Recent progresses in quantum information technologies have demonstrated the benefits of leveraging coherence effects such as collective spin precession in ferromagnets in order to process information more efficiently. This coherent transfer between different waveforms is an important ingredient of the quantum information processing as it allows transport of quantum states without loss of frequency or phase. An efficient hybridization process requires to reach a strong coupling regime, where the interaction rate between two collective states becomes larger than their relaxation rates. While increasing the overlap integral between two spatio-temporal patterns is primarily a design issue, diminishing the internal friction inside an object is a much more complex task, which requires know-how in material research and growth technology. In spintronics, this has revived interest for insulating materials and in particular garnets, which are the magnetic materials benefiting from the lowest magnetic damping. The sound wave attenuation coefficient in garnets is also exceptional, i.e. up to an order of magnitude lower than that in single crystalline quartz. In addition to the low damping of magnetic and sound waves, a strong coupling can be established between spin-waves (magnons) and lattice vibrations (phonons) through the magnetic anisotropy and strain dependence of the magnetocrystalline energy in magnetic garnets. The magnetoelasticity leads to new hybrid quasiparticles (“magnon polarons”) when spin wave and acoustic wave dispersions cross [1]. This coupling has been exploited in the past to produce microwave acoustic transducers [2]. The adiabatic conversion between magnons and phonons in magnetic field gradients proves their strong coupling in yttrium iron garnet (YIG) [3]. Here we first demonstrate that the spin waves can be strongly coupled to coherent transverse sound waves that have very long characteristic decay length and propagate ballistically over millimetric distances. The experiment was performed at room temperature with a magnetic field applied perpendicular to the film. Our sample consists of two 200 nm thick YIG layers deposited on both sides of a 0.5 mm thick gadolinium gallium garnet (GGG) substrate. The circularly polarized standing sound waves couple to the magnetization oscillations in both layers. An interference pattern is observed and it is explained as the strong coupling of the magnetization dynamics of the two YIG layers either in phase or out of phase by the standing transverse sound waves [4]. This long range coherent transport of spin by phononic angular momentum can add new functionalities to insulator spintronic circuits and devices. Furthermore, such mediation of coherent spins could induce a novel dynamic exchange coupling in a spin-valve system when the magnetic resonances of two layers are brought within the strength of the magnetoelastic coupling. To detect such coupling, a Pt strip electrode was deposited on one YIG layer to monitor its dynamics through the inverse spin Hall effect (ISHE). This improves the measurement sensitivity of the phonon mediated spin transfer. In our sample, the two YIG layers have initially different spontaneous magnetizations. We tune the difference between two magnetic resonances either i) by varying the polar angle of an external magnetic field or ii) by applying a temperature gradient along the stack direction. The existence of the novel dynamic coupling is evidenced by an emergence of the “bright” and “dark” collective states in both measurements. Our observation of such collective modes resembles the level attraction/repulsion behavior between two hybridized modes [5]. This feature is similar to the coupling control via microwave phase [6]. We show that the observed behavior is in agreement with theoretical predictions. Finally we discuss the detection of heat carried by coherent phonons. We measure thermal voltages across Pt in YIG|GGG|Pt system, where no ISHE voltage should be present. The signal appears only at the acoustic phonon resonances indicating that the heat can be efficiently carried by circularly polarized coherent phonons excited by magnons. When the magnetic field direction is tilted away from the film normal direction, the signal vanishes, suggesting that the heat carried by acoustic phonons becomes less coherent. We perform several control experiments, which shows the universality of the signal and possible enhancement schemes.

**References:**

[1] T. Kikkawa, K. Shen, B. Flebus et al., Phys. Rev. Lett. 117, 207203 (2016) [2] M. Pomerantz, Phys. Rev. Lett. 7, 312 (1961) [3] J. Holanda, D. S. Maior, A. Azevedo et al., Nat. Phys. 14, 500 (2018) [4] K. An, A.N. Litvinenko, R. Kohno et al., Phys. Rev. B 101, 060407(R) (2020) [5] M. Harder, Y. Yang, B. M. Yao et al., Phys. Rev. Lett. 121, 137203 (2018) [6] I. Boventer, C. Dörflinger, T. Wolz et al., Phys. Rev. Research 2, 013154 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/6b745abdcceba5bf7d855dd387b11ad1.jpg)
Theoretical calculation of (a,b) the dark and (c,d) bright states formation. The insets show the magnetic precession states of both layers when (a) even or (c) odd phonon mode mediates the coupling between two magnetic layers. The dashed lines show the calculated eigenvalues. The linecuts in (b) and (d) are along the zero detuning case.

 Long range coupling of magnetic bilayers by coherent phonons

The mutual synchronization of spin-torque nano-oscillators (STNOs) arranged in a large array improves the individual properties of each STNO, increasing the output-power and reducing the linewidth of the emitted signal. These improvements are required to implement STNOs in wireless communication schemes [1] and furthermore open applications for different oscillator based neuromorphic computing schemes [2]. Many theoretical and experimental studies considered single STNO devices [3], while experimentally the synchronization of a large number of STNOs remains a challenging task [4]. This is because the synchronized state and the phase-locking depend on the geometry, device resistance, input signals, coupling mechanism, among others [5]. As a first step to guide experiments on the synchronization behavior of STNO arrays, we have undertaken a theoretical study, combining numerical and analytical approaches based on the spin-wave formalism [3]. The STNO devices considered here are of circular cross-section (100nm in diameter) with a perpendicular polarizer and an in-plane magnetized free layer under a strong out-of-plane field. This field is larger than the saturation field. The free layer magnetization is orientated out-of-plane leading to an out-of-plane precession mode that is advantageous to induce strong dipolar coupling between STNOs, which is the coupling mechanism considered here. We derived analytically the coupled equations of amplitudes and phases where the latter are similar to the Kuramoto-phase equation, but limited to a finite number of devices. Solving for the stationary states, this model provides analytical expressions for the locking-range, the stationary amplitudes, and the frequency of oscillations of the synchronized state. These solutions depend on the array geometry, number N of STNOs in the array, separation between STNOs, distribution of the DC current, as well as the different magnetic material parameters, and the external magnetic field. In this work, we investigate the solution of these equations for two specific array geometries: a straight line and a ring structure (N=3,6 and 10), shown in figure 1b. Our results show that the locking-range depends on the separation among the STNOs (because this scales the coupling strength), but it is independent of the angle among them. Furthermore, we show that the locking-range is larger when the STNOs are placed in a ring structure (or triangle for N=3) as compared to a straight-line structure. Finally, the most interesting result is that for the ring structure, we identify two dynamic modes that represent a standing wave for the STNO phases along the ring structure (observed for N&gt;5). These two dynamics modes are shown in Fig. 2 and are called here (a) the in-phase mode, with identical phases for all STNOs, and (b) the out-of-phase mode, where the phase difference between two adjacent STNOs is 2π/N. We study how these states and their existence range are modified upon variation of the current density through the different STNOs (identical and non-identical currents), the STNO separation, and the number of STNOs in the ring. The analytical results are in good agreement to the numerical solutions of the Landau-Lifshitz-Gilbert (LLG) equation, as long as the separation among the STNOs is above a certain critical value. For smaller separations, the dipolar interactions become too strong and non-linear effects would require to go beyond the first-order approximations used to solve the amplitude and phase equations. The results reported here represent a first step to validate the phase equations and to define their limitations, and can be used to address now the Kuramoto equations to find solutions for large scale structures (N very large). We acknowledge financial support in Chile from FONDECYT 1200867, and Financiamiento Basal para Centros Científicos y Tecnológicos de Excelencia AFB 180001. D. M.-A. acknowledges Postdoctorado FONDECYT 2018, 3180416. M. A. Castro acknowledges Conicyt-PCHA/Doctorado Nacional/2017-21171016. The project was supported in part by ERC Advanced Grant MAGICAL No. 669204

**References:**

[1] T. Chen, et al., Proceedings of the IEEE., 104, 1919-1945(2016). [2] J. Grollier, et al., Nat. Electron. 3, 360 (2020). [3] A. Slavin and V., Tiberkevich, IEEE Trans. Magn., 45,1875(2009). [4] S. Tsunegi, et al., Scientific Reports., 8, 13475(2018). [5] R. Lebrun, et al., Nat. Commun. 8, 15825 (2017).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/67e3f596fc435dd303beec991462b132.jpg)
Fig.1: (a) Schematics of an STNO device and (b) two configurations for a coupled STNO array.

![](https://assets.underline.io/uploads/markdown_image/1/image/fdc26dc3ca23f437e028887120de5d0d.jpg)
Fig. 2: Schematics of the two dynamic modes obtained for the ring structure. The snapshots show the instantaneous distribution of the x- and y- components of the magnetization in three consecutive time steps t1 < t2 < t3, for (a) the in-phase and (b) the out-of-phase modes.

 Mutual synchronization of an array of spin-torque oscillators with perpendicular polarizer

In modern radar and communication systems it is important to determine the frequency composition of complex external signals on the µs time scale and faster [1]. Common swept-tuned spectrum analyzers (SA) are limited to sweep times of 10-100 ms determined by the characteristic times of macroscopic VCOs and YIG-tuned reference oscillators. In contrast, recent progress in spintronics has led to the development of spin-torque nano-oscillators (STNO) generating in the GHz frequency range, and naturally having time constants of the order of several nanoseconds determined by the intrinsic properties of magnetization dynamics at nano-scale [2]. In [3] it was proposed theoretically and in [4] demonstrated experimentally for a vortex-state configuration that STNOs can be used as a central element of an ultra-fast spectrum analyzer. A fastest sweep rate of 0.67us was achieved for spectral analysis in the range of 25MHz around center frequency of 300MHz. Here we focus on increasing the bandwidth and operational frequency of the STNO SA concept. For this purpose a special uniform-state STNO was nanofabricated. We show that our uniform-state STNO has a very wide frequency-current tuning range and high operational frequency. With such an STNO we pushed the STNO-based SA concept to a central frequency of 9 GHz. The corresponding SA performances sufficiently exceed the results obtained with a vortex-state STNO with a reduced sweep time of T = 20 ns, and a record sweep range of 1GHz (limited mostly by STNO power and not by the tuning range capabilities) keeping the RBW (resolution bandwidth) close to the theoretical limit (50 MHz). This GHz-frequency technique of spectrum analysis was implemented as shown in Fig.1. The STNO was used as a local oscillator whose frequency was sweep-tuned via an additional saw-tooth sweep signal. The STNO output is, then, mixed with the input signal, digitized, and processed with a matched filter, resulting in a narrow output peak whose temporal position corresponds to the input frequency while the width determines the RBW. In the top panel of the inset of Fig.1 we show a series of peaks obtained with an input signal whose frequency was changing in time in a saw-tooth manner with a period of 500ns. The sweeping rate of the STNO SA was chosen 10 times faster so that the changes of the input signal frequency could be correctly tracked. As can be seen from the spectrogram in the bottom panel of the inset, the shape of the instantaneous input frequency was successfully tracked with sufficient RBW of 34.6MHz. Financial support is acknowledged from the EC program ERC MAGICAL 669204, from the NSF of the USA (Grants # EFMA-1641989 and “ECCS-1708982), and by the US AFOSR (MURI grant # FA9550-19-1-0307).

**References:**

[1] V.C., Chen and W.J., Miceli, “Time-varying spectral analysis for radar imaging of manoeuvring targets”, IEEE Proceedings - Radar, Sonar and Navigation 145, 262-268 (1998). [2] T. Chen, et al., “Spin-Torque and Spin-Hall Nano-Oscillators”, IEEE Proceedings, 104, 1919-1945 (2016). [3] S. Louis, et al., “Ultra-fast wide band spectrum analyzer based on a rapidly tuned spin-torque nano-oscillator”, Applied Physics Letters 113, 112401 (2018). [4] A. Litvinenko, et al., “Ultrafast sweep-tuned spectrum analyzer with temporal resolution based on a spin-torque nano-oscillator,” Nano Letters 20; 6104-6111 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/ae175606696079038bdd43c4e48d7b6b.jpg)
Fig.1. Ultra-fast GHz STNO-based spectrum analyzer. In the inset, top panel, left axis: Vspec vs time for 10 consecutive sweeps. Right axis: The time variation of the input signal frequency fin. 
Bottom panel: fspec vs time in the form of waterfall spectrogram.

 Ultra-fast spectrum analysis at GHz frequencies using spin-torque nano-oscillators

Perpendicular magnetic tunnel junctions (pMTJs) constitute the basic element for magnetic random access memories [1], thanks to their non-volatility, high density, and low power consumption. Their multifunctional properties make it possible to operate also as magnetic field sensors, spin torque nano-oscillators (STNO) or microwave signal detectors [2]. However, quite generally their interfacial perpendicular anisotropy (iPMA) is very sensitive to temperature, and thus to Joule heating when an electric current is passed through them [3]. The induced heating decreases the perpendicular anisotropy and thereby reduces the thermal stability and the potential for memory applications of pMTJs. Nevertheless, here we demonstrate that Joule heating induced modifications of iPMA can be of advantage for radiofrequency (RF) signal generation and detection, that will find applications within wireless communication systems used for the Internet of things (IoT). Quite generally, one can distinguish two different RF dynamical regimes and excitations. The first one is the RF signal generation, where upon injection of a DC current, the spin transfer torque (STT) induces steady state oscillations. The second is the RF signal detection, where an injected RF voltage, (in absence or presence of an additional DC current), excites resonantly via STT the magnetization, which results in a rectified DC voltage in the output. Both regimes have been demonstrated in numerous experiments and are promising for RF applications such as wireless communications [4] or ultra-fast spectrum analysis [5], as well as for neuromorphic computation [6]. A major advantage of MTJ structures is their GHz operational frequency, their high frequency tunability, the possibility to sweep-tune the frequency on short time scales as well as their high sensitivity to low RF power signals [7]. Here we report on the Joule heating effects in pMTJs for both: STT induced RF signal generation and active (RF + DC) RF signal detection. Results are presented for two types of pMTJs, one for which the free layer (FL) thickness is t = 1.4 nm and one with t = 1.8 nm. This FL thickness determines the orientation of the FL magnetization (in-plane for t=1.8nm, out-of-plane for t=1.4nm) due to the competition between the iPMA and the demagnetizing energy. For pMTJs with FL thickness of t = 1.8 nm (in-plane FL), under in plane and/or out of plane bias fields, only damped oscillations have been detected when injecting a DC current. The most interesting result here is a very large frequency shift with DC current characterized by a slope of -4 GHz/mA that occurs for both current signs. We attribute this current-sign-independent frequency shift to the changes in the iPMA due to Joule heating. However, the STT effect is noticeable in the power of the excitations, see Fig. 1a. This will be important for the RF signal detection, where for one current sign it enhances the output voltage by a factor of 4, and strongly reduces it for the opposite sign. The frequency tuning via current will be of interest for the RF signal detection because it allows one to easily tune the detection frequency band in a relatively large range, as illustrated in Fig. 1b, without the need of an external applied field. We emphasize that this tuning is attributed to the Joule heating and not to the STT that does not lead to strong frequency shifts in the damped regime. However, a similarly high frequency tuning has also been observed in the steady state oscillation regime for devices with FL thickness t = 1.4 nm (out-of-plane FL) under DC current and out-of-plane field . The corresponding frequency tuning is close to - 3 GHz/mA (frequency redshift) with a minimum linewidth of 30 MHz. In view of applications, we tested the frequency modulation using sinusoidal rf signals. Modulation was observed for modulation frequencies larger than 1 GHz, which greatly exceeds the amplitude relaxation frequency given by ΓP ( ~ 200 MHz) of the uniform STNO. Analysis of the phase noise indicates that there are two cut-off frequencies one due to the amplitude relaxation and one due to the heating. To conclude, this work demonstrates how Joule heating in pMTJs can be exploited to add functionalities to RF signal generation and detection. The authors acknowledge partial funding from ERC MAGICAL No 669204, the Nanoscience Foundation (Grenoble, France) and the EU Horizon 2020 project GREAT No 687973.

**References:**

[1] IKEDA, S., MIURA, K., YAMAMOTO, H., et al. Nature materials, 2010, vol. 9, no 9, p. 721-724. [2] CHAVENT, A., IURCHUK, V., TILLIE, L., et al. Journal of Magnetism and Magnetic Materials, 2020,vol. 505, p. 166647. [3] STRELKOV, N., CHAVENT, A., TIMOPHEEV, A., et al. Physical Review B, 2018, vol. 98, no 21, p. 214410. [4] JENKINS, Alex S., ALVAREZ, Lara San Emeterio, FREITAS, Paulo P., et al. Scientific reports, 2020, vol. 10, no 1, p. 1-7. [5] LITVINENKO, Artem, IURCHUK, Vadym, SETHI, Pankaj, et al. Nano letters, 2020, vol. 20, no 8, p. 6104-6111. [6] GROLLIER, Julie, QUERLIOZ, Damien, CAMSARI, K. Y., et al. Nature electronics, 2020, vol. 3, no 7, p. 360-370. [7] FANG, Bin, CARPENTIERI, Mario, HAO, Xiaojie, et al. Nature communications, 2016, vol. 7, no 1, p. 1-7.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/52188146d083bb35c2153b447c2a32a4.jpg)
Fig.1 : Frequency tuning of damped oscillations observed for both current signs, measurement carried out under an 800 Oe in-plane bias field.

![](https://assets.underline.io/uploads/markdown_image/1/image/ab8dbe5ee73ac660f44ede16b088140f.jpg)
Fig.2 : RF rectification voltage vs DC current, for input signals of different frequencies: 10.4 GHz to 9 GHz.

 Broadband RF detection and GHz modulation rates enabled by Joule heating in perpendicular anisotropy magnetic tunnel junctions

In modern radar and communication systems it is important to determine the frequency composition of complex external signals on the µs time scale and faster [1]. Common swept-tuned spectrum analyzers (SA) are limited to sweep times of 10-100 ms determined by the characteristic times of macroscopic VCOs and YIG-tuned reference oscillators. In contrast, recent progress in spintronics has led to the development of spin-torque nano-oscillators (STNO) generating in the GHz frequency range, and naturally having time constants of the order of several nanoseconds determined by the intrinsic properties of magnetization dynamics at nano-scale [2]. In [3] it was proposed theoretically and in [4] demonstrated experimentally for a vortex-state configuration that STNOs can be used as a central element of an ultra-fast spectrum analyzer. A fastest sweep rate of 0.67us was achieved for spectral analysis in the range of 25MHz around center frequency of 300MHz. Here we demonstrate that an ultra-fast sweep-tuned spectrum analysis can be performed at a central frequency of 3 GHz using uniform-state STNOs. The obtained SA performances sufficiently exceed the results obtained with a vortex-state STNO with a reduced sweep time of T =0.1µs, sweep range of 400 MHz (limited by the STNO power and not by tuning range capabilities) keeping the RBW (resolution bandwidth) close to the theoretical limit (14 MHz). This GHz-frequency technique of spectrum analysis was implemented as shown in Fig.1. The STNO was used as a local oscillator whose frequency was sweep-tuned by injecting a saw-tooth sweep signal. The STNO output (a) is, then, mixed with the input signal (b), digitized (c), and processed with a matched filter, resulting in a narrow output peak (d) whose temporal position corresponds to the input frequency while the width determines the RBW. Financial support is acknowledged from the EC program ERC MAGICAL 669204, from the NSF of the USA (Grants # EFMA-1641989 and “ECCS-1708982), and by the US AFOSR (MURI grant # FA9550-19-1-0307). The EC program GREAT is acknowledged for provision of perpendicular MTJ devices operating at GHz frequencies.References: [1] Chen, V.C. and Miceli, W.J., “Time-varying spectral analysis for radar imaging of manoeuvring targets”, IEEE Proceedings - Radar, Sonar and Navigation 145, 262-268 (1998). [2] Tingsu Chen, et al., “Spin-Torque and Spin-Hall Nano-Oscillators”, IEEE Proceedings, 104, 1919-1945 (2016). [3] Louis, S. et al., “Ultra-fast wide band spectrum analyzer based on a rapidly tuned spin-torque nano-oscillator”, Applied Physics Letters 113, 112401 (2018). [4] A. Litvinenko, et al., “Experimental demonstration of a rapid sweep-tuned spectrum analyzer with temporal resolution based on a spin-torque nano-oscillator,” arXiv preprint arXiv:2004.03508, (2020).

Ultra-fast Spectrum Analysis at GHz frequencies using Spin-Torque Nano-Oscillators

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Artem Litvinenko

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Presentations

Long range coupling of magnetic bilayers by coherent phonons

Mutual synchronization of an array of spin-torque oscillators with perpendicular polarizer

Ultra-fast spectrum analysis at GHz frequencies using spin-torque nano-oscillators

Broadband RF detection and GHz modulation rates enabled by Joule heating in perpendicular anisotropy magnetic tunnel junctions

Ultra-fast Spectrum Analysis at GHz frequencies using Spin-Torque Nano-Oscillators

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