France



The recent development of techniques (various methods of deposition have been used),enabling the elaboration of very thin epitaxial YIG films has brought a renewed interest for exploiting the resonance properties of such films. When the thin YIG film is coated with a heavy metal (such as Pt), a non local extra damping of the microwave magnetization is observed [associated to the (YIG/Pt) interfacial coupling].Different techniques [1,2] of microwave absorption measurements have been used to characterize the resonance properties of such films. We highlight here basic results we have obtained in our &lt;i&gt;cavity-FMR studies&lt;/i&gt; at X-band (9.725 GHz) on the 5 films whose characteristics are given below. These films correspond to (111) oriented YIG layers deposited by LPE [3] on GGG substrates. We have: F1 [YIG58], F2 [YIG44], F3 [YIG15], with thicknesses in nm, corresponding to the virgin YIG layers. Films F4 [YIG15/Pt3] and F5 [YIG58/Pt3] refer, respectively, to films F3 and F4 which have been coated by a Pt (3nm) over layer deposited by evaporation.&lt;br/&gt;We performed a detailed study of the angular variation of the resonance spectrum (angle θ&lt;sub&gt;H &lt;/sub&gt;of the dc field with the film normal) and we exploit the main characteristics of the observed resonance lines. A basic observation in these YIG films is that the resonance spectrum corresponds indeed to the superposition of individual resonances (arising from different parts of the film, weakly coupled by the dipolar interactions). We summarize below the results obtained for the main characteristics (Hres , linewidth ΔH) of the &lt;i&gt;principal resonance&lt;/i&gt;.&lt;br/&gt;&lt;i&gt;Angular variation of Hres&lt;/i&gt; : results and analysis&lt;br/&gt;In perpendicular (PER) geometry, the resonance condition reads [4, 5]: (ω/γ) = H&lt;sub&gt;PER &lt;/sub&gt;– Heff (Eq.1), where Heff = 4πM - H&lt;sub&gt;A &lt;/sub&gt;– 2/3 H&lt;sub&gt;an &lt;/sub&gt;, with H&lt;sub&gt;A &lt;/sub&gt;= 2K/M a uniaxial perpendicular anisotropy (spin-orbit origin) and H&lt;sub&gt;an &lt;/sub&gt;= 2K&lt;sub&gt;1 &lt;/sub&gt;/M the YIG cubic anisotropy. Taking the measured value for 4πM and the bulk value for H&lt;sub&gt;an &lt;/sub&gt;(- 87 Oe), we get for the 3 virgin YIG films: F1: (- H&lt;sub&gt;A&lt;/sub&gt;) = 37 Oe (easy plane); F2: H&lt;sub&gt;A &lt;/sub&gt;= 48 Oe (easy &lt;i&gt;axis&lt;/i&gt;); F3: H&lt;sub&gt;A &lt;/sub&gt;= 130 Oe (easy axis). One observes thus that the uniaxial perpendicular anisotropy changes sign versus the YIG thickness.&lt;br/&gt;&lt;i&gt;Linewidth ΔH of the principal resonance&lt;/i&gt; : angular variation and analysis&lt;br/&gt;The linewidth ΔH of the principal resonance is the sum of two different contributions: ΔH = Δ+ ΔH&lt;sub&gt;inh &lt;/sub&gt;. The first one (Δ) corresponds to the relaxation rate of the magnetization vector (proportional to the &lt;i&gt;intrinsic damping&lt;/i&gt; parameter α). The second one is an inhomogeneous width corresponding to a distribution ΔHres .The basic observation for the virgin YIG layers is that ΔH displays a &lt;i&gt;sharp minimum&lt;/i&gt; at a specific field orientation θ&lt;sub&gt;H &lt;/sub&gt;where it reduces to the &lt;i&gt;intrinsic width&lt;/i&gt; Δ .This behavior is well accounted for theoretically [ref 4], where the inhomogeneous contribution induced by a distribution P(Hi) has been discussed (where Hi = 4πM - H&lt;sub&gt;A&lt;/sub&gt;). Thus for F2 we find Δ= 0.8 Oe [leading to α= 2 x 10&lt;sup&gt;-4 &lt;/sup&gt;] . Intrinsic width for the films F4 and F5 coated by a Pt(3nm) overlayer :&lt;br/&gt;Δ may be decomposed as: Δ= Δ&lt;sub&gt;0 &lt;/sub&gt;+ Δ&lt;sub&gt;S&lt;/sub&gt;, where the second term corresponds to the increment of the damping induced by the (YIG/Pt) interfacial coupling .We find Δ&lt;sub&gt;S&lt;/sub&gt;(F5) = 1.57 Oe and Δ&lt;sub&gt;S&lt;/sub&gt;(F4) = 5.25 Oe varying approximately as (1/t) with the YIG thickness t .&lt;br/&gt;&lt;br/&gt;&lt;i&gt;Characteristics of the resonance spectra&lt;/i&gt; : remarkable phenomena observed&lt;br/&gt;A) For the virgin thick (58nm)YIG layer (filmF1),in a broad range of field orientations, the FMR spectrum displays a &lt;i&gt;fine structure&lt;/i&gt;: on superposition of the principal resonance, a series of regularly spaced narrow (0.8 Oe) resonance lines are observed. We ascribe them to standing elastic waves, excited in the YIG layer through the &lt;i&gt;magneto-elastic coupling&lt;/i&gt; [6], which develop across the whole sample [500µm thick GGG substrate +YIG layer].Taking into account the transverse sound velocity in such a medium, the estimated frequency splitting (3.5 MHz) between two successive waves is well consistent with the observed field splitting (~1.2 Oe) between the individual resonance lines.&lt;br/&gt;B) For the two thin (15 nm) YIG layers (films F3 and F4),besides the principal resonance, two standing spin waves (we label SW1 and SW2) are observed in the resonance spectrum. These spin waves are collective modes associated to the &lt;i&gt;non-uniform exchange &lt;/i&gt;in the YIG films. Such standing spin waves are here observed since the YIG layer thickness is comparable to the YIG exchange length (18nm).The resolved spin wave spectrum is observed continuously from the PAR to the PER geometry, except for a specific orientation (31 deg for F2) where it collapses to the &lt;i&gt;uniform mode&lt;/i&gt;.

**References:**

[1] Y. Sun et al, Phys.Rev.Lett.111, 106601 (2013).&lt;br/&gt;[2] C. Du et al, Phys.Rev. Applied. 1, 044004 (2014).&lt;br/&gt;[3] N. Beaulieu et al, IEEE Magn. Letter.9, 3706005 (2018).&lt;br/&gt;[4] H. Hurdequint, J.Magn.Magn.Mater. 242-245 , 521 (2002).&lt;br/&gt;[5] H. Makino and Y.Hidaka, Mat.Res.Bull. Vol16 , pp 957-966 (1981).&lt;br/&gt;[6] A.Gurevich and G. Melkov,Magnetization oscillations and Waves, CRC Press (1996).

**Images:**





INTERMAG 2021

 Cavity-FMR studies of LPE epitaxial YIG films

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The recent development of techniques (various methods of deposition have been used),enabling the elaboration of very thin epitaxial YIG films has brought a renewed interest for exploiting the resonance properties of such films. When the thin YIG film is coated with a heavy metal (such as Pt), a non local extra damping of the microwave magnetization is observed [associated to the (YIG/Pt) interfacial coupling].Different techniques [1,2] of microwave absorption measurements have been used to characterize the resonance properties of such films. We highlight here basic results we have obtained in our cavity-FMR studies at X-band (9.725 GHz) on the 5 films whose characteristics are given below. These films correspond to (111) oriented YIG layers deposited by LPE [3] on GGG substrates. We have: F1 [YIG58], F2 [YIG44], F3 [YIG15], with thicknesses in nm, corresponding to the virgin YIG layers. Films F4 [YIG15/Pt3] and F5 [YIG58/Pt3] refer, respectively, to films F3 and F4 which have been coated by a Pt (3nm) over layer deposited by evaporation. We performed a detailed study of the angular variation of the resonance spectrum (angle θH of the dc field with the film normal) and we exploit the main characteristics of the observed resonance lines. A basic observation in these YIG films is that the resonance spectrum corresponds indeed to the superposition of individual resonances (arising from different parts of the film, weakly coupled by the dipolar interactions). We summarize below the results obtained for the main characteristics (Hres , linewidth ΔH) of the principal resonance. Angular variation of Hres : results and analysis In perpendicular (PER) geometry, the resonance condition reads [4, 5]: (ω/γ) = HPER – Heff (Eq.1), where Heff = 4πM - HA – 2/3 Han , with HA = 2K/M a uniaxial perpendicular anisotropy (spin-orbit origin) and Han = 2K1 /M the YIG cubic anisotropy. Taking the measured value for 4πM and the bulk value for Han (- 87 Oe), we get for the 3 virgin YIG films: F1: (- HA) = 37 Oe (easy plane); F2: HA = 48 Oe (easy axis); F3: HA = 130 Oe (easy axis). One observes thus that the uniaxial perpendicular anisotropy changes sign versus the YIG thickness. Linewidth ΔH of the principal resonance : angular variation and analysis The linewidth ΔH of the principal resonance is the sum of two different contributions: ΔH = Δ+ ΔHinh . The first one (Δ) corresponds to the relaxation rate of the magnetization vector (proportional to the intrinsic damping parameter α). The second one is an inhomogeneous width corresponding to a distribution ΔHres .The basic observation for the virgin YIG layers is that ΔH displays a sharp minimum at a specific field orientation θH where it reduces to the intrinsic width Δ .This behavior is well accounted for theoretically [ref 4], where the inhomogeneous contribution induced by a distribution P(Hi) has been discussed (where Hi = 4πM - HA). Thus for F2 we find Δ= 0.8 Oe [leading to α= 2 x 10-4 ] . Intrinsic width for the films F4 and F5 coated by a Pt(3nm) overlayer : Δ may be decomposed as: Δ= Δ0 + ΔS, where the second term corresponds to the increment of the damping induced by the (YIG/Pt) interfacial coupling .We find ΔS(F5) = 1.57 Oe and ΔS(F4) = 5.25 Oe varying approximately as (1/t) with the YIG thickness t . Characteristics of the resonance spectra : remarkable phenomena observed A) For the virgin thick (58nm)YIG layer (filmF1),in a broad range of field orientations, the FMR spectrum displays a fine structure: on superposition of the principal resonance, a series of regularly spaced narrow (0.8 Oe) resonance lines are observed. We ascribe them to standing elastic waves, excited in the YIG layer through the magneto-elastic coupling [6], which develop across the whole sample [500µm thick GGG substrate +YIG layer].Taking into account the transverse sound velocity in such a medium, the estimated frequency splitting (3.5 MHz) between two successive waves is well consistent with the observed field splitting (~1.2 Oe) between the individual resonance lines. B) For the two thin (15 nm) YIG layers (films F3 and F4),besides the principal resonance, two standing spin waves (we label SW1 and SW2) are observed in the resonance spectrum. These spin waves are collective modes associated to the non-uniform exchange in the YIG films. Such standing spin waves are here observed since the YIG layer thickness is comparable to the YIG exchange length (18nm).The resolved spin wave spectrum is observed continuously from the PAR to the PER geometry, except for a specific orientation (31 deg for F2) where it collapses to the uniform mode.

**References:**

[1] Y. Sun et al, Phys.Rev.Lett.111, 106601 (2013). [2] C. Du et al, Phys.Rev. Applied. 1, 044004 (2014). [3] N. Beaulieu et al, IEEE Magn. Letter.9, 3706005 (2018). [4] H. Hurdequint, J.Magn.Magn.Mater. 242-245 , 521 (2002). [5] H. Makino and Y.Hidaka, Mat.Res.Bull. Vol16 , pp 957-966 (1981). [6] A.Gurevich and G. Melkov,Magnetization oscillations and Waves, CRC Press (1996).

**Images:**

poster

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

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.

 Néel vector alignment induced symmetry breaking in the electronic band structure of the antiferromagnet Mn2Au

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.

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

Among nanomaterials, metal nanowires (NWs), consisting of alternating layers of various compositions (layered NWs), are of particular interest. Such structures can be obtained by the method of matrix synthesis - filling of nanosized pores in a special matrix. Layered NWs can have various applications, for example, as optically active surfaces (SERS). Another practically important property is giant magnetoresistance (GMR). According to preliminary estimates, NWs consisting of alternating layers of various magnetic metals can also be used to generate electromagnetic radiation. It is known that when current passes through the magnetic layer, its spin polarization occurs. When this current flows through subsequent layers, a change in the energy state of the electrons is possible. Relaxation of this state can lead to the generation of electromagnetic radiation, in particular, terahertz frequency. In this work, NWs arrays consists of several (three) layers (for example- Ni/Co/Ni ) were grown from aqueous solutions of corresponding metal salts, using “two-bath” electrochemical approach. A track membrane with a pore diameter of 100 nm was used as a matrix. Particular attention was paid to the method of bringing contacts to the resulting array of layered NWs. When passing a current through such arrays, a signal with a frequency of 15-25 THz was detected. The measurements were carried out on a Golay cell and a Bruker spectrometer. It was found that with the standard method of making the contacts (a thin flat layer over the entire surface), the generated signal is not stable. Local burnout of a thin conductive layer occurs. To solve this problem, a method was proposed for forming contacts in the form of discontinuous periodic stripes. This method also made it possible to change the total effective electrical resistance of the array. An example of the obtained sample with contact strips is shown in Fig. 1. An SEM image of an array of layered NW is also shown. Fig. 1. SEM image of the sample surface with separate strips-current leads (left); SEM image of an array of layered NW between two contact layers (right). Figure 2 shows the generation signal and its dependence on time (for the NWs array and the GLOBAR (heat source)). Fig. 2. Left- Signal intensity versus time: 1- NWs array, 2- heat source-GLOBAR; On the right, the figure shows the nature of the angular distribution of the signal intensity. Comparison of the dependence of the signal intensity on time for the NWs array and for the heat source shows a sharp increase of the signal in the first case. This proves the nonthermal nature of the signal that arises when current flows through an array of NWs with magnetic transitions. The paper also provides a theoretical assessment of the possibility of using such an NWs array to solve the inverse problem, namely, to obtain a THz radiation detector.

**References:**



**Images:**

 Magnetic nanowires as a source of irradiation of THz frequency

Spin-torque oscillators (STOs) have been extensively studied due to their potential applications in hardware neural networks [1]. For future practical STO devices, multiple magnetic tunnel junctions in series are demanded. Because it will involve a complicated stack structure, there are very limited experimental attempts so far. In this work, the spin-torque oscillation modes of a composite synthetic antiferromagnetic free layer in dual magnetic tunnel junctions with MgO barriers are studied experimentally by analyzing its field- and current-dependent power spectra. Two oscillation modes are observed under different magnetic fields and bias currents due to the unique layer structure as follows: seed layer/PtMn/Co70Fe30/Ru/Co60Fe20B20/MgO/Co20Fe60B20/Ru/Co20Fe60B20/MgO/Co60Fe20B20/Ru/Co70Fe30/PtMn/capping layer. With increasing field, the first mode shows a frequency reduction at low magnetic fields followed by an increasing frequency at high magnetic fields, while the second mode reveals a frequency increase at both low and high magnetic fields (Fig. 1(b)). The current-dependent power spectra of these two modes are also different. With increasing current, the frequency of the first mode drops at low magnetic fields (Fig. 2(a)) and rises at high magnetic fields (Fig. 2(c)), while the other decreases at low and high magnetic fields. These two modes could be tentatively understood by considering the coupling, the bias asymmetry of the spin torque, and the different thicknesses of Co20Fe60B20 in the composite synthetic antiferromagnetic free layer.

**References:**

[1] M. Romera, P. Talatchian, S. Tsunegi et al., Nature, Vol. 563, p. 230, (2018).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/5e2f10db377ec008ba72f706161f7df6.jpg)
Fig. 1 (a) The power spectral density of the free layer measured at the current of 0.3 mA and the bias fields of 400, 800, and 1000 Oe. The hollow signs are experimental results. The solid curves are Lorentzian fittings. (b) The power spectral density of the free layer as a function of magnetic field from 0 to 1100 Oe. The triangles and the crosses correspond to the frequencies of the two modes.

![](https://assets.underline.io/uploads/markdown_image/1/image/ec7159002dc17d22c71088883f41636f.jpg)
Fig. 2 The current-dependent power spectral density of the two modes measured at the magnetic fields of (a) 400 Oe, (b) 800 Oe, and (c) 1000 Oe. The triangles are the frequencies of the first mode, and the crosses are the frequencies of the second mode.

 Spin-Torque Oscillation Modes of a Composite Synthetic Antiferromagnetic Free Layer in Dual Magnetic Tunnel Junctions

Up-to-date technologies require modern information devices to process large amounts of data at high rates. Methods of the ultrafast magnetism are very promising in this respect since they allow controlling the magnetization of a magnetic material by the femtosecond laser pulses at a picosecond time scales. Ferrimagnetic alloy of gadolinium-iron-cobalt (GdFeCo) is one of the most promising materials for further development of the information storage devices, since it allows to perform a single-shot all-optical magnetization switching during a few picoseconds in the area of pulse action on the GdFeCo film. A mechanism of all-optical switching originates from the ultrafast spin dynamics of the exchange-coupled Gd and FeCo sublattices which are thrown out of balance due to the light-induced thermal heating of the spin sublattices. If the delivered energy exceeds the threshold, the magnetizations of the two sublattices are reversed at the picosecond timescales due to the difference of the relaxation times for these sublattices. Thus, ultrafast all-optical magnetization switching depends on the amount of energy delivered by the optical pulse and is characterized by a threshold femtosecond pulse intensity required for the magnetization switching. Nowadays many efforts are put to study how to control the process of all-optical switching via tailoring the properties of the femtosecond pulse and via the additional patterning of the magnetic structure. In this work we propose a design of photonic nanostructure where the parameters of the dielectric layers determine the spatial light distribution and the resonances of the absorption in the GdFeCo layers. We propose to use the magnetophotonic crystal (MPC) structures, that were shown to perform tunable localization of light at the resonant frequencies enabling the enhancement of the optomagnetic interaction in a magnetic material. The proposed magnetophotonic crystal with thin smooth or patterned layers of GdFeCo ferrimagnetic alloy provides the local magnetization control and targeted remagnetization of the single layers of the multilayer structure. By the frequency tuning of the input femtosecond laser pulses one can select the magnetic layer of GdFeCo in which the energy of the laser pulse is mostly concentrated and exceeds the magnetization reversal threshold, while in others it is 1.5-2 times lower. In other words, the proposed MPC allows to ‘turn on’ one certain magnetic layer of the structure and leave all other layers ‘turned off’. As GdFeCo material is perspective for data storage applications allowing a significant increase of the writing speed, the proposed structure can be implemented for the purposes of the record density increase in such a device. Usually, the magnetic bit cells are arranged in the plane of a single magnetic layer. Using the proposed MPC, bit cells can be arranged in several magnetic layers separated by the submicron dielectric spacers and addressed individually. This configuration is quite simple for fabrication and doesn’t require a precise positioning of the laser pulse. Besides that, another configuration of the chirped MPC structure with the patterned GdFeCo layers is addressed. For the higher density of the information recording the magnetic layer can be nanostructured to separate bit cells in the lateral direction. The patterning of the magnetic layer can be implemented along both axes in the plane of the structure layers. In our work we limited ourselves by one-dimensional patterning for the sake of the modelling simplicity. It should be stressed that the patterned chirped MPC allows combining two approaches instantaneously, the bit cells arranged in plane and the bit cells arranged in different layers. It opens up the ample opportunities for the significant increase of the information recording density. We also provide the method of an all-optical single-wavelength information reading in this multilayered structure. Thus, the designed MPC with GdFeCo layers could serve as a basis of 3D information storage devices. To sum up, a design of the MPC structure providing a selective magnetization switching in the different magnetic layers at different frequencies is proposed. The MPC contains the thin layers of GdFeCo as magnetic counterparts. By illuminating the MPC by femtosecond laser pulses at the certain frequencies we create the conditions for the highest concentration of the electromagnetic field in the necessary layer of the structure while in the other GdFeCo layers the intensity is at least 1.5 times smaller. Thus, one can achieve selective all-optical magnetization reversal in a single layer of the multilayered stack determined by the laser frequency without any impact on the other layers. The magnetic layers of the MPC are separated from each other by the non-magnetic layers, and can be patterned, so, they can serve as the unit cells for information storage. We also provide a mechanism of single-wavelength reading of the information stored in such a multilayered stack. The approach was demonstrated for the 4 layers of SiO2, TiO2 and GdFeCo for the sake of simplicity, however it could be extended to the larger number of layers by the proper design of the chirped photonic crystal. The work was supported by Russian Science Foundation, grant No. 19-72-10139.

**References:**

A. Kirilyuk, A.V. Kimel, T. Rasing. Rev. Mod. Phys. Vol. 82, p. 2731 (2010). A.V. Kimel, A. Kirilyuk, P.A. Usachev, et al. Nature Vol. 435, p. 655 (2005). J.Y. Bigot, M. Vomir, E. Beaurepaire. Nature Physics Vol. 5, p. 515 (2009). A.I. Chernov, M.A. Kozhaev, D.O. Ignatyeva, et al. Nano Letters Vol. 20, p. 5259 (2020). U. Atxitia, T.A. Ostler. Appl. Phys. Lett. Vol. 113, p. 062402 2018). M. Inoue, et al. J. Phys. D. Appl. Phys. Vol. 39, p. R151 (2006).

**Images:**

 Chirped Photonic Crystals with GdFeCo for Layer-Selective Magnetization Control

Spin control in magnetic materials is a fundamental basis of the most current energy efficient devices, such as magnetic memory, Boolean and quantum logical elements [1]. In the last few decades, femtosecond laser systems opened up opportunities for ultrafast spin control in various magnetic materials such as ferromagnetic metals, iron garnets, and even antiferromagnetic dielectric oxides [2]. Special attention is paid to nonthermal spin wave control via inverse magnetooptical effects, such as inverse Faraday, inverse transverse magnetooptical Kerr, or inverse Voigt effects. Moreover, recent advances in fabrication techniques provide capabilities for light localization at the nanoscale regions together with optical modes excitation in the nanostructures [3,4]. The aforementioned advances of the nanostructures increase the efficiency of light-matter interaction and bring new horizons to all-optical spin control in magnetic materials. Here we report on spin wave amplitude enhancement in all-dielectric iron garnet nanostructure based on one-dimensional iron garnet grating. The grating consists of solitary strips of 400 nm width on gadolinium gallium garnet substrate placed with subwavelength period (600 nm). The height of the nanostructure was 225 nm. For spin wave launch pump-probe technique is utilized in Voigt configuration [2]. For pumping a circularly polarized pulse of ~200 fs duration at 600 nm and normal incidence was used. Probe pulse of 200 fs duration at 820 nm (transparency region of the structure) was linearly polarized. The probe angle of incidence was ~30 deg. The external magnetic field was equal to 100 mT. The nanostructure support propagation of waveguiding modes that are well defined in transmittance spectra at ~600 nm (Figure 1). The electromagnetic field localization and enhancement inside the nanostrips due to waveguiding mode excitation result in spin wave amplitude enhancement (up to 2 times). Moreover, as can be noted from figure 2 there is a shift in spin wave frequency between pure film and nanostructure. The effect can be associated with the existence of additional boundaries between magnetic strips and external media. This work was financially supported by the Russian Ministry of Education and Science, Megagrant project N 075-15-2019-1934

**References:**

1. A. V. Chumak et. al. Nature Physics, Vol. 11(6), p. 453, (2015) 2. A. Kirilyuk et. al. Reviews of Modern Physics, Vol. 82(3), p. 2731, (2010). 3. A. I. Chernov et. al. Nano Letters, Vol. 20(7), p. 5259, (2020). 4. A. L. Chekhov et. al. Nano letters, Vol. 18(5), p. 2970, (2018).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/ff4ec02eadaa48a1da002f1ada82a1fc.jpg)
Figure 1 Transmission of the nanostructure as a function of incident angle and wavelength

![](https://assets.underline.io/uploads/markdown_image/1/image/0f50b3bfdc75944256271a9c07bf3f25.jpg)
Figure 2 Spin wave precession for a pristine garnet film of 225 nm thickness (black) and nanostructure (red)

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