United States

Dissipative coupling of resonators arising from their cooperative dampings to a common reservoir induces intriguingly new physics such as energy level attraction. In this
study, we report the nonlinear properties in a dissipatively coupled cavity magnonic system. A magnetic material YIG (yttrium iron garnet) is placed at the magnetic field node of a FabryPerot-like microwave cavity such that the magnons and cavity photons are dissipatively coupled. Under high power excitation, a nonlinear effect is observed in the transmission spectra,
showing bistable behaviors. The observed bistabilities are manifested as clockwise, counterclockwise, and butterfly-like hysteresis loops with different frequency detuning. The
experimental results are well explained as a Duffing oscillator dissipatively coupled with a harmonic one and the required trigger condition for bistability could be determined
quantitatively by the coupled oscillator model. Our results demonstrate that the magnon damping has been suppressed by the dissipative interaction, which thereby reduces the threshold for
conventional magnon Kerr bistability. This work sheds light upon potential applications in developing low power nonlinearity devices, enhanced anharmonicity sensors and for exploring
the non-Hermitian physics of cavity magnonics in the nonlinear regime. &lt;br&gt;
**References** &lt;br&gt; [1] H. Pan, Y. Yang and Z.H. An, arXiv:2206.01231 (2022)
[2] P. Hyde, B. M. Yao, Y. S. Gui, Phys. Rev. B 98, 174423 (2018)

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/d354dd9cd5e5f679db783aefba0047ef.png) &lt;br&gt;

FIG. 1. (a) Illustration of the experimental setup, where a YIG sphere is imbedded in an assembly cavity. (b) Transmission coeffcient mapping of the hybridized cavity-magnon system. (c)
Dispersion relation of hybridized cavity and magnon mode, where points A and E indicate off-resonance, and point C indicates on-resonance, and points B and D indicate intermediate
frequencies. (d) The fixed field cut of transmission coeffcient mapping at the coupling condition. &lt;br&gt;

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/30da0f70b1cedc9cec9c3ce912929efb.png) &lt;br&gt;

FIG. 2 The jump position of field foldover hysteresis versus P at cavity frequencies (a) A, (b) B, (c) C, (d) D, (e) E. Purple (blue) circle symbols are experimental results of forward
(backward) H field sweeping. The yellow and cyan solid curves are fitted. (f) The threshold for coherent and dissipative coupling system when off- and on-resonance. The threshold for
coherent coupling is from Ref. [2].

MMM 2022

Bistability in Dissipatively Coupled Cavity Magnonics

Dissipative coupling of resonators arising from their cooperative dampings to a common reservoir induces intriguingly new physics such as energy level attraction. In this
study, we report the nonlinear properties in a dissipatively coupled cavity magnonic system. A magnetic material YIG (yttrium iron garnet) is placed at the magnetic field node of a FabryPerot-like microwave cavity such that the magnons and cavity photons are dissipatively coupled. Under high power excitation, a nonlinear effect is observed in the transmission spectra,
showing bistable behaviors. The observed bistabilities are manifested as clockwise, counterclockwise, and butterfly-like hysteresis loops with different frequency detuning. The
experimental results are well explained as a Duffing oscillator dissipatively coupled with a harmonic one and the required trigger condition for bistability could be determined
quantitatively by the coupled oscillator model. Our results demonstrate that the magnon damping has been suppressed by the dissipative interaction, which thereby reduces the threshold for
conventional magnon Kerr bistability. This work sheds light upon potential applications in developing low power nonlinearity devices, enhanced anharmonicity sensors and for exploring
the non-Hermitian physics of cavity magnonics in the nonlinear regime. 
**References** [1] H. Pan, Y. Yang and Z.H. An, arXiv:2206.01231 (2022)
[2] P. Hyde, B. M. Yao, Y. S. Gui, Phys. Rev. B 98, 174423 (2018)

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/d354dd9cd5e5f679db783aefba0047ef.png) 

FIG. 1. (a) Illustration of the experimental setup, where a YIG sphere is imbedded in an assembly cavity. (b) Transmission coeffcient mapping of the hybridized cavity-magnon system. (c)
Dispersion relation of hybridized cavity and magnon mode, where points A and E indicate off-resonance, and point C indicates on-resonance, and points B and D indicate intermediate
frequencies. (d) The fixed field cut of transmission coeffcient mapping at the coupling condition. 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/30da0f70b1cedc9cec9c3ce912929efb.png) 

FIG. 2 The jump position of field foldover hysteresis versus P at cavity frequencies (a) A, (b) B, (c) C, (d) D, (e) E. Purple (blue) circle symbols are experimental results of forward
(backward) H field sweeping. The yellow and cyan solid curves are fitted. (f) The threshold for coherent and dissipative coupling system when off- and on-resonance. The threshold for
coherent coupling is from Ref. [2].

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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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 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/5c0e253fe8db7509bc80794fd3463df5.png)
![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/fad4c59ec8346dbd4cf75f26716d6d3f.png)

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

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. 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/8b450645fa586c94ab6a85259b3f505c.png) 
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

Commercial melt-spun ribbons are typically available in the range of 17–30 µm thickness which limits their high-frequency application due to high eddy current loss. In addition, the ribbons can be annealed for nanocrystallisation to optimise their power loss behaviour 1. However, possible oxidation during annealing and the brittle nature of as-annealed ribbons, makes core fabrication difficult. It is possible, however, to straightforwardly design an alloy composition with moderate Amorphisation Ability (AMA) to in-situ fabricate ultra-thin 2 nano-crystallised ribbons 3, using a high-speed melt spinner. 
By changing the percentages of mainly Si, B and Nb, three alloy compositions with various Amorphisation Ability (AMA) have been designed, based on different liquidus temperatures calculated using CALPHAD, enthalpies of mixing, and atomic mismatch factors. Ultra-thin ribbons of the designed alloys have been synthesised by a high-speed melt spinner, to obtain the advantages of improved material performance and lower costs over commercial ribbons. The melt-spun ultra-thin ribbons (t~5 µm) of Alloys 1 and 2 exhibit nanocrystalline structure owing to their moderate AMA, whereas Alloy 3 with a higher AMA is amorphous (Fig. 1). Interestingly, in-situ nanocrystallised alloys show lower Hc and higher Hk compared to the amorphous alloy (Fig. 2) which makes them perfect candidates for high-frequency applications as they will show lower hysteresis loss (due to low Hc) and lower anomalous loss (less domain wall motion due to high Hk). Additionally, owing to low eddy current loss in ultra-thin ribbons, almost one-fifth of the best available commercially, the total loss is expected to be very low. The lower Hc of nanocrystallised alloys can be attributed to the cancellation of the magnetostriction of the amorphous matrix by the formed nanocrystals. Additionally, the high Hk of such alloys can be owing to the pinned domain walls by the nanocrystals. We have found a cutting-edge methodology to in-situ fabrication of nano-crystallised ultra-thin ribbons which are ideal for minaturised and efficient high-frequency magnetic cores. 
**References:** 1 G. Herzer, J. Magn. Magn. Mater. 133, 248 (1994). 
2 A. Masood, H.A. Baghbaderani, V. Ström, P. Stamenov, P. McCloskey, C. Mathúna, and S. Kulkarni, J. Magn. Magn. Mater. 483, 54 (2019). 
3 K.L. Alvarez, H. Ahmadian Baghbaderani, J.M. Martín, N. Burgos, P. McCloskey, J. González, and A. Masood, J. Non. Cryst. Solids 574, (2021). 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/26edc474401a2a615b12e41da81a2288.png) 
Figure 1. XRD patterns of melt-spun alloys. 
![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/aa677410e66f6351ee096321e76ab2cc.png) 
Figure 2. B-H loops of three alloys.

Design and in situ Fabrication of Nano

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)

Magnetically Sensitive Electronic Skins for Supervised Folding of Origami Actuators

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) 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/22b70a5a23d04b9bb67cee1c6723a45d.png)

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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