United States

Soft actuators are required to deform, fold, or unfold in order to interact with their surroundings.[1] One strategy to achieve the movement of mechanically soft systems is
the use of magnetic fields for untethered actuation. Flexible magnetic composites have been demonstrated as functional grippers, rollers, and walkers upon applied external magnetic fields.
[2] Being controlled with electromagnetic coils, magnetic actuators can profit from high-speed actuation to quickly respond to their environment.[3]
The development of an appropriate sensory tracking system for soft actuators is a research topic with open challenges. Light, conformal, and mechanically imperceptible sensing systems
are to be developed to be compatible with soft actuators. In this work, we present flexible magnetosensitive electronic skin which relies on thin-film magnetic field sensors to enable
onboard folding control of origami-like soft actuators. The flexible electronic skin consists of thin film giant magnetoresistive GMR and Hall effect sensors that are used to measure the
magnetization state of the actuator, the applied magnetic fields, and the completeness of the bending process. The resulting intelligent material is mechanically designed to fold even when
the flexible magnetic skin is attached to the soft actuator.[4]
The magnetic origami actuators are made of thin DiAPLEX foils, a shape memory polymer, with embedded NdFeB particles. Such composite can be used to achieve magnetically induced
motion using magnetic fields and a directed light source to increase locally the temperature. We experimentally found the best thickness (60 μm) and concentration (40 NdFeB wt%)
parameters to achieve magnetic folds.[4]
The integration of magnetic soft actuators with e-skins allowed the self-guided assembly of the origami foils. We showed two case studies showing that this approach is useful for
assembling boxes and boat-like origami shapes. This integration process was monitored, followed, and controlled by the output of the laminated sensors. [4]&lt;br&gt;

**References:**&lt;br&gt;

[1] A. Miriyev, K. Stack, H. Lipson, et al. Nat. Commun., Vol. 8, p.596 (2017)&lt;br&gt;
[2] S. Wu, W. Hu, Q. Ze, et al. Multifunct. Mater. Vol. 3, p.042003 (2020)&lt;br&gt;
[3] X. Wang, G. Mao, G. Jin, et al. Commun. Matter. Vol. 1, p.67 (2020)&lt;br&gt;
[4] M. Ha, G.S. Cañón Bermúdez, J.A.-C- Liu, et al. Adv. Mater. Vol. 33, p.2008751 (2021)&lt;br&gt;



MMM 2022

Magnetically Sensitive Electronic Skins for Supervised Folding of Origami Actuators

Soft actuators are required to deform, fold, or unfold in order to interact with their surroundings.[1] One strategy to achieve the movement of mechanically soft systems is
the use of magnetic fields for untethered actuation. Flexible magnetic composites have been demonstrated as functional grippers, rollers, and walkers upon applied external magnetic fields.
[2] Being controlled with electromagnetic coils, magnetic actuators can profit from high-speed actuation to quickly respond to their environment.[3]
The development of an appropriate sensory tracking system for soft actuators is a research topic with open challenges. Light, conformal, and mechanically imperceptible sensing systems
are to be developed to be compatible with soft actuators. In this work, we present flexible magnetosensitive electronic skin which relies on thin-film magnetic field sensors to enable
onboard folding control of origami-like soft actuators. The flexible electronic skin consists of thin film giant magnetoresistive GMR and Hall effect sensors that are used to measure the
magnetization state of the actuator, the applied magnetic fields, and the completeness of the bending process. The resulting intelligent material is mechanically designed to fold even when
the flexible magnetic skin is attached to the soft actuator.[4]
The magnetic origami actuators are made of thin DiAPLEX foils, a shape memory polymer, with embedded NdFeB particles. Such composite can be used to achieve magnetically induced
motion using magnetic fields and a directed light source to increase locally the temperature. We experimentally found the best thickness (60 μm) and concentration (40 NdFeB wt%)
parameters to achieve magnetic folds.[4]
The integration of magnetic soft actuators with e-skins allowed the self-guided assembly of the origami foils. We showed two case studies showing that this approach is useful for
assembling boxes and boat-like origami shapes. This integration process was monitored, followed, and controlled by the output of the laminated sensors. [4] 

**References:** 

[1] A. Miriyev, K. Stack, H. Lipson, et al. Nat. Commun., Vol. 8, p.596 (2017) 
[2] S. Wu, W. Hu, Q. Ze, et al. Multifunct. Mater. Vol. 3, p.042003 (2020) 
[3] X. Wang, G. Mao, G. Jin, et al. Commun. Matter. Vol. 1, p.67 (2020) 
[4] M. Ha, G.S. Cañón Bermúdez, J.A.-C- Liu, et al. Adv. Mater. Vol. 33, p.2008751 (2021)

technical paper

#### Welcome to the 67th Annual Conference on Magnetism and Magnetic Materials, MMM 2022!

The Conference was held from October 31 to November 4 and offers both in-person and on-demand content.

MMM 2022 is sponsored jointly by AIP Publishing and the IEEE Magnetics Society. Members of the international scientific and engineering communities interested in recent developments in fundamental and applied magnetism are invited to attend and contribute to the technical sessions. The technical program will include invited and contributed papers in oral and poster sessions, invited symposia, a tutorial, and several special sessions. This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

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This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

The ability of short-range proximity interactions to imbue magnetic functionality into otherwise nonmagnetic materials [1-3] has exciting prospects for devices that combine the optical and electrical properties of monolayer semiconductors with additional magnetic tuning parameters that couple directly to spin and valley pseudospin. The atomically-smooth surfaces that are nowadays routinely achieved with van der Waals (vdW) materials allow for nearly ideal interfaces between monolayer transition-metal dichalcogenide semiconductors (such as WSe2 or MoS2) and magnetic substrates (such as EuO or CrI3). Magnetic proximity interactions (MPIs) between atomically-thin semiconductors and two-dimensional magnets therefore provide a means to manipulate spin and valley degrees of freedom in nonmagnetic monolayers, without the use of applied magnetic fields. 

In such vdW heterostructures, MPIs originate in the nanometer-scale coupling between the spin-dependent electronic wavefunctions in the two materials, and historically their overall effect is regarded as an effective magnetic field acting on the semiconductor monolayer. Here we demonstrate that this picture, while appealing, is incomplete: The effects of MPIs in vdW heterostructures can be markedly asymmetric, in contrast to that from an applied magnetic field [4]. Valley-resolved optical reflection spectroscopy of MoSe2/CrBr3 vdW structures reveals strikingly different energy shifts in the K and K' valleys of the MoSe2, due to ferromagnetism in the CrBr3 layer. Strong asymmetry is observed at both the A- and B-exciton resonances. Density-functional calculations indicate that valley-asymmetric MPIs depend sensitively on the spin-dependent hybridization of overlapping bands, and as such are likely a general feature of such hybrid vdW structures. These studies suggest routes to selectively control specific spin and valley states in monolayer semiconductors. 
**References** [1] I. Zutic et al., Proximitized Materials, Materials Today, 22, 85 (2019).
[2] M. Gibertini et al., Magnetic 2D materials and heterostructures, Nat. Nanotechnol. 14, 408–419 (2019).
[3] K. F. Mak, J. Shan, D. Ralph, Probing and controlling magnetic states in 2D layered magnetic materials, Nat. Rev. Phys. 1, 646-661 (2019).
[4] J. Choi, C. Lane, J.-X. Zhu, S. A. Crooker, Asymmetric magnetic proximity interactions in MoSe2/CrBr3 van der Waals heterostructures, arXiv:2206.09958 

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Asymmetric Magnetic Proximity Interactions in Ferromagnet/Semiconductor van der Waals Heterostructures

Recent spintronics revealed that the intrinsic anomalous Hall effect (AHE) emerged from an interplay between the Berry curvature and the spin-orbit coupling. Because the Berry phase theory does not require a spontaneous magnetization for AHE (1), AHE can be applied to antiferromagnetic (AFM) materials. Recently, we reported the hysteresis of AHE voltage as a function of magnetic field for the Pt/AFM-Cr2O3/Pt trilayer (2). The observed AHE should not be simply interpreted because Cr2O3 is an insulator, and we proposed the spin chiral texture in the energy bands as an origin (3). To address the insight of AHE, the correlation with the magnetization is helpful (1), which is difficult for Cr2O3 due to its AFM nature. To address this issue, the spontaneous magnetization is induced in the Cr2O3 thin film by Al doping (4) and investigated the correlation with AHE.
Pt(2 nm)/Al-doped Cr2O3(200 nm) bilayer was fabricated on α-Al2O3(0001) substrate by a DC magnetron sputtering. Al was doped by the cosputtering with Cr in the Ar and O2 mixed gas. Composition ratio was determined by XRF: Al/Cr = 4/96. Structural characterizations revealed that each layer grew in Pt(111)/(Al,Cr)2O3(0001). Magnetization was measured by VSM. AHE was measured using the Hall device fabricated by photolithography and Ar ion milling.
Fig.1 shows the M-H curve and the AHE loop at 200 K for the perpendicular magnetic field. The spontaneous magnetization, ~18 emu/cc is similar to the previous report (4). Loops show the rectangular hysteresis showing the perpendicular magnetic anisotropy. Reversal fields are similar for two loops. Temperature dependences of the remanent magnetization Mr and the remanent anomalous Hall resistivity σxy are shown in Fig.2. Although Mr monotonically decreases with increasing temperature, σxy first increase, show the maximum and decrease again. The similar temperature dependence of σxy was reported for other systems where the AHE is associated with the Berry phase. This similarity supports the Berry phase origin of AHE at the Pt/Cr2O3 interface. 

**References:** 
(1) N. Nagaosa, J. Sinova, S. Onoda, et al., Rev. Mod. Phys. 82, 1539 (2010). 
(2) X. Wang, K. Toyoki, R. Nakatani, Y. Shiratsuchi, AIP Advances, 12, 035216 (2022). 
(3) T. Moriyama, Y. Shiratsuchi, T. Ono et al., Phys. Rev. Appl. 13, 034052 (2020). 
(4) T. Nozaki, M. Al-Mahdawi, Y. Shiokawa, et al., Phys. Status Solidi RRL, 12, 180036 (2018). 

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Anomalous Hall effect in Pt/(Al0.04Cr0.96)2O3 epitaxial bilayer

Spin accumulation, which is created by an electrical current flowing in a nanomagnet, affects the strength of spin-orbit interaction (SO) and anisotropy field Hani in a nanomagnet. The reduction of Hani and SO by the current may cause a magnetization reversal. As a result, the data, which is encoded into the current, is memorized by means of two equilibrium magnetization directions of the nanomagnet. Recently, we have developed a high-precision measurement method of Hani and coefficient of spin-orbit interaction kso [1]. kso is a numerical parameter characterizing the SO strength.
Figure 1 shows kso vs. Hani measured in FeCoB nanomagnets.The SO strength is larger in nanomagnet, which contains several ferromagnetic layers (shown by stars) in comparison with nanomagnets containing only one ferromagnetic layer(shown by triangles). It means that the SO strength depends on the number of interfaces. The SO strength increases with an increase of the number of FeB layers up to 5 FeB layers. Further increase of the number of FeB layers causes a decrease of kso due to accumulated interface roughness.
Figure 2 compares current dependency of Hani for a single and multilayer nanomagnet. In the multilayer nanomagnet with a strong SO, the reduction of Hani is large of about 25 % and is nearly independent of current polarity. In contrast, in the single- layer nanomagnet with a weak SO, Hani changes almost linearly with the current only with a small symmetrical contribution due to heating, but the change is small of about 6%. Even such a small change of Hani is sufficient for magnetization reversal, when the conditions for the parametric resonance are met [2,3]. 
**References** [1] https://www.youtube.com/watch?v=LmvYN5hG-90
[2] V. Zayets, arXiv:2104.13008 (2021).
[3] V. Zayets, IOA-07, MMM (2021)
 
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Peculiarities of measured dependencies of strength of spin orbit interaction and anisotropy field on current density in FeCoB nanomagnet

Spintronics is a promising field centered around next-generation devices that use electronic spin to store and manipulate information. Since there are no ohmic losses inherent in the transfer of spin â€“ for example in magnons or pure spin currents â€“ spintronic devices have the potential to be very energy efficient, and lots of efforts have been taken over the last few decades to apply spintronic principles to make â€˜beyond CMOSâ€™ devices. However, one of the major challenges in spintronics is to find material systems with efficient spin-to-charge conversion, and the lack of such model systems has kept practical, energy efficient spintronic applications from being realized. We propose a new pathway for discovering model systems with efficient spin-to-charge conversion in epitaxial oxide heterostructures. We present on one such system, BaPb1-xBixO3 / La0.7Sr0.3MnO3 (BPBO/LSMO), grown by pulsed laser deposition with excellent crystalline quality characterized by X-ray diffraction and TEM. Using spin-torque ferromagnetic resonance (STFMR) experiments, we measured a spin-orbit torque efficiency of 3 â€“ over an order of magnitude greater than typical spin-orbit coupled metals. We confirm this measurement with samples grown and measured across 3 different labs, along with transverse STFMR and Second Harmonic experiments (see Fig. 1). We also find an enhancement of the spin-orbit torque efficiency for thinner layers of BPBO, indicating that the epitaxial interface plays an important role in the generation of spin-orbit torques. With a better understanding of the role of the interface in spin-orbit torque generation, and by exploring similar complex oxide systems, we hope to find a model epitaxial oxide heterostructure that can be used for energy efficient spintronic applications. We acknowledge SRC-ASCENT for funding support.

Large Spin Hall Effects in a Model Epitaxial BaPb1 xBixO3 / La0.7Sr0.3MnO3 System

Recent advances in quantum magnonics [1-3], e.g., strong magnon-photon coupling [2] and single magnon sources [3], enable study of fundamental magnon properties. It is interesting to use these effects to answer fundamental questions of single magnon decoherence (SMD) mechanisms, understanding of which is necessary to use finite magnon number
states.
Here, we propose a simple measurement scheme for SMD. It is based on entangling a magnon and a qubit (with a much longer lifetime) with resonant frequencies ωm and ωq
, respectively,
and coupling rate κ. When the detuning Δω=ωm–ωq
is large (│Δω│»κ), the magnon and qubit states evolve independently. A magnetic field pulse can temporary couple (│Δω│«κ) the
system, thereby entangling or unentangling it.
The scheme (Fig. 1) is a temporal-domain Mach-Zehnder interferometer and works as follows. Initially, the qubit is excited, and the system is unentangled. A magnetic pulse entangles the
system and then it evolves freely for some time τ before another “unentangling” pulse is applied. When τ is comparable to the magnon lifetime, the final qubit population P(τ) depends on
the SMD mechanisms.
Using the Lindblad quantum master equation [4], we numerically simulated the proposed scheme (Fig. 2). We included two possible SMD mechanisms, namely, damping (Fig. 2a) and
dephasing (Fig. 2b) with decoherence rates Γ and Γ′, respectively. The fast oscillations in Fig. 2 are caused by usual quantum interference, while decay of the interference pattern is due to
SMD. Note, that the two mechanisms lead to different dependences of P(τ); in particular, dephasing alone does not change the average qubit population. We derived analytical expressions
that determine both rates Γ and Γ′ from the measurements of P(τ), even when both processes are present simultaneously (Fig. 2c).
In summary, we proposed a simple measurement scheme for SMD, which can be realized using currently available technology and which can be used to study fundamental questions of
quasi-particle decoherence at a single quantum level. 
**References** [1] D. D. Awschalom et al., IEEE Trans. Quantum Eng. 2, 5500836 (2021).
[2] P. G. Baity et al., Appl. Phys. Lett. 119, 033502 (2021).
[3] A. V. Chumak et al., IEEE Trans. Magn. 58, 6, 0800172 (2022).
[4] H.-P. Breuer and F. Petruccione, Oxford University Press (2002).

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/4145058cb4ce4da58735a9fa28924cb4.png) 
Fig. 1 Proposed SMD measurement scheme. 

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Fig. 2 Numerical simulation of SMD measurement scheme. (a): damping Γ≈38 μs-1. (b): dephasing Γ′≈50 μs-1 . (c): mixture of (a) and (b). Dashed lines: average P

Measurement Scheme for Single Magnon Decoherence

Nanocomposites (NCs) are multicomponent materials in which a nanoscale reinforcement is added to a host matrix to combine their different properties. In this work, we
investigate the magneto-optical (MO) properties of an NC made of Soda Lime Glass (SLG), which is a transparent, nonmagnetic, and cheap matrix doped by nanostructures of Cobalt (Co),
a magnetic material. Among various MO effects, the Faraday Effect (FE) describes the polarization modifications of a linearly polarized light when it travels through a magnetized
material. This effect manifests itself as two angles (θ, ε) depicting the polarization rotation and the ellipticity of the emerging light. The Co-SLG NC was formed in two successive steps: a
Co layer was deposited on the glass surface, then diffused into the glass using the thermal poling technique [1]. The FE effect was measured at different wavelengths (λ), while the applied
magnetic field (H) varied between -800 and +800 mT. Such FE-H curves describe the magnetic properties of the material under consideration. “Fig. 1-2” shows the θ-H curves measured at
λ=700 nm, for the Co layer “Fig. 1”, as well as for Co-SLG NC “Fig. 2”. The Co layer exhibits a hysteresis loop, which is characteristic of ferromagnetic materials (FM). After thermal
poling, the curve is linear, which indicates that the diffusion of the Co layer within the glass matrix changes drastically its magnetic behavior, most likely due to the oxidation of the Co ions
since the SLG matrix is oxygen-rich. “Fig. 3” presents the spectral behavior of this FE effect for the cobalt layer (saturation value of θ as a function of λ) and the NC (slope of θ-H curve as
a function of λ). Two main bands are observed in the case of the NC, centered at around 700 nm and 1400 nm, whereas no bands are observed for the Co layer. These two bands are
assigned to MO dipolar transitions of Co2+ ions in the tetrahedral sites of the Co3O4 structure [2]. If this NC is irradiated with a continuous wave laser, Co3O4 can be transformed
reversibly to CoO [1]. Since Co3O4 and CoO have different magnetic and MO behaviors, such NCs may lead to a promising photomagnetic feature that can be used in data storage
applications or optical MO switching. 

**References:** 

[1] R. Faraj, F. Goutaland, N. Ollier, Physica Status Solidi B., Vol. 257, p.2000155 (2020) 
[2] W. F. J. Fontijn, P. J. van der Zaag, L. F. Feiner, R. Metselaar, M. A. C. Devillers, Journal of Applied Physics, Vol. 85, p.5100-5105 (1999) 

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Magneto Optical Properties of Cobalt

For cancer therapy with magnetic hyperthermia by using magnetic nanoparticles (MNPs) [1, 2], alternating magnetic fields (AMF) HAC, typically sinusoidal wave, can deliver the magnetic energy into the deeper location in the body. In this study, we proposed a highly effective heat generation method for the MNPs by the application of an ultra-short pulse. We numerically evaluated the heating power with a variety of parameters, such as pulse width, field amplitude, and frequency [3]. Figure 1 shows effective magnetic hyperthermia with the ultra-short pulse magnetic field (Fig.1 (a)). The hysteresis curve and magnetization dynamics clearly indicate larger energy dissipation (Figs. 1 (b) and (c)). Figure 2 shows the energy dissipation and efficiency [4, 5] on the two-dimensional parameter space of field strength and duty ratio. Hysteresis loss and the input energy increases increasing with field strength and duty ratio (Figs. 2(a) and (b)) and there is a large efficiency power condition (Fig.2 (c)). To evaluate the effective heat generation and practical temperature increment, a larger imaginary part of magnetic susceptibility (Ï‡â€™â€™ &gt; 30) and specific loss power (SLP &gt; 105 W/kg) are required (Figs. 2 (d) and (e)). In addition, larger intrinsic loss power (100 nHm2/kg) is achieved (Fig. 2 (f)). Finally, we found the optimal condition of applied AMF (duty ratio = 1.2% and HAC = 16 kA/m) considering the practical uses. The results indicate that magnetic harmonics signals with a higher frequency range significantly enhance the heat generation of MNPs. We explore further studies of the development of an effective pulse generator for clinical applications and evaluation of the heating effect in animal experiments.

Ultra short pulse magnetic fields on effective magnetic hyperthermia for cancer therapy

Due to their high spin polarization and easy manipulation, ferromagnetic materials dominate as the magnetically active element in spintronic devices but come with drawbacks such as large stray fields, limited scalability, and limited operational frequencies [1-3]. These shortcomings have recently inspired researchers to consider antiferromagnetic spintronics [4], as antiferromagnetic materials have no stray fields and possess ultrafast spin dynamics. However, antiferromagnets have no net magnetic moment, which leads to weak read-out signals and more difficult operation. Compensated ferrimagnets (FiMs) provide an alternative as they combine the properties of ferromagnets and antiferromagnets. In particular, FiMs can have near THz resonances as in antiferromagnets, while still having a net magnetic moment which can be used for strong read-out signals and frequency control, such as efficient tunable microwave signal output from FiM based nano-oscillators. Due to these unique properties, research in FiMs for spintronic applications is intensifying [5-7]. However, to use ferrimagnets in spintronic devices such as in spin Hall nano-oscillators (SHNOs), it is important to ensure that such films retain their advantageous properties in ultrathin films and in nano devices.
In the present study, ferrimagnetic GdFeCo thin films were grown using co-sputtering of Gd and Fe87.5Co12.5 on high resistance Si (100) substrates, and their magnetodynamic properties were studied using broadband ferromagnetic resonance measurements at room temperature. By tuning the stoichiometry of the GdFeCo films, a nearly compensated behavior is for the first time demonstrated in 2 nm thin film, as shown in Fig. 1. Values for the effective magnetization and effective Gilbert damping constant (α) of 0.02 Tesla and 0.0078±0.0002 are obtained for a 2 nm Gd24.4(FeCo)75.6 film [8], where α is comparable to the lowest value obtained in thick films [9]. The vertical dotted lines in Fig. 1 show literature values [6, 9-10] for the spin angular momentum (xa) and magnetic momentum (xm) compensation points in thick films. The composition of the films for the magnetic moment and angular momentum compensation in this work is very close to those reported in the literature.
In search of high-frequency auto-oscillations in spin Hall nano-oscillators (SHNOs), constrictions with 50-300 nm widths were also prepared using GdFeCo(2-10nm)/Pt(5nm) based stacks. Brillouing Light Scattering microscopy measurements on SHNOs show auto-oscillations in the 8 GHz range, as shown in Fig. 2 [11]. Very interestingly, different Gd compositions result in different signs of the threshold current, which indicates different signs of the effective spin-orbit torque as a function of the composition. 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/0ec1329d0bf0522e3ffef8763deade00.png) 
Fig. 2. (a,b) Brillouin Light Scattering Spectroscopy (BLS) vs. current of two GdFeCo based SHNOs with different Gd content, believed to operate at opposite sides of the angular momentum conpensation point (SHNO temperature > RT due to Joule heating). While thermal SWs [ferromagnetic resonace (FMR)] are seen at all currents, the Gd rich SHNO only shows auto-oscillations (AO) at negative current, and the Gd poor SHNO only shows AO at positive current. (c,d) Log plots of the BLS counts from (a,b) for the thermal spin waves SWs (green) and the AO SWs (red). While the FMR show a slight current dependence due to heating, the AO intensity shows an initially exponential increase, as expected around threshold. Insets shows the BLS spectrum profile at the highest current.

**References:** 

[1] M. Romera et al., Nature 2018, 563, 230. 
[2] M. Zahedinejad et al., Nat. Nanotechnol. 15, 47 (2020). 
[3] B. Dieny et al., Nat. Elec. 3, 446 (2020). 
[4] T. Jungwirth et al., Nat. Nanotechnol. 11, 231 (2016). 
[5] S. K. Kim et al., Nat. Mat. 21, 24 (2022). 
[6] C. Stanciu et al., Phys. Rev. B 73, 220402 (2006). 
[7] D. Cespedes-Berrocal et al., Adv. Mat. 33, 2007047 (2021). 
[8] Lakhan Bainsla et al., Adv. Funct. Mater. 32, 2111693 (2022). 
[9] D.H. Kim et al., Phys. Rev. L 122, 127203 (2019). 
[10] Y. Hirata et al., Phys. Rev. B 97, 220403 (R) (2018). 
[11] L. Bainsla, A. A. Awad, J. Åkerman et al., unpublished.

Composition dependent threshold current polarity in ferrimagnetic spin Hall nano oscillators based on GdFeCo

The combination of inversion symmetry breaking and spin-orbit coupling (SOC) give rise to spin-orbit torque (SOT), charge pumping, and chiral magnetism. In conventional SOT studies, the inversion symmetry breaking usually comes from the structure or the geometry, e.g. crystal inversion assymmety in the bulk of diluted ferromagnet with zinc-blende structure (Fig. 1a) and space inversion assymmetry in a heavy metal/ferromagnet bilayer (Fig. 1b). It was known that the SOT strength can be controlled by the magnitude of the SOC, therefore, heavy metals with large SOC has been widely used for SOT-based magnetic random-access memory (MRAM).
In our study, we demonstrated that the vertical composition gradient in a single FePt layer acts as a new type of inversion symmetry breaking (Fig. 1c). The SOT efficiencies scale almost linearly with the composition gradient (G), which is defined to be the change of the Co/Pt ratio per 1 nm. We found that by changing G from 0.31 %/nm to 0.71 %, the SOT efficiency increases by 300 %. In experiments, the composition gradient can be easily controlled during sample growth. Therefore, our work provides a powerful tool to tune the SOT strength.
Then we demonstrated the current-induced magnetization switching in a FePt single layer (Fig. 1e). However, this switching requires an in-plane external magnetic field to break the symmetry. For real application, it is pursued to realize magnetic field-free switching. To achieve this goal, we move our attention from L10 FePt (P4/mmm) to fcc CoPt3. Both of them possess good perpendicular magnetic anisotropy (PMA) and hold promise in magnetic storage (media and memory). We found that the CoPt3 has two structural properties, as illustrated in Fig. 2(a). One is the composition gradient along the thickness direction which can break the inversion symmetry and allows for the generation of the in-plane damping-like torque. The other is the formation of the Co platelets in the Pt-rich matrix near the substrate during growth. We can make a symmetry analysis of the Co platelet/Pt structure, and we can easily find that the mirror symmetry is broken relative to the (11-2) plane and preserved relative to the (1-10) plane. Therefore, when the current is applied along the [1-10] direction (low-symmetry axis), the lateral mirror symmetry is broken so that the out-of-plane SOT can be allowed. Then we can achieve the field-free magnetization switching (0 deg in Fig. 2c). In contrast, when the current is applied along the [11-2] direction (high-symmetry axis), the lateral mirror symmetry is preserved and there is no field-free switching (90 deg in Fig. 2c). We also found that the current-induced switching exhibit a three-fold angular dependence on the current angle (θI), which is in perfect agreement with the three-fold rotational symmetry of the crystal structure in Fig. 2b.
To summarize, we observed the field-assisted magnetization switching in FePt single layer by introducing a new type of inversion symmetry breaking: composition gradient. Furthermore, we demonstrated the symmetry-dependent field-free magnetization switching in the CoPt3 single layer. The composition gradient along the film's normal direction gives rise to the in-plane damping-like torque while the low symmetry (3m1) property at the interface of Co platelet/Pt gives rise to the 3m torque in CoPt3. The cooperation of these two effects leads to a three-fold field-free switching in the CoPt3 single layer. Our result of the self-switching in CoPt3 has provided one of the most simplified structures for field-free switching of perpendicular magnetization. The good endurance and high thermal stability make it a good candidate for magnetic memory devices and other spintronic applications.

**References:** 

[1] L. Liu, et.al., Electrical switching of perpendicular magnetization in a single ferromagnetic layer Physical Review B 101 (22), 220402 (2020). 

[2] L.Liu, et.al., Current-induced self-switching of perpendicular magnetization in CoPt single layer Nature Communication 13, 3539 (2022).

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Spin orbit torque induced magnetization switching in single ferromagnetic layer

The spin splitting torque (SST) was theoretically proposed to combine advantages of conventional spin transfer torque (STT) and spin-orbit torque (SOT) as well as enable controllable spin current (1). This talk presents experimental evidences of SST and the inverse effect in collinear antiferromagnet RuO2 films. First, according to spin torque ferromagnetic resonance (ST-FMR) measurements of RuO2 films, we exhibit that spin current direction is correlated to the crystal orientation of RuO2 and spin polarization direction is dependent on (parallel to) the Néel vector, indicating the existence of SST in RuO2 (2). Second, based on spin Seebeck effect and THz emission measurements, we demonstrate that inverse SST effect can convert spin current polarized along Néel vector into charge current, which manifests as Néel vector-dependent spin Seebeck voltage signals and THz emission signal (3). These findings not only presents a new member for the spin torques besides traditional STT and SOT, but also proposes RuO2 for both promising spin source and spin sink for spintronics. 

**References:** 
(1) R. González-Hernández, et al., Phys. Rev. Lett. 126, 127701 (2021). 
(2) H. Bai, C. Song, et al. accpeted by Phys. Rev. Lett. 128, 197202 (2022). 
(3) H. Bai, C. Song, et al. In preparation. 

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