Giant spin-torque diode sensitivity in the absence of bias magnetic field

Microwave detectors based on the spin-torque diode effect are among the key emerging spintronic devices. By utilizing the spin of electrons in addition to charge, they have the potential to overcome the theoretical performance limits of their semiconductor (Schottky) counterparts. However, so far, practical implementations of spin-diode microwave detectors have been limited by the necessity to apply a magnetic field. Here, we demonstrate nanoscale magnetic tunnel junction microwave detectors, exhibiting high-detection sensitivity of 75,400 mV mW−1 at room temperature without any external bias fields, and for low-input power (micro-Watts or lower). This sensitivity is significantly larger than both state-of-the-art Schottky diode detectors and existing spintronic diodes. Micromagnetic simulations and measurements reveal the essential role of injection locking to achieve this sensitivity performance. This mechanism may provide a pathway to enable further performance improvement of spin-torque diode microwave detectors.

The RF input is applied by a signal generator, the spin-torque microwave emission voltage through the pre-amplifier is measured by a spectrum analyzer, and the spin-torque diode output is simultaneously recorded by a lock-in amplifier.

Supplementary Note 1. Estimation of the voltage-controlled perpendicular magnetic anisotropy (VCMA)
The VCMA, i.e. the change of magnetic anisotropy induced by electric field in our devices may increase the sensitivity of the microwave detector. The amplitude of VCMA can be estimated using the method described in Supplementary Ref. 1 . The effective perpendicular magnetic anisotropy energy per unit volume of the free layer, E p , including interface and demagnetization contributions, can be calculated from the area under the in-plane fieldmagnetoresistance hysteresis loop, whose shape is identical to that of the magnetic tunnel junction (MTJ) conductance G(H x ) hysteresis loop as shown in Supplementary Fig. 1a (1) , 2 where M s is the saturation magnetization of the free layer, M x is the projection of magnetization onto the x axis, and H p is the effective perpendicular anisotropy field. The VCMA induces a change in the slopes of the two G(H x ) curves in Supplementary Fig. 1a. Supplementary Figure 1b shows the dependence of the perpendicular magnetic anisotropy field on the applied voltage, where ΔH p (V dc ) = H p (V dc )-H p (0). This dependence is well fit by a straight line with a slope of 0.55 kOe V -1 , which corresponds to a change in the magnetic anisotropy energy per unit area per applied electric field of 34 fJ V -1 m -1 . This is comparable to VCMA values previously observed in similar systems ( Supplementary Refs 1-3 ).

Supplementary Note 2. Noise characterization and signal-to-noise ratio
In magnetic tunnel junctions (MTJs) used as radiofrequency (RF) detectors, four types of noise are found, namely Johnson noise, shot noise, nonlinear magnetic noise, and diode-mixing noise. In the device discussed here, the Johnson and shot noise are found to be small compared to the mixing noise and nonlinear magnetic noise, which is consistent with the previous study by Miwa et al (Supplementary Ref. 4 ). Thus the characterization of both the nonlinear magnetic noise and the diode-mixing noise become important. In this section, we present the noise measurements (the bandwidth is 100 kHz) for the device presented in the main text, and discuss the signal-to-noise ratio (SNR) through the characterization of noise-equivalent power (NEP) (Supplementary Ref. 4 ).

a) Nonlinear magnetic noise
The nonlinear magnetic noise is attributed to the nonlinear response of thermal fluctuations in the magnetic free layer. Supplementary Figure 3a shows the measurement circuit for the nonlinear magnetic noise. A d.c. bias is applied to the MTJs by a source meter, and the noise is measured by a spectrum analyzer. Supplementary Figure 3b shows the nonlinear magnetic noise voltage as a function of frequency. The d.c. bias dependence of the peak value around 0 Hz is shown in Supplementary Fig. 3c. The magnetic noise level increases with increasing the d.c. bias current. Its slight decrease at I dc = -0.28 mA compared to I dc = -0.24 mA is due to a change in the orientation between the free and reference layer magnetizations, which is indicated from the change in the resistance curve (see Fig. 5d in the main text). Our measurements show that this noise is independent of the RF input power, as was the case for the nonlinear magnetic noise reported in Supplementary Ref. 4 .

b) Diode-mixing noise
The diode-mixing noise is attributed to the mixing of the input RF current and resistance fluctuations, which originate from thermal fluctuations in the magnetic free layer (Supplementary Ref. 4 ). Supplementary Figure 4a shows the measurement circuit for the diodemixing noise. An RF input at the resonant frequency (f ac = f 0 ) is applied by a signal generator, and the noise voltage through the pre-amplifier is measured by a spectrum analyzer. Supplementary Figure 4b shows the diode-mixing noise voltage as a function of frequency. The d.c. bias dependence of the peak values around 0 Hz is shown in Supplementary Fig. 4c. The mixing noise level exhibits a similar trend as the nonlinear magnetic noise shown in Supplementary Fig. 3c.

c) Noise equivalent power (NEP) in MTJs
Supplementary Figure 5a shows the measured diode-mixing noise around 0 Hz as a function of the RF input power. It can be seen that the nonlinear magnetic noise governs the noise properties when a small RF input power (P RF <0.01 µW) is applied. On the other hand, for large RF input power, the diode-mixing noise becomes more important and proportional to the RF input power. Similar noise properties in MTJ didoes have been observed in Supplementary Ref. 4 .
The NEP is characterized to evaluate the signal-to-noise ratio (SNR) in the MTJ. As demonstrated in Supplementary Ref. 4 , the NEP in a spin-torque diode is expressed as RF dc noise y Sensitivit voltage Noise NEP where V dc is the measured d.c. voltage, P RF is the incident RF power, and V noise is the noise generated in the MTJ device. In our measurement, V noise = V Measured ×(50+R MTJ )/50, where V Measured is the noise measured with the spectrum analyzer as shown in Supplementary Fig. 5a, and R MTJ is the MTJ resistance (R MTJ = 770 Ω at zero magnetic field). As discussed above and shown in Supplementary Ref. 4 , the diode-mixing noise is dominant for a large RF input. Hence, the experimental data of the diode-mixing noise are used to evaluate the RF input power dependence of the SNR. Supplementary Figure 5b displays the NEP values as a function of the RF input for various d.c. currents. As an example, at P RF = 0.01 µW and I dc = -0.25 mA, the measured NEP is estimated to be 8 ×10 -12 W Hz -0.5 , which is of the same order as that in previous MTJ diodes (3.6×10 -12 W Hz -0.5 in Supplementary Ref. 4 ).

Supplementary Note 3. Experimental data on an additional device
We found that the detection sensitivity is significantly enhanced for a range of currents, which our simulations link to the presence of the injection locking mechanism. In order to verify this point, we also performed injection locking experiments as shown in Supplementary Figure 6. Our data confirm that the injection locking plays a key role in enhancing the detection sensitivity, as shown in Fig. 5 in the main text.
Here we present additional data from a second device, showing that the injection locking contribution to enhancement of detection sensitivity is robust. The device whose data are presented below is fabricated on the same substrate as the device discussed in the main text. The device has elliptical geometry of 150 nm ×50 nm and a free layer with a thickness of 1.64 nm (Device #2), slightly different from that discussed in the main text. The resistances in parallel and antiparallel configurations are 700 Ω and 1330 Ω, respectively. Supplementary Figure 2a shows the measured rectified voltage as a function of the microwave frequency at I dc = 0 mA for different input microwave powers. The maximum voltage is measured at the resonant frequency f 0 = 1.3 GHz and the detection sensitivity at P RF = 0.01μW was obtained to be 880 mVmW -1 , similar to that discussed in the main text. A quadratic dependence (power detection, see Supplementary Fig. 2b) on the RF power is observed as described in Fig. 3a of the main text.
Supplementary Figure 7a shows the microwave emission output as a function of I dc in the absence of RF power. As described in Fig. 5a of the main text, the precession mode changes from Mode #1 to Mode #2, corresponding to the precession axis change in the f p vs I dc response. The large spin-diode signal (see Supplementary Fig. 7c) and the injection locking behaviors were observed in the Mode #2 region for Device #2. Supplementary Figure 7b shows the microwave output for the oscillation f p versus the driving frequency f ac at P RF = 3.2 μW. It is clear from Supplementary Fig. 7b that the self-oscillation frequency f p follows the driving frequency f ac near f ac = f p , similar to that in Supplementary Ref. 5 . Note that the red dots at f ac = f p are an artifact of the measurement and are due to the signal of the driving source, which cannot be suppressed. When the amplitude of the driving signal increases, the locking range increases ( Supplementary  Fig. 7d), while the linewidth of the oscillator decreases inside the injection-locking range. At P RF = 3.2 μW, the injection locking range reaches to 0.2 GHz while the oscillation linewidth decreases to about 10 MHz. This corresponds to an improvement by a factor of 15 as compared to the linewidth of the oscillator with no RF power, but is still much larger than the linewidth of the microwave driving signal (which is on the order of several hertz). This behavior can be attributed to the influence of noise (Supplementary Ref. 6 ), consistent with a previous study (Supplementary Ref. 7 ). If the linewidth of the oscillator is further improved, a larger detection voltage output may be achieved.