Spin-torque oscillator (STO) is a class of emerging spintronic devices that can find applications in wireless communication systems in the form of radio frequency (rf) generator1,2 and rf detector3. The STO offers a compatibility with CMOS technology and high frequency tunability2. However, the single STO output is not sufficient for the rf applications. In order to overcome this, the mutual synchronization of STOs is critical for communication, energy harvesting and neuromorphic applications. The short range magnetic coupling-based synchronization has spatial restrictions (few μm), whereas the long-range electrical synchronization using vortex STOs has limited frequency responses in hundreds MHz (&lt; 500 MHz), restricting them for on-chip GHz-range applications. Here, we demonstrate electrical synchronization of four non-vortex uniformly-magnetized STOs at 2.4 GHz WiFi band4, resolving the frequency-area quandary for designing STO based on-chip systems. We use a single dc source to synchronize canted free layer STOs, thereby simplifying the synchronization scheme. Due to mutual synchronization, STOs show a power enhancement and linewidth reduction [Fig. 1a,b]. When injection-locked with an external rf source, the synchronised STOs show a wide locking range around 2.4 GHz [Fig. 1c,d], which can be useful for neuromorphic computing. Under injection locking, synchronized STOs demonstrate an excellent time-domain stability and improved phase noise performance [Fig. 1e,f]. Our results highlight the significance of electrical topology (series vs. parallel) while designing an on-chip STOs system.

![](https://assets.underline.io/uploads/markdown_image/1/image/5c47ef17602057fa745ff11bcef50d6b.jpg)

Fig. 1. a,b Oscillation power (P) and linewidth (△f) versus numbers of oscillators (N) in parallel (a) and series (b), respectively. Solid lines are linear fit and N−1 scaling for the power and linewidth, respectively. c,d STO frequency (f0) versus radio frequency (frf) response for a single oscillator (red) and four oscillators (blue) at Prf = −20 dBm for the parallel (c) and series (d) connection. The locking range defines the region where f0 ~ frf. e,f Phase noise for 1 ms time-domain trace in parallel (e) and series (f). The solid black and blue lines in (f) shows the 1/f2 and 1/f3 phase noise, respectively.

Electrically connected spin-torque oscillators array for 2.4 GHz WiFi band transmission

All Optical Helicity Independent Switching (AO-HIS) of magnetization, using single femtosecond laser pulses, has been demonstrated in GdFeCo ferrimagnetic alloys for various concentrations [1] as well as in other structures with antiferromagnetic coupling, Gd/Co, [Tb/Co]n/Ta/CoFeB and Mn2RuxGa [2,3,4]. Up to now, AO-HIS has never been observed for ferromagnetic layers. However, it was shown that a single pulse magnetization reversal of a ferromagnet could be observed in a spin-valve structure [5]. The switching is then achieved by the ultrashort spin current pulse generated from the ultrafast demagnetization of GdFeCo [5,6]. In this work, we study Gdx(FeCo)1-x/Cu/FM spin-valve structures, where FM can be different ferromagnetic layers [7] and the composition x of the GdFeCo alloy is also changed [8]. By increasing the Gadolinium concentration x, we aim at increasing the spin current injected in the copper layer [6]. We show that this can reduce the laser fluence threshold required to observe the FM magnetization reversal. In particular, no AO-HIS of the GdFeCo layer is required and the threshold fluence for the FM layer is around 1.6 mJ/cm2 i.e. comparable to GdFeCo and Gd/Co multilayers [1,2] and smaller than what is achieved for Tb/Co/CoFeB [2] and Mn2RuxGa [3]. We also show that by changing the Curie temperature, the laser pulse duration and the Cu/FM interface, one can control the interaction between the spin current and the FM layer and so the laser fluence threshold. Finally, we measured the dynamics of the reversal of the FM layer, which happens in around a picosecond. We show a model, based on a recent theory for the ultrafast magnetization dynamics of ferromagnets [9], that explains this behavior. We thus designed spin-valve structures that could provide technological advantages regarding both speed and energy efficiency of data storage.

Ultrafast Single Pulse All Optical Magnetization Switching of Ferromagnets

The mutual synchronization of spin-torque oscillators (STOs) is critical for communication, energy harvesting and neuromorphic applications. Short range magnetic coupling-based synchronization has spatial restrictions (few μm), whereas the long-range electrical synchronization using vortex STOs has limited frequency responses in hundreds MHz (<500 MHz), restricting them for on-chip GHz-range applications. Here, we demonstrate electrical synchronization of four non-vortex uniformly-magnetized STOs using a single common current source in both parallel and series configurations at 2.4 GHz band, resolving the frequency-area quandary for designing STO based on-chip communication systems. Under injection locking, synchronized STOs demonstrate an excellent time-domain stability and substantially improved phase noise performance. By integrating the electrically connected eight STOs, we demonstrate the battery-free energy-harvesting system by utilizing the wireless radio-frequency energy to power electronic devices such as LEDs using the setup shown in Fig. 1a. We also demonstrate the capability of this energy harvesting system in holding dc power using a time-varying signal [Fig. 1b], which is useful in harvesting energy from discrete commercial sources such as a WiFi router. Our results highlight the significance of electrical topology (series vs. parallel) while designing an on-chip STOs system.

Electrically connected spin-torque oscillators array for 2.4 GHz WiFi band transmission and energy harvesting

Spin-transfer torque magnetoresistive random access memories (STT-MRAMs) have been successfully introduced into integrated circuits owing to their non-volatility, high endurance, high-speed operation, and scalability. Since the discovery of a perpendicular easy-axis in a CoFeB/MgO material system [1], which has become the standard material system for magnetic tunnel junction (MTJ), a core building block of STT-MRAM, MTJ scaling has been accelerated while improving device performance in data retention by engineering MTJ device structure (Table 1) [2]. Here we review the MTJ scaling technology and discuss our recent results on ultra-small shape-anisotropy MTJs. Maintaining high data-retention performance, represented by thermal stability factor Δ, is essential for nonvolatile applications. Δ is proportional to total magnetic anisotropy energy density and a volume of a nanomagnet. Hence, magnetic anisotropy energy densities arising from the bulk, interface, and shape are needed to be enhanced to achieve high thermal stability as the MTJ size is scaled. Following the first demonstration of the perpendicular MTJs using a single CoFeB/MgO interface [1], those using double CoFeB/MgO interfaces were invented to enhance the interfacial anisotropy [2], resulting in high thermal stability [2] and thereby high-performance STT-MRAMs using MTJs with tens of nm in diameter for production. Once the MTJs are scaled beyond 2X nm, however, interfacial anisotropy, which is proportional to the MTJ area, becomes insufficient to achieve high thermal stability [4]. To overcome the limitation, the MTJ using quad interfaces was proposed to further enhance interfacial anisotropy for scaling down to 1X nm [5]. Still, scaling of those interfacial-anisotropy MTJs while achieving high performance is challenging for scaling beyond 10 nm. Shape anisotropy, which negatively impacts the total magnetic anisotropy in the interfacial-anisotropy MTJs, was shown to work positively in these dimensions [6]. By making a nanomagnet cylindrical with its thickness larger than its diameter, shape anisotropy turns the easy axis to the perpendicular direction instead of the in-plane easy-axis. In this way, both interfacial and shape anisotropy positively contribute to the total magnetic anisotropy, allowing one to scale MTJs beyond 10 nm. We made the MTJs with a 15-nm-thick FeB layer and achieved the MTJ scaling down to single-digit nanometers (X nm) while maintaining high Δ, yet observing STT switching [6]. Moreover, to understand the physics governing the temperature dependence of the properties of the shape-anisotropy MTJs, we studied the scaling relationship between the energy barrier E between parallel and anti-parallel states and spontaneous magnetization with respect to the temperature and compared it with that of the conventional interfacial-anisotropy MTJs. We found that E of the shape-anisotropy MTJs is less sensitive to temperature and that the shape-anisotropy MTJs have the potential to be used for wide-temperature applications at an X-nm scale [7]. The shape-anisotropy MTJ is proved to be promising for scaling down beyond 10 nm, but several challenges in the shape-anisotropy MTJ remain: (1) switching current is needed to be further reduced at short pulse and (2) an upper limit of a nanomagnetic thickness for coherent switching exists. These challenges are arising from a large volume (thickness) of a nanomagnet meeting high Δ. To address the challenges, we recently proposed the shape-anisotropy MTJ using multilayered ferromagnets, instead of a single ferromagnet [8]. The newly proposed shape-anisotropy MTJs have multilayered ferromagnets separated by MgO layer(s) so that the total ferromagnetic layer thickness can be reduced owing to the enhancement of total interfacial anisotropy. With the multilayered ferromagnet, we showed that a 5-nm-thickness reduction is achieved while obtaining the same Δ as the single ferromagnet and that the MTJs are scaled down to 2.3 nm. In addition, we demonstrated high performance in the X-nm shape-anisotropy MTJs with the multilayered ferromagnets: (1) stable switching (Fig. 1a) and high thermal stability (Fig. 1b) at high temperatures, (2) switching efficiency improvement (Fig. 1c), and (3) high-speed switching down to 10 ns with the voltage below 1 V (Fig. 1d). The shape-anisotropy MTJs in our studies use the CoFeB/MgO material system without introducing any new material. This means that the device structure can be readily employed in the existing MTJ technology by making a taller and smaller nanomagnet. Note that, not limited to the CoFeB/MgO material system, the concept of the shape-anisotropy MTJs can be adopted to other material systems; indeed, the concept was proved in Co or NiFe material systems [9]. Having the results and the versatility of the concept, the shape-anisotropy MTJs holds promise in the era of the ultimate scaling. This work was supported in part by JST-OPERA JPMJOP1611, JSAP KAKENHI JP19K04486 and JP19J12926, Cooperative Research Projects of RIEC, and DIARE of Tohoku University. J.I. acknowledges financial support from GP-Spin of Tohoku University and JST-OPERA.

**References:**

[1] S. Ikeda et al., Nat. Mater. 9, 721 (2010). [2] B. Jinnai et al., Appl. Phys. Lett. 116, 160501 (2020). [3] H. Sato et al., Appl. Phys. Lett. 101, 022414 (2012). [4] H. Sato et al., Appl. Phys. Lett. 105, 062403 (2014). [5] K. Nishioka et al., VLSI Symp., T120 (2019). [6] K. Watanabe et al., Nat. Commun. 9, 663 (2018). [7] J. Igarashi et al., Appl. Phys. Lett., to be published (2021). [8] B. Jinnai et al., IEEE IEDM, 24.6 (2020). [9] N. Perrissin et al., Nanoscale 10, 12187 (2018).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/5fe6f9d12904bf2ac31236552f543ec7.jpg)
Table 1. Evolution of (Co)FeB/MgO-based MTJ structures with a perpendicular easy-axis.

![](https://assets.underline.io/uploads/markdown_image/1/image/18e8ce4784e37f1a345a22a3c60bdfce.jpg)
Figure 1. (a) R-H curves at various temperatures [left panel: CoFeB (5)/MgO/CoFeB (5) at D = 7.1 nm; right panel: CoFeB (7.5)/MgO/CoFeB (7.5) at D = 7.6 nm]. (b) Temperature dependence of Δ in the respective MTJs. (c) Switching efficiency Δ/IC0 with respect to D. (d) R-V curves at various pulse widths down to 10 ns with D = 7.6 nm.

 Material, Device Engineering, and Performance INVITED

Shape-anisotropy magnetic tunnel junction (MTJ) [1], having a cylindrical free layer, is promising for deeply scaled spin-transfer torque magnetoresistive random access memory (STT-MRAM). In shape-anisotropy MTJs, positively utilizing the shape anisotropy as well as the interfacial anisotropy allows one to reduce the MTJ diameter D below 10 nm while simultaneously keeping the thermal stability factor Δ high and capability of STT switching [1-4]. Of particular interest in the shape-anisotropy MTJs is the magnetization reversal mode, which is critical in quantifying Δ with high accuracy. In the conventional interfacial-anisotropy MTJs with such a small size (D &lt; 30 nm), magnetization dynamics of the free layer can be reasonably described by a single-domain (coherent reversal) model. On the other hand, in shape-anisotropy MTJs, micromagnetic simulation in previous studies suggests that magnetization reversal mode depends not only on D but also on the thickness t; the MTJs with too-thick a free layer (t &gt; ~30 nm) switch incoherently, imposing an upper limit of Δ and also causing a switching delay [2,5]. In this study, we experimentally study the magnetization reversal mode in shape-anisotropy MTJs with various free layer thicknesses and diameters to reveal the crossover of coherent/incoherent reversal. A stack structure of, from the substrate side, Ta (5)/Ru (10)/Ta (15)/synthetic ferrimagnetic reference layer/MgO/(Co0.25Fe0.75)75B25 (t = 15, 30, and 50)/MgO/Ru (5) is deposited by dc/rf magnetron sputtering on a thermally oxidized Si substrate. The numbers in parentheses are nominal thicknesses in nm and t represents the free-layer CoFeB layer thickness. For some samples with t = 50 nm, Ta (5) capping layer is used instead of MgO, which is confirmed to have little impact on the findings described below. The stacks are processed into circular MTJs with various D by electron beam lithography, reactive ion etching, and multistep Ar ion milling [1]. To study the magnetization reversal mode, we evaluate astroid curves by measuring the magnetic-field-angle dependence of switching fields [6,7]. We also investigate the thickness range in which the coherent reversal model is applicable by comparing Δ values experimentally determined under an assumption of the coherent reversal and those expected from the calculation. Figure 1 shows the magnetic-field-angle dependence of a switching field in a cartesian coordinate, the so-called astroid curve, for the shape-anisotropy MTJs with t of 15 nm and 50 nm. The solid curve is the best fit based on the coherent reversal model as used in [6]. As can be seen, the fitting degree is different for each t. For t = 15 nm, the experimental result is well explained by the fit, indicating a coherent reversal, which is consistent with the previous result on a FeB-based shape-anisotropy MTJ with the same free-layer thickness [5]. On the other hand, for the t = 50 nm case, the fit is poor; the switching field along the easy-axis (μ0Hx = 0 mT, where μ0 is the permeability in vacuum) is smaller compared with the other angles (|μ0Hx| &gt; 0). Such a distortion is also seen for t = 30 nm with D &gt; ~15 nm. Similar behavior was reported in a Py nanowire, and was explained by a buckling mode [9]. The similarity suggests that magnetic moments in the shape-anisotropy MTJs with a thicker and larger-diameter free layer is reversed incoherently via an oscillatory buckling along the thickness direction. Next, we measure the switching probability using a pulsed magnetic field and evaluate Δ with a coherent reversal model [10]. The obtained Δ is plotted as a function of D in Fig. 2. The solid curves represent the calculation based on the coherent reversal model, where the whole volume contributes to the energy barrier. For D &lt; ~15 nm, the measured Δ value agrees well with the calculated one, whereas D &gt; ~15 nm is much smaller, backing up interpretation of the difference observed in the astroid-curve measurement as crossover of the magnetization reversal mode. In summary, we investigate the magnetization reversal mode and thermal stability factor in shape-anisotropy MTJs with various free-layer thicknesses and diameters. We reveal that the magnetization reversal in the MTJs with thicker and larger-diameter free layer proceeds incoherently, affecting the retention property. This study provides a key understanding of the magnetization reversal in the shape-anisotropy MTJs. This work was supported in part by JST-OPERA, JSPS KAKENHI (JP19J12926 and JP19K04486), and DIARE. J.I. and K.W. acknowledge financial support from GP-Spin and JST-OPERA.

**References:**

[1] K. Watanabe et al., Nature Commun. 9, 663 (2018). [2] N. Perrissin et al., Nanoscale 10 12187 (2018). [3] J. Igarashi et al., Appl. Phys. Lett., to be published (2021). [4] B. Jinnai et al., IEEE IEDM, 24.6.1 (2020). [5] K. Watanabe et al., International Conference on Magnetism 2018, F6-01 (2018). [6] N. Kikuchi et al., IEEE Trans. Magn. 41, 3613 (2005). [7] R. Dittrich et al., J. Appl. Phys. 97, 10J705 (2005). [8] J. Igarashi et al., Appl. Phys. Lett. 111, 132407 (2017). [9] A. B. Oliveria et al., Phys. Rev. B 78, 024423 (2008). [10] Z. Li et al., Phys. Rev. B 69, 134416 (2004).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/09cef5af19c31a24332dd558ca93eedc.jpg)
Figure 1 Experimental results of magnetic-field-angle dependence of switching field in the shape-anisotropy MTJs for the thickness of (a) 15 nm and (b) 50 nm with MgO capping layer. The lines correspond to the best fitting based on the coherent reversal model.

![](https://assets.underline.io/uploads/markdown_image/1/image/7af8e6f3b37af4ec0b1579568cbc20eb.jpg)
Figure 2. Thermal stability factor Δ as a function of D in the shape-anisotropy MTJs for the thickness of 15 [4], 30, and 50 nm. For the samples with t = 50 nm, Ta (5) capping layer is used. The curves correspond to the calculation based on the coherent reversal model.

 Crossover of magnetization reversal mode with thickness and diameter in shape-anisotropy magnetic tunnel junctions

Unconventional computing utilizing the probabilistic nature of physical systems – probabilistic computing – has recently gathered much attention for its potential to effectively address computationally complex problems [1]. A stochastic magnetic tunnel junction (MTJ) is a promising element to construct a probabilistic bit (p-bit), a fundamental building block of the probabilistic computers, owing to fast fluctuation rate and high controllability as well as the manufacturability based on current spin-transfer torque (STT) magnetoresistive random access memory (MRAM) technology. Recently, a proof of concept of the probabilistic computer using stochastic MTJs was presented, where integer factorization was demonstrated as an illustrative example of a combinatorial optimization problem [2]. Performance of stochastic MTJs is characterized by a time-varying fluctuation of magnetization and time-averaged response to the external field and current, and in this regard, understanding the physical mechanism governing these properties is of high importance. In this research, we investigate the mechanism governing the sigmoid-like time-averaged response to external field and current in stochastic MTJs with various sizes. We use the same stack structure used in the demonstration of integer factorization [2], i.e., Ta(5)/ Pt(5)/ syntheic ferrimagnet/ Ta(0.3)/ Co19Fe56B25(1)/ MgO(1.1)/ Co19Fe56B25(t)/ Ta(5)/ Ru(5) (thickness in nm), which is deposited by dc/rf magnetron sputtering on a thermally oxidized Si substrate. Both top and bottom CoFeB layers have perpendicular easy axis. We design the thickness of the free layer t so that the thermal stability factor Δ0 is low enough to show superparamagnetic behavior. All films are processed into MTJs with various junction diameters D by electron beam lithography and Ar ion milling. We determine D of each device from their electrically measured resistance R, with a resistance area product RA determined from several MTJs with D ~ 80 nm. Typical TMR ratio is 90% and RA = 6.3 Ωμm2. The measurement circuit for the time-averaged resistance 〈R〉 is shown in Fig. 1(a). We monitor the magnetization fluctuation of the MTJ by measuring R vs. time under dc bias current I with various magnitudes using an oscilloscope connected in parallel to the MTJ. The relaxation time τ of the studied MTJ is found to range from 1 ms to 1 s, corresponding to Δ0 of 14 to 21, by assuming the Néel-Arrhenius law, τ = τ0expΔ0 with τ0 being attempt time 1 ns [3]. The 〈R〉 against external perpendicular magnetic field H and I for the MTJ with nominal D = 50 nm are shown in Figs. 1(b) and (c), respectively. Clear sigmoidal-like characteristics with respect to H and I are observed as a result of the change of the ratio of τ in parallel (P) and anti-parallel (AP) states τP/τAP. We normalize 〈R〉 using resistances at P and AP states as 〈r〉 ≡ τP/(τP + τAP). The normalized sigmoid curves 〈r〉 against H and I are shown in Figs. 1(d) and (e), respectively. In order to characterize the external field and current dependences of stochasticity of MTJs, we derive an analytical expression of the slope of the sigmoidal curve around the center (〈r〉 = 1/2) [see Figs. 1(d) and (e)]. We define the shift current IS and the shift field HS as I and H to take 〈r〉 = 1/2 (P state probability of 50%), respectively. When MTJs are in P (AP) state, τ is given by τP(AP) = τ0 exp{Δ0[1 ± (I - IS)/IC0]nI}, where nI is a switching exponent for I and IC0 the intrinsic critical current. Here, we assume nI = 2, which was derived by analyzing the Fokker-Planck equation [4]. Then, the partial derivative of 〈r〉 (= τP/(τP + τAP)) with respect to I at I = IS is derived to be ∂〈r〉/∂I|I=Is = Δ0/IC0, which has been used as a figure of merit of STT switching in nonvolatile MTJs [5-7]. We apply the same procedure for ∂〈r〉/∂H and obtain ∂〈r〉/∂H|H=Hs = Δ0/HKeff with HKeff being the perpendicular effective anisotropy field. Experimentally measured ∂〈r〉/μ0∂H|H=Hs and ∂〈r〉/∂I|I=Is for MTJs with different t are plotted as a function of D in Figs. 2(a) and (b), respectively. The H derivative of sigmoid curve ∂〈r〉/∂H|H=Hs monotonically increases with increasing D. Since the analytical expression of the H derivative, Δ0/HKeff, can be converted to MSAefft/2kBT (Aeff denotes an effective area for thermal activation), where the spontaneous magnetization MS, thermal energy kBT, and thickness t are independent of D, this result indicates that Aeff increases with the device size; in other words, relatively coherent magnetization switching takes place in this D regime. On the other hand, the I derivative, ∂〈r〉/∂I|I=Is, decreases with increasing D. The reason for this behavior is not clear but we note that a similar result is also observed in the size dependence of Δ0/IC0 in nonvolatile MTJs [5-7]. In conclusion, this work has studied the physical mechanism governing the sigmoid-like response of stochastic MTJs, which strongly affects the performance of probabilistic computing. We derived an analytical expression of the slope of sigmoid curve and experimentally show that the slope varies with the device size. This work is supported in part by JST-CREST JP1082016.

**References:**

[1] P. R. Feynman, Int. J. Theor. Phys. 21, 467 (1982). [2] W. A. Borders et al, Nature 573, 390 (2019). [3] W. F. Brown Jr., Phys. Rev. 130, 1677 (1963). [4] T. Taniguchi et al., Phys. Rev. B 83, 054432 (2011). [5] J. Z. Sun et al, Phys. Rev. B 84, 064413 (2011). [6] H. Sato et al, Appl. Phys. Lett. 105, 062403 (2014). [7] B. Jinnai et al., IEEE IEDM 24.6 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/dbe0f712d916203b266d2d43fc513b3a.jpg)
Fig. 1 (a) Measurement circuit and (b),(c) ((d),(e)) time averaged resistance 〈R〉 (sigmoid curve 〈r〉) as a function of external perpendicular magnetic field µ0H and bias current I, respectively (μ0 denotes a permeability in vacuum).

![](https://assets.underline.io/uploads/markdown_image/1/image/f482273c059d8cc39adbc62d2afcd307.jpg)
Fig. 2 (a)(b) Slopes of sigmoid curve 〈r〉 against μ0H and I, respectively, as a function of junction diameter D measured for the devices with different CoFeB free layer thicknesses t.

 Physical Mechanism Governing Sigmoid Curves of Stochastic Magnetic Tunnel Junctions

**Session chairs:** Hélène Béa, Université Grenoble Alpes, Spintec and Emilie Jué, National Institute of Standards and Technology


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Electrically connected spin-torque oscillators array for 2.4 GHz WiFi band transmission

Ultrafast Single Pulse All Optical Magnetization Switching of Ferromagnets

Electrically connected spin-torque oscillators array for 2.4 GHz WiFi band transmission and energy harvesting

Material, Device Engineering, and Performance INVITED

Crossover of magnetization reversal mode with thickness and diameter in shape-anisotropy magnetic tunnel junctions

Physical Mechanism Governing Sigmoid Curves of Stochastic Magnetic Tunnel Junctions

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