Tunnel magnetoresistance angular and bias dependence enabling tuneable wireless communication

Spin-transfer torques (STTs) can be exploited in order to manipulate the magnetic moments of nanomagnets, thus allowing for new consumer-oriented devices to be designed. Of particular interest here are tuneable radio-frequency (RF) oscillators for wireless communication. Currently, the structure that maximizes the output power is an Fe/MgO/Fe-type magnetic tunnel junction (MTJ) with a fixed layer magnetized in the plane of the layers and a free layer magnetized perpendicular to the plane. This structure allows for most of the tunnel magnetoresistance (TMR) to be converted into output power. Here, we experimentally and theoretically demonstrate that the main mechanism sustaining steady-state precession in such structures is the angular dependence of the magnetoresistance. The TMR of such devices is known to exhibit a broken-linear dependence versus the applied bias. Our results show that the TMR bias dependence effectively quenches spin-transfer-driven precession and introduces a non-monotonic frequency dependence at high applied currents. This has an impact on devices seeking to work in the ‘THz gap’ due to their non-trivial TMR bias dependences.


Part 1: STNO efficiency: metallic spin valve versus magnetic tunnel junction
The efficiency of STNOs can be expressed by the power conversion ratio of the output power (emitted by the device) to the input power (required to excite steady-state precession): P out /P in . Typically, for the same lateral size of the nano-pillar, the resistance of a metallic spin-valve is of the order of 10 Ω, and that of an Fe/MgO/Fe magnetic tunnel junction ~100 Ω. The characteristic operation DC currents are experimentally ~10 mA and ~1 mA, respectively. Thus we obtain following input power of these two types of STNOs: According to the literature, the output power of STNOs is of order of nW for metallic devices 1 , and µW for MgO-based systems 2,3 . Thus, the power conversion ratios are as follows: Consequently, the power conversion efficiency of STNOs based on MgO-based magnetic tunnel junctions is four orders of magnitude larger than that of fully metallic devices.

Part 2: STNO output power
The RF signal generated by an STNO device is detected by the spectrum analyzer as a voltage quantity per a defined frequency division. Thus, in order to express the spectral signal in the unit of power, we used the following formula: Here, ./ 9 ( :; < is the Power Spectral Density, = > ? @A is the voltage signal generated by the STNO sample, = B? is the background voltage, C is the impedance of the circuit (50 Ω), and D is the Resolution Band Width (in this case, 3 MHz).
Supplementary Fig. S1 shows an example of data analysis for a single frequency spectrum of the STNO sample measured at +30 mT with a +2.3 mA current. The black line represents the measured spectrum, where the background signal has been previously subtracted. Since in this case a quite significant contribution from the low frequency noise is observed, the overall signal is fitted with Lorentz functions, so that two overlapping peaks can be distinguished: the main mode peak (red curve) and the low frequency noise (green curve). The total output power of the spintorque oscillator is defined as the area under the red curve over the whole frequency. The power integration was conducted using a Matlab script based on the formula displayed in the inset of Supplementary Fig. S1.
Supplementary Figure S1. An example of data analysis. The output power of spin-torque nano-oscillators is defined as an integral of the Power Spectral Density of the main frequency mode (red curve) over the frequency. Inset formula: ./ -Power Spectral Density, EF -frequency step (in our case EF = 9 MHz).

Part 3: Static resistance at dynamical states
Simultaneously with the frequency spectra, we measured the static resistance versus field for every current value, shown in Supplementary Fig. S2. The magnitude of the TMR is directly proportional to the relative orientation of the magnetizations of the free and the reference layers, reaching its maximum for the AP state and minimum for the P state. Since the orientation of the reference layer magnetization is fixed, when dynamics are excited, the magnitude of the static resistance gives information about the G-component of the average position of the magnetization in the free layer (i.e., the position of the precession axis).
Supplementary Fig. S2 shows the evolution of magnetoresistance curves with the applied current. We observe here a reduction of the base resistance with increasing current, which results from the TMR bias dependence (see Fig. 1 (d) in the Main Text). For currents up to 0.8 mA, the TMR curve is similar to the curve measured at out-of-plane applied fields for a small probe current of 0.01 mA (see the red curve in Fig. 1 (c) in the Main Text). While approaching zero-field, we observe a dip in the resistance, which occurs due to the canting of the free layer magnetization, induced by an inplane shape anisotropy of the nano-pillar (note that cross section of the nano-pillar is elliptical), combined with a slight parallel interlayer coupling with the reference layer. For currents above 0.8 mA, where the current density is high enough to drive magnetization dynamics, we observe an increase of the resistance close to zero-field, indicating a gradual tilting of the precession cone toward the in-plane AP orientation (i.e., −G direction in Fig. 1 (a) in the Main Text).
Since the static resistance is proportional to the projection of the free layer magnetization on the magnetization vector in the reference layer, for every applied current, we calculate the change in resistance Δ J | L M : NO = − 0.5 Q with respect to the resistance at the same field when using a small current = 0.5 mA, which does not stimulate strong dynamics (see Fig. 3 (c) in the Main Text). The value of Δ % is directly proportional to Q R . The resistance change Δ % and its equivalent magnetic static state (expressed with averaged Q R component of the magnetization in the free layer) are presented with the colour plot in Fig. 2 (b) in the Main Text. At small fields (0-30 mT), the average position of the magnetization tilts towards the antiparallel configuration (blue region); it finally reaches the AP state for currents above 2 mA (black region). This leads to the preliminary conclusion that the gap in the dynamics at small field, observed in diagrams in Fig. 2 (a), is actually an effect of the stabilization of the static in-plane AP state, under the influence of the spin-transfer torque, which favours the AP state for this current configuration. Figure S2. Static magnetoresistance versus field for different current values. We observed a general decrease of the overall resistance with the current (due to the TMR bias dependence) and an increased resistance in the small field range (directly proportional to the magnitude of the applied current) indicating a gradual tilting of the precession cone toward the in-plane antiparallel direction. > 0 ] , the onset currents for precession exhibit a distinct curvature versus the applied field (see Supplementary Fig. S3 (b)), which has not been previously observed in metallic structures and thus constitutes a distinct signature for MTJs. Meanwhile, the quenching currents where the magnetization transits from steady-state precession to static in-plane states still depend linearly on the applied field (see dash-dot lines in Supplementary  Fig. S3 (b)). = 105 ] . The plots are limited to positive currents, as no dynamics was observed for negative bias, although the full current range was considered for the calculations.

Part 5: Linewidth and details of spectral features
We estimate the magnetization precession angle c from the experimentally obtained frequency as a function of , shown in Fig. 3 (a) in the Main Text, using the following formula: Here, F is the precession frequency, p = 1.76 • 10 $$ s@t >• is the gyromagnetic ratio, D aRb = 30 mT is the external field, and D uv = 120 mT is the effective out-of-plane anisotropy.
The derived angle is plotted in Supplementary Fig. S4. The increase of the angle above 90° indicates that the macrospin approximation breaks down above ~ 1 mA. A similar behavior was obtained in metallic systems 1 . This interpretation is further supported by the increase in 1/f noise (see Supplementary Fig. S5), occurring above this bias. 1/f noise is indicative that the dynamics are becoming increasingly less coherent 5 .
It is also worth to note that equation (6) is only valid when assuming a constant precession angle c for a given frequency value (the same approximation we also used in our analytical calculations, see Methods section in the Main Text). In the real system, as well as in the macrospin simulation, the precession angle can be assumed as constant only for low currents. For higher applied currents, the magnetization precession trajectory deviates from circular shape and becomes more quasielliptical.