Uncooled sub-GHz spin bolometer driven by auto-oscillation

Bolometers are rectification devices that convert electromagnetic waves into direct current voltage through a temperature change. A superconducting bolometer has a responsivity of approximately 106–107 V/W under cryogenic temperatures at infrared wavelengths; however, no devices have realized such a high responsivity in the sub-GHz frequency region. We describe a spin bolometer with a responsivity of (4.40 ± 0.04) × 106 V/W in the sub-GHz region at room temperature using heat generated in magnetic tunnel junctions through auto-oscillation. We attribute the unexpectedly high responsivity to a heat-induced spin-torque. This spin-torque modulates and synchronizes the magnetization precession due to the spin-torque auto-oscillation and produces a large voltage output. In our device, heat-induced spin-torque was obtained because of a large heat-controlled magnetic anisotropy change: −2.7 µJ/Wm, which is significant for enhancing dynamic range and responsivity. This study can potentially lead to the development of highly sensitive microwave detectors in the sub-GHz region.

microwave synchronizes through the HCMA with the magnetization precession of spin-torque auto-oscillation and generates the diode voltage. As reported in a previous study 3 , HCMA in MgO|FeB|MgO systems exerts spin-torque on magnetization more effectively than the spin-transfer torque and voltagecontrolled magnetic anisotropy. In our study, the spin-torque auto-oscillation synchronizes with the spin-torque induced by the HCMA effect to generate a high diode voltage.

Supplementary Note 2: Measurement circuit and device characteristics
The circuit used for the spin-torque diode measurements is shown in Fig.   S1(a). Microwaves were applied to the magnetic tunnel junction (MTJ) from a signal generator. The diode voltage was measured by a lock-in amplifier synchronized with the signal generator. We used an attenuator of −50 dB to reduce the intensity of microwaves. A magnetic field was applied with intensity B, azimuthal angle θ, and rotation angle φ. Figures S1(b) and S1(c) show the inplane and out-of-plane magnetic field dependence of the resistance of the MTJ, respectively. The in-plane magnetic field is applied in the +y direction, which is opposite to that of the pinned layer magnetization. The solid and dashed lines represent the sweep direction of the magnetic field. We obtained a magnetoresistance ratio of 43%, and a resistance-area product of 3.9 Ωµm 2 . circuit. Microwaves with amplitude modulation frequency of 7.5 kHz are applied to the MTJ from a signal generator synchronized with a lock-in amplifier. Bold red and black arrows represent free and pinned layer magnetization, respectively. The magnetic field is applied with intensity B, azimuthal angle θ, and rotation angle φ. (b) In-plane and (c) out-of-plane magnetic field dependence of the MTJ resistance. The in-plane magnetic field is applied in the +y direction. The solid and dashed lines represent the sweep direction of the magnetic field.

Supplementary Note 3: Elevation angle dependence of diode voltage
We measured the dependence of the diode voltage on the elevation angle of the magnetic field to confirm the existence of the nonlinear diode voltage.
The measurement circuit is the same as that shown in Fig. S1(a), and the attenuation is set to −30 dB. The amplitude modulation frequency is 7.5 kHz. The film structure of the MTJ is the same as that described in the main text, and the diameter is 130 nm. A magnetic field of 100 mT is applied along the y-z plane as shown in Fig S2(a). Under this condition, the magnetization in the FeB free-layer is almost saturated. The elevation angle of the magnetic field, θH, is defined as shown in Fig. S2(a). The dc current is approximately −1.39 mA. The energy density of magnetization under perpendicular magnetic anisotropy and an external magnetic field is described by magnetization, H is the external magnetic field, and θm is the elevation angle of magnetization as shown in Fig. S2(a). We define the slight difference between the magnetization and the magnetic field as mH     = − . Eq. (S1) is expanded in terms of Δθ as follows: The last term in Eq. (S2) represents the higher-order potential that generates the nonlinear diode voltage. Under this potential, an increase in the magnetizationprecession angle induces a change in the precession center. If the coefficient 2/3 Kz sin2θH is positive, the precession center θm decreases from its initial value θH.
On the contrary, if it is negative, θm increases. In this experiment, the in-plane magnetic anisotropy occurs because Kz is negative at a bias current of −1.39 mA.
Here, a dc bias current of −1.39 mA in the MTJ corresponds to a bias voltage of −347 mV at a θH of 90°. Therefore, θm increases in the ranges 0 90

Supplementary Note 4: Effect of spin-torques on responsivity
We discuss the effect of various spin-torques, such as HCMA, VCMA, and spin-transfer torque, on the responsivity. Using the HCMA value calculated from Fig 6(b), the oscillation amplitude of the magnetic anisotropy field (S1) Here, f , r f , and f  represent the frequency of the microwave, the resonant frequency, and the full width at half maximum of the resonant peaks, respectively; A is the amplitude of the peak. Figure S3 We used the amplitude at 100 mT because, as shown in Fig S1(c), the free-layer magnetization is almost saturated at that field intensity, and a larger magnetic field increases the modulation of the pinned-layer magnetization. Using the amplitude of 3.4 μVGHz at the 100 mT, we obtained the effective magnetic field of spin-transfer torque stt B = 308 μT at a microwave power of −25 dBm, including an insertion loss of 1.16 dB. This value can be converted to stt B = 9.8 μT at a microwave power of −55 dBm, the condition of the experiment shown in Fig 2(b). Therefore, the spin-torque due to HCMA is dominant in this experiment.
Although we suggested that large HCMA (large rf-spin-torque) produces large responsivity, it is not obvious under the mechanism in this manuscript. Thus, here, we discuss the relation between rf-spin-torque and responsivity induced by HCMA. From the power dependence of responsivity as shown in Fig 3, larger spin-torques induce higher responsivity. The diode voltage is proportional to the microwave power, and heat induced spin-torque in dc-biased MTJ is proportional to the microwave voltage, implying that the diode voltage is proportional to the square of rf spin-torque. In our system, because the HCMA is high and exerts a large spin-torque, the diode voltage increases, and a high responsivity is obtained.

responsivity
As shown in Fig 2(b), the diode voltage is obtained at 0.59 GHz with a line width of only 0.1 GHz. This frequency is tunable by magnetic-field and biasvoltage conditions. Figure S4 shows the diode spectra at various magnetic field conditions. The peak frequency can be modulated from 0.59 GHz to 0.74 GHz; there is a tradeoff between increasing peak frequency and decreasing responsivity.
As shown in Fig. 3, the dynamic range of the diode voltage is approximately from 0.1 mV to 10 mV. To expand this dynamic range, improvement of the signal to noise ratio (SNR) is necessary. In this experiment, the diode voltage reaches a noise equivalent voltage (NEV) of 0.1 mV at the microwave power of 0.1 nW. The decrease in the NEV enhances the dynamic range. This SNR can be improved by increasing the ferromagnetic-layer thickness. Spin-transfer torque and VCMA are inversely related to the FeB thickness. HCMA also diminishes with thickness, but the decrease is smaller than that in spin transfer torque or VCMA. This is because the increase in temperature of the ferromagnetic layer is affected by the MgO layer through which the heat flows. Therefore, HCMA is preferable for improving the dynamic range of the responsivity.

power
We explain the results of the noise equivalent power (NEP) measurements considering the spin-torque diode effect. We searched for the optimal conditions for NEP in the magnetic field range of 44 mT -60 mT, azimuthal angles between 6° -12°, and rotation angles in the range 20° -60°. Figure S5 shows the frequency dependence of the diode voltage. We obtained a minimum NEP of GHz with a time constant of 100 ms. The responsivity is (3.33 ± 0.01)×10 6 V/W under these conditions. Taking into consideration the insertion loss of 1.16 dB, the responsivity is (4.35 ± 0.01)×10 6 V/W.