Abstract
Short wavelength exchangedominated propagating spin waves will enable magnonic devices to operate at higher frequencies and higher data transmission rates. While giant magnetoresistance (GMR)based magnetic nanocontacts are efficient injectors of propagating spin waves, the generated wavelengths are 2.6 times the nanocontact diameter, and the electrical signal strength remains too weak for applications. Here we demonstrate nanocontactbased spin wave generation in magnetic tunnel junctions and observe largefrequency steps consistent with the hitherto ignored possibility of second and thirdorder propagating spin waves with wavelengths of 120 and 74 nm, i.e., much smaller than the 150nm nanocontact. Mutual synchronization is also observed on all three propagating modes. These higherorder propagating spin waves will enable magnonic devices to operate at much higher frequencies and greatly increase their transmission rates and spin wave propagating lengths, both proportional to the much higher group velocity.
Introduction
Steadystate largeangle magnetization dynamics can be generated via spintransfer torque (STT)^{1,2,3} in a class of devices commonly referred to as spin torque nanooscillators (STNOs)^{4,5,6,7,8,9,10}. The typical building block of an STNO is a thinfilm trilayer stack, where two magnetic layers are separated by a nonmagnetic spacer. The charge current becomes partially spin polarized by the magnetic layers and can act as positive or negative spin wave (SW) damping depending on its polarity. Above a certain critical current density, the negative damping can locally overcome the intrinsic damping, resulting in autooscillations on one or more SW modes of the system. To sustain such autooscillations, a large current density of the order of 10^{6}−10^{8} A/cm^{2} is required, which can be achieved by spatial constriction of the current, e.g. using a nanocontact (NC) on top of a GMR trilayer stack. Such NCbased STNOs are also the most effective SW injectors for miniaturized magnonic devices^{11,12,13,14}, in particular for short wavelength, exchangedominated SWs, since the wave vector (k) is inversely proportional to the NC radius (r_{NC}) through the Slonczewski relation k = 1.2/r_{NC}. As the SW group velocity, which governs the data transmission rate, scales with k, and the operating frequency with k^{2}, future ultrahigh data rate magnonic devices will have to push the SW wavelength down to a few 10s of nanometers^{15}.
For efficient electrical SW readout, magnonic devices will also have to be based on magnetic tunnel junctions (MTJs), as tunneling magnetoresistance (TMR) is one or more orders of magnitude higher than GMR^{16,17}. The relatively low conductivity of the MTJ tunneling barrier compared with the top metal layers leads to large lateral current shunting for an ordinary NC (Fig. 1a). To force more of the current through the MTJ, we instead fabricate socalled sombrero NCs (Fig. 1b), in which the MTJ cap layer is gradually thinned as it extends away from the NC^{18,19}, and use a MgO layer with a lowresistance area (RA) product of 1.5 Ω m^{2} to further promote tunneling through the barrier. The resulting devices exhibit the typical SW modes associated with NC STNOs, such as the spinwave bullet^{20,21,22,23} and the Slonczewski propagating SW mode^{3}. In addition, we observe two additional, higherfrequency modes, which we identify as the second and thirdorder propagating SW modes mentioned in Ref. ^{3}, but never previously observed. We estimate the wavelengths of these two modes to be 120 and 74 nm, i.e., much smaller than the 150nm nanocontact. Using double nanocontact devices, we furthermore observe mutual synchronization on all three propagating modes, corroborating their propagating character.
Results
Magnetostatics
Figure 1c shows the magnetic hysteresis loop of the unpatterned MTJ stack in a magnetic field applied along the inplane easy axis (EA) of the magnetic layers (for details see Methods). Figure 1d shows the corresponding resistance (R) of an MTJSTNO with a nominal diameter of d_{NC} = 150 nm, displaying a magnetoresistance (MR) of 36%, confirming that a significant fraction of the current indeed tunnels through the MgO barrier. The very good agreement between the field dependence of the unpatterned stack and the fully processed MTJSTNO suggests minimal processinduced changes of the magnetic layers, a strong indication that the free layer (FL) remains intact.
Magnetodynamics
Figure 2 shows the generated power spectral density (PSD) vs. field strength during autooscillations at six different drive currents, with the field angle fixed to θ_{ex} = 85° (the color plot is assembled from PSD measurements at constant current and field, a few of those shown in Supplementary Figure 2 of Supplementary Information). At the lowest currents, I_{dc} = −5 & −6 mA, the strongest mode can be identified as a SW bullet soliton^{20,21,22,23}. Its frequency, f_{SWB} lies well below the ferromagnetic resonance frequency (f_{FMR}; red dashed line) and can be very well fitted (Eq. 4 in Methods) for fields below 0.7 T. At intermediate fields, 0.7 T < H_{ex} < 1.35 T, the bullet signal gradually weakens and its frequency approaches f_{FMR}, until at 1.35 T it finally disappears as its frequency crosses f_{FMR}, where selflocalization of the bullet is no longer possible. The calculated (Eq. 2 in Methods) internal angle of magnetization, \(\theta _{{\mathrm{int}}}^{{\mathrm{crit}}} = 60^\circ\), at the critical field μ_{0}H_{ex} = 1.35 T, is in good agreement with the theoretical prediction^{24} \(\theta _{{\mathrm{int}}}^{{\mathrm{crit}}} = 55^\circ\). Above the critical field, we find a weaker mode about 0.2 GHz above f_{FMR} consistent with the ordinary Slonczewski propagating SW mode^{3} (see also Supplementary Figure 2 in Supplementary Information).
At stronger negative currents, I_{dc} = −7 mA, the PSD in the highfield region changes dramatically, as a much stronger mode appears with a frequency much higher than f_{FMR}. This change is accompanied by additional lowfrequency noise, indicative of mode hopping. Further increasing the negative current strength to I_{dc} = −8 mA, first modifies this new mode, after which another sharp jump up to an even higher frequency is observed at about 1.6 T. As we increase the current magnitude further to −9 and −10 mA, this new mode dominates the entire highfield region. The lowfrequency noise is now concentrated to the field region just above the critical field, where the 2nd and 3rd modes appear to be competing.
To analyze this behavior, we draw renewed attention to the higherorder propagating SW modes put forward by Slonczewski^{3} but up to this point entirely overlooked in experiments. The excited propagating SWs have a discrete set of possible wave vectors r_{NC}k ≃ 1.2, 4.7, 7.7..., where only the firstorder mode (r_{NC}k ≃ 1.2) is discussed in the literature because of its lower threshold current. Taking the literature value^{25} for the freelayer exchange stiffness, A_{ex} = 23 × 10^{−12} J/m, and allowing for a reasonable lateral current spread^{26} (an effective NC radius of r_{NC} = 90 nm), we find that we can fit the fielddependent frequencies of both the second and thirdmode almost perfectly using the predicted k = 4.7/r_{NC} and k = 7.7/r_{NC}. The ordinary firstorder mode can be equally well fitted (not shown). It is noteworthy that increasingly higher currents are required to excite the higher mode numbers, in agreement with Slonczewski’s original expectations^{3}. We also point out that in the original derivation only radial modes were considered, excluding any azimuthal modes. The additional smaller frequency step observed within the 2^{nd} radial mode in Fig. 2(d) could hence be related to a further increase in the exchange energy of a possible azimuthal mode^{27}.
In all fits, we allowed M_{s} to be a function of I_{dc} and used the same M_{s} to calculate f_{FMR}, f_{SWR}, and \(f_{{\mathrm{PSW}}}^{i = 1,2,3}\). This allows us to estimate the amount of heating due to the drive current. Figure 3a shows the variation of M_{s} as a function of temperature (blue circles) measured from 10 to 340 K using temperaturedependent FMR spectroscopy on unpatterned areas of the MTJ stack. We can fit M_{s}(T) to a Bloch law function and extrapolate this dependence to higher temperatures (black solid line). The red triangles in Fig. 3a then show the extracted M_{s} values at each I_{dc} placed on the extrapolated fit, which allow us to extract the local temperature of the FL underneath the NC. As can be seen in the inset, the temperature shows a parabolic rise with increasing current, indicative of Joule heating. The currentinduced temperature rise at e.g., I_{dc} = −9 mA is about 220 K, which is consistent with literature values of nanoscale temperature gradients in similar structures sustaining similar current densities^{28}.
We then show how we can control which propagating mode to excite by varying the current at constant applied field (Fig. 3b). We can again fit the three modes very accurately using the currentdependent M_{s}(I_{dc}) extracted from Fig. 3a. The weak current tunability of our MTJbased NCSTNOs is consistent with the weak nonlinearity values found in the literature on MTJ pillars^{29,30} and is advantageous as it reduces any nonlinearity driven increase in phase noise from amplitude noise^{31,32}. It is also consistent with theoretical predictions that the nonlinear frequency shift, at a constant current, should decrease strongly with increasing NC size and only be prominent for sub 100nm NCs^{33}. Since our large MTJbased STNOs can autooscillate at about the same currents as the smaller GMRbased STNOs, we conclude that the generated SWs should have a much weaker nonlinear frequency shift, i.e., should be considered as quasilinear.
Mutual synchronization
In Fig. 4, we show experimentally that it is also possible to achieve spinwavemediated mutual synchronization^{34,35,36,37} on all three modes, further corroborating their propagating character. Figure 4a shows the PSD vs. field for a doubleNC MTJSTNO autooscillating on the first Slonczewski mode (the double NCs were fabricated on the same type of stack as the device above). At fields below 1.22 T, the PSD shows two distinct peaks at high frequency and substantial microwave noise below 2.5 GHz. Above 1.22 T, the two signals instead merge into a single signal with a frequency in between the first two, and the microwave noise disappears. These observations are consistent with highly interacting but individually autooscillating regions below 1.22 T and a robust mutually synchronized state above 1.22 T.
As the original double NC devices did not survive the currents required for autooscillations on the higher modes, we instead made a second batch of devices based on an improved MTJ stack with a thicker bottom electrode (150 nm CuN instead of 30 nm) to promote more of the current to pass through the tunneling barrier and further reduce the lateral current spread^{26}. As a result, we could effectively reduce the threshold current density for all three modes. Figure 4b shows the PSD vs. current from one such optimized double nanocontact device operating at 1.18 T. The NCs first autooscillate on the first mode at relatively close frequencies (Fig. 4b). They then jump to the second mode at different currents: one NC at about −13 mA and the other at about −17 mA. As soon as both NCs autooscillate on the second mode, their frequencies approach each other, and at about −18 mA, both the first and the second harmonic indicate mutual synchronization. Figure 4c shows the same device at a higherfield of 1.45 T. At this field, the second mode does not show mutual synchronization at any current. However, when both NCs jump to the third mode, their overlapping signals indicate that mutual synchronization on the third mode is also possible.
Discussion
The possibility of generating higherorder Slonczewski modes has a number of important implications. Their much shorter wavelengths, in our case estimated to 120 nm (2nd mode) and 74 nm (3rd mode), already bring them into the important sub 100 nm range^{15}, which only a few years ago was considered outofreach for magnonics^{38}. As the SW group velocity increases linearly with the wave vector as v_{gr} ≃ 4γA_{ex}k/M_{s}, much faster transmissions can be achieved in magnonic devices and the SWs can travel significantly farther before being damped out. The calculated group velocities for the three observed modes are v_{1} = 258 m/s, v_{2} = 1010 m/s, and v_{3} = 1655 m/s. This is particularly beneficial for mutual synchronization of multiple MTJbased NCs. For example, one can find the maximum distance of synchronization, a_{max}, between the two coupled oscillators, using the method developed by Slavin and Tiberkevich^{39}. Using typical parameters of coupling strength, \({\mathrm{\Delta }}_{{\mathrm{max}}}/\sqrt {1 + \nu ^2} = 50\,{\mathrm{MHz}}\), and a Gilbert damping of α_{G} = 0.015, we find a_{max} = 240, 350, and 420 nm for the PSWs with the corresponding frequencies f_{PSW} = 13.5, 17.7, and 24.7 GHz observed at μ_{0}H_{ext} = 1.6 T (Fig. 3). As the drive current of both single and mutually synchronized STNOs can be modulated very rapidly^{40,41,42,43,44,45}, high data rate frequency shift keying^{46} will likely be possible using only a small modulation amplitude of the drive current. In addition, novel modulation concepts such as wave vector keying could be readily realized, with possible use in magnonic devices.
We conclude by pointing out that both the nominal NC diameter (150 nm) and the estimated effective NC diameter (180 nm) are much larger than what could be realized using stateoftheart MTJ lithography. We see no fundamental reason against fabricating NCs down to 30 nm, which would then translate to wavelenghts down to 15 nm and SW frequencies well beyond 300 GHz. The use of higherorder propagating SW modes might therefore be the preferred route toward ultrahigh frequency STNOs.
Methods
MTJ multilayer
The magnetronsputtered MTJ stack contains two CoFeB/CoFe layers sandwiching a MgO tunneling barrier with a resistancearea (RA) product of 1.5 Ω μm^{2}^{47,48,49}. The top CoFeB/CoFe bilayer acts as the FL and the bottom one as the reference layer (RL). A pinned layer (PL) is made of CoFe, which is separated from the RL by a Ru layer. An antiferromagnetic PtMn layer is located right below the PL. The complete layer sequence is: Ta(3)/CuN(30)/Ta(5)/PtMn(20)/CoFe_{30}(2)/Ru(0.85)/CoFe_{40}B_{20}(2)/CoFe_{30}(0.5)/MgO/CoFe_{30}(0.5)/CoFe_{40}B_{20}(1.5)/Ta(3)/Ru(7), with thicknesses in nanometer. For the demonstration of mutual synchronization on the higher spin wave modes, the same stack but with a thicker CuN(150) layer was used.
Nanocontact fabrication
After stack deposition, 16 μm × 8 μm mesas are defined using photolithography. To make the hybrid NC structure, electronbeam lithography (EBL) with a negative tone resist is used to define nanocontacts with a nominal diameter of 150 nm. The negative tone resist is used as an etching mask in the ion beam etching (IBE) process. Etching of the cap layers in IBE is carefully monitored by in situ secondary ion mass spectroscopy to prevent any damage to the layers underneath the cap. After this step, a structure similar to that shown in Fig. 1b is realized. Following the etching process, 30 nm of SiO_{2} is deposited to provide electrical insulation between the cap and top contact. The remaining negative tone resist acts as a liftoff layer this time. The devices are left in a hot bath of resist remover combined with a highenergy ultrasonic machine for a successful liftoff. In order to provide electrical access to the devices, top contacts are defined using photolithography.
Static characterization
The static magnetic states throughout key points of the reversal are highlighted as insets in Fig. 1c and d. Decreasing the field from a fully saturated state (1) allows the RL to gradually rotate to be antiparallel (2) with the PL due to the strong antiferromagnetic coupling (AFC). In going from state 2 → 3, the FL switches rapidly in a relatively small field and once again becomes parallel to the RL, hence a minimum R is restored. Note that the FL minor loop is shifted toward positive fields in both Fig. 1c and d, indicating some weak ferromagnetic coupling to the RL. Upon further decreasing the field, the magnetic state moves from 3 → 4, as the PL, working against the strong AFC and weaker exchange bias, slowly switches to be parallel to the RL. In Fig. 1d, we find small increases in R when moving from states 3 → 4 and 4 → 5. These can be attributed to minor scissoring of the RL and PL layers due to their strong AFC. As one goes from state 5 → 6 → 1, the FL switches to align with the applied field, followed by the RL switching at high field.
Ferromagnetic resonance (FMR) measurements
The magnetodynamic properties of the free layer (CoFeB) are determined using an unpatterned thinfilm stack. The inset of Fig. 1d shows the extracted FL resonance field from broadband FMR measurements (blue squares), fitted with the standard Kittel equation (red line). From the fit, we extract the values of the gyromagnetic ratio, γ/2π = 29.7 GHz/T, and effective saturation magnetization, μ_{0}M_{eff} = 1.41 T. Subsequent microwave measurement are performed such that the inplane component of the field lies along the EA of the MTJ stack. We also study the temperature dependence of the magnetodynamcis at low temperature using a NanOsc Instrument CryoFMR system. The lowtemperature measurements are performed between 10 K–340 K. At each temperature, the FMR response was measured at several frequencies over the range 4–16 GHz, where an external magnetic field is applied in the film plane. At each frequency, the resonance field (H_{res}) is extracted by fitting the FMR to a Lorentzian function. We extracted the effective magnetization (M_{eff}) of CoFeB thin films by fitting the dispersion relation (frequency vs. field) to the Kittel equation \(f = \frac{{\gamma \mu _0}}{{2\pi }}\sqrt {H(H + M_{{\mathrm{eff}}})}\), where \(\frac{\gamma }{{2\pi }}\) is the gyromagnetic ratio. We fit the variation of M_{eff} with the temperature to a Bloch's law to extract M_{eff} at higher temperatures (T > 340 K).
Microwave measurements
All measurements were performed at room temperature. Inplane magnetization hysteresis loops of the blanket MTJ multilayer film stacks were measured using an alternating gradient magnetometer (AGM). The MR was measured using a custombuilt fourpoint probe station. The magnetodynamic properties of the unpatterned FL were determined from using a NanOsc Instruments PhaseFMR spectrometer.
Microwave measurements were performed using a probe station with a permanent magnet Halbach array producing a uniform and rotatable outofplane field with a fixed magnitude μ_{0}H = 0.965 T. A direct electric current, I_{dc}, was applied to the devices through a bias tee, and the resulting magnetodynamic response was first amplified using a lownoise amplifier and then measured electrically using a 40 GHz spectrum analyzer (see Supplementary Information). Microwave measurements at higher fields were performed using another custombuilt setup capable of providing a uniform magnetic field of up to μ_{0}H = 1.8 T.
Bullet frequency and PSW spectrum calculation
The angular dependence of the nonlinear frequency coefficient, N, is calculated from the following expression^{24}:
where f_{FMR} is the FMR frequency. \(f_{\mathrm{H}} = \frac{\gamma }{{2\pi }}\mu _0H_{{\mathrm{int}}}\), \(f_{\mathrm{M}} = \frac{\gamma }{{2\pi }}\mu _0M_{\mathrm{s}}\) and finally H_{int} and θ_{int} are the internal magnetic field magnitudes and outofplane angles, respectively. H_{int} and θ_{int} are extracted using a magnetostatic approximation:
The frequency of the Slavin–Tiberkevich bullet mode is calculated from^{20}:
where f_{SWB} is the bullet angular frequency and B_{0} is the characteristic spinwave amplitude. The calculated f_{SWB} quantitatively describes the measured field dependence by setting B_{0} = 0.46, providing further evidence that this mode is, in fact, a solitonic bullet. The value of B_{0} is calculated according to Tyberkevych et al.^{20} and reaches B_{0} = 0.46, which is the upper limit of the theory. The spectrum of the propagating spin waves in the linear limit is defined as^{50}
where D = 2A_{ex}/(μ_{0}M_{eff}) is the dispersion coefficient and A_{ex} is the exchange stiffness constant.
Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.
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Acknowledgements
This work was partially supported by the European Commission FP7ICT2011contract No. 317950 “MOSAIC”. It was also partially supported by the European Research Council (ERC) under the European Community’s Seventh Framework Programme (FP/20072013)/ERC Grant 307144 “MUSTANG”. Support from the Swedish Research Council (VR), the Swedish Foundation for Strategic Research (SSF), the Göran Gustafsson Foundation, and the Knut and Alice Wallenberg Foundation is also gratefully acknowledged.
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A.H. and A.G. fabricated the devices. A.H. and H.F. performed all the microwave measurements. R.K. performed analytic calculations. M.H. performed the FMR measurements. R.F. and P.P.F. provided the MTJ stack. R.K.D. cosupervised the project. J.Å. initiated and supervised the project. All authors contributed to the data analysis and cowrote the manuscript.
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Houshang, A., Khymyn, R., Fulara, H. et al. Spin transfer torque driven higherorder propagating spin waves in nanocontact magnetic tunnel junctions. Nat Commun 9, 4374 (2018). https://doi.org/10.1038/s41467018065890
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