Tuning spin torque nano-oscillator nonlinearity using He+ irradiation
Sheng Jiang, Roman Khymyn, Sunjae Chung, Quang Tuan Le, Liza Herrera Diez, Afshin Houshang, Mohammad Zahedinejad, Dafine Ravelosona, Johan Åkerman
TTuning spin-torque nano-oscillator nonlinearity using He + irradiation Sheng Jiang,
1, 2
Roman Khymyn, Sunjae Chung,
1, 3
Quang Tuan Le,
1, 2
Liza Herrera Diez, Afshin Houshang,
2, 5
Mohammad Zahedinejad, Dafin´e Ravelosona,
4, 6 and Johan ˚Akerman
1, 2, 5, ∗ Department of Applied Physics, School of Engineering Sciences,KTH Royal Institute of Technology, Electrum 229, SE-16440 Kista, Sweden Department of Physics, University of Gothenburg, 412 96, Gothenburg, Sweden Department of Physics and Astronomy, Uppsala University, 751 20 Uppsala, Sweden Institut d’Electronique Fondamentale, CNRS, Universit´e Paris-Sud, Universit´e Paris-Saclay, 91405 Orsay, France NanOsc AB, Kista 164 40, Sweden Spin-Ion Technologies, 28 rue du G´en´eral Leclerc, 78000 Versailles Cedex, France (Dated: December 24, 2018)We use He + irradiation to tune the nonlinearity, N , of all-perpendicular spin-torque nano-oscillators (STNOs) using the He + fluence-dependent perpendicular magnetic anisotropy (PMA)of the [Co/Ni] free layer. Employing fluences from 6 to 20 × He + /cm , we are able to tune N in an in-plane field from strongly positive to moderately negative. As the STNO microwave signalproperties are mainly governed by N , we can in this way directly control the threshold current, thecurrent tunability of the frequency, and the STNO linewidth. In particular, we can dramaticallyimprove the latter by more than two orders of magnitude. Our results are in good agreement withthe theory for nonlinear auto-oscillators, confirm theoretical predictions of the role of nonlinearity,and demonstrate a straightforward path towards improving the microwave properties of STNOs. DOI:
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Spin-torque nano-oscillators (STNOs) are among themost promising candidates for nanoscale broadband mi-crowave generators [1–6] and detectors [7–9]. STNOs cangenerate broadband microwave frequencies ranging fromhundreds of MHz to the sub-THz [10–12], controlled byboth magnetic fields and dc currents [5, 13]. Moreover,the device size can be reduced to a few tens of nanome-ters, which is of great opportunity for industrial appli-cations. They can also host a range of novel magneto-dynamical spin wave modes, such as propagating spinwaves of different orders [14, 15], and magnetodynamicalsolitons, such as spin wave bullets[14] and droplets[3].However, the applicability of these devices has sufferedfrom their low power emission and large linewidth. Non-linear auto-oscillator theory [16–19] explains the largelinewidth as a result of the strong nonlinearity N , i.e. thedependence of the microwave frequency on its preces-sion amplitude. N can be controlled not only by themeasurement conditions [13, 20–24], such as the mag-nitude and direction of the magnetic field, but also bythe magnetic properties of the free layer of the STNO,such as the magnetic anisotropy and the effective mag-netization [19]. For instance, in an easy-plane free layer, N changes gradually from positive to negative values asthe direction of magnetic field rotates from out-of-planeto in-plane [16, 19]. Experimental studies have corrobo-rated [13, 14, 16, 21, 25–27] this theoretical prediction,as the linewidth shows a minimum when N crosses zeroat the critical field angle. This suggests a way to improvethe linewidth by selectively reducing the nonlinearity.Whereas all previous studies aimed at minimizing thenonlinearity have focused only on the effects of the exter-nal conditions in single devices, a more general and prac- tical solution should be based on the intrinsic magneticproperties of the device itself. In our work, we thereforestudy systematically how N is affected by the strengthof perpendicular magnetic anisotropy (PMA) H k in a setof nanocontact (NC) STNOs. We show how N can becontinuously tuned as H k is controlled by He + irradia-tion fluence [28–31] in otherwise identical devices. Mostimportantly, the linewidth is dramatically improved atmoderate H k values, where N →
0. Finally, we show ex-cellent agreement of our experimental results with non-linear auto-oscillator theory [19].The STNO devices were fabricated from all-perpendicular (all-PMA) [Co/Pd]/Cu/[Co/Ni] [32, 33]and orthogonal [Co/Pd]/Cu/NiFe spin valves (SVs).The full stack consists of a Ta (5)/Cu (15)/Ta (5)/Pd(3) seed layer, an all-PMA [Co (0.5)/Pd (1.0)] × × × Fe (4.5) SV with aCu(3)/Pd(3) capping layer, sputtered onto a thermallyoxidized 100 mm Si wafer (numbers in parentheses arelayer thicknesses in nanometers). The deposited stackswere first patterned into 8 µ m × µ m mesas using pho-tolithography and ion-milling etching, followed by chemi-cal vapor deposition (CVD) of an insulating 40-nm-thickSiO film. Electron beam lithography and reactive ionetching were used to open nanocontacts (with nominalradius of R NC
35 nm) through the SiO in the centerof each mesa. The processed wafer was then cut intodifferent pieces for He + irradiation with the fluence F varied from 6 to 20 × He + /cm [33]. Fabricationwas completed with lift-off lithography and deposition ofa Cu (500 nm)/Au (100 nm) top electrode in a singlerun with all irradiated pieces. Our protocol hence en- a r X i v : . [ phy s i c s . a pp - ph ] D ec TABLE I. Sample structure information and the calculatedeffective magnetization µ M eff of free layer ([Co/Ni] or NiFe)for various He + -irradiation fluences. µ M eff are measured byST-FMR (see the supplemental materials [41]).Structure Fluence( × He + /cm ) µ M eff (T)[Co/Pd]/Cu/[Co/Ni] 0 -0.68[Co/Pd]/Cu/[Co/Ni] 6 -0.44[Co/Pd]/Cu/[Co/Ni] 10 -0.14[Co/Pd]/Cu/[Co/Ni] 20 0.03[Co/Pd]/Cu/NiFe - 0.98 sures that all other properties, except the He + fluence,are identical from device to device.We used our custom-built probe station for static andmicrowave characterization. A direct current I dc wasinjected into the devices using a Keithley 6221 currentsource, and the dc voltage was detected using a Keithley2182 nanovoltmeter. The magnetic field was applied inthe plane of the film. The generated microwave signalsfrom the STNO device were decoupled from the dc volt-age via a bias-tee, amplified using a low-noise amplifier,and then recorded with a spectrum analyzer [34, 35].To accurately determine M eff of the [Co/Ni] free layer,spin-torque ferromagnetic resonance (ST-FMR) [36–40]measurements were performed on the He + -irradiatedSTNOs (see details in supplemental materials [41]). Thefluence information and the obtained effective magneti-zation µ M eff are presented in Table I. The value of M eff ( H k ) increases (decreases) as the fluence increases. Here,the NiFe free layer is used as a reference for a larger M eff sample.In Fig. 1, we compare the calculated FMR frequency, f FMR , using the measured M eff , with the microwave sig-nals generated from the STNO devices. The inset inFig. 1 shows a typical power spectral density (PSD) of themicrowave signals for a fluence of F = 10 × He + /cm .All PSD spectra are well fitted with a Lorentz function,and the extracted frequency f versus magnetic field ispresented in Fig. 1 with different symbols for each dif-ferent fluence. All data show a quasi-linear dependenceon the magnetic field, and the generated microwave fre-quency f extends to lower values as M eff ( H k ) increases(decreases). This behavior is consistent with the cal-culated value of the FMR frequency f FMR , plotted asdashed lines in Fig. 1. The overall trends of f FMR arein good agreement with the auto-oscillation f . The dif-ference between the calculated f FMR and the measuredauto-oscillation f is a direct measure of the nonlinearityof the magnetization precession [5, 14, 23, 42], which isdiscussed in detail below.We now turn to the current-induced frequency tunabil-ity. Figures 2(a)–2(e) show the generated microwave fre-quency f versus dc current I dc at a fixed magnetic field, µ H = 0 .
72 T; f linearly depends on the I dc at different F ( · H e + / c m ) (cid:1) M eff = 0.98 T (cid:1) M eff = 0.03 T (cid:1) M eff = -0.14 T (cid:1) M eff = -0.44 T
0 6 1 0 2 0 N i F e
Frequency (GHz)
M a g n e t i c F i e l d ( T ) (cid:1) M eff = -0.68 T
0 5 1 0 d B F = 1 0 × 1 0 H e + / c m Frequency (GHz) (cid:1) H ( T ) FIG. 1. Auto-oscillation frequency versus in-plane magneticfield for various irradiated STNOs with R NC = 35 nm. Thedashed lines are the calculated FMR frequencies f FMR , basedon the values of µ M eff obtained from ST-FMR measurements[41]. Inset: A typical power spectral density (PSD) of anSTNO with F = 10 × He + /cm at I dc = −
14 mA. values of M eff . The current-induced frequency tunabil-ity df /dI dc can be extracted from the slopes of linear fitswhich plot as each dashed line in Figs. 2(a)–2(e). df /dI dc for M eff are then summarized in Fig. 2(f). We found that i ) df /dI dc decreases from 0.50 GHz/mA for nonirradiated[Co/Ni] to -0.13 GHz/mA for NiFe as M eff increases (or H k decreases), ii ) the sign of df /dI dc changes from posi-tive (for [Co/Ni]) to negative (for NiFe), consistent withthe easy axis transition from out-of-plane for [Co/Ni] toin-plane for NiFe, and further details will be discussedlater.We carried out detailed measurements at differentmagnetic fields to understand further the behavior of df /dI dc . Figure 3(a) shows one example of extracted f versus I dc at different fields, ranging from 0.37 to 1.12 Twith a 0.05 T step, for F = 6 × He + /cm . Alldata show clear linear dependencies on I dc . Here wewould like to define one numerical relation about thetunability, df /dζ = I th ( df /dI dc ), to compare our ex-perimental results directly with theoretical calculation,where ζ = I dc /I th is the dimensionless supercriticalityparameter [19] and I th is the threshold current. I th were extracted from plots of inverse power 1 /P versus I dc as described in supplemental materials [41]. Afterobtained all I th and df /dI dc for different M eff , df /dζ are represented as solid dots in Fig. 3(b). All df /dζ for different M eff show similar behaviors that is inverseproportional to magnetic field. It is noteworthy thatthe overall df /dζ decreases as M eff ( H k ) increases (de-creases). It reaches around zero when the µ M eff ≈ F = 20 × He + /cm . The sign of df /dζ for NiFe iseven negative. - 1 8 - 2 0 - 2 2 - 2 4 - 2 6 - 2 81 01 21 41 61 8 - 1 8 - 2 0 - 2 2 - 2 4 - 2 6 - 2 81 61 82 02 2- 1 6 - 1 8 - 2 0 - 2 2 - 2 41 61 82 02 22 4 - 1 2 - 1 4 - 1 6 - 1 8 - 2 0 - 2 22 02 22 42 6- 2 6 - 2 8 - 3 0 - 3 2 - 3 42 02 22 42 6 - 1 . 0 - 0 . 5 0 . 0 0 . 5 1 . 0- 0 . 20 . 00 . 20 . 40 . 60 . 8 Frequency (GHz)Frequency (GHz)Frequency (GHz)
C u r r e n t ( m A )( c ) F = 1 0 · H e + / c m (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) ( d ) F = 2 0 · H e + / c m (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:2) M e f f = - 0 . 1 4 T (cid:2) M e f f = 0 . 0 3 T 1 1 1 1 ( e ) N i F e ( f ) 1 1 1 1 (cid:2) M e f f = 0 . 9 8 T d f /d I dc (GHz/mA) (cid:2) M e f f ( T )( a ) F = 0 (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) ( b ) F = 6 · H e + / c m (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:2) M e f f = - 0 . 6 8 T (cid:2) M e f f = - 0 . 4 4 T 1 1 1 1 FIG. 2. (a)–(e) PSD versus I dc in STNOs with differentirradiated fluences at µ H = 0 .
72 T. The red dotted linerepresents the linear fits of the auto-oscillation frequency. (f)slope df/dI dc versus µ M eff extracted from the fits of (a)–(e). To understand the behavior of tunability versus M eff ( H k ) from He + -irradiated STNOs, we considered thenonlinear auto-oscillator theory of A. Slavin and V.Tiberkevich [18, 19, 42, 43], which was derived from uni-versal auto-oscillation systems and has proved to be con-sistent with the Landau–Lifshitz–Gilbert–Slonczewski(LLGS) equation [19]. This theory allows us to de-scribe the experimental observation analytically. Theauto-oscillation frequency f generated from an STNO isexpressed as: f ( I dc ) = f FMR + N π ζ − ζ + Q , (1)where N is the nonlinearity factor, ζ − ζ + Q = P is thenormalized power of the stationary precession, and Q is the nonlinear damping coefficient. From Eq. (1), thefrequency shift is mainly decided by the nonlinearity N .Taking the derivation of Eq. (1), df /dζ is derived as: dfdζ = I th dfdI dc = N π Q ( ζ + Q ) . (2)The nonlinear frequency shift coefficient N for STNOsdominates the frequency tunability, and may be positive,zero, or negative, depending on magnetic field directionand magnetic anisotropy of free layer in STNOs.To explain the experimental observations using this an-alytical theory, we derive N with our experimental con- FIG. 3. (a) Extracted auto-oscillation frequency f vs. I dc at different magnetic fields for F = 6 × He + /cm . Someminor frequency jumps at µ H = 0 .
87 T are shown as rectan-gular boxes, possibly due to film inhomogeneities generatingdifferent dynamical behaviors. (b) df/dζ [ i.e. I th ( df/dI dc )]vs. magnetic field, where I th is extracted from the inter-cept of the inverse power of the auto-oscillation signals andthe df/dI dc are the slopes of the linear fits of frequency as I dc > I th (see supplemental materials [41]). The solid linesare the theoretical calculation from Eqs. (2)–(4). ditions. The nonlinearity is expressed as [42] N = − ω H ω M ( ω H + ω M / ω ( ω H + ω M / , (3) ω H = γHω M = 4 πγM eff ω = γ (cid:112) ω H ( ω H + ω M ) . (4)We note that Eqs. (3) and (4) are valid for the magneti-zation of the free layer being aligned to the magnetic fielddirection. Utilizing Eqs. (3) and (4), we calculate df /dζ ( ∝ N ), where ζ and Q are used as fitting parametersfor all data in Fig. 3(b), and we find reasonable goodagreements with 1.5 for ζ and 3.0 for Q, respectively.All calculated results are shown as the solid lines along-side the experimental results in Fig. 3(b). It should benoted that the theoretical calculation coincides with ex-perimental results in the overall trend, although there arediscrepancies between experiment and theory. One rea-son for these discrepancies is likely that the theory doesnot take into account the current-induced Joule heating - 1 0 - 1 5 - 2 0 - 2 5 - 3 0 - 3 51 01 0 01 0 0 0 F ( 1 0 H e + / c m ) Linewidth (MHz)
C u r r e n t ( m A )
0 6 1 0 2 0 N i F e (cid:1) M e f f = - 0 . 6 8 T (cid:1) M e f f = - 0 . 4 4 T (cid:1) M e f f = - 0 . 1 4 T (cid:1) M e f f = 0 . 0 3 T (cid:1) M e f f = 0 . 9 8 T FIG. 4. Linewidth ∆ f versus I dc with different effectivemagnetization µ M eff at µ H = 0 .
72 T. The linewidth wereextracted from the data in Figs. 3(a)–3(e). and Oersted fields that are present in the experiments. Inaddition, the calculated nonlinearity N can also explainthe frequency difference between the calculated f FMR andthe generated microwave frequency f in Fig. 1. Due tothe negative value of N (or df /dζ ) for NiFe, f is expectedto be lower than f FMR , as predicted in Eq. (1) and consis-tent with our experimental observations in Fig. 1. Thisauto-oscillation mode is often characterized as a localizedbullet [13, 14, 42]. In contrast, N is positive for easy out-of-plane [Co/Ni], so f > f FMR in Fig. 1 [13, 32, 42]. Inthis case, its mode favors to be a propagating spin-wave[13, 27, 44]. All of these experimental observations con-firm the theoretical predictions very well.Furthermore, according to nonlinear auto-oscillatortheory, the linewidth ∆ f of the generated microwave sig-nals can be expressed as [19]∆ f = Γ + ( P ) k B TE ( P ) (cid:34) (cid:18) N Γ eff (cid:19) (cid:35) , (5)where k B is the Boltzmann constant and T is the tem-perature. Γ + ( P ) and E ( P ) are the damping functionand time-averaged oscillation energy as a function of thepower P , respectively. Γ eff is the effective damping. InEq.(5), the linewidth ∆ f exhibits a quadratic dependenceon the nonlinearity N . To compare with our experimen-tal results, we extracted the linewidth from the data inFigs. 2(a)–2(e), as shown in Fig. 4. The linewidth wasindeed dramatically improved by two orders of magni-tude as N decreases (as M eff increases), it reaches to alowest value for µ M eff = 0 .
03 T where
N →
0. ∆ f again increases for the NiFe free layer when N becomesmoderately negative. The excellent agreement betweenour experimental results and theory confirms that thelinewidth can be minimized intentionally by controllingthe nonlinearity in general, and tuning it to zero in par- ticular. When the PMA compensates the demagnetiza-tion field, the nonlinearity identically equals zero regard-less of the external conditions. We can therefore mini-mize the linewidth by choosing free layer materials with µ M eff →
0. We hence would emphasize that our studycan offers a universal path to solving one of the key is-sues in utilizing STNOs as microwave generators. As forthe generated microwave power—another key drawbackof this type of microwave generators—we did not observean improvement in this study, mainly due to the slightlydegradation in magnetoresistance (MR) values [33]. Weexpect that the power can be dramatically improved us-ing magnetic tunnel junction-based STNOs, whose MRcan be over two orders of magnitude greater than that ofspin valve-based STNOs. [2, 15].In conclusion, we have presented a systematic studyof the variation of nonlinearity against PMA in STNOs.By using He + irradiation to continuously tune the PMAof the [Co/Ni] free layer, the nonlinearity N (along withthe frequency tunability df /dI dc ) shows a continuous de-creasing trend as H k ( M eff ) decreases (increases). 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