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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 &gt; 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.&lt;br&gt;
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.&lt;br&gt;
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.&lt;br&gt;
* This work was supported in part by the National Science Foundation (NSF) under Grant No. 2137275.&lt;br&gt;
**References:**&lt;br&gt;[1] Michael A. McGuire, Huibo Cao, Bryan C. Chakoumakos, and Brian C. Sales, Phys. Rev. B 90, 174425 (2014).&lt;br&gt;
[2] Akimasa Sakuma, Yuki Manabe, and Yohei Kota, Journal of the Physical Society of Japan 82, 073704 (2013).&lt;br&gt;
[3] W.E. Stutius, T. Chen, and T.R. Sandin, AIP Conf. Proc. 18, 1222 (1974)&lt;br&gt;

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/081c10dda94527f46067ae6a0ecd1f71.png)&lt;br&gt;
Figure 1. Magnetic structure for (a) LTP-MnBi (in-plane), (b) substitutionally (out-of-plane), and (c) interstitially (in-plane) Sn-doped MnBi.&lt;br&gt;
![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/228c6b8e39f3866599951f9ce67548c7.png)&lt;br&gt;
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).&lt;br&gt;

MMM 2022

Tuning Magnetocrystalline Anisotropy of LTP MnBi*

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).

technical paper

#### Welcome to the 67th Annual Conference on Magnetism and Magnetic Materials, MMM 2022!

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Thermal stability of the half-metallic band gap at the Fermi energy and high spin polarization of Co2FeAl0.5Si0.5 (CFAS) Heusler alloys (1,2) have made these systems attractive for spintronic applications. However, a stringent requirement is a controllable growth of highly ordered CFAS Heusler alloys. Moreover, giant magnetoresistance (GMR) (3,4) and the anomalous Hall effect (5,6) crucially depend on the magnitude of electrical resistivity (ρxx) and its temperature dependence. Thus, a complete understanding of the different contributions to ρxx is needed. To investigate the effect of film thickness on the structural- and electrical- properties, CFAS thin films of thickness, t, in the range 12 - 75 nm, were deposited by ultrahigh vacuum dc magnetron sputtering on Si(100) substrates with SiO2 buffer layer (300 nm), at the optimum substrate temperature of 500°C. The GIXRD patterns, shown in figure 1, reveal that B2 structural order grows with increasing t and peaks at t = 50 nm. The film with t = 75 nm showed A2 disorder. Irrespective of the magnitude of t, ρxx(T) goes through a minimum at Tmin. An elaborate quantitative analysis (6-8) of the ρxx(T, H=0) data, taken over the temperature range 5 K to 300 K, demonstrates that the electron-diffuson (e – d) and weak localization (WL) effects (responsible for the negative temperature coefficient of resistivity (TCR) for T < Tmin) compete with the electron-magnon (e – m) and electron-phonon (e – p) scattering (positive TCR) contributions to produce a minimum at Tmin. Figure 2 shows the normalized resistivity ρxx(T, H=0) / ρxx(T = 300 K, H=0) (open circles) along with the optimum theoretical fits (continuous lines), go through a minimum at Tmin. Consistent with the maximum B2 order at t = 50 nm, residual resistivity, ρ5K, and the e – d, wl, e - m and e - p scattering contributions to ρxx(T, H=0), ρe-d, ρwl, ρe-m and ρe-p, all go through a minimum at t = 50 nm. Regardless of t, the thermal renormalization of the spin-wave stiffness makes a significant contribution to ρe-m. 

**References:** 
(1) G. H. Fecher and C. Felser, J. Phys. D: Appl. Phys. 40, 1582 (2007). 
(2) Balke et al, Appl. Phys. Lett. 90, 242503 (2007). 
(3) Tezuka et al., Appl. Phys. Lett. 89, 112514 (2006). 
(4) Tezuka et al., Appl. Phys. Lett. 94, 162504 (2009). 
(5) A. Valet and T. Fret, Phys. Rev. B 48, 7099 (1993). 
(6) Hazra et al., Phys. Rev. B 96, 184434 (2017). 
(7) Srinivas et al., J. Non. Cryst. Solids 248, 211 (1999). 
(8) Kaul et al., Phys. Rev. B 33, 4987 (1986). 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/e37971143d1386fe7d1f4891815a9b3c.png)

Effect of film thickness on the electrical transport in Co2FeAl0.5Si0.5 thin films

Spin-orbit torques (SOTs) in heavy metal (HM)/ferromagnet (FM) have gathered much attention due to its potential for non-volatile, high-speed, and low-power spintronic devices [1-3]. While the majority of research has focused on the development of digital memories, previous studies on antiferromagnet (AFM)/FM structures showed field-free as well as analog-like (memristive) switching behavior [4,5], opening a new paradigm, the neuromorphic spintronics [6]. For applications, one needs to address a challenge that the memristive characteristics diminish with a reduction of device dimensions; for the case of PtMn/[Co/Ni] system, it totally disappears at around 200 nm [7,8]. In this study, we introduce a nanocomposite FM CoPtCrB towards SOT-based nanoscale memristors. A stack with Si sub./ Ta(4)/ Pt(4)/ CoPtCrB(7)/ Ru(1) is processed into single nanodot devices with various dot diameters (Ddot: 30-1000 nm) through the electron beam lithography and Ar ion milling. Memristive characteristics are studied by switching experiments with perpendicular magnetic fields or pulse currents (Ich) under an in-plane external field (Hx). Fig. 1 shows the results of SOT switching at Âµ0Hx = 90 mT for Ddot = 400 nm. Memristive behavior is observed, in contrast to the previous work with uniform FM exhibiting much fewer intermediate states [7]. Fig. 2 shows the obtained relationship between the square root of the number of intermediate states NIS and Ddot. Ddot below which devices show binary switching is around 60 nm, which is much smaller than the previous study (~ 200 nm) [7]. The present study demonstrates the potential of nanocomposite FM for nanoscale spintronic memristors. The authors thank A. Kurenkov, T. Koga, K. K. Tham, and S. Saito for their support. This work is partly supported by JST-CREST JPMJCR19K3, JSPS Kakenhi 19H05622, and RIEC Cooperative Research Projects. K. V. D. Z. acknowledges WISE program for AIE for financial support.

Memristive Spin Orbit Torque Switching in Nanocomposite CoPtCrB

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

Writing using spin-orbit torque (SOT) has been widely investigated in the field of magnetic random-access memory (MRAM) as it provides several advantages over Spin transfer torque (STT) based writing, including a much faster writing speed, better writing endurance, and protection to MgO from oxide breakdown due to a large current flowing across it during STT writing process, among others. Heavy metal(HM)/CoFeB/MgO is the core of this SOT-MRAM structure. The heterostructure consisting of Ta as the spin current source and CoFeB/MgO as the perpendicular magnetic anisotropy (PMA) material is the most researched structure owing to the high tunneling magneto-resistance ratio. However, Ta is difficult to be integrated into the CMOS process due to its poor thermal stability against annealing at temperatures greater than 350 Â°C. Currently, Î²-Tungsten (W) is the only heavy metal with CoFeB/MgO system, which can provide both thermal stability and spin-orbit torque switching simultaneously. Nevertheless, achieving a high resistive Î² phase of W is a challenging task, and the high resistivity of Î²-W makes the devices susceptible to Joule's heating. Here, we report another material Rhenium (Re) capable of providing thermally stable PMA up to temperature 425 Â°C with a perpendicular anisotropic field greater than 5000 Oe; Re possesses a spin hall angle (Î¸SH) of 0.065 Â± 0.003 and spin-orbit torque switching can be achieved with current density around 1.36Ã—1011 A/m2. Our findings pave a new avenue for the material design of perpendicular SOT-based MRAM.

Spin orbit torque driven perpendicular magnetization switching in Re/CoFeB/MgO with high thermal stability.

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) 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/18f06e1093e3ce8aa0b1723fd2effd4a.png) 

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. 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/8d14eaddeb192050581d31930976f00f.png) 

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

Applying spintronics devices to neuromorphic computing have recently gained much attention. For example, a speech recognition task using a spin-torque oscillator (STO)
and based on the algorithm of physical reservoir computing was experimentally demonstrated [1]. In this experiment, the nonlinear magnetization dynamics in STO is used as a
computational resource, where the modulation of the dynamics due to the injection of human voice, converted to electric voltage, is used to recognize the input data. Therefore, it is
essential to investigate the relationship between the physical properties reflected in the magnetization dynamics and the computational capability of physical reservoir computing.
It has been widely believed that the computational capability of physical reservoir computing is enhanced at the edges of chaos because complex dynamics near the chaos is useful to
distinguish several kinds of input data. However, the physical reservoir computing in previous works has been performed in the dynamical state far away from chaos. Therefore, the
computational capability of STO near the edge of chaos is still unclear.
In this work, we investigated the relationship between the dynamical properties of STO and the computational capability in reservoir computing. We consider two kinds of STO, where the
one is a conventional STO consisting of a pinned (P) and free (F) layer, while the other, P/F/F, includes two free layers; see Fig. 1. This is because, in principle, the former cannot show
chaos while the latter has a possibility to show chaotic dynamics, and therefore, the comparison between them is useful to study the role of the chaos on the computational capability. We
evaluate the short-term memory capacity [2] as a figure of merit and the Lyapunov exponent [3] to distinguish the dynamical state. It was found that the short-term memory capacity in
P/F/F STO is greatly enhanced near the edge of chaos (see Fig. 2) and becomes much larger than the maximum value of the capacity in the conventional P/F STO.
References [1] J. Torrejon et al., Nature 547, 428 (2017).
[2] K. Fujii and K. Nakajima, Phys. Rev. Applied 8, 024030 (2017).
[3] S. H. Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering (Westview Press, Boulder, CO, 2001). 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/09c01428e1ce12b4a80fc7ddb5e1c030.png) 
Fig.1 Conceptual picture of (a) P/F and (b) P/F/F. 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/03a7125ddd653ac21b4860e9c3be7f4c.png) 

Fig.2 (a) Short-term memory capacity and (b) Lyapunov exponent in P/F/F combination.

Computational Capability of Physical Reservoir Computing in Spin Torque Oscillator with Two Free Layers

Soft magnetic elastomers (ME) are a class of smart materials consisting of magnetic particles dispersed within soft elastomer networks. Their excellent magnetic and
mechanical properties enable fast, untethered and reversible responses to external magnetic induction1. Magnetic field sensors have rather broad applicability in many biomedical
applications such as biological activity monitoring or medical devices navigation. Fiber-optic magnetic field sensors are promising alternatives to their electrical counterparts due to their
small size, low cost, no field-induced heating, intrinsic material safety and immunity to electromagnetic (EM) interference.2 Nevertheless, their development is largely limited by the low
sensitivity and reliability due to poor integration of magnetic materials with the optical fiber, and the complexity of the sensor design.
In this work, we proposed a compact design for a fiber-optic magnetic sensor based on highly responsive ME composites, which enables real-time measurement of small changes in
magnetic fields using interferometric interrogation scheme. Dip-coating method was introduced to directly deposit uniform ME composite films on the end of a single mode fiber and create
a interferometric structure for sensing of mechanical deformations induced by external magnetic field (Fig1 and 2). ME composites of different compositions and magnetic sensors with
various coating structures were developed and further optimized. A fiber-optic interferometric sensing system was established for magnetic actuation and sensing performance evaluation.
The proposed sensor exhibited excellent sensing performance enabling measurement of magnetic fields in millitesla level. These highly sensitive, miniature sensors are cost-effective,
simple in design, immune to EM interference and are well-suited to a wide range of biomedical applications. Further studies will entail simultaneous measurement of magnetic field and
gradient. 
**References:** 

1. Bira, N., Dhagat, P. & Davidson, J. R. Front. Robot. AI 7, 1–9 (2020). 
2. Peng, J. et al. Sensors 19, 2860 (2019). 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/fabbf2674d23dae2b34b4d1060725834.png) 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/d4d5ad237d2edb915dd06bf67ba6f49d.png)

Soft Magnetic Elastomer Composites Enabling Magnetic Actuation and Field Sensing Based on Fiber Optic Interferometry

Spin Hall nano-oscillators (SHNOs) are miniaturized, ultra-broadband, microwave signal generators based on the spin Hall effect that converts a direct charge current into a transverse pure spin current, producing a spin-transfer torque into an adjacent ferromagnetic layer, which in turn excites spinwave (SW) auto-oscillations. Nano-constriction SHNOs [1] offer several advantages, thanks to their simple bilayer structure, such as significant freedom in device fabrication, material, and layout, and direct optical access to the active auto-oscillating region. SHNOs also exhibit robust frequency response [2], easy injection locking [3], and robust mutual synchronization [4]. These properties make them ideal candidates for broadband microwave signal generation, processing, and nonconventional oscillator computing.
Here we show how the controlled synchronization of SHNOs enables multiple forms of computing and demonstrations of robust mutual synchronization of two-dimensional SHNO arrays [5] (fig1.a) ranging from 2 × 2 to 8 × 8 nano-constrictions, which is observed both electrically and using micro-Brillouin light scattering microscopy (fig1.b.) Furthermore, using injection locking, we show that these SHNO arrays exposed to two independently tuned microwave frequencies exhibit the same synchronization maps (fig 1.d) as ones used for neuromorphic vowel recognition [6].
SHNOs are also potentially very appealing for oscillator network based Ising machines. Ising Machines are physical systems designed to find solutions to combinatorial optimization (CO) problems by using binary spins (Ising model). One promising approach is to use interacting non-linear oscillators that have been locked in phase to a signal at double their natural frequency. We show how phase-locked spin-Hall nano-oscillators, through the injection locking of a microwave frequency at the second harmonic, show a phase binarizations, see fig.2.(a-e), and can be used as computing units in Ising machines [7].
The core functionality required for real-world implementation of SHNOs for such potential computing applications is the individual control of the oscillators through external signal, we will show that such oscillators can be externally controlled in several ways including through optical control (fig2.f) [8]. Our demonstration of optical tuning of SHNOs might open up novel optical annealing schemes applicable to Ising machines, as well as for other computing applications. Furthermore, we discuss SHNOs readout using as well different means, which opens the way for two-dimensional synchronized SHNO networks for ultra-fast neuromorphic computing. 

**References:** 

[1]. V. E. Demidov et al., Appl. Phys. Lett. 105, 172410 (2014). 
[2]. A.A. Awad et al., Appl. Phys.Lett 116, 232401 (2020). 
[3]. T. Hache et al., Appl. Phys. Lett. 114,192405 (2019). 
[4]. A. A. Awad et al., Nat.Phys. 13, 292 (2017). 
[5]. M. Zahedinejad et al., Nat. Nanotechnol. 15, 47 (2020). 
[6]. M. Romera et al., Nature 563, 230 (2018). 
[7]. A. Houshang et al., Phys. Rev. Appl. 17, 014003 (2022). 
[8]. S. Muralidhar et al., Appl. Phys. Lett. 120, 262401 (2022). 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/dd5719583e518cbe5419797ac9deef1d.png)

Synchronization of Spin Hall nano

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). 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/d451774e933c88b771a4f3f6377fb0c7.png)

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Tuning Magnetocrystalline Anisotropy of LTP MnBi*

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Effect of film thickness on the electrical transport in Co2FeAl0.5Si0.5 thin films

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