Magnetic field sensor based on a low-frequency-tail spintronic diode

Abstract

Spin-torque diode have shown great potentials and performance in many applicative fields, from microwave detectors to energy harvesters. In this work, we use micromagnetic simulations to study, at room temperature, a state-of-the-art non-resonant low-frequency-tail spin-torque diode in terms of dc output voltage as a function of the amplitude of an in-plane external field applied along different directions. We find that there exists a threshold value of the injected ac current that promotes a linear behavior of the output voltage of field down to the pT range, and we suggest exploiting such a behavior for the design of a magnetic field sensor.

Keywords

Magnetic tunnel junction spin-torque diode magnetic field sensor

1. Introduction

Spintronic diodes were born in 2005 [1] with the discovery that a spin-polarized microwave current can be converted into a rectified voltage in magnetic tunnel junctions (MTJs), thanks to a rectification phenomenon linked to the ferromagnetic resonance. The spin-torque diodes (STDs) are the dual effect of spin-torque oscillators [2–5]. They exhibit a number of advantages from their compatibility with the CMOS technology, which allows them to be integrated together in a chip [6], to be the smallest rectifiers developed so far (nanoscale size). STDs can operate in different regimes such as resonant, non-resonant, passive and active. For this reason, they can be used for many applications, ranging from microwave detectors to energy harvesters [7,8].

Initially, the STD effect was only exploited to measure the spin-transfer torque efficiency in MTJs [9–11], but later STDs have shown promising features for the integration in hybrid systems with better performances than the CMOS counterparts, i.e. Schottky diodes [12,13]. It has been experimentally proved that biased STDs can achieve a sensitivity (defined as the ratio between the rectified output and the input microwave power) larger than 10 kV/W, with output resistances smaller than 1 kOhm [13–17]. This is possible thanks to the excitation of strongly nonlinear dynamics, such as non-adiabatic stochastic resonance [14], out-of-plane precession [18], nonlinear resonance [15], resonant vortex expulsion [16], as well as injection locking [12]. However, for energy saving in Internet-of-Things nodes and electromagnetic energy harvesting, it is more convenient to design passive detectors that can work at ultralow power with a large signal-to-noise ratio [18,19]. The STD effect can be excited by Dzyaloshinskii-Moriya interaction [20] and spin-Hall effect [21,22], and used in probing domain wall’s dynamics in the free layer and the corresponding domain pattern [23]. It can also be employed in neurocomputing such a spin-torque nano oscillators hardware neural network [24] or sparse neuromorphic computing [25], in sensing, thanks to their very high sensitivity (up to 210 000 mVmW⁻¹ [26]), as radiofrequency detectors [19,27–29], passive demodulation of digital signals and microwave imaging [30,31], as well as in antiferromagnets [32].

A promising application of STDs is the sensing of magnetic field due to the wide and common range of use of these sensors, such as in space [33], navigation and mechanical systems [34], automotive industry [35], industrial automation [36] and biomedicine [37]. The required characteristics of a magnetic sensor are sensitivity, field range, power consumption, costs and linearity [38,39]. In particular, linearity is crucial for a sensor output as it allows to determine the field intensity univocally, which leads to a simple circuitry, a better error propagation [39] as well as an easier optimization process compared to non-linear sensors [40].

The detection of magnetic field in the pT range is important for a wide range of industrial, homeland security, and biomedical applications [41,42]. For instance, neural activities are characterized by magnetic fields, induced by the electrical current spikes, on the order of pT and fT [43]. Similarly, the signal generated by proteins and DNA, as well as that of labels utilized to tag analyte and other cells/bacteria, is on the same order [42,44]. There have been proposals of pT magnetic field sensors based on MTJs [41,45–47], however these exploit the MTJs as magnetoresistive (MR) sensors and rely on arrays of MTJs and magnetic flux concentrators (MFCs) to enhance their detectivity and sensitivity.

In a non-resonant low-frequency STD working in the passive regime, i.e., when the magnetization is excited with an ac current with a frequency far from the ferromagnetic resonance (∼GHz), in the lower end of the spectrum, the amplitude of the generated dc voltage increases with decreasing the frequency of the input ac current. This makes non-resonant low-frequency STD appealing and promising solutions for low frequency applications. Hence, STDs can provide a higher sensitivity than traditional MR sensors, avoiding the need of arrays of MTJs and MFCs, with sub-micrometric device dimensions with respect to the millimeter to micrometer characteristic dimensions of the MR-based devices.

In this work, we propose to use a non-resonant low-frequency tail STD [48], where the interfacial perpendicular magnetic anisotropy (IPA) is compensated by the demagnetization energy, working in the passive regime as a magnetic field sensor with detectivity in the range of pT. Here we show, by means of micromagnetic simulations, that an in-plane magnetic field down to the pT range results in a linear change of the rectified output voltage generated by an input ac current at the MHz frequencies at room temperature. Our results pave the way for a novel application of this type of non-resonant STDs.

2. Device and model

In this section, we present the simulated device and the behavior of the rectified voltage when varying the in-plane x and y components of the applied field in the mT range. The simulated STD has an elliptical cross section of dimensions 130 nm × 46 nm, similar to previous studies on analogous systems where the IPA is balanced by the demagnetization contribution due the shape of the device [48–50]. The stack, from bottom to top is composed of PtMn(15) / Co₇₀Fe₃₀(2.3) / Ru(0.85) / Co₄₀Fe₄₀B₂₀(2.4) / MgO(0.8) / Co₂₀Fe₆₀B₂₀(1.65) (thickness in nm), where the bottom PtMn(15) / Co₇₀Fe₃₀(2.3) / Ru(0.85) / Co₄₀Fe₄₀B₂₀(2.4) stack is the reference layer in which the PtMn layer is exchange biased to the synthetic antiferromagnetic structure Co₇₀Fe₃₀(2.3) / Ru(0.85) / Co₄₀Fe₄₀B₂₀(2.4). Figure 1(a) shows a sketch of the MTJ structure.

Fig. 1.

(a) Schematics of the STD stack which consists of an in-plane magnetized reference layer and an in-plane magnetized free layer. (b) Time evolution of the dimensionless resistance (red curve) and normalized input current density (blue curve).

The micromagnetic model is based on the numerical solution of the Landau–Lifshitz–Gilbert equation with the Slonczewski terms [51,52]: $\begin{eqnarray}\displaystyle \frac{d\boldsymbol{m}}{d{\tau}}=-(\boldsymbol{m}\times \boldsymbol{h}_{\mathit{eff}})+{\alpha}\left(\boldsymbol{m}\times \frac{d\boldsymbol{m}}{d{\tau}}\right)-{\sigma}[\boldsymbol{m}\times (\boldsymbol{m}\times \boldsymbol{m}_{p})] & & \displaystyle\end{eqnarray}$ (1) where m = M ∕M_s is the normalized magnetization of the MTJ free layer, M_S = 950 kA/m is the saturation magnetization, τ = 𝛾M_st is the dimensionless time with μ₀𝛾 = 2.21 ×10⁵ rad $\cdot \frac{m}{C}$ being the gyromagnetic ratio and t the time. The system is discretized in micromagnetic cells of dimension 2 nm × 2 nm × 1.65 nm. h _eff = H _eff∕M_s is the normalized effective field and includes the following contribution: exchange ( h _ex), magnetostatic ( h _dmag), uniaxial anisotropy ( h _ani), external ( h _ext) and thermal ( h _th) fields. h _ex favors the parallel alignment of the magnetization and is given by $\boldsymbol{h}_{ex}=\frac{2A}{{\mu}_{0}M_{s}^{2}}{\nabla}^{2}\boldsymbol{m}$ , where A is the exchange stiffness. h _dmag takes into account the interactions existing in the material due to the magnetic dipoles and is computed from the volume and surface charges. h _ani describes the tendency of the magnetization to align along a specific direction (easy-axis) and can be expressed as $\boldsymbol{h}_{ani}=∼\frac{2k_{1}}{{\mu}_{0}M_{s}^{2}}(\boldsymbol{m}\cdot \hat{\boldsymbol{e}}_{u})\hat{\boldsymbol{e}}_{u}+\frac{4k_{2}}{{\mu}_{0}M_{s}^{2}}(\boldsymbol{m}\cdot \hat{\boldsymbol{e}}_{u})^{3}\hat{\boldsymbol{e}}_{u}$ , where the first term on the right hand side (RHS) is the first order anisotropy contribution and the second is the second order term characterized by the energy densities k₁ and k₂, and $\hat{\boldsymbol{e}}_{u}$ is the unit vector identifying the easy-axis direction. h _ext is the external field applied to the system. Finally, h _th accounts for thermal effects and it is described as a stochastic term. It reads $\boldsymbol{h}_{th}=\frac{\boldsymbol{\chi}}{M_{s}}\sqrt{\frac{2{\alpha}k_{B}T}{{\mu}_{0}{\gamma}{\rm\Delta}VM_{s}{\rm\Delta}t}}$ , with k_B being the Boltzmann constant, ΔV the volume of the computational cubic cell, Δt the simulation time step, T temperature of the sample, and 𝛘 a three-dimensional white Gaussian noise with zero mean and unit variance [53,54]. This noise is assumed to be uncorrelated for each computational cell and the simulations described in the following are performed at room temperature (T = 300 K). The last term on the RHS of Eq. (1) describes the spin transfer torque contribution. σ = Jσ_⊥∕(1 + 𝜂² cos𝛽) is the current-torque proportionality coefficient, where 𝜂 = 0.66 is the spin-polarization factor and 𝛽 = arccos( m ⋅ m _p) is the angle between the free layer magnetization and pinned layer magnetization m _p, which is assumed to be fixed along the x direction ( $\boldsymbol{m}_{p}=∼\hat{\boldsymbol{x}}$ , with $\hat{\boldsymbol{x}}$ the x axis unit vector). ${\sigma}_{\bot }=(2{\eta}g{\mu}_{B})/(2{\gamma}eM_{s}^{2}t_{FL})$ , where g is the Landé factor, μ_B is the Bohr magneton, e is the electron charge, t_FL is the free layer thickness. J = J_AC sin(2πft) is the ac current density of amplitude I_AC = J_ACA_FL applied perpendicularly to the elliptic free layer with surface A_FL, with a frequency f = 100 MHz. The geometrical and physical parameters are the same as those utilized in a previous work on an analogous system [48]: exchange energy constant A = 20 pJ/m, first order uniaxial anisotropy energy density k₁ = 0.48 MJ/m³ and second order term k₂ = 1.5 × 10⁴ J/m³, and Gilbert damping 𝛼 = 0.02.

3. Results

3.1. Effect of the in-plane magnetic field

Figure 1(b) shows the time evolution of the dimensionless resistance of the MTJ, calculated as r = 1 −〈m_x〉∕2 (with 〈m_x〉 being the normalized x component of the magnetization) and the normalized current density in the absence of an external field for a current density J = 2 MA/cm². r describes the oscillations of the MTJ resistance R_MTJ = R_P + (R_AP − R_P)(1 − cos𝛽)∕2 and is defined to be centered in 1, with minimum value 1/2 corresponding to R_P and maximum value 3/2 corresponding to R_AP, for the sake of clarity in the plot. We can see that the current induces an in-plane precession of the magnetization with the same frequency as the injected current, but with a difference in its phase Δ𝜙 ≃ −80 deg, as in Ref. [48].

Let us consider now the effect of applying an in-plane magnetic field to our system. Figure 2 shows the effect of the external in-plane magnetic field applied along the x direction (Fig. 2(a) and (c)), which is the easy-axis of the free layer, and the y direction (Fig. 2(b) and (c)), on the rectified voltage V_DC and the phase difference Δ𝜙 between the applied current and the magnetization x component. V_DC is calculated from: $\begin{eqnarray}\displaystyle V_{DC}=0.5R_{S}J_{AC}A_{FL}\cos ({\rm\Delta}{\phi}) & & \displaystyle\end{eqnarray}$ (2) where R_s is the amplitude of the oscillating resistance R_MTJ estimated directly from the simulations as R_S = dm (R_AP − R_P)∕2, where R_AP = 1660 Ω and R_P = 900 Ω are the experimental nominal values of the MTJ resistance in the antiparallel and parallel state, respectively, and dm is the amplitude of the oscillations of 〈m_x〉 [48].

Fig. 2.

Rectified voltage plotted against the applied field along (a) x and (b) y axes, and the phase difference between the magnetization x component and the current density as a function of the applied field along (c) x and (d) y axes.

In Fig. 2(a) we can see that, by applying the external magnetic field along the x direction, we achieve an almost monotonical behavior of the absolute value of V_DC, showing an increase of its value for an increasing intensity of the negative x-field, and a decrease for positive x-field. However, there is a small change in the slope around 5 mT. On the other hand, in Fig. 2(b), we can see that the effect of the field applied along the y direction has an almost symmetric trend for an increasing intensity of the field, both for negative and positive directions, with a minimum at H = 0 mT.

The behavior of the V_DC when the external field is applied along x and y is accompanied by a similar trend of the phase difference, as shown in panels (c) and (d), respectively, suggesting that the effect of the magnetic field is to induce a change of the phase of the x component of the magnetization with the respect to the ac current, without modifying the frequency of the induced magnetization precession.

3.2. pT magnetic sensor

After characterizing the response over the mT range, we focus on the pT range by applying a positive field along the free layer easy-axis. With the aim to use the non-resonant STD as a pT magnetic sensor, we are looking for a linear response of the rectified voltage on the applied field. Then, we perform simulations for fields in the range 8 to 20 pT. The dc voltage exhibits an overall linear behavior, as shown in Fig. 3(a). We ascribe the difference from the ideal linear behavior to the effect of the thermal fluctuations which introduce a random response of the resistance when the effect of the ac current is dominated by the thermal field.

Fig. 3.

(a) Rectified voltage (blue dots) for fields applied along the x direction and the linear fit (red straight line) for J_AC = 2.0 MA/cm². (b) Output voltage for H_x = 13 pT for various realization number. Red dashed line is the mean, while the green dashed one is the standard deviation. Highlighted gray area is where the data are inside the standard deviation.

To achieve a better understanding of the role of temperature, we performed additional simulations by fixing the in-plane external field to 13 pT for ten different realizations at room temperature (T = 300 K). The results are shown in Fig. 3(b), where the voltage outputs are scattered with the respect to the mean value of the voltage (red dashed line), resulting in a wide standard deviation (green dashed lines).

However, in order to obtain a linear magnetic field sensor in the pT range, it is enough to calibrate the input ac current. Indeed, by increasing the amplitude of the current density J_AC from 2.0 MA/cm² to 2.1 MA/cm², the V_DC behavior as a function of the field exhibits an excellent linear trend. This is shown in Fig. 4, where we plot the rescaled voltage ΔV_DC = V_DC − V_DC(1 pT).

Fig. 4.

Rescaled rectified voltage (blue dots) for fields applied along the x-direction and linear fit (red straight line) of the data for J_AC = 2.1 MA/cm².

Moreover, if we measure the voltage difference between 5 pT and 1 pT, i.e. ΔV = V_DC(5 pT) − V_DC(1 pT) = 0.14 μV, we can see that the STD is sensitive to small changes of the external field. These results suggest that there exists a threshold current that allows to achieve a linear behavior and thus to utilize the STD as a magnetic field sensor at room temperature. This aspect is worth further investigation, and it will be object of a future work.

4. Conclusions

We have shown, by means of micromagnetic simulations, the effect of an in-plane magnetic field applied to a non-resonant low-frequency tail STD excited by an ac current at the MHz frequencies working at room temperature. The results show that it is possible to achieve a linear response of the output voltage generated by the STD as a function of the external field down to the pT range with a measurable output signal on the order of the μV. We find that there exist upper- and lower-bounds thresholds values for the input ac current for the system to yield a linear output. The lower threshold is dictated by the requirement for the external excitation to overcome thermal effects, whereas the weak amplitude of the fields determines the upper threshold. Our results prove how such a STD is a potential candidate for low-frequency magnetic field sensors down to the pT thanks to their sub-micrometric dimensions, robustness and low power. However, optimization of the device is necessary and will be object of further work.

Footnotes

Acknowledgement

This work was supported by the Italian Ministry of University and Research, Project No. PRIN 2020LWPKH7, and by the PETASPIN association ().

References

Tulapurkar

A.A.

Suzuki

Fukushima

Kubota

Maehara

Tsunekawa

, Spin-torque diode effect in magnetic tunnel junctions, Nature438 (2005), 339–342, doi:10.1038/nature04207.

Puliafito

Azzerboni

Consolo

Finocchio

Torres

and Diaz

L.L.L.

, Micromagnetic modeling of nanocontact spin-torque oscillators with perpendicular anisotropy at zero bias field, IEEE Trans. Magn.44 (2008), 2512–2515, doi:10.1109/TMAG.2008.2002596.

Puliafito

Pogoryelov

Azzerboni

Akerman

and Finocchio

, Hysteretic synchronization in spin-torque nanocontact oscillators: A micromagnetic study, IEEE Trans. Nanotechnol.13 (2014), 532–536. doi:10.1109/TNANO.2014.2308474.

Finocchio

Consolo

Carpentieri

Romeo

Azzerboni

Torres

, Trends in spin-transfer-driven magnetization dynamics of CoFe/AlO/Py and CoFe/MgO/Py magnetic tunnel junctions, Appl. Phys. Lett.89 (2006), 262509, doi:10.1063/1.2425017.

Torres

Lopez-Diaz

Martinez

Finocchio

Carpentieri

and Azzerboni

, Coupling of spin-transfer torque to microwave magnetic field: A micromagnetic modal analysis, J. Appl. Phys.101 (2007), 053914, doi:10.1063/1.2435812.

Golonzka

Alzate

J.-G.

Arslan

Bohr

Bai

Brockman

MRAM as embedded non-volatile memory solution for 22FFL FinFET Technology, in: 2018 IEEE Int. Electron Devices Meet., IEEE, 2018, pp. 18.1.1–18.1.4. doi:10.1109/IEDM.2018.8614620.

Finocchio

Tomasello

Fang

Giordano

Puliafito

Carpentieri

, Perspectives on spintronic diodes, Appl. Phys. Lett.118 (2021), 160502, doi:10.1063/5.0048947.

Finocchio

Ricci

Tomasello

Giordano

Lanuzza

Puliafito

, Skyrmion based microwave detectors and harvesting, Appl. Phys. Lett.107 (2015), 262401, doi:10.1063/1.4938539.

Sankey

J.C.

Cui

Y.-T.

Sun

J.Z.

Slonczewski

J.C.

Buhrman

R.A.

and Ralph

D.C.

, Measurement of the spin-transfer-torque vector in magnetic tunnel junctions, Nat. Phys.4 (2008), 67–71, doi:10.1038/nphys783.

10.

Kubota

Fukushima

Yakushiji

Nagahama

Yuasa

Ando

, Quantitative measurement of voltage dependence of spin-transfer torque in MgO-based magnetic tunnel junctions, Nat. Phys.4 (2008), 37–41. doi:10.1038/nphys784.

11.

Wang

Cui

Y.-T.

Sun

J.Z.

Katine

J.A.

Buhrman

R.A.

and Ralph

D.C.

, Bias and angular dependence of spin-transfer torque in magnetic tunnel junctions, Phys. Rev. B79 (2009), 224416, doi:10.1103/PhysRevB.79.224416.

12.

Fang

Carpentieri

Hao

Jiang

Katine

J.A.

Krivorotov

I.N.

, Giant spin-torque diode sensitivity in the absence of bias magnetic field, Nat. Commun.7 (2016), 1–7, doi:10.1038/ncomms11259.

13.

Fang

Carpentieri

Louis

Tiberkevich

Slavin

Krivorotov

I.N.

, Experimental demonstration of spintronic broadband microwave detectors and their capability for powering nanodevices, Phys. Rev. Appl.11 (2019), 014022, doi:10.1103/PhysRevApplied.11.014022.

14.

Cheng

Katine

J.A.

Rowlands

G.E.

and Krivorotov

I.N.

, Nonlinear ferromagnetic resonance induced by spin torque in nanoscale magnetic tunnel junctions, Appl. Phys. Lett.103 (2013), 082402, doi:10.1063/1.4819179.

15.

Miwa

Ishibashi

Tomita

Nozaki

Tamura

Ando

, Highly sensitive nanoscale spin-torque diode, Nat. Mater.13 (2014), 50–56, doi:10.1038/nmat3778.

16.

Jenkins

A.S.

Lebrun

Grimaldi

Tsunegi

Bortolotti

Kubota

, Spin-torque resonant expulsion of the vortex core for an efficient radiofrequency detection scheme, Nat. Nanotechnol.11 (2016), 360–364, doi:10.1038/nnano.2015.295.

17.

Algarín

J.M.

Ramaswamy

Chen

Y.J.

Weinberg

I.N.

Krivorotov

I.N.

Katine

J.A.

, High rectification sensitivity of radiofrequency signal through adiabatic stochastic resonance in nanoscale magnetic tunnel junctions, Appl. Phys. Lett.115 (2019), 192402, doi:10.1063/1.5123466.

18.

Prokopenko

O.V.

Krivorotov

I.N.

Bankowski

Meitzler

Jaroch

Tiberkevich

V.S.

, Spin-torque microwave detector with out-of-plane precessing magnetic moment, J. Appl. Phys.111 (2012), 123904, doi:10.1063/1.4729301.

19.

Prokopenko

Melkov

Bankowski

Meitzler

Tiberkevich

and Slavin

, Noise properties of a resonance-type spin-torque microwave detector, Appl. Phys. Lett.99 (2011), 032507, doi:10.1063/1.3612917.

20.

Tomasello

Carpentieri

and Finocchio

, Influence of the Dzyaloshinskii-Moriya interaction on the spin-torque diode effect, J. Appl. Phys.115 (2014), 17C730, doi:10.1063/1.4867750.

21.

Liu

Moriyama

Ralph

D.C.

and Buhrman

R.A.

, Spin-torque ferromagnetic resonance induced by the spin hall effect, Phys. Rev. Lett.106 (2011), 036601, doi:10.1103/PhysRevLett.106.036601.

22.

Siracusano

Tomasello

Puliafito

Giordano

Azzerboni

Corte

A.L.

, Intrinsic synchronization of an array of spin-torque oscillators driven by the spin-Hall effect, J. Appl. Phys.117 (2015), 17E504, doi:10.1063/1.4914880.

23.

Lequeux

Sampaio

Bortolotti

Devolder

Matsumoto

Yakushiji

, Increased magnetic damping of a single domain wall and adjacent magnetic domains detected by spin torque diode in a nanostripe, Appl. Phys. Lett.107 (2015), 182404, doi:10.1063/1.4935203.

24.

Marković

Leroux

Riou

Araujo

F.A.

Torrejon

Querlioz

, Reservoir computing with the frequency, phase, and amplitude of spin-torque nano-oscillators, Appl. Phys. Lett.114 (2019), 012409, doi:10.1063/1.5079305.

25.

Cai

Jialin

Zhang

Fang

Bin

Wenxing

Zhang

Baoshun

Finocchio

Giovanni

Xiong

Rui

Liang

Shiheng

and Zeng

Zhongming

, Sparse neuromorphic computing based on spin-torque diodes, Appl. Phys. Lett.114(19) (2019) 513.192402-1–192402-4.

26.

Zhang

Fang

Bin

Cai

Jialin

Carpentieri

Mario

Puliafito

Vito

Garescì

Francesca

Amiri

Pedram Khalili

Finocchio

Giovanni

and Zeng

Zhongming

, Ultrahigh detection sensitivity exceeding 105 V/W in spin-torque diode, Appl. Phys. Lett.113(10) (2018) 93.102401-1–102401-4.

27.

Wang

Cui

Y.-T.T.

Sun

J.Z.

Katine

J.A.

Buhrman

R.A.

and Ralph

D.C.

, Sensitivity of spin-torque diodes for frequency-tunable resonant microwave detection, J. Appl. Phys.106 (2009), 053905, doi:10.1063/1.3197137.

28.

Gui

Y.S.

Xiao

Bai

L.H.

Hemour

Zhao

Y.P.

Houssameddine

, High sensitivity microwave detection using a magnetic tunnel junction in the absence of an external applied magnetic field, Appl. Phys. Lett.106 (2015), 152403, doi:10.1063/1.4918677.

29.

Skowroński

Frankowski

Wrona

Stobiecki

Ogrodnik

and Barnaś

, Spin-torque diode radio-frequency detector with voltage tuned resonance, Appl. Phys. Lett.105 (2014), 072409, doi:10.1063/1.4893463.

30.

Herrera

D.R.

Tapia

D.F.

Gui

Y.S.

Pistorius

, Microwave radar imaging using a solid state spintronic microwave sensor, Appl. Phys. Lett.105 (2014), 122406, doi:10.1063/1.4896691.

31.

Gui

Y.S.

Bai

L.H.

Guo

Abou-Rachid

and Hu

C.-M.

, Microwave holography using a magnetic tunnel junction based spintronic microwave sensor, J. Appl. Phys.117 (2015), 213902, doi:10.1063/1.4921887.

32.

Tomasello

Verba

Lopez-Dominguez

Garesci

Carpentieri

Ventra

M.D.

, Antiferromagnetic parametric resonance driven by voltage-controlled magnetic anisotropy, Phys. Rev. Appl.17 (2022), 034004. doi:10.1103/PhysRevApplied.17.034004.

33.

Díaz-Michelena

, Small magnetic sensors for space applications, Sensors9 (2009), 2271–2288, doi:10.3390/s90402271.

34.

Bird

and Arden

, Indoor navigation with foot-mounted strapdown inertial navigation and magnetic sensors [Emerging Opportunities for Localization and Tracking], Wirel. Commun. IEEE18(2) (2011), 28–35. doi:10.1109/MWC.2011.5751293.

35.

Luo

Yang

and Wu

, Magnetic angular position sensor enabled by spin-orbit torque, Appl. Phys. Lett.112 (2018), 262405, doi:10.1063/1.5038908.

36.

Reininger

Welker

and von Zeppelin

, Sensors in position control applications for industrial automation, Sensors Actuators A Phys.129 (2006), 270–274, doi:10.1016/j.sna.2005.09.056.

37.

Uchiyama

and Ma

, Development of pico tesla resolution amorphous wire magneto-impedance sensor for bio-magnetic field measurements, J. Magn. Magn. Mater.514 (2020), 167148, doi:10.1016/j.jmmm.2020.167148.

38.

Khan

Mohammed Asadullah

Sun

Jian

Bodong

Przybysz

Alexander

and Kosel

Jürgen

, Magnetic sensors-A review and recent technologies, Engineering Research Express3(2) (2021) 61.022005-1–022005-22.

39.

Fraden

, Handbook of Modern Sensors Fifth Edition, 2016. https://rizkia.staff.telkomuniversity.ac.id/files/2017/11/Handbook-of-modern-sensors-physics-designs-and-applications-Fraden-Jacob-Springer-2016.pdf.

40.

Sani

S.M.

Oluyombo

O.W.

Tekanyi

A.M.S.

and Jimoh

, Improvement of sensitivity and noise of a fluxgate magnetometer using modified firefly optimization algorithm, Int. J. Eng. Res. Technol.4 (2015), 32–37. www.ijert.org.

41.

Liou

S.H.

Yin

Russek

S.E.

Heindl

Silva

F.C.S.S.D.

Moreland

, Picotesla magnetic sensors for low-frequency applications, IEEE Trans. Magn.47 (2011), 3740–3743, doi:10.1109/TMAG.2011.2157997.

42.

Dieny

Prejbeanu

I.L.

Garello

Gambardella

Freitas

Lehndorff

, Opportunities and challenges for spintronics in the microelectronics industry, Nat. Electron.3 (2020), 446–459, doi:10.1038/s41928-020-0461-5.

43.

Hämäläinen

Hari

Ilmoniemi

R.J.

Knuutila

and Lounasmaa

O.V.

, Magnetoencephalography—theory, instrumentation, and applications to noninvasive studies of the working human brain, Rev. Mod. Phys.65 (1993), 413–497, doi:10.1103/RevModPhys.65.413.

44.

Liu

Lam

K.H.

Zhu

Zheng

, Overview of spintronic sensors with internet of things for smart living, IEEE Trans. Magn.55 (2019), 1–22, doi:10.1109/TMAG.2019.2927457.

45.

Zhang

Qian

Xiao

Zhang

Santamarina

J.C.

, PicoTesla magnetic tunneling junction sensors integrated with double staged magnetic flux concentrators, Appl. Phys. Lett.113 (2018), 242401, doi:10.1063/1.5052355.

46.

Chaves

R.C.

Freitas

P.P.

Ocker

and Maass

, Low frequency picotesla field detection using hybrid MgO based tunnel sensors, Appl. Phys. Lett.91 (2007), 102504, doi:10.1063/1.2775802.

47.

Tondra

Daughton

J.M.

Wang

Beech

R.S.

Fink

and Taylor

J.A.

, Picotesla field sensor design using spin-dependent tunneling devices, J. Appl. Phys.83 (1998), 6688–6690, doi:10.1063/1.367861.

48.

Tomasello

Fang

Artemchuk

Carpentieri

Fasano

Giordano

, Low-frequency nonresonant rectification in spin diodes, Phys. Rev. Appl.14 (2020), 024043, doi:10.1103/PhysRevApplied.14.024043.

49.

Zeng

Finocchio

Zhang

Amiri

P.K.

Katine

J.A.

Krivorotov

I.N.

, Ultralow-current-density and bias-field-free spin-transfer nano-oscillator, Sci. Rep.3 (2013), 1426, doi:10.1038/srep01426.

50.

Zeng

Finocchio

and Jiang

, Spin transfer nano-oscillators, Nanoscale5 (2013), 2219, doi:10.1039/c2nr33407k.

51.

Giordano

Finocchio

Torres

Carpentieri

and Azzerboni

, Semi-implicit integration scheme for Landau–Lifshitz–Gilbert-Slonczewski equation, J. Appl. Phys.111 (2012), 07D112, doi:10.1063/1.3673428.

52.

Slonczewski

J.C.

, Current-driven excitation of magnetic multilayers, J. Magn. Magn. Mater.159 (1996), L1–L7, doi:10.1016/0304-8853(96)00062-5.

53.

Brown

W.F.

, Thermal fluctuations of a single-domain particle, Phys. Rev.130 (1963), 1677–1686. doi:10.1103/PhysRev.130.1677.

54.

Finocchio

Krivorotov

I.N.

Cheng

Torres

and Azzerboni

, Micromagnetic understanding of stochastic resonance driven by spin-transfer-torque, Phys. Rev. B83 (2011), 134402, doi:10.1103/PhysRevB.83.134402.