France



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 Mn&lt;sub&gt;5&lt;/sub&gt;Si&lt;sub&gt;3&lt;/sub&gt; [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.&lt;br/&gt;&lt;br/&gt;In our presentation, we aim to experimentally demonstrate the presence of the even contribution to transversal resistance in a low-symmetry antiferromagnetic phase of Mn&lt;sub&gt;5&lt;/sub&gt;Si&lt;sub&gt;3&lt;/sub&gt; 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&lt;br/&gt;&lt;br/&gt;Mn&lt;sub&gt;5&lt;/sub&gt;Si&lt;sub&gt;3&lt;/sub&gt; is a compensated antiferromagnet that can order both collinearly and non-collinearly in different temperature regimes, with the two phase transitions at T&lt;sub&gt;N1&lt;/sub&gt; ≈ 70 K and T&lt;sub&gt;N2&lt;/sub&gt; ≈ 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 Mn&lt;sub&gt;5&lt;/sub&gt;Si&lt;sub&gt;3&lt;/sub&gt; 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 (ρ&lt;sub&gt;xx&lt;/sub&gt;) and transverse (ρ&lt;sub&gt;xy&lt;/sub&gt;) resistivities were measured simultaneously as a function of external magnetic field B&lt;sub&gt;z, &lt;/sub&gt;applied in the out-of-plane direction.&lt;br/&gt;The longitudinal and transverse signals measured at two different temperatures corresponding to the collinear (180 K) and non-collinear (40 K) antiferromagnetic phase of Mn&lt;sub&gt;5&lt;/sub&gt;Si&lt;sub&gt;3&lt;/sub&gt;, 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 ρ&lt;sub&gt;xy&lt;/sub&gt; by subtracting the signal linear in B&lt;sub&gt;z.&lt;/sub&gt;&lt;br/&gt;The longitudinal signal Δρ&lt;sub&gt;xx &lt;/sub&gt;(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].&lt;br/&gt;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 B&lt;sub&gt;z&lt;/sub&gt; 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 ρ&lt;sub&gt;xx &lt;/sub&gt;and even ρ&lt;sub&gt;xy &lt;/sub&gt;by subtraction the normalized curves, i.e. Δρ(B&lt;sub&gt;z&lt;/sub&gt;) = ρ&lt;sub&gt;xx&lt;/sub&gt;(B&lt;sub&gt;z&lt;/sub&gt;)/ ρ&lt;sub&gt;xx&lt;/sub&gt;(0) - Δρ&lt;sup&gt;(sym)&lt;/sup&gt;&lt;sub&gt;xy&lt;/sub&gt;(B&lt;sub&gt;z&lt;/sub&gt;)/ ρ&lt;sup&gt;(sym)&lt;/sup&gt;&lt;sub&gt;xy&lt;/sub&gt;(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.&lt;br/&gt;&lt;br/&gt;This observation is in agreement with the assumed lowering of the symmetry in the non-collinear phase of Mn&lt;sub&gt;5&lt;/sub&gt;Si&lt;sub&gt;3&lt;/sub&gt;. 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 Mn&lt;sub&gt;5&lt;/sub&gt;Si&lt;sub&gt;3&lt;/sub&gt;. The transversal voltage does not need to show purely antisymmetric elements.

**References:**

[1] N. Nagaose et al., Rev. Mod. Phys. 82, 1539 (2010)&lt;br/&gt;[2] S. Nakatsuji, N. Kiyohara, and T. Higo, Nature 527, 212-215 (2015)&lt;br/&gt;[3] Ch. Surges et al., Nat. Comm. 5, 3400 (2015)&lt;br/&gt;[4] H. Reichlova et al., arXiv:2012.15651v1 (2020)&lt;br/&gt;[5] https://arxiv.org/abs/2002.08712&lt;br/&gt;[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 B&lt;sub&gt;z &lt;/sub&gt;at two different temperatures, corresponding to the collinear (180 K) and non-collinear (40 K) phase of Mn&lt;sub&gt;5&lt;/sub&gt;Si&lt;sub&gt;3&lt;/sub&gt;.

![](https://assets.underline.io/uploads/markdown_image/1/image/fe910a604ff8e4df2548b44104926b42.jpg)
Fig. 2. (a) symmetrized and (b) antisymmetrized components of transverse resistance data in Mn&lt;sub&gt;5&lt;/sub&gt;Si&lt;sub&gt;3&lt;/sub&gt; measured at 40 K and 180 K, respectively. Panel (c) demonstrates the difference in shape by subtracting normalized curves for ρ&lt;sub&gt;xx&lt;/sub&gt;(B&lt;sub&gt;z&lt;/sub&gt;) and ρ&lt;sup&gt;(sym)&lt;/sup&gt;&lt;sub&gt;xy&lt;/sub&gt;(B&lt;sub&gt;z&lt;/sub&gt;).

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 Symmetry of transversal conductivity signal in antiferromagnetic Mn5Si3

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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).

technical paper

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

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

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

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

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