United States

Spin Hall antiferromagnetic oscillators (AFMO) (1) are a promising candidate for a CMOS-compatible THz-range frequency source. The output power of a nano-scale AFMO is relatively low, and mutual synchronization of AFMOs may be used to increase the power and to reduce the generation linewidth. The first step in understanding AFMO synchronization is to investigate the injection locking of a single oscillator, i.e., synchronization to an external driving signal.
Here, we numerically study the injection locking of AFMOs using the model derived in (1). In contrast with previous studies (2, 3), we study injection locking in a wide range of AFMO frequencies and assume that the driving signal is mixed with the DC bias current, i.e., that the bias and locking spin currents have the same spin polarization, which is more suitable for practical realization.
Figure 1 shows a dependence of the driven AFMO frequency f on the injected frequency fs. Straight segment near the AFMO free-running frequency f0 = 0.23 THz corresponds to the injection locking at the fundamental signal harmonic. The huge locking bandwidth Δf1≈100 GHz is due to strong influence of AFMO nonlinearity related to anisotropy of the antiferromagnet (1). An additional signature of a strongly nonlinear regime is the appearance of higher-order locking bands f=2fs and f=3fs. Synchronization at higher harmonics may be important in practical applications, since it allows one to synchronize THz-range AFMO by a driving signal of a lower frequency.
The synchronization bandwidth Δf1 drastically reduces with the increase of AFMO free-running frequency f0 (Fig. 2). This effect is caused by reduction of AFMO nonlinearity and may be a serious obstacle for practical use of AFMOs in the frequency range f &gt; 1 THz. Therefore, alternative methods of AFMO injection locking should be studied, such as locking to a microwave magnetic field or to a spin current with different spin polarization (2).&lt;br&gt;

**References:** &lt;br&gt;
(1) R. Khymyn, et al., “Antiferromagnetic THz-frequency Josephson-like oscillator driven by spin current”, Sci. Rep. 7, 43705 (2017).&lt;br&gt;
(2) O. Gomonay, T. Jungwirth, and J. Sinova, “Narrow-band tunable terahertz detector in antiferromagnets via staggered-field and antidamping torques”, Phys. Rev. B 98, 104430 (2018).&lt;br&gt;
(3) R. Khymyn, et al., “Injection-locking of a nonlinear sub-THz antiferromagnetic spin-Hall oscillator”, DE-08, Abstracts of the International Magnetics Conference INTERMAG-18, Singapore, Singapore, April 2018.&lt;br&gt;

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MMM 2022

Injection Locking of Antiferromagnetic Oscillators

Spin Hall antiferromagnetic oscillators (AFMO) (1) are a promising candidate for a CMOS-compatible THz-range frequency source. The output power of a nano-scale AFMO is relatively low, and mutual synchronization of AFMOs may be used to increase the power and to reduce the generation linewidth. The first step in understanding AFMO synchronization is to investigate the injection locking of a single oscillator, i.e., synchronization to an external driving signal.
Here, we numerically study the injection locking of AFMOs using the model derived in (1). In contrast with previous studies (2, 3), we study injection locking in a wide range of AFMO frequencies and assume that the driving signal is mixed with the DC bias current, i.e., that the bias and locking spin currents have the same spin polarization, which is more suitable for practical realization.
Figure 1 shows a dependence of the driven AFMO frequency f on the injected frequency fs. Straight segment near the AFMO free-running frequency f0 = 0.23 THz corresponds to the injection locking at the fundamental signal harmonic. The huge locking bandwidth Δf1≈100 GHz is due to strong influence of AFMO nonlinearity related to anisotropy of the antiferromagnet (1). An additional signature of a strongly nonlinear regime is the appearance of higher-order locking bands f=2fs and f=3fs. Synchronization at higher harmonics may be important in practical applications, since it allows one to synchronize THz-range AFMO by a driving signal of a lower frequency.
The synchronization bandwidth Δf1 drastically reduces with the increase of AFMO free-running frequency f0 (Fig. 2). This effect is caused by reduction of AFMO nonlinearity and may be a serious obstacle for practical use of AFMOs in the frequency range f > 1 THz. Therefore, alternative methods of AFMO injection locking should be studied, such as locking to a microwave magnetic field or to a spin current with different spin polarization (2). 

**References:** 
(1) R. Khymyn, et al., “Antiferromagnetic THz-frequency Josephson-like oscillator driven by spin current”, Sci. Rep. 7, 43705 (2017). 
(2) O. Gomonay, T. Jungwirth, and J. Sinova, “Narrow-band tunable terahertz detector in antiferromagnets via staggered-field and antidamping torques”, Phys. Rev. B 98, 104430 (2018). 
(3) R. Khymyn, et al., “Injection-locking of a nonlinear sub-THz antiferromagnetic spin-Hall oscillator”, DE-08, Abstracts of the International Magnetics Conference INTERMAG-18, Singapore, Singapore, April 2018. 

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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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A type-II Weyl semimetal, WTe2 is receiving great attention in spin physics because of the generation of spin polarization due to fictitious Weyl monopoles. In a previous study, in-plane spin polarization (Sy, parallel to the b-axis of WTe2) originating from the Weyl node was reported by introducing an electrical method even though detection is limited at very low temperature [1]. Meanwhile, the existence of spin polarization along the c-axis (Sz, perpendicular to the plane) in WTe2 was suggested by using angle-resolved photoemission spectroscopy (ARPES) [2], and Sz spin polarization can affect the spin-torque ferromagnetic resonance (ST-FMR) of adjacent ferromagnets [3]. However, the Sz spin generation using an electrical method, which is suitable for investigation of more precise origin of Sz spin polarization, has not been explored.
In this study, we successfully detected the Sz spin polarization of Td-type WTe2 using an all-electric method that is an expansion of the experimental technique for detecting topological surface spin polarization in BiSbTeSe [4]. Perpendicular magnetic anisotropy (PMA) electrodes made of [Pt/Co]10 (“10” denotes a stacking number) and nonmagnetic Pt electrodes were deposited on the mechanically exfoliated WTe2, and the out-of-plane magnetic field dependence of spin voltages was measured from 5 K to 300 K (see Fig.1). Figure 2 shows the result at 5 K and 300 K, and the hysteresis attributed to spin accumulation beneath the PMA electrode was successfully observed up to 300 K [5]. In addition, the polarity of spin voltage hysteresis was reversed by switching the electric current direction, and the hysteresis vanished when the direction of current changes to parallel to the b-axis of WTe2. These evidence that the Sz spin polarization was originating from the in-plane symmetry breaking of WTe2. Other supporting evidence and detailed discussion will be given in the presentation. 
**References** [1] P. Li et al., Nat. Commun. 9, 3990 (2018).
[2] P.K. Das et al., Nat. Commun. 7, 10847 (2016).
[3] D. MacNeil et al., Nat. Phys. 13, 300-306 (2017).
[4] Y. Ando, M. Shiraishi et al., Nano Lett. 14, 6226 (2014).
[5] K. Ohnishi, Y. Ando, M. Shiraishi et al., under review. 

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All electric measurement of perpendicularly spin polarization in Weyl semimetal, WTe2, at room temperature

Recently, transition metal oxide thin films with strong bulk or interfacial spin-orbit coupling have demonstrated to exhibit exceptionally large spin Hall angle, which can potentially enable energy-efficient spin-orbit torque devices. To characterize the spin Hall efficiency, spin-torque ferromagnetic resonance (ST-FMR) or spin pumping measurements that operate at microwave frequencies have been widely used in oxide epitaxial thin films on various oxide substrates. At high frequency, the dielectric loss of those oxide substrates could significantly influence the resonance spin torque signals. However it has not been well considered when evaluating the spin Hall efficiency. Here we report that some insulating oxide substrates could generate significant spurious symmetric voltage signals on ST-FMR measurements, leading to serious overestimation of spin-Hall angle. We investigate the spurious signals in five widely used insulating oxide substrates SrTiO3, KTiO3, DySrO3, LSAT, and Al2O3 by performing ST-FMR measurements in oxide substrate/ferromagnetic bars. We find that all the devices present considerable resonance voltage signals even with the absence of spin source layer, see Fig.1. Among which, STO, KTO, DSO show significant symmetric voltage signals, while Al2O3 presents S/A smaller than other oxides due to its large A signal. In contrast, the low frequency second harmonic Hall measurements give no signals for all the devices, indicating that the extra resonance signals on ST-FMR are not originated from spin Hall effect. Our work reveals significant influence of oxide insulator substrates on ST-FMR measurement that should be taken into account on study of spin Hall angle. 
**References** 
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Spurious symmetric voltage signals on the spin torque ferromagnetic resonance measurement induced by oxide substrates

Spin-transfer nano-oscillators (STNO) can generate a microwave voltage output based on a DC input current. However, a single oscillator generates a relatively small amount of power. To address this issue, a solution is to have an array of STNOs and synchronize them, thus leading to much greater generated power. Achieving synchronization in a large array of oscillators can be challenging due to the complexity of interactions. Here, we proposed a structure that can allow synchronization in a large array of STNO by means of spin waves in a thin magnetic film. The structure is based on a honeycomb configuration, which has low-damping hexagonal regions with high-damping embedded triangle regions (Fig. 1). STNOs are placed at each narrow neck of the pattern. The spin waves generated by the STNO propagate within the low-damping region, whereas they are damped in the high-damping regions. The narrow neck width is smaller than the spin wave wavelength, so that the spin waves do not pass there. Thus, each STNO only has nearest-neighbor interactions (Fig. 2). By limiting the range of interaction, synchronization in a large array of STNOs is possible. Furthermore, the coupled oscillations can be tuned by either changing the STNO driving current or using extra current on the high damping region to reduce the effective damping constant to allow more connections among adjacent STNOs within a certain region. 
**References** 
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Synchronization of Spin Torque Nano

Inspired by the success of FETs in electronics, voltage controlled magnetic anisotropy (VCMA) induced magnetization dynamics has emerged as an important integrant in low-power spintronic devices. In this talk, I will discuss our recent demonstration of VCMA induced parametric resonance excitation for generating magnons with exchange-interaction wavelengths [1]. Earlier, we had shown that the growth-induced magnetocrystalline anisotropy can be used for giving rise to a direction-specific magnon scattering [2]. This was shown
using epitaxy dependent anisotropic damping in (111), (110) and (100) YIG/GGG thin films. However, metallic ferromagnets grown on Si have a better compatibility with CMOS
processes. Therefore, we choose CoFeB/MgO junctions, that have emerged to be technologically relevant owing to its high perpendicular magnetic anisotropy, low damping, and high
TMR ratios.
Following an introduction to our earlier work on YIG, I will focus on the excitation of VCMA induced magnetization dynamics for in-plane magnetized CoFeB/MgO junctions (Fig. 1a), a
long-standing limitation of VCMA. This is done using VCMA of interfacial in-plane anisotropy [1], that is induced by magnetic annealing [3]. At high powers, VCMA induced parametric
resonance is observed (Fig. 1b). The wavelengths of corresponding magnons are estimated to be tuned down to the exchange-interaction length scales using magnetic field, power and
frequency of excitation (Fig. 1c). Power dependent parametric pumping amplitudes reveal unique trends at different dynamical excitation regimes (Fig. 1d). The crucial role of excitation
frequency in distinguishing VCMA induced magnetization dynamics will be discussed. Finally in Fig 1(e-f), using angular dependent measurements, we prove the presence of electric-field
torque from VCMA in both linear and non-linear magnetization dynamics [1].
**References** [1] A. Deka et al., Phys. Rev. Research 4, 023139 (2022).
[2] R.M.*, A. Deka* et al., Appl. Phys. Lett. 119, 162403 (2021). (*Equal first author)
[3] A. Deka et al., Phys. Rev. B 101 (17), 174405 (2020). 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/be5352b95a3d88e4f47b7b677c539406.png) 
Fig. 1 (a) Illustration of VCMA excitation. (b) Power dependent inverse spin Hall effect voltage VISHE. (c) Calculated frequency and magnetic field Hex dependence on wavength of
magnons. (d) Power dependence of VISHE at different wavelengths. In-plane angle dependence of VISHE amplitudes at (e) uniform and (f) parametric resonances. Lines are fits to equations
in Ref. 1.

Generation of Magnons with Nanoscale Wavelengths using Voltage Controlled Parametric Resonance

The push into three dimensions in nanomagnetic systems is a growing theme in basic nanomagnetism research and potential spintronics devices. In two dimensions,
magnetic Skyrmions are an established platform to explore the physics of real-space topological spin textures. In three dimensions, the analogous spin texture is the recently observed magnetic Hopfion [1]. A Hopfion is a toroidal spin texture equivalent to a Skyrmion string twisted and closed into a torus (fig. 1). 3D magnetic systems are also predicted to host additional novel spin textures including Skyrmion tubes, chiral bobbers, and torons.
These 3D spin textures, which have so far only been observed statically, now hold promise for dynamical studies. Investigating transitions between these novel 3D spin textures under
applied magnetic fields or currents is within reach with experimental studies with time-resolved x-ray microscopy and scattering techniques. (fig. 2). I will present numerical calculations
investigating how the dynamics of Hopfions and related 3D spin textures couple to their topology [2]. This work has implications for experimental design and 3D spintronic device
engineering. This work was funded by the US DOE, Office of Science, Basic Energy Sciences under Contract No. DE-AC02-05-CH11231.
**References** [1] N. Kent et al., “Creation and observation of Hopfions in magnetic multilayer systems,” Nature Communications, vol. 12, no. 1, p. 1562, 2021, doi: 10.1038/s41467-021-21846-5. [2] D. Raftrey and P. Fischer, “Field-Driven Dynamics of Magnetic Hopfions,” Physical Review Letters, vol. 127, no. 25, p. 257201, Dec. 2021, doi: 10.1103/PhysRevLett.127.257201. 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/6b68dae4e657b2030f6f18140455a328.png) 
(a) Magnetization color map of a Hopfion at the z=0 plane. 
(b) Magnetization color map of Hopfion at the y=0 plane. 
(c) Hopfion spin textures with linked magnetization isosurfaces. The Hopf invariant or linking number, Q, is the number of times the isosurfaces are linked. 
(d) Detail of Hopfion vortex rings. 
(e) Magnetization color map of a toron at the z=0 plane. 
(f) Magnetization color map of toron at the y=0 plane. 
(g) Toron spin textures with unlinked isosurfaces. A toron has Q=0. 
(h) Detail of toron Bloch points (monopole antimonopole pair). 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/b5bc8bf9d42624a210e36cf7d42ab514.png) 
(a) Power Spectral Density response of a Hopfion to a field pulse under static applied external field. 
(b) Magnetic excitation pulse applied in the x direction in the time domain. Pulsed field is the cardinal sign or sinc function. 
(c) Fourier transform of the excitation pulse in the frequency domain. The sinc function creates a square wave with equal sampling frequency up to a maximum frequency of 15 GHz.

Dynamics of 3D topological spin textures

Amorphous alloys have excellent low loss characteristics and are suitable for high-performance motor cores [1]. Due to the limitation of the thickness of extremely thin soft magnetic materials, stamping is not suitable for processing. At present, the most commonly used processing method is EDM [2], but this method will generate high temperature at the edge of the material, thereby changing the internal structure of the edge of the material, making iron loss worsens. 
In this paper, a ring-like experiment method was used to explore the effect of EDM on the deterioration of iron loss. The first part of the paper analyzes the research situation of the scholars on the deterioration of the iron loss at the edge of the soft magnetic material core; The second part introduces the basic principles and specific methods of the ring-like experiment（The sample and principle are shown in Fig. 1）, and explores the relationship between the ratio of the area affected by cutting to the total area and the deterioration of iron loss. Taking 0.05mm ultra-thin silicon steel as a control（Some experimental results are shown in Fig. 2）, comparing the degree of iron loss deterioration of the two materials, and analyzing the iron loss deterioration law of ultra-thin soft magnetic materials; The third part analyzes the metallographic diagram of the material, observing the crystallization of amorphous alloys at the edge after EDM cutting and the behavior of 0.05mm ultra-thin silicon steel grains, and explains the reasons for the difference in the degree of deterioration of the two materials from a microscopic point of view; Finally, summarize the relevant conclusions. 
To sum up, this paper compares the iron loss deterioration of amorphous alloys and other ultra-thin soft magnetic materials, and explores the iron loss deterioration law of amorphous alloys with different proportions of the area affected by cutting from the perspective of experimental data and microstructure. In the follow-up work, according to this law, the exact value of the iron loss deterioration at the cutting edge of the material is deduced to provide guidance for the application of amorphous alloys. 
**References:** [1] Li T , Zhang Y , Liang Y , et al. Multiphysics Analysis of an Axial-Flux In-Wheel Motor With an Amorphous Alloy Stator[J]. IEEE Access, 2020, 8:1-1. 
[2] Chai F , Li Z , Chen L , et al. Effect of Cutting and Slot Opening on Amorphous Alloy Core for High-Speed Switched Reluctance Motor[J]. IEEE Transactions on Magnetics, 2020, PP(99):1-1. 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/d02ef63c98d1b3b945fec492fdd4a75a.png) 
Fig. 1 Test ring samples and principle 
![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/696424145d13f052da5f61f4252674b7.png) 
Fig. 2 Part of the experimental data

Study on Deterioration of Iron Loss of Amorphous Alloy by Wire Electrical Discharge Machining

Hybrid anisotropy heterostructures consist of two exchange coupled magnetic layers with in-plane and out-of-plane magnetic anisotropy where the exchange coupling is controlled by a non-magnetic spacer layer [1,2], Fig.1. Previous studies have investigated the quasi-static magnetic properties of these structures using magnetometry and polarised neutron reflectivity (PNR) to determine the magnitude and extent of the coupling in these layer [3]. In this work we extend the study of hybrid anisotropy thin films to include the dynamic properties of these structures. We undertake angle dependent FMR measurements using VNA-FMR where the angle of the applied magnetic field can be varied whilst keeping the waveguide in a fixed position. The experimental details of our measurement are identical to those report in [4] except that we replace the Picoprobe waveguide with a NanOsc Coplanar Waveguide v4. Our results demonstrate that the angle dependence of the resonance frequency depends on the degree of coupling between the two magnetic layers. In systems with significant exchange coupling (e.g.: Pd spacer thickness of 1.2 & 2 nm) we observe a dominant â€˜acousticâ€™ mode which shows a maximum frequency for an applied field angle of approximately 40o to the sample plane, Fig.2. The increase in frequency is ~25% for an applied field of 6 kOe. To further understand this effect, we have conducted micro-magnetic simulations using MuMax3 [5] which are able to reproduce the key features of the experimental results which will be presented in the full paper for spacer thicknesses of 0, 1.2, 2, 4, 6 and 100 nm). This shows that the angle of the applied field may be used to tune the resonance response of these materials over a significant frequency range.

Frequency Tunability with Field Angle in Hybrid

A viable compound for magnetic refrigeration at ambient temperature must present a large change in magnetic entropy, with minimum hysteresis and should be composed of earth abundant and non-toxic elements. [1] Recently a computational proxy was developed to identify new magnetocaloric materials whereby first principle structure relaxation is carried out with and without spin polarization to ascertain the degree of magnetic deformation. [2] By applying this method to ferromagnets in the PbFCl family we found magnetic deformation of around 2% which is similar to other magnetocaloric compounds. We therefore have focussed our experimental study on MnZnSb, which is reported to be an itinerant ferromagnet with a second order phase transition and Curie temperature about room temperature. [3] Detailed magnetization measurements were carried out and Arrott analysis (Fig 1. a)) yields a Curie temperature of 304K, with the system being described as one universality class across all order parameters and identified as â€˜2-dimensional long-range.â€™ We find a reasonably large magnetic entropy change of 4.5 Jkg-1K-1 with a relative cooling power of 153 Jkg-1. Temperature dependant powder neutron diffraction was used to investigate the origin of the significant magnetic entropy change around the magnetic transition which is attributed to the release of crystallographic strain through the magnetic transition. We identify the c/a parameter as an accurate crystallographic proxy to control the magnetic transition (Fig. 1 b)). Using this concept, chemical substitution on the square-net allows to experimentally tune the Curie temperature over a broad temperature span between 252-322 K (Fig. 1 c)). A predictive machine learning model for the c/a parameter is developed to guide future exploratory synthesis.

Chemically controllable magnetic transition temperature and magneto caloric properties in MnZnSb based compounds

Refrigeration based on the magnetocaloric effect (MCE) attracts a lot of attention since it can be more energy efficient and environmentally friendly than current vapor compression technology. The concept uses a solid-state magnetic material that heats up and cools down cyclically when exposed to a changing magnetic field. The development of multicaloric materials using more than one transformation-inducing stimulus opens up further possibilities to enhance the efficiency of a multicaloric cycle. One approach is to use magnetic field and uniaxial pressure alternatingly to trigger the cyclic phase transition in a multicaloric material [1,2]. In this work, we present a novel multi-stimuli cooling concept including potential material systems and methods to tailor their functional and mechanical properties. The main objective is adopting the properties for a classical MC cycle towards the extended needs of the multi-stimuli cycle using intrinsic and extrinsic means. We investigated for Ni-Co-Mn-In and Ni-Co-Mn-Ti Heusler alloys the influence of different microstructures from chemical variation and different processing routes on the magnetocaloric and elastocaloric performance [3,4]. We found that preferential grain orientation in [001] direction along the compression direction is beneficial for the stress-induced transformation [3], whereas introducing secondary phases enhances the long-term stability under cyclic stress application while maintaining the caloric performance [5]. For single phase Ni-Co-Mn-Ti, we tailor the phase transition by optimizing the heat treatment and varying the stoichiometry. By this, we can achieve large isothermal entropy changes of up to 40 Jkg-1K-1 in 2 T [4]. In combination with very good mechanical strength, this makes Ni-Co-Mn-Ti alloys a suitable candidate for the multi-stimuli cooling cycle. We acknowledge funding by ERC (Adv. Grant â€œCool Innovâ€, GrantNo. 743116) and by DFG (CRC â€œHoMMageâ€, Project-ID 405553726 â€“TRR 270)

Tailoring thermal hysteresis and microstructure of Ni Mn

The observation of the Higgs boson solidified the standard model of particle physics. However, explanations of anomalies (e.g. dark matter) rely on further symmetry breaking 1calling for an undiscovered axial Higgs mode. In condensed matter, the Higgs was seen in magnetic, superconducting, and charge density wave(CDW) systems. Uncovering a low energy mode’s vector properties is challenging, requiring going beyond typical spectroscopic or scattering techniques. Here, we discover an axial Higgs mode in the CDW system RTe3 using the interference of quantum pathways. In RTe3 (R=La, Gd), the electronic ordering couples bands of equal or different angular momenta. As such, the Raman scattering tensor associated with the Higgs mode contains both symmetric and antisymmetric components, which can be excited via two distinct, but degenerate pathways. This leads to constructive or destructive interference of these pathways, depending on the choice of the incident and Raman scattered light polarization. The qualitative behavior of the Raman spectra is well-captured by an appropriate tight-binding model including an axial Higgs mode. The elucidation of the antisymmetric component provides direct evidence that the Higgs mode contains an axial vector representation (i.e. a pseudo-angular momentum) and hints the CDW in RTe3 is unconventional. Thus we provide a means for measuring collective modes quantum properties without resorting to extreme experimental conditions.

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Injection Locking of Antiferromagnetic Oscillators

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