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Magnetic skyrmions are topological spin textures with great potential for spintronics applications (1). The appearance of skyrmions requires a careful balance between the magnetic anisotropy and the Dzyaloshinskii-Moriya interaction, and being able to tune these values with a voltage is an important tool for material optimisation for skyrmion devices.

In this work we have explored generation of both volatile and non-volatile skyrmions in MgO/Mn2CoAl/Pd thin films using different ionic liquid gating voltage sequences and magneto-optical Kerr effect (MOKE) microscopy. With a negative gate voltage of -2.5 V, we are able to generate non-volatile skyrmions ~ 1 μm diameter in films with perpendicular magnetic anisotropy Keff ~ 1 x 104 Jm-3. The same result is achieved in higher Keff films by ‘training’ or repeatedly cycling the gate voltage, achieving a giant voltage tunability of magnetic anisotropy of 109.8 mT V-1. Interestingly, volatile skyrmions can also be generated, by first applying a large negative ‘trigger’ voltage, and then skyrmions appear at a positive gate voltage. Using X-ray photoelectron spectroscopy, we explain the generation of skyrmions in terms of magneto-ionic and electrostatic effects (2). Our results show the potential of ionic liquid gating for achieving large anisotropy changes to reversibly or irreversibly generate skyrmions from materials with a range of starting anisotropy values.&lt;br&gt;

**References:**&lt;br&gt;
(1) X. Zhang, Y. Zhou, K. M. Song, T.-E. Park, J. Xia, M. Ezawa, X. Liu, W. Zhao, G. Zhao, and S. Woo, J. Phys. Cond. Mat. 32, 143001 (2020).&lt;br&gt;
(2) Y. Zhang, G. Dubuis, C. Doyle, T. Butler, and S. Granville, Phys. Rev. Appl. 16, 014030 (2021).&lt;br&gt;

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MMM 2022

Magneto ionic and electrostatic generation of non

Magnetic skyrmions are topological spin textures with great potential for spintronics applications (1). The appearance of skyrmions requires a careful balance between the magnetic anisotropy and the Dzyaloshinskii-Moriya interaction, and being able to tune these values with a voltage is an important tool for material optimisation for skyrmion devices.

In this work we have explored generation of both volatile and non-volatile skyrmions in MgO/Mn2CoAl/Pd thin films using different ionic liquid gating voltage sequences and magneto-optical Kerr effect (MOKE) microscopy. With a negative gate voltage of -2.5 V, we are able to generate non-volatile skyrmions ~ 1 μm diameter in films with perpendicular magnetic anisotropy Keff ~ 1 x 104 Jm-3. The same result is achieved in higher Keff films by ‘training’ or repeatedly cycling the gate voltage, achieving a giant voltage tunability of magnetic anisotropy of 109.8 mT V-1. Interestingly, volatile skyrmions can also be generated, by first applying a large negative ‘trigger’ voltage, and then skyrmions appear at a positive gate voltage. Using X-ray photoelectron spectroscopy, we explain the generation of skyrmions in terms of magneto-ionic and electrostatic effects (2). Our results show the potential of ionic liquid gating for achieving large anisotropy changes to reversibly or irreversibly generate skyrmions from materials with a range of starting anisotropy values. 

**References:** 
(1) X. Zhang, Y. Zhou, K. M. Song, T.-E. Park, J. Xia, M. Ezawa, X. Liu, W. Zhao, G. Zhao, and S. Woo, J. Phys. Cond. Mat. 32, 143001 (2020). 
(2) Y. Zhang, G. Dubuis, C. Doyle, T. Butler, and S. Granville, Phys. Rev. Appl. 16, 014030 (2021). 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/21c77abfee9e932ada1d2b3ce6ec1e37.png)

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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Please register for the MMM 2022 conference to join the event.

This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

Magnetic skyrmions are promising candidates for achieving low-power, next-generation edge computing devices due to their particle-like nature, efficient coupling to electrical and spin currents and room-temperature stability in multilayer films [1]. However, in most skyrmion-hosting multilayers, the predominant magnetic textures at zero-field (ZF) are labyrinthine stripes [2]. External applied magnetic fields or geometric confinement [3] are typically used to stabilize isolated skyrmions, which limits their practicality.

In this work, we design multilayers comprising three adjoining functional stacks – two repeats of skyrmion-hosting multilayers and a bias layer – coupled by two tunable interlayer exchange couplings (IECs) [4,5]. Using Lorentz transmission electron microscopy (LTEM), we demonstrate that these two IECs act as coarse and fine-tuning knobs that determine skyrmion stability and density. With micromagnetic simulations, we elucidate the unique roles played by each of the couplings and establish the advantage of a duo-IEC system in applications. This work establishes and extends the use of IEC as a means of stabilizing and shaping ZF skyrmions and paves the path to skyrmion-based devices. 
**References** [1] A. Fert, N. Reyren, and V. Cros, Magnetic Skyrmions: Advances in Physics and Potential Applications, Nat. Rev. Mater. 2, natrevmats201731 (2017).
[2] X. Chen, M. Lin, J. F. Kong, H. R. Tan, A. K. C. Tan, S.-G. Je, H. K. Tan, K. H. Khoo, M.-Y. Im, and A. Soumyanarayanan, Unveiling the Emergent Traits of Chiral Spin Textures in Magnetic Multilayers, Adv. Sci. 9, 2103978 (2022).
[3] P. Ho, A. K. C. Tan, S. Goolaup, A. L. G. Oyarce, M. Raju, L. S. Huang, A. Soumyanarayanan, and C. Panagopoulos, Geometrically Tailored Skyrmions at Zero Magnetic Field in Multilayered Nanostructures, Phys. Rev. Appl. 11, 024064 (2019).
[4] G. Chen, A. Mascaraque, A. T. N’Diaye, and A. K. Schmid, Room Temperature Skyrmion Ground State Stabilized through Interlayer Exchange Coupling, Appl. Phys. Lett. 106, 242404 (2015).
[5] W. Legrand, D. Maccariello, F. Ajejas, S. Collin, A. Vecchiola, K. Bouzehouane, N. Reyren, V. Cros, and A. Fert, Room-Temperature Stabilization of Antiferromagnetic Skyrmions in Synthetic Antiferromagnets, Nat. Mater. 19, 34 (2019). 
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Zero field Magnetic Skyrmions in Multilayer Films Stabilized by Interplay of Interlayer Exchange Couplings

Toward the applications to high-performance MRAMs [1, 2], spin-orbit torque (SOT)-induced magnetization switching has been widely investigated in various material systems. While 4d transition metals, such as Ru, exhibit low SOT due to the small spin-orbit coupling [3], recent works have reported the SOT generation in antiferromagnetic RuO2 film thanks to its unique band structure [4], although the detailed understanding is still lacking. Herein, we fabricate the (100)-oriented RuO2 film and evaluate SOT in a RuO2/Co-Fe-B bilayer by harmonic Hall measurement. 
RuO2 (4 nm)/Co20Fe60B20 (1.2 nm) bilayer was fabricated on a α-Al2O3 (0001) substrate by DC/RF sputtering, where (100)-oriented RuO2 film with a likely existence of a three-domain structure is expected to be grown [5]. The resistivity of the RuO2 film was estimated as 247.4 mΩcm from the sheet resistance. A Ru (4 nm)/Co20Fe60B20 (1.2 nm) bilayer was also fabricated for comparison. The harmonic Hall measurement was performed for Hall bar devices in a rotating magnetic field [Fig. 1]. A clear second harmonic signal is observed for RuO2/Co-Fe-B while it is negligible for Ru/Co-Fe-B, suggesting the SOT generation owing to the unique band structure of RuO2. For RuO2/Co-Fe-B bilayer, the effective fields with the Slonczewski-like torque (HSL) and field-like torque (HFL) symmetries were quantified by fitting [Fig. 2(a, b)]. Linear relation with the applied current density J [Fig. 2(c)] proves that these fields are induced by the current. These results would be important for further research on the current-induced magnetization switching using antiferromagnets. 
The authors acknowledge JSPS KAKENHI Grants 21K14522, 21K18189, the Core Research Cluster program, the MRAM program in CIES, Tohoku Univ.
Fig. 1: The second harmonic Hall resistance vs. field direction curves for Hall bar devices of RuO2/Co-Fe-B and Ru/Co-Fe-B.
Fig. 2: Fitting of HSL (a) and HFL (b). J dependence of μ0HSL and μ0HFL (c). 
**References:** [1] H. Honjo et al., IEDM Technical Digest 28.5, (2019). 
[2] M. Natsui et al., JSSC 56, 1116 (2020). 
[3] T. Tanaka et al., Phys. Rev. B 77, 165117 (2008) 
[4] A. Bose et al., Nature Electronics 5, 267 (2022). 
[5] H. Bai et al., Phys. Rev. Lett. 128, 197202 (2022). 

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Spin orbit torques in RuO2/Co

It is of great significance in the memory industry to find a conductive spin current source (SCS) possessing a large damping-like spin-orbit torque efficiency (ξDL) higher than W, for the purpose of realizing a faster and more efficient spin-orbit torque magnetic random-access memory (SOT-MRAM). Among numerous candidates, 5d transition metal Pt is one of the more competitive spin Hall materials for efficiently generating spin-orbit torques (SOTs) in Pt/ferromagnetic layer (FM) heterostructures, due to its high spin Hall conductivity (SHC) and moderate resistivity. However, for a long while with tremendous engineering endeavors, the of Pt and Pt alloys are still limited to ξDL<0.5 . In this work, we report that with proper alloying elements, particularly the 3d transition metals V and Cr with giant orbital Hall effect (OHE), the strength of the high spin Hall conductivity of Pt (σSH~6.45×105 (h-bar/2e) Ω-1 m-1) is observed even in the relatively resistive regime. Especially for the Cr-doped case, an extremely high ξDL~0.9 in a perpendicular magnetized Pt0.69Cr0.31/Co device can be achieved with a moderate Pt0.69Cr0.31 resistivity of ρxx~133 μΩ cm . This sizable SOT efficiency can be attributed to the additional spin current generation from orbital-to-spin current conversion, resulting in the increasing SHC as the Cr concentration in the Pt-Cr alloy increases. Moreover, a low critical SOT-driven switching current density of is also demonstrated, and the damping constant (α) of Pt0.69Cr0.31/CoFeB structure is found to be reduced to 0.052 from the pure Pt/CoFeB case of 0.078. The overall high σSH, giant ξDL, moderate ρxx , and the reduction of α make the Pt-Cr/FM heterostructure promising for versatile extremely low power consumption SOT memory applications. 
**References:** 1. Miron, I.M., et al., Perpendicular switching of a single ferromagnetic layer induced by in-plane current injection. Nature, 2011. 476(7359): p. 189-U88. 
2. Liu, L.Q., et al., Current-Induced Switching of Perpendicularly Magnetized Magnetic Layers Using Spin Torque from the Spin Hall Effect. Physical Review Letters, 2012. 109(9). 
3. Pai, C.F., et al., Determination of spin torque efficiencies in heterostructures with perpendicular magnetic anisotropy. Physical Review B, 2016. 93(14). 
4. Liu, L.Q., et al. Spin-Torque Ferromagnetic Resonance Induced by the Spin Hall Effect. Physical Review Letter, 2011, 106, 036601. 
5. Lee, Soogil, et al. "Efficient conversion of orbital Hall current to spin current for spin-orbit torque switching." Communications Physics 4.1 (2021): 1-6. 
6. Hu, Chen-Yu, et al. "Toward 100% Spin–Orbit Torque Efficiency with High Spin–Orbital Hall Conductivity Pt–Cr Alloys." ACS Applied Electronic Materials 4.3 (2022): 1099-1108. 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/94e0f175e8889995a66f95dcd6ff810c.png) 
Damping-like spin-orbit torque efficiency of PtxCr1-x alloys in Pt-Cr/Co structures.

Enhancing Spin Orbit Torque Efficiency via Orbital Currents

Researchers are attracted to antiferromagnets due to their high frequency dynamical properties with a possibility of developing terahertz frequency range spintronics devices. We use magnetic multilayer heterostructures consisting of successive ferromagnetic layers separated by a non-magnetic metal of suitable thickness to have an antiferromagnetic coupling. These structures are called synthetic antiferromagnets (S-AFM). We use permalloy as a ferromagnetic material and ruthenium as a non-magnetic metal to prepare tetralayer synthetic antiferromagnets. We theoretically predict and experimentally verify the existence of two types of magnon-magnon couplings for antiferromagnetic magnons localized on surface and interior layers of tetralayer synthetic antiferromagnet. Macrospin modeling and micromagnetic simulations are used to show that the dynamic part of Rudermanâ€“Kittelâ€“Kasuyaâ€“Yosida (RKKY) interaction is responsible for the self-hybridization of acoustic and optical magnons localized on surface and interior layers due to an accompanying field-like torque. Likewise, surface optical magnons hybridize with interior acoustic magnons by spin pumping, which creates antidamping torque on neighboring ferromagnetic layer. It is reflected in the double-gap in magnon spectrum, that is, an additional magnon-magnon interaction is observed. Thus, interlayer spin pumping is a magnon-magnon interaction control mechanism in in S-AFMs that can be used to help develop energy efficient and high-speed spintronics devices. Research at University of Michigan was supported from NSF CAREER grant DMR-1847847. Work at Oakland University was funded by NSF under award number ECCS-1941426, and that at University of Delaware was supported from NSF grant DMR-2011824.

Hybridizing antiferromagnetic magnons with spin pumping and exchange fields

Spin torque nano-oscillators are spintronic devices in which radiofrequency magnetization oscillations can be generated through spin-transfer effects. Due to their
nonlinearity, these devices display interesting properties such as frequency stability and high tunability, opening up possibilities from wireless telecommunication to neuromorphic
computing [1].
In this study, we will focus on vortex-based spin-torque nano-oscillators (STVO) and study the response of mutually coupled STVOs. To couple them, we use the RF current emitted by
one STVO, which is first amplified and then sent through the antenna located above the second STVO and vice versa. The resulting external RF field hence mediates the coupling between
the two STVOs.
Using this approach, beyond the expected improvement of their RF properties, i.e., power emission and spectral purity [2], we have recently shown that strong coupling can lead to new
phenomena beyond synchronization, such as amplitude death, mode branching, and non-trivial states associated with exceptional points (EPs) [3]. EPs, defined as singularities of nonHermitian problems, can indeed emerge from such systems. Combining experimental results (Fig.1) and theoretical modeling (Fig.2), we succeed in demonstrating that the presence of
mode branching (see Fig.1) can be connected to the coalescence of the system complex eigenvalues, i.e., the existence of an EP, in a specific current range.
The next step is to investigate, both in frequency and time domain, how these EPs' existence is sensitive to the individual properties of each STVO and the path used to approach this EP
state [4]. We believe that this study opens spintronic devices to the field of non-Hermitian Hamiltonian physics, already observed in several variable loss/gain systems in photonics and
electronics [5]. By proving the engineering of EPs for high sensitivity mode control, the objective will be to show the potential of this technique in sensor-type systems. 
**References** 
[1] N. Locatelli, V. Cros, and J. Grollier, Nature Materials, 13, 1, 11 (2016)
[2] R. Lebrun, et al., Nat. Comm. 8, 15825 (2017)
[3] S. Wittrock, et al., arXiv:2108.04804 (2021)
[4] C. Dembowski et al., Phys. Rev. Lett. 86, 787 (2001)
[5] Z. Liu, et al., arXiv:2009.07713 (2020) 

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Fig.1 Frequency spectra of the coupled STVOs versus STVO2 current IDC,2 and fixed IDC,1. An EP is observed at (I1,I2) = (8,8) mA. 

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Fig.2 Corresponding complex eigenvalues versus STVO2 current IDC,2. Eigenvalues are in dashed (uncoupled) and solid (coupled) lines.

Complex Dynamics In Mutually Coupled Spin Torque Vortex Oscillators

The prospect of thermal imaging and control in magnetic particle imaging (MPI) is an important advancement for non-invasive medical diagnostics and therapeutics.
Current MPI systems focus mainly on imaging from measurement of nanoparticle concentrations. Accurate derivation of temperature relies on detailed understanding of magnetization
dynamics in the presence of AC drive fields and variable temperature [1]. It is well established that MPI performance is critically impacted by nanoparticle relaxation dynamics [2]. The
dynamic response of magnetic nanoparticles in magnetic fields depends strongly on the particles’ magnetic and structural properties, inter-particle interactions, and the local environment. We report an arbitrary-wave magnetic particle spectrometer for characterizing dynamics over the 200 K to 350 K temperature range. These measurements can separately identify features of
Brownian and Néel relaxation and quantify the timescales and amplitudes associated with these processes.
Here, we discuss measurements of magnetization dynamics using AC susceptibility and pulsed excitation for ferrite and cobalt-doped ferrite nanoparticles ranging in diameter from 7 nm to
70 nm. For example, Fig. 1 show the imaginary component, χ’’, peak frequency for two different sizes of ferrite nanoparticles [3]. Fig. 2 shows the time domain measurement of 7 nm
cobalt-doped ferrite under pulsed excitation in which both field-on and field-free relaxation are observed and quantified. Frequency and time domain measurements for cobalt-doped
ferrites show the presence of both Néel and Brownian dynamics, and the temperature dependence reveals their intrinsic coupling. To resolve this coupling, we used stochastic Monte Carlo
methods to simulate the field and temperature dependence of magnetization dynamics. This knowledge will eventually inform strategies for design of magnetic nanoparticles with
properties targeted for accurate and sensitive thermal imaging using MPI. 
**References** [1] Thinh Q. Bui, Weston L. Tew, Solomon I. Woods. “AC magnetometry with active stabilization and harmonic suppression for magnetic nanoparticle spectroscopy and
thermometry.” J. Appl. Phys. 128, 224901 (2020).
[2] Zhi Wei Tay, Daniel W Hensley, Erika C Vreeland, Bo Zheng, Steven M Conolly. “The Relaxation Wall: Experimental Limits to Improving MPI Spatial Resolution by Increasing
Nanoparticle Core size.” Biomed Phys. Eng. Express, 3 (3), 035003 (2017)
[3] Thinh Q. Bui, Adam J. Biacchi, Cindi L. Dennis, Weston L. Tew, Angela R. Hight Walker, Solomon I. Woods. “Advanced characterization of magnetization dynamics in iron oxide
magnetic nanoparticle tracers.” Applied Physics Letters, 120, 012407 (2022).

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Fig. 1: ACS spectrum of 15 and 20 nm ferrites. The real (χ’) imaginary (χ”) parts, and fits (blue) using a semi-empirical analytical model. 

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Fig. 2: Magnetic field (~ 5 mT) with 20 ns rise time (blue). Magnetization step-response of 7 nm cobalt-doped ferrite (red).

Coupled Néel Brown magnetization dynamics of magnetic nanoparticles for thermal and magnetic particle imaging

Attaining high areal density (AD) in bit-patterned magnetic recording (BPMR) technology means reducing its bit period and track pitch [1,2]. When the readers move from the initial to other zones of the disk, a skew angle (SA) takes place, leading to a degradation of the system performance [3]. Therefore, controlling SA properly is necessary. Prior works introduced SA detection along with the suppression [4] and the study of SA in a read-head array [5]. To the best of our knowledge, this is the first proposed scheme of combining a multi-layer perceptron (MLP) with a V-shaped read-head array to estimate and alleviate SA in BPMR. 

We propose SA estimation and alleviation schemes in BPMR by combining the V-shaped read-head array, as shown in Fig. 1, with MLP. The V-shaped read-head array is investigated in three zones of the disk, i.e., inner, middle, and outer zones, which are notated as ID, MD, and OD, respectively. The initial positions of all three readers in the middle zone are fixed at 5, -5, and 5 degrees for upper, middle, and lower readers, respectively. The sensitivity functions of these readers are shown in Fig. 2, in which their changes as they move from one zone to another are also illustrated. Note that when the sensitivity changes, the channel coefficient, and their readback signals will also change. Therefore, the SA estimation process can utilize readback signals that are produced from the array reader as the input of an MLP-based SA estimator. The next process is attenuating the SA effect in the system by designing an appropriate 2-D equalizer for each SA level in the mentioned zones of the disk, based on a minimum mean-square error approach, before sending an equalized sequence to the Viterbi detector. 

We found that five levels of estimated SA to signal-to-noise (SNR) values, by using a V-shaped read-head array in BPMR, can estimate nearly 100% of the SA value equal to 0 degree, while the positive and negative SA values also gain high percentages. Furthermore, the accuracy percentage of our proposed scheme is independent to SNR. 
**References:** [1] Y. Shiroishi et al., IEEE Trans. Magn., vol. 45, no. 10, pp. 3816-3822, 2009. 
[2] H. J. Richter et al., IEEE Trans. Magn., vol. 42, no. 10, pp. 2255–2260, 2006. 
[3] M. R. Elidrissi, K. Sann Chan, S. Greaves, et al., Journal of Applied Physics, 115(17), 2014. 
[4] S. Koonkarnkhai, C. Warisarn, and P. Kovintavewat, AIP Advances 11, 015229, 2021. 
[5] E. Hwang, T. Oenning, G. Matthew, et al., IEEE Trans. Magn., vol. 51, no. 4, 2015. 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/3aff06df588a127002514c90ce70afe1.png)
Fig. 1. V-shaped read-head array in various zones.
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Skew Angle Estimation and Alleviation Based Multi Layer Perceptron in V

Spin orientation of LTP-MnBi can be controlled by partially substituting Bi of hexagonal LTP-MnBi with either the third alloying element or temperature. The spin reorientation occurs at about 90 K from ab-plane (0 - 90 K) to c-axis (T > 90 K) of LTP MnBi [1]. Sakuma et al. have performed first-principles calculations on Sn-doped Mn (Bi1-xSnx) and found that magnetocrystalline anisotropy constant (Ku) increases to about 3 MJ/m3 (x = 0.1) from -0.5 MJ/m3 (x = 0.0) at 0 K and then remains unchanged up to x = 0.3 [2]. However, Stutius et al. reported -0.15 MJ/m3 (x = 0.0) of the measured Ku at 4.3 K [3]. Therefore, Sakuma’s calculated Ku (x = 0.0) does not agree with the experimental Ku in [3]. This may be attributed to 300 K lattice constants in [2] used in the calculation. Sakuma did not relax the MnBi formula unit to obtain lattice constants at the ground state. 
In this study, we have performed first-principles calculations on Mn0.5Bi0.5, Mn0.5Bi0.25Sn0.25 (substitutional doping: SD), and (Mn0.5Bi0.5)66.7Sn33.3 (interstitial doping: ID) in Fig. 1 and used the relaxed lattice constants. Both a and c decrease from 4.287 and 6.118 Å to 3.954 and 5.456 Å, respectively, when Sn substitutes for Bi of LTP-MnBi. However, the a of ID increases to 4.611 Å, while the c decreases to 5.683 Å. 
Figure 2 shows density of states for MnBi-Sn. The net magnetic moment is 7.224 μB/f.u. for LTP-MnBi, 5.034 μB/f.u. for SD, and 6.609 μB/f.u for ID. The Ku is changed from in-plane (-0.202 MJ/m3) to out-of-plane (1.711 MJ/m3) by substitutionally doping Sn and maintains in-plane with interstitially doping Sn-MnBi (-0.043 MJ/m3). Our results agree with experimental one [3], but Sakuma’s. The Curie temperature decreases from 716 K for LTP-MnBi to 445 K for SD and 285 K for ID. 
* This work was supported in part by the National Science Foundation (NSF) under Grant No. 2137275. 
**References:** [1] Michael A. McGuire, Huibo Cao, Bryan C. Chakoumakos, and Brian C. Sales, Phys. Rev. B 90, 174425 (2014). 
[2] Akimasa Sakuma, Yuki Manabe, and Yohei Kota, Journal of the Physical Society of Japan 82, 073704 (2013). 
[3] W.E. Stutius, T. Chen, and T.R. Sandin, AIP Conf. Proc. 18, 1222 (1974) 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/081c10dda94527f46067ae6a0ecd1f71.png) 
Figure 1. Magnetic structure for (a) LTP-MnBi (in-plane), (b) substitutionally (out-of-plane), and (c) interstitially (in-plane) Sn-doped MnBi. 
![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/228c6b8e39f3866599951f9ce67548c7.png) 
Figure 2. Density of states for (a) LTP-MnBi (Mn0.5Bi0.5), (b) substitutionally Sn-doped MnBi (Mn0.5Bi0.25Sn0.25), and (c) interstitially Sn-doped MnBi ((Mn0.5Bi0.5)66.7Sn33.3).

Tuning Magnetocrystalline Anisotropy of LTP MnBi*

Nanoflowers vs Nanobiots: Inorganic vs biological agents for cancer theragnosis applications

The Ising machine is an unconventional computing architecture that can be used to solve NP-hard combinatorial optimization problems more efficiently than traditional von Neumann architectures. Fast, compact oscillator networks that provide programmable connectivities among arbitrary pairs of nodes are highly desirable for the development of practical oscillator-based Ising machines. In this talk, I will discuss how an electrically coupled array of gigahertz spin Hall nano-oscillators can realize such a network (1). By developing a general analytical framework that describes injection locking of spin Hall oscillators with large precession angles, I will explicitly show the mapping between the coupled oscillators’ physical properties and the Ising model. I will describe how our analytical model is integrated into a versatile Verilog-A device that can emulate the coupled dynamics of spin Hall oscillator networks at the circuit level using conventional electronic components and considering phase noise and scalability. Finally, I will demonstrate how our results provide design insights and analysis tools toward the realization of a CMOS-integrated spin Hall oscillator Ising machine operating with a high degree of time, space, and energy efficiency. 

**References:** 

1. B. C. McGoldrick, J. Z. Sun, and L. Liu, Physical Review Applied, Vol. 17 (1), p.014006 (2022). 
2. J. Chou, S. Bramhavar, S. Ghosh, et. al., Scientific Reports, Vol. 9 (1), p.1 (2019). 

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