Magnetoresistive field sensors have a wide range of uses, such as in biomedical applications, in the automotive industry, robotics, or smart city technologies. Figures of merit like sensitivity, detectivity and spatial resolution are used to evaluate the performance of such sensors [1]. At low frequencies, the 1/f noise component is dominant and is in fact responsible for hindering the device's detectivity, and, consequently, its performance. There is an active research effort to reduce this noise component and tackle this limitation [2]. Vortex-based devices, in which the free layer exhibits a vortex magnetization distribution in its equilibrium state, are promising magnetic field sensors due to their large linear detection range [3] and the fact that they show practically no hysteresis in this range. Besides, these devices are often considered as model systems for the study of magnetization dynamics. In this study, we focus on the analysis of the 1/f noise in a particular type of magnetic sensor based on a vortex magnetic configuration integrated in a magnetic tunnel junction (MTJ) spin torque nano-oscillator. These devices present excellent rf characteristics for future radio-frequency devices and applications, such as rf generation [4], detection [5] or neuromorphic computing [6]. While the use of vortex-based spin-torque nano-oscillators for applications such as these mentioned here has been largely studied, they are newcomers in the magnetic field sensing landscape. In this work, we analyse the 1/f low-frequency noise in vortex-based spin-torque nano-oscillators by determining the Hooge parameter in different conditions. The Hooge parameter is typically used to characterize and compare sensor’s noise properties. Firstly, we find that in the uniform states the Hooge parameter of the studied device is comparable to that measured in state-of-the-art TMR sensors with similar RA product, α = 10-11 - 10-10 µm2. In the vortex state, the measured noise level is around one order of magnitude greater than in the parallel (and antiparallel) state, see Fig. 1a. This is due to the increased probability of pinning of the vortex core into defects or inhomogeneities of the free layer. Secondly, we determine that the dynamics of the vortex core strongly influence the noise level of the device. For a current above a certain threshold, the spin transfer torque surpasses the intrinsic damping of the free layer resulting in self-sustained oscillations of the vortex core [7]. In the self-sustained oscillations' regime, the noise decreases to a level close to that of the antiparallel state, see Fig. 1b. Furthermore, we present a novel strategy for reducing the 1/f low-frequency magnetic noise, through the application of an in-plane rf field or injection of an rf current [8]. By using this approach while the device is operating in the self-sustained regime, we are capable of further decreasing the measured noise level to values close to the minimum attainable, see Fig. 2. We find that this noise reduction is non-resonant, see Fig. 2a. As such, we can have a vortex-based STNO with relevant noise properties, comparable to those of state-of-the-art TMR field sensors. At the same time, we profit from the specific advantages of vortex-based spin-torque nano-oscillators for sensing applications: large linear detection range, virtually no hysterisis and high spatial resolution. This noise reduction technique based on the spin-torque dynamics of the vortex can have an impact on the sensors' industry, which may profit from the advantages of the vortex configuration. The work is supported by the French ANR project “SPINNET” ANR-18-CE24-0012.

**References:**

[1] D. C. Leitão et al., Nanotechnology 27, 045501 (2015) [2] L. Huang et al., Journal of Applied Physics 122, 113903 (2017); J. Moulin et al., Appl. Phys. Lett. 115, 122406 (2019) [3] D. Suess et al., Nat. Electronics 1, pages 362–370 (2018) [4] S. Wittrock et al., Phys. Rev. B 99, 235135 (2019) [5] A. S. Jenkins et al., Nat. Nanotech. 11, 360 (2016); D. Marković et al., Phys. Rev. Applied 13, 044050 (2020) [6] M. Romera et al., Nature 563, 230–234 (2018); J. Torrejon et al., Nature 547, 428-431 (2017) [7] A. Dussaux et al., Nat. Comm. 1, 8 (2010) [8] M. Jotta Garcia et al., arXiv:2012.09616 [cond-mat.mes-hall] (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/f1e2a4020c2f2daf24d07405919ec60f.jpg)
Fig.1 a) Hooge parameter as a function of an in-plane magnetic field that is swept from the parallel to the anti-parallel state and back. b) Evolution of the Hooge parameter with the applied bias current. The inset shows the oscillation power of the rf emission due to the emerging vortex dynamics. The red dotted line represents the Hooge parameter measured in the AP state.

![](https://assets.underline.io/uploads/markdown_image/1/image/8659329698821b38c65d8cb8989eb4a3.jpg)
Fig. 2 a) Hooge parameter as a function of the frequency of the applied oscillating field, with Prf = 1 mW. The red line indicates the value measured in the absence of this field. b) Hooge parameter as a function of the power amplitude of the rf field at a fixed frequency, f = fres = 243.1 MHz. The green dotted lines represent the Hooge parameter measured in the P state.

 Spin-torque Dynamics for Noise Reduction in Vortex-based Sensors

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

Spin-torque nano-oscillators (STNOs) are spintronic devices operating in frequencies ranging from less than 100 MHz up to a few GHz [1]. Vortex-based STNOs have a distinct configuration exhibiting a vortex magnetization distribution of the free layer in the equilibrium state. STNOs are promising candidates for future-generation implementations, such as rf generation [2], detection [3] or bio-inspired computing [4]. However, their use as magnetic field sensors remains understudied. Vortex-based devices provide a large linear range for magnetic field detection [5] and their nanometric size allows for improved spatial resolution. Such advantages motivate the study of vortex STNOs for sensing applications. One of the main limiting factors for magnetic sensors, notably vortex-based ones, is their intrinsic 1/f noise, which inhibits the device’s detection capabilities at low-frequencies. Here, we study the low-frequency noise of vortex-based STNOs. We determine the Hooge parameter α [6] - a figure of merit used to characterize sensor’s noise properties. In the uniform states, α is in the same order of magnitude as those measured in state-of-the-art TMR sensors with similar RA product, α = 10-11 - 10-10 µm2. In the vortex state, the measured noise level is around one order of magnitude greater than in the parallel state (Fig. 1), due to the increased probability of pinning of the vortex core due to material defects and/or inhomogeneities at the free layer. Furthermore, we examine the impact of the vortex dynamics in the low-frequency noise. Above a certain critical current, the spin transfer torques surpass the intrinsic damping of the free layer resulting in self-sustained oscillations of the vortex core [7]. We find that these dynamics strongly modify the characteristics of the STNOs and, in consequence, the achievable performances of magnetic field sensors relying on magnetic vortex dynamics. We present a detailed analysis of these characteristics and how they relate to the device’s noise properties. The work is supported by the French ANR project “SPINNET” ANR-18-CE24-0012.References: [1] S. Kiselev et al., Nature Vol. 425, 380 (2003) [2] S. Wittrock et al., Phys. Rev. B Vol. 99, 235135 (2019) [3] A. S. Jenkins et al., Nat. Nanotech., Vol. 11, 360 (2016) [4] M. Romera et al., Nature Vol. 563, 230–234 (2018); J. Torrejon et al., Nature, Vol. 547, 428-431 (2017) [5] D. Suess et al., Nature Electronics volume 1, pages 362–370 (2018) [6] F. Hooge and A. Hoppenbrouwers, Physica 45, 386-392 (1969) [7] A. Dussaux et al., Nat. Comm., Vol. 1, 8 (2010)

Analysis of 1/f Low-frequency Noise in Vortex-based Spin-torque Nano-oscillators for Magnetic Sensing Applications

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Spin-torque Dynamics for Noise Reduction in Vortex-based Sensors

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

Analysis of 1/f Low-frequency Noise in Vortex-based Spin-torque Nano-oscillators for Magnetic Sensing Applications

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