In superparamagnetic tunnel junctions (SMTJ), the energy barriers that separate the parallel and the antiparallel magnetization configurations are sufficiently small that the thermal noise causes stochastic magnetization fluctuations between the two states. Through magnetoresistance effects, those stochastic fluctuations give rise to telegraphic noise signals with two voltage levels (see Fig.1) [1, 2]. The relative average time spent in each of the two configurations can be controlled by an applied dc current via the spin-transfer torque. Due to their inherent stochastic nature, SMTJs are promising candidates for truly random number generator applications [3, 4], brain-inspired and probabilistic computing [5-10]. However, an external bias magnetic field was always required to fully operate the SMTJ’s with current, which represents a drawback to their integration with the required microelectronic circuits. In this work, we report for the first time, SMTJs that are fully controlled by DC current at zero applied magnetic field using perpendicular magnetic tunnel junctions (pMTJ). Stable pMTJs are used in densely magnetic memories [11], nevertheless their thermal stability can be strongly reduced by tuning their free layer thickness, leading to a superparamagnetic state. Here, we use pMTJ’s with a free layer thickness of t=1.6 nm, and with diameters ranging from 150 nm to 80 nm. By applying a DC current in one direction (sign), without any external bias field, we observe stochastic fluctuations in the resistance for dc currents between -0.3 mA and -0.27 mA. As shown in Fig. 2, the average probability in being in high and low resistance state is well controlled by the applied current. In order to obtain good statistics on the extracted probability, we record to stochastic transitions. We extracted the dwell time distribution, which follows an exponential distribution with a mean dwell time that is in agreement with the modified Néel-Brown model. The authors acknowledge partial funding from ERC MAGICAL No 669204, and the Nanoscience Foundation (Grenoble, France).

![](https://assets.underline.io/uploads/markdown_image/1/image/032d011551d8698e3dc1b74244af9c81.jpg)

Figure 1 : Experimental voltage time trace of the SMTJ.

![](https://assets.underline.io/uploads/markdown_image/1/image/f8c0fe8daabe77b0c738c5d388eadce3.jpg)

Figure 2 : The probability of occupancy of the high resistance state versus current.

Current controlled perpendicular superparamagnetic tunnel junctions operating at zero applied magnetic field

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

Wireless sensor networks (WSN) are part of our daily lives and their applications are growing years after years, especially with the advent of the Internet of Things. The price to pay is an increase in energy demand. Hence, the development of autonomous, adaptive, and energy-efficient communicating sensor solutions is a topic of intense research. One way to drastically reduce energy consumption is to wake up the main radio receiver of a WSN for communication only when needed. For that purpose, a wake-up receiver (WuRx) is used, which itself should operate with ultra-low power consumption and provide immunity to parasitic radio signals. Spintronic Resonators (SR) based on Magnetic Tunnel Junctions (MTJ) offer a promising solution to be incorporated in integrated wake-up radio circuits since they are extremely compact and can serve as passive RF-DC converters [1]. Another significant advantage of these spintronic devices is that they provide RF filtering capability, responding in a narrow frequency band around their resonance frequency making it possible to demodulate amplitude or frequency modulated signals with high sensitivity [1, 2]. To achieve this, there is a need for an electrical model of MTJs used as RF-to-DC converters, to offer the possibility to investigate their potentialities once integrated in an actual radio receiver (sensitivity, energy consumption) and facilitate the choice for a modulation scheme in order to optimize the communication power efficiency. The model must be compact, include the physical equations, be generic (can be extended to other types of spintronic junctions), and easy to implement. As a preamble to this model extraction, we have explored the characteristics of one type of SR device, based on the vortex configuration (V-SR), for the case of passive detection and zero DC current biasing. Under zero external magnetic field, V-SRs are working in the 150-400 MHz range [2]. The observed characteristics concern i) RF-DC conversion efficiency ii) V-SRs input impedance matching, iii) demodulation capabilities. All these criteria will contribute to the final sensitivity of the V-SR based WuRx. The equivalent model is then proposed by considering the MTJ-based SR as an RF power controlled DC voltage source with internal resistance. To investigate input impedance matching, the RF equivalent circuit is derived, as illustrated in Fig. 1. This model has been developed on the basis of RF reflection coefficient measurements (S-parameters obtained through a vector network analysis), I(V) measurements, and the physical equations of the ferromagnetic resonance frequency and the rectification DC voltage. In order to evaluate the parasitic parameters external to the junction, an additional measurement is performed on an Open circuit, consisting of the same feeding accesses as in Fig. 1 but without including the V-SRs. Hence, S-Parameters measurements enable to extract the internal parasitic elements of the junction itself (junction capacitance and inductive effect of the magnetic layers due to their high permeability). Also, I(V) DC measurements reveal the non-linear behavior of the V-SRs, enabling to determine the coefficients of the polynomial characteristic, outside resonance [3]. Indeed, the model must consider the effect of the ferromagnetic resonance, the center of interest for the RF-DC conversion. Physical equations from [2] enable to determine the value of the ferromagnetic resonance pulsation and the DC rectification voltage from the geometry of the junction, the RF power, and the DC current injected into the junction. Finally, the behavioral model gathers all equations considering parasitic effects (junction and feeding lines), the non-linear junction resistance through the I(V) characteristics, and the ferromagnetic resonance response in order to predict the rectifying effect of the V-SR in the whole frequency band of interest. Thirdly, the V-SR model derived from RF and DC measurements is implemented using an electronic design automation software system (ADS) by implementing symbolically defined devices (SDD) [4]. The necessary variables for DC rectification are embedded in the SDD component and rectification is observed through harmonic balance (HB) simulations. Simulation results of the DC rectification voltage are presented in Fig. 2 and compared with the measurement results. Finally, in order to test the demodulation capabilities, the input RF carrier frequency is fixed at the ferromagnetic resonance in order to benefit from the maximum rectified DC voltage and then modulated with an On-Off Keying (OOK) modulation scheme. We obtain for V-SRs data rates up to 20 Mbit/s for an input RF power of -15 dBm leading to a signal to noise ratio of more than 14 dB, which guarantees a bit error rate as low as 10-6 . It has to be noticed that 20 Mbit/s is within a comfortable margin regarding the typical data rates reported for existing WuRx in the literature [5]. Based on this performance, a complete RF wake-up system will be designed and tested. Future studies will extend the developed model to other MTJ devices such as described in Ref. [6] that allow for operation at higher frequencies (1-10GHz). Authors acknowledge financial support from ANR-SPINNET ANR-18-CE24-0012.

**References:**

[1] B. Fang et al., Phys. Rev. Applied, vol. 11, p. 014022 (2019) [2] A.S. Jenkins, et al. Nature Nanotech, vol. 11, p. 360 (2016) [3] H. Simon, K. Wu. IEEE, vol. 102, p. 11 (2014) [4] J. Wood, D. E. Root, et N. B. Tufillaro, IEEE, vol. 52, p. 2274 (2004) [5] H. Bello, al., Sensors 2019, vol. 19, p. 3078 (2019) [6] A. Chavent, al., doi.org/10.1016/j.jmmm.2020.166647

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/eaa806106a8ae13b6e25aa6660a1e1dc.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/2d47b79ba214cd19f3e4ce528801ea51.jpg)

 Compact Model of a Spintronic Resonator for Rectifying Purposes in Wireless Sensor Network Applications

**Session chair:** Denys Makarov, Helmholtz-Zentrum Dresden-Rossendorf


GOL - MRAM, Magnetic Logic and Related Devices II

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Current controlled perpendicular superparamagnetic tunnel junctions operating at zero applied magnetic field

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

Compact Model of a Spintronic Resonator for Rectifying Purposes in Wireless Sensor Network Applications

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