMI constant ( is obtained from the slop of frequency shifts (Δf) of nonreciprocal spin waves vs wave vector (figure 2(c)). Though the DMI amplitude is much smaller in GdFeCo if compared with Pt/Co and Ta/Co systems, the chiral DWs are stabilised due to lower net magnetization of GdFeCo, as the threshold Dc for Néel DW stabilisation is proportional to Ms. The occurrence of these phenomena also requires a broken inversion symmetry. Electron Energy-Loss Spectroscopy (EELS) studies in a scanning transmission electron microscopy (STEM) reveal an inhomogeneity in Gd concentration along the film thickness. This elemental inhomogeneity breaks the spatial inversion symmetry and the combination of broken inversion asymmetry and electronic hybridization of RE-5d and TM-3d electrons favors the emergence of net SOC effects (SOTs, DMI and chiral Néel DWs) inside the GdFeCo layer. These results show that phenomena that can only exist in systems with broken inversion symmetry and strong SOC -- spin-orbit torques, chiral textures, and DMI -- can occur in a ferrimagnetic thin layer without a heavy metal adjacent layer. This should be taken into account when analysing these phenomena even in bi-layers, and may be very useful for applications as it may allow removing the requirement for a heavy-metal layer and improving the efficiency of SOT-driven magnetisation switching.

**References:**

1. Soumyanarayanan, A. et al. Nature 539, 509–517 (2016). 2. Stamm, C. et al. Phys. Rev. Lett. 119, 087203 (2017). 3. Sánchez, J. C. R. et al. Nat. Commun. 4, 1–7 (2013). 4. Garello, K. et al. Nat. Nanotechnol. 8, 587–593 (2013). 5. Emori, S. et al. Nat. Mater. 12, 611–616 (2013). 6. Ryu, K.-S. et al. Nat. Nanotechnol. 8, 527–533 (2013). 7. Thiaville, A. et al. Epl 100, (2012). 8. Caretta, L. et al. Nat. Commun. 11, 1–9 (2020). 9. Yu, J. et al. Nat. Mater. 18, 29–34 (2019).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/906aed22f1aa90a30aad88a7fc2c9d8a.jpg)
Figure 1. (a) HDL and (b) HFL effective fields per current density as a function of temperature. Purple points correspond to an up saturated film state and khaki to down one. The diagrams represent the direction and magnitude of Gd (black) and FeCo (red) magnetic moments. The dotted lines are guides to the eyes.

![](https://assets.underline.io/uploads/markdown_image/1/image/4b4afae03c3181e42876985bb777aa9a.jpg)
Figure 2. (a) Multidomain XMCD-PEEM images at the Gd M4,5 edge (1178.7 eV) at T = 230 K. The green arrow shows the direction of the X-ray beam at a grazing angle of 16°. The dark (bright) contrast corresponds to a down (up) magnetic domain. (b) Intensity profiles (black lines) averaged over the yellow regions in (a). The thick yellow line is a fit to the experimental data using the theoretical profile. The presence of a peak or a dip in the line scan is an evidence of chiral Néel DWs. (c) The DMI induced frequency shifts (𝛥f) of nonreciprocal spin waves vs wave vector magnitudes |ksw| for GdFeCo thin film

 Direct Observation of Spin-Orbit Torques, Dzyaloshinskii-Moriya Interaction and Chiral Spin Textures in Single Layer Ferrimagnets

We study the magnetic reversal of the canted antiferromagnet α-Fe2O3. At room temperature, the Dzyaloshinskii-Moriya interaction (DMI) induces canting of the two magnetic sublattices MA and MB giving rise to a weak ferromagnetic (FM) moment m. We employ spin Hall magnetoresistance (SMR) measurements to study electrical and magnetic field control of the Néel order in α-Fe2O3/Pt bilayers. The angle-dependent magnetoresistance (ADMR) shows the characteristic saturated negative SMR signal of AFMs (dotted curve in figure 1) in agreement with previous findings1–4. We note that the FM moment lifts the degeneracy of the sublattices and consequently the orientation of the Néel vector with respect to the applied magnetic field. The solid blue curve in figure 1 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 ADMR signal and the remanent resistance by a factor of 5. The lack of signatures of anisotropy in the remanent signal implies that the relaxation of the SMR signal is dominated by destressing effects favoring an equilibrium state with multiple domains distributing the orientation of the Néel vector along random directions. Furthermore, we observe hysteresis in the SMR signal. The irreversibility upon switching the direction of the magnetic field in combination with investigating the transient effects of current-induced changes in the domain structure allows us to study the nature and formation of antiferromagnetic as well as ferromagnetic domain walls at low magnetic fields. Our work emphasizes the importance of the FM moment induced by DMI and the relaxation effects for the equilibrium domain structure in α-Fe2O3.

**References:**

1. Lebrun, R. et al. Anisotropies and magnetic phase transitions in insulating antiferromagnets determined by a Spin-Hall magnetoresistance probe. Commun. Phys. 2, 50 (2019). 2. Cheng, Y., Yu, S., Zhu, M., Hwang, J. & Yang, F. Electrical Switching of Tristate Antiferromagnetic Néel Order in a-Fe2O3 Epitaxial Films. Phys. Rev. Lett. 124, 027202 (2020). 3. Fischer, J. et al. Large Spin Hall Magnetoresistance in Antiferromagnetic a-Fe2O3/Pt Heterostructures. Phys. Rev. Appl. 13, 014019 (2020). 4. Zhang, P., Finley, J., Safi, T. & Liu, L. Quantitative Study on Current-Induced Effect in an Antiferromagnet Insulator/Pt Bilayer Film. Phys. Rev. Lett. 123, 247206 (2019).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/7877b8c698ce2bc70681f32ecc5f5632.jpg)
Transverse resistance (solid blue line) after H has been reduced from a saturated state (dotted blue line) to zero field as a function of angle of the applied magnetic field. The inset in the top right corner shows a schematic of the canting of the sublattice magnetization MA and MB due to DMI giving rise to the ferromagnetic moment m.

 Roles of Destressing, Pinning, and Weak Ferromagnetism for Magnetic Reversal in α-Fe2O3

The Hall effect family is of fundamental importance among the magneto-transport phenomena, as it represents a way to dissipationless transport. [1] Hall effects manifest as a transverse component to conductivity, perpendicular to the direction of the electrical current. Apart from the long-known ordinary Hall effect that is present in all conductive materials, the anomalous Hall effect was a long time thought to be exclusive to ferromagnetic systems. In the last years, the Hall effect family has been explored in materials with zero net magnetic moment. Both anomalous Hall effect [2] and topological Hall effect were detected [3] also in non-collinear antiferromagnets (AFM). Very recently, a novel type of spontaneous Hall effect was reported also in the collinear phases of antiferromagnetic Mn5Si3 [4] and RuO2 [5]. All the above-mentioned Hall effects rely on detection of transversal voltage which is expected to be odd in magnetic field. Any even contribution to the transversal voltage is often considered as an artefact related to misalignment of the Hall cross and, consequently, only antisymmetrized transversal voltage data are presented. However, it has been theoretically shown [6] that for certain low-symmetry magnetic systems, even components would be present in the transverse voltage data. In our presentation, we aim to experimentally demonstrate the presence of the even contribution to transversal resistance in a low-symmetry antiferromagnetic phase of Mn5Si3 indicating that the symmetry of the signal could serve as a probe of the degree of spin symmetry of the material. The ratio between odd and even contributions in various samples will be shown and the role of the crystal quality will be discussed Mn5Si3 is a compensated antiferromagnet that can order both collinearly and non-collinearly in different temperature regimes, with the two phase transitions at TN1 ≈ 70 K and TN2 ≈ 200 K in thin-film layers [4]. Our samples are 20 nm thick epilayers, prepared by molecular beam epitaxy on Si(111) substrate, which results in the c-axis of Mn5Si3 to be oriented perpendicular to the sample plane. The layers were patterned to Hall bar devices with a channel width of 10 µm using standard laser lithography and Ar+ milling. Both longitudinal (ρxx) and transverse (ρxy) resistivities were measured simultaneously as a function of external magnetic field Bz, applied in the out-of-plane direction. The longitudinal and transverse signals measured at two different temperatures corresponding to the collinear (180 K) and non-collinear (40 K) antiferromagnetic phase of Mn5Si3, are shown in Fig. 1(a) and (b), respectively. Note that all the curves presented in Fig. 1 were shifted for clarity, and the ordinary Hall resistance was removed from ρxy by subtracting the signal linear in Bz. The longitudinal signal Δρxx (see Fig.1(a)) corresponds to the magnetoresistance (MR). The strong magnetoresistance observed at 40 K is significantly suppressed in the collinear phase at 180 K in accord with the expected behaviour [5]. In contrast, the transverse resistivity persists even in the collinear phase (see Fig 1(b)), with a clear hysteretic behaviour and coercive field of 2 T. This spontaneous Hall response has recently been attributed to a novel antiferromagnetic Zeeman effect [4]. As for the case of any Hall effect, generated transverse voltage is expected to be odd in the inducing magnetic field. However, the data in Fig. 1 (b) clearly contain both odd and even component. This feature is highlighted in Fig. 2, where the corresponding hysteresis curves are split into symmetric (a) and antisymmetric (b) parts. Notably, the symmetrical component that reflects signals even Bz is comparable in magnitude to the antisymmetrical one at 40 K, but disappears entirely at 180 K. To exclude the possible origin in MR-related artefacts, we compare the shapes of the ρxx and even ρxy by subtraction the normalized curves, i.e. Δρ(Bz) = ρxx(Bz)/ ρxx(0) - Δρ(sym)xy(Bz)/ ρ(sym)xy(0). The resulting non-trivial curve, shown in Fig. 2(c), demonstrates the difference in shapes of MR and even transverse voltage. The comparison is, however, possible only in the low-temperature regime, as the transverse detected at 180 K do not display any sizable even component. This observation is in agreement with the assumed lowering of the symmetry in the non-collinear phase of Mn5Si3. As shown in [6], the shape of the linear response tensor can be extended to deal with more complex situations, such as the low magnetic symmetry of the Mn5Si3. The transversal voltage does not need to show purely antisymmetric elements.

**References:**

[1] N. Nagaose et al., Rev. Mod. Phys. 82, 1539 (2010) [2] S. Nakatsuji, N. Kiyohara, and T. Higo, Nature 527, 212-215 (2015) [3] Ch. Surges et al., Nat. Comm. 5, 3400 (2015) [4] H. Reichlova et al., arXiv:2012.15651v1 (2020) [5] https://arxiv.org/abs/2002.08712 [6] M. Seeman et al., Phys. Rev. B 92, 155138 (2015)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/94973c6c1a579fe576fa9e7b95036f21.jpg)
Fig. 1. (a) Longitudinal and (b) transverse resistivity measured as a function of the out-of-plane magnetic field Bz at two different temperatures, corresponding to the collinear (180 K) and non-collinear (40 K) phase of Mn5Si3.

![](https://assets.underline.io/uploads/markdown_image/1/image/fe910a604ff8e4df2548b44104926b42.jpg)
Fig. 2. (a) symmetrized and (b) antisymmetrized components of transverse resistance data in Mn5Si3 measured at 40 K and 180 K, respectively. Panel (c) demonstrates the difference in shape by subtracting normalized curves for ρxx(Bz) and ρ(sym)xy(Bz).

 Symmetry of transversal conductivity signal in antiferromagnetic Mn5Si3

Regulation of electronic properties in spintronic interfaces (spinterfaces) can give rise to the optimization and even emergence of abundant spintronic effects. However, a proof-of-concept demonstration of such a strategy has rarely been achieved. Here, we experimentally demonstrate a reversible switching from antiferromagnetic coupling through insulating spinterface to ferromagnetic coupling through metallic spinterface in [Pt/Co]2/VO2/[Co/Pt]2 heterostructure, where atomically VO2 is considered as a controllable spinterface via its reversible metal-to-insulator transition. Furthermore, we attribute such an evolution to two distinct coupling mechanisms of spin-dependent tunneling and Rudermann-Kittel-Kasuya- Yosida interaction determined by the electronic states of VO2. The effect of VO2-tailored interlayer exchange coupling highlights the great potential of spinterface as a magic building block in beyond-CMOS electronic devices. 1.Preparation and characterization of atomically thin VO2 and heterostructures Both atomically thin VO2 and [Pt/Co]2/VO2/[Co/Pt]2 heterostructure are deposited by sputtering. Ultrathin VO2 is chosen as an electrically-controllable spacer to regulate the interlayer exchange coupling via its metal-insulating transition around 340K1. First, the phase change of atomically thin VO2 lies at the heart of whole works. XPS result in Fig. 1a is displayed to check the valence state of vanadium of VO2 thin film from which we can see that the proportion of VO2 reaches 97%. Meanwhile electrical transport with a junction device of Au/VO2/ Au is also performed to confirm the phase change of VO2. From It is clearly in Fig. 1b that the I-V curve changes from tunneling (300K) to linear (340K) suggesting a transition from insulating state to metallic state of VO2. We also show the dependence of resistance ratio of ultrathin VO2 (2nm) on temperature comparing with a bulk sample (40 nm) (Fig. 1c). Based on such an atomically thin VO2, we prepare the heterostructure of [Pt/Co]2/VO2/[Co/Pt]2 (Fig. 1d). To prove the good quality and continuity of heterostructure, high-resolution transmission electron microscopy measurement is required profiled in Fig. 1e. In addition, PMA of heterostructure is also measure by p-MOKE in Fig. 1f. 2.Interlayer exchange coupling switching via phase change The change on electronic state of spinterface induced by phase change will arise the interlayer exchange coupling switching. In order to investigate the coupling change, we measure the hysteresis loops of heterostructure with various thicknesses of VO2 as temperature rises to trigger the phase change. The loops change from double spin flips to single flip (Fig. 2a) that indicates a transition from antiferromagnetic coupling at low temperature to ferromagnetic coupling at high temperature. Besides such a dynamic process of coupling switching, we extract the exchange coupling field of different samples with temperature increasing (Fig. 2b left). To further verify the reliability of the experimental data, we compare the coupling strength value calculated by experimental data with that calculated by theoretical fitting at room temperature with various thicknesses of VO2 (Fig. 2b right). As for theoretical fitting, due to different electronic state of VO2, spin-dependent tunneling model2 is applied at insulating VO2 while RKKY interaction model3 is used at metallic VO2. In the final, to confirm reversibility of such a promising interlayer exchange coupling regulation, we also show the hysteresis loop after the temperature decrease back to the low temperature (Fig. 2c).

**References:**

1. Morin, F. J. Oxides Which Show a Metal-to-Insulator Transition at the Neel Temperature. Phys. Rev. Lett. 3, 34–36 (1959). 2. Faure-Vincent, J. et al. Interlayer Magnetic Coupling Interactions of Two Ferromagnetic Layers by Spin Polarized Tunneling. Phys. Rev. Lett. 89, 107206 (2002). 3. Parkin, S. S. P. & Mauri, D. Spin engineering: Direct determination of the Ruderman-Kittel-Kasuya-Yosida far-field range function in ruthenium. Phys. Rev. B 44, 7131–7134 (1991).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/e447c176a4b7fda336683342073dba20.jpg)
Figure 1. Atomically Thin VO2 and Magnetic Heterostructures

![](https://assets.underline.io/uploads/markdown_image/1/image/08ebecb12fa445146d3e52fdbe78663d.jpg)
Figure 2. Interlayer exchange coupling switching

 Reversible interlayer exchange coupling regulation induced by phase change of atomically thin VO2

The anomalous Hall effect (AHE) reflects the immense diversity of mechanisms for intrinsic or extrinsic current generation that can be found in the world of magnets. This world offers numerous exciting classes of antiferromagnets, where the anomalous and recently discovered crystal Hall [1] effect as well as the topological Hall effect in non-coplanar antiferromagnets [2] have been studied in the past decades. In this work, we uncover a novel type of Hall effect emerging in generic canted spin systems. Identifying a clear fingerprint of this chiral Hall effect (CHE) in discrete tight-binding models as well as ab-initio calculations is central in establishing a solid understanding of this new phenomenon closely tied to real space topology of magnetic textures. In this study, we provide robust numerical evidence for the CHE in a honeycomb lattice of canted spins and present a material candidate, SrRuO3. We uncover contributions to the Hall conductivity sensitive to the canting angle between neighboring spins which can be directly related to the imprinted vector chirality. Exploring the symmetry properties of the CHE we demonstrate the complex interplay of symmetry, topology and chirality in canted spin systems.

**References:**

[1] L .Smejkal, R. Gonzalez-Hernandez, T. Jungwirth, J. Sinova, Science Advances 6 (2020) [2] L. Smejkal, Y. Mokrousov, B. Yan, A. H. MacDonald, Nature Physics 14, 242–251 (2018) [3] J. Kipp et al., arXiv:2007.01529 (2020)

**Images:**

 The chiral Hall effect in canted ferromagnets and antiferromagnets

The theoretical prediction of Néel order manipulation in antiferromagnetic (AFM) Mn2Au by current induced bulk spin-orbit torques [1] and subsequent experimental realization of the same [2, 3] have led to a surge of interest in the study of this material for spintronics applications. However, the absence of a net magnetic moment in antiferromagnets poses a major challenge to the visualization of antiferromagnetic domains and it is usually resolved by complex synchrotron-based microscopy methods such as X-ray magnetic linear dichroism - photoemission electron microscopy (XMLD-PEEM) [4, 5]. In this work we present an alternative technique to image antiferromagnetic domains in-house by imprinting them on thin ferromagnetic overlayers via interfacial exchange coupling. The domains of the Mn2Au/ferromagnet bi-layer system were first observed using X-ray magnetic linear/circular dichroism – photoelectron emission microscopy for the antiferromagnetic and ferromagnetic layers, respectively. The ferromagnet was found to mimic the underlying Mn2Au domain pattern, thereby enabling us to indirectly image the AFM domains of Mn2Au using an in-house scanning electron microscope with polarization analysis (SEMPA) (Figure 1). Furthermore, superconducting quantum interference device (SQUID) magnetometry measurements were carried out to quantify the pinning field acting upon the ferromagnet and an unusually large exchange coupling was revealed at the Mn2Au/ferromagnet interface. Our results unlock novel possibilities for in-house study of antiferromagnets and take us a step further towards the realization of next generation spintronics devices based on this remarkable material. This project is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) TRR 173 268565370 (projects A01 & A05).

**References:**

[1] J. Zelezný et al., Phys. Rev. Lett., 113, 157201 (2014). [2] S. Yu. Bodnar et al., Nat. Commun., 9, 348 (2018). [3] M. Meinert et al., Phys. Rev. Appl., 9, 064040 (2018). [4] A. A. Sapozhnik et al., Phys. Rev. B, 97, 134429 (2018). [5] S. Yu. Bodnar et al., Phys. Rev. B, 99, 140409(R) (2019).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/f2d6948c2def4381e9442d9174f034ac.jpg)
Figure 1. Scanning electron microscopy with polarization analysis to study the domain structure of Mn2Au imprinted on the ferromagnetic overlayer. The SEMPA resolves in-plane magnetization into horizontal and vertical components.

 Imprinting the domain structure of a metallic antiferromagnet on thin ferromagnetic layers

Contemporary spintronics, utilizing the electronic spin for information processing and microelectronics, is mostly based on ferromagnetic device architectures. In view of long term perspectives to enable enhanced data processing speeds and downscaling for on-chip information processing, spintronics with antiferromagnets is a promising avenue [1]. Antiferromagnets exhibit the key advantage over ferromagnets that their resonance frequency is enhanced by the exchange coupling of the sublattices, and thus generally in the terahertz regime. In compensated antiferromagnets, the absence of a net moment however strongly impedes simple access to their ultrafast dynamics, especially in thin films, and the development of ultra-fast antiferromagnet-based devices [2]. Experimental access to the spin dynamics can be facilitated by spin-to charge conversion mechanisms such as the spin pumping effect [3,4] or by probing the light-matter interaction of the spin system via a coupling to cavity resonator photons [5]. The spin pumping effect generates alternating (AC) and continous (DC) spin currents in an adjacent conductor which can be electrically detected, for instance, by the inverse spin hall effect (ISHE) [6]. On the other hand, light-matter interaction is also at the heart of cavity spintronics which describes the generation and manipulation of cavity-magnon polaritons (CMP) for a general understanding of these interactions and applications for information processing and spintronics. The CMP is the associated quasiparticle to the hybridization of cavity resonator photons and collective spin excitations, i.e. magnon modes and the hallmark for a coherent information transfer in the strong coupling regime [5]. Such coherent information transfer is key for the implementation of microwave-to-optics transducers or quantum-based information processing schemes such as quantum memories [7]. Probing the spin dynamics electrically by spin-to-charge mechanisms or via the light-matter interaction of a strongly coupled photon-magnon system allows to study the physics of spin dynamics from different perspectives as it is at the crossroads of spintronics, magnonics and photonics. In this work, we access the spin dynamics of a collinear (easy axis) antiferromagnetic system by using a bulk chromium oxide (Cr2O3) sample as a model system. We both investigate the hybridization between the spin precession in the low frequency left-handed mode with cavity resonator photons and its temperature dependence via recording the corresponding ISHE voltages. We measure a CMP in Cr2O3 at 150 K and we observe several, small couplings to resonator modes below the spin flop field at 6 T. For instance, for a resonator mode ~39.6 GHz, we find a coupling strength of approximately 50 MHz. For the spin pumping experiment, we find a non-monotonous temperature dependence of the ISHE voltage signal with a peak at 30 K of the low frequency left-handed mode. The opposite signs of the ISHE voltages between the left-handed mode of Cr2O3 and the right-handed mode of ferrimagnetic YIG confirm the mode polarity. We compare our findings to the work of J.Li et al., who studied the temperature dependence of the high frequency right-handed mode of Cr2O3 [8]. We find qualitatively the same temperature dependence towards higher signals with the signal vanishing above 100 K as the net spin current polarization decreases to higher temperatures [8]. Hence, we study the spin dynamics of our model system Cr2O3 for GHz frequencies based on electrical detection and light matter interaction. Notably, establishing antiferromagnets in cavity spintronics could bridge frequency regimes from the GHZ to the optical range. Further, the demonstration of a coupling and, eventually, coherent information exchange is a promising way towards quantum information processing schemes with antiferromagnets [9].

**References:**

[1] V. Baltz, A. Manchon, M. Tsoi et al., Rev. Mod. Phys, 90, 015005 (2018). [2] T. Kampfrath, A. Sell, G. Klatt et al., Nat. Photonics 5, 31 (2011). [3] Y. Tserkovnyak, A. Brataas, and G. E. W. Bauer, Phys. Rev. B 66, 224403 (2002). [4] M. V. Costache, M. Sladkov, S. M. Watts et al., Phys. Rev. Lett. 97, 216603 (2006). [5] M. Harder and C. M. Hu, Solid State Physics, 69, 47 - 121 (2018). [6] E. Saitoh, M. Ueda, H. Miyajima et al., Appl. Phys. Lett. 88, 182509 (2006). [7] D. Lachance-Quirion, Y. Tabuchi, A. Gloppe et al., Appl. Phys. Expr. 12, 070101 (2019). [8] J. Li, C. B. Wilson, R. Cheng et al., Nature 578, 7793 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/64f1679716243edc0e3b382587c8dbac.jpg)
Dispersion relation of the CMP for a bulk chromium oxide sample (Cr2O3 ) at 150 K with several couplings for higher frequencies across the spin flop field at ~6 T. Inset displays the gradient calculated from the amplitude spectrum in the main. It shows expemplarily a zoom on one clearly separated anticrossing at 39.6 GHz with a coupling strength of ~50 MHz.

![](https://assets.underline.io/uploads/markdown_image/1/image/9eb4756535fc1148c73ad825bbc5330a.jpg)
Temperature dependence of the ISHE voltage from spin pumping with the same crystal up to 100 K.

 Cavity Magnon Polaritons and Inverse Spin Hall Effect in Easy-Axis Antiferromagnets

In the paramagnetic space group of Mn2Au, the two Mn atoms are connected by inversion symmetry. However, in the antiferromagnetically (AFM) ordered state the inversion symmetry is broken. Our ab-initio calculated energy bands show the corresponding coupling of the energy bands to the Néel vector direction [Elm20], which is significant due to the strong spin-orbit interaction in Mn2Au. Here, we focus on the experimental investigation of the Néel vector alignment induced anisotropies in the electronic band structure by angular resolved photoemission spectroscopy (ARPES). We investigate epitaxial Mn2Au(001) thin films [Jou15, Bom20], with photon energies in the vacuum-ultraviolet, soft, and hard X-ray range [Elm20]. Our samples consist in the as grown state of AFM domains with the Néel vector equally distributed parallel to both magnetic easy axes [110] and [1-10] of the tetragonal crystal structure. To enable the observation of Néel vector orientation induced symmetry breaking, we align the staggered magnetization by a 50 T magnetic field pulse via a spin-flop transition parallel to one of the two easy axis [Sap18]. Thus, in the ARPES experiments, we see the effect of averaging over AFM domains with antiparallel Néel vector, resulting in a 2-fold symmetry of the electronic states within the ab-plan of the tetragonal crystal structure. We observed a maximum asymmetry of ≈10 % probed by bulk-sensitive hard X-ray photoemission spectroscopy (probing depth ≈5 nm) at a binding energy of 0.25 eV (see Fig. 1), which is reduced to ≈5 %, if probing with more surface sensitive soft X-rays (probing depth ≈1 nm). Additionally, probing uncapped samples even more surface sensitive with vacuum-ultraviolet light reveals a maximum spin−orbit interaction induced band splitting of ≈100 meV. These anisotropies can lead to large magnetoresistance, transport and topological effects [Elm20].

**References:**

[Bom20] S. P. Bommanaboyena et al., J. Appl. Phys. 127, 243901 (2020). [Elm20] H.-J. Elmers et al., ACS Nano, 14, 17554 (2020). [Jou15] M. Jourdan et al., J. Phys. D: Appl. Phys. 48, 385001 (2015). [Sap18] A. A. Sapozhnik et al., Phys. Rev. B 97, 134429 (2018).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/e90e587c9dd42f4b1e6b792f6778d469.jpg)
Experimental photoemission results (upper panels) for two epitaxial Mn2Au sample halves with the staggered magnetization aligned vertically (a) and horizontally (b) as indicated on the real space unit cells. The intensities are represented as constant energy sections I(EB, kx, ky) at a binding energy of 0.25 eV. The photon energy is 5230 eV. The lower panels show corresponding calculations of the spectral function densities, averaging over two antiparallel directions of the Néel vector.

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