Direct observation of magnetic droplet solitons in all-perpendicular spin torque nano-oscillators
Sunjae Chung, Q. Tuan Le, Martina Ahlberg, Markus Weigand, Iuliia Bykova, Ahmad A. Awad, Hamid Mazraati, Afshin Houshang, Sheng Jiang, T. N. Anh Nguyen, Eberhard Goering, Gisela Schütz, Joachim Gräfe, Johan Åkerman
DDirect observation of magnetic droplet solitons in all-perpendicular spin torquenano-oscillators
Sunjae Chung,
1, 2, 3, ∗ Q. Tuan Le,
1, 2, ∗ Martina Ahlberg,
1, 4
Markus Weigand, IuliiaBykova, Ahmad A. Awad,
1, 4
Hamid Mazraati,
2, 4
Afshin Houshang,
1, 4
Sheng Jiang, T. N. Anh Nguyen,
1, 2, 6
Eberhard Goering, Gisela Sch¨utz, Joachim Gr¨afe, and Johan ˚Akerman
1, 2, 4 Department of Physics, University of Gothenburg, 412 96 Gothenburg, Sweden Department of Applied Physics, School of Engineering Sciences,KTH Royal Institute of Technology, 164 40 Kista, Sweden Department of Physics and Astronomy, University Uppsala, 751 20 Uppsala, Sweden NanOsc AB, 164 40 Kista, Sweden Max Planck Institute for Intelligent Systems, Stuttgart, Germany Laboratory of Magnetism and Superconductivity, Institute of Materials Science,Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Hanoi, Vietnam
Magnetic droplets are non-topological dynamical solitons that can be nucleated and sustainedin nano-contact based spin torque nano-oscillators (NC-STNOs) with perpendicular anisotropy freelayers. While originally predicted in all-perpendicular NC-STNOs, all experimental demonstrationshave so far relied on orthogonal devices with an in-plane polarizing layer that requires a strongmagnetic field for droplet nucleation. Here, we instead show the nucleation and sustained operationof magnetic droplets in all-perpendicular NC-STNOs in modest perpendicular fields and over a widerange of nano-contact size. The droplet is observed electrically as an intermediate resistance stateaccompanied by broadband low-frequency microwave noise. Using canted fields, which introducea non-zero relative angle between the free and fixed layer, the actual droplet precession frequencycan also be determined. Finally, the droplet size, its perimeter width, and its fully reversed coreare directly observed underneath a 80 nm diameter nano-contact using scanning transmission x-raymicroscopy on both the Ni and Co edges. The droplet diameter is 150 nm, i.e. almost twice thenominal size of the nano-contact, and the droplet has a perimeter width of about 70 nm.
INTRODUCTION
Non-topological magnetodynamical solitons , such asdroplets and spin wave (SW) bullets , are con-densed states of SWs deriving their stability from theintrinsic precession of their spins. For their nucleation,these condensed states require a high local SW density,which in metals can only be achieved using highly focusedspin currents . In contrast to topological static soli-tons, such as vortices and skyrmions , the non-topological dynamical solitons will dissipate from SWdamping if the spin current is removed. The dynam-ics can also stabilize a topological state that otherwisewould not be stable, an example being the dynamicalskyrmion .High spin current densities can be achieved in so-callednano-contact spin torque nano-oscillators (STNOs fromhereon) where a charge current is injected into an ex-tended GMR trilayer through a nano-contact . His-torically, STNOs were fabricated with all the constituentmagnetic layers having in-plane remanent states. Inthis system, the magnetodynamic non-linearity fa-vors propagating SWs when the free layer mag-netization is saturated towards the film normal (positivenon-linearity), and SW bullets when it is saturatedtowards the plane (negative non-linearity). PropagatingSWs, in particular in the form of SW beams , are e.g. crucial for the synchronization of multiple STNOs .In STNOs where the free layer has a large perpendicularmagnetic anisotropy (PMA) the non-linearity is negative at all fields and any auto-oscillation is inherently self-localized underneath the nano-contact, which promotesa high local SW density.
At a critical SW density,the magnetodynamics can then condense into a magneticdroplet soliton, which is characterized by a largely re-versed core and a perimeter where all spins precess withthe same frequency, and, in ideal conditions, with thesame phase.
All experimental realizations of droplets have so far re-lied on so-called orthogonal spin valves, where the fixedlayer magnetization has an easy-plane orientation ( e.g.
Co or NiFe).
To nucleate a droplet, a perpen-dicular field has to be applied, which tilts, or satu-rates, the fixed layer out-of-plane. The combination ofa tilted fixed layer magnetization and a large Oerstedfield from the drive current modifies the effective mag-netic field landscape in such a way that the droplet ex-periences a so-called drift instability , i.e. it may leavethe nano-contact region and dissipate out, after whicha new droplet can form. The drift instability compli-cates the experimental characterization of the intrinsicproperties of the droplet. As a recent example, attemptsat determining the degree of reversal of the droplet coreusing scanning transmission x-ray microscopy (STXM)resulted in much smaller estimates ( ≈ ◦ ) than theoret-ically predicted ( ≈ ◦ ), and an apparent non-circulardroplet shape. It would therefore be highly valuable torealize, and directly observe, droplets in less asymmet-ric STNOs. In this work we realize magnetic droplets inSTNOs based on all-perpendicular spin valves and use a r X i v : . [ c ond - m a t . m e s - h a ll ] J u l FIG. 1.
Device structure. Magnetic and electri-cal characterization. ( a ) Schematic of an all-perpendicularNC-STO composed of Co/Pd (fixed) and Co/Ni (free) mul-tilayers with a Cu spacer. The current I dc flows through thenanocontact (NC) fabricated on top of the stack. The mag-netic field H is applied at an angle ϕ H from the film plane.( b ) Full (black circles) and minor (red and blue dots) hys-teresis loops of the unpatterned material stack in a perpen-dicular field, showing entirely decoupled switching of the freeand fixed layers before processing. ( c ) Full (black circles)and minor loop (red dots) low-current ( I dc = -0.6 mA) mag-netoresistance (MR) measurements of the patterned NC-STOshowing MR of about 1% and some process induced interlayercoupling of about -0.03 T. both electrical and STXM measurements to study theirproperties. Our electrical measurements indicate a muchmore stable droplet in perpendicular fields than in tiltedfields. Using both the Ni and Co edges, our STXM re-sults show that the droplet core is essentially completelyreversed ( ≈ ◦ ) and that the droplet has a highly cir-cular shape. RESULTS
Fig.1a shows a schematic of the type of all-perpendicular STNO studied in this work, having aCo/Pd multilayer fixed layer and a Co/Ni multilayerfree layer, both with sufficient perpendicular magneticanisotropy (PMA) to have their remanent states alongthe film normal. The drive current is provided througha nano-contact with diameters ranging from 50 to 150nm. Fig.1b shows major and minor magnetization hys-teresis loops of the full unpatterned material stack withtwo distinct switching fields corresponding to the fixedand free layer respectively. The symmetry of the minorloops indicate negligible coupling between the fixed andthe free layer before patterning. Fig.1c shows a mag-netoresistance (MR) hysteresis loop of a fully processedSTNO having about 1% MR and about 0.03 T interlayercoupling after patterning.Fig.2a shows the resistance variation of a 100 nm nano- contact STNO as the drive current is swept back andforth at three different perpendicular field strengths. Ata negative current of about -12 mA and in a field of 0.25T, there is a sharp step in resistance indicating the nu-cleation or collapse of a droplet depending on the cur-rent sweep direction. The step value is about 60% of thetotal difference between the P and the AP states, con-sistent with a droplet, and its location moves linearlyto higher current magnitudes if the field is increased,consistent with the stiffening of the SWs and the fielddependence of the Slonczewski threshold current for aspin transfer torque driven SW instability . The insetshows the same resistance step after the subtraction ofthe shared parabolic background at all fields. A furtherdirect indication of a droplet is the appearance of broad-band microwave noise at low frequency, only observed inthe intermediate resistance state, which arises due to theparticle-like Brownian motion of the droplet underneaththe nano-contact .Fig.2b shows the droplet nucleation as the field is in-creased from 0.16 to 0.42 T at three different strong neg-ative currents and compared to a field sweep at muchlower current. Again, the droplet is characterized by anintermediate resistance value, which first decreases slowlywith field until it drops more rapidly towards the resis-tance value of the P state. The gradual collapse indicatesmode hopping between the droplet and the P state. Justas in Fig.2a, the droplet is again accompanied by the ap-pearance of broadband low-frequency microwave noise.In this all-perpendicular geometry, where the two mag-netizations and also the applied magnetic field are allaligned along the film normal, the high-frequency pre-cession of the droplet does not generate any microwavesignal since the projection of the precessing spins ontothe fixed layer magnetization remains constant in time.We can however prove that the droplet precesses by tilt-ing the applied field closer to the film plane, since thiscreates a substantial non-collinearity between the freeand the fixed layer magnetizations and hence a time-dependent variation of the STNO resistance. The in-set shows a microwave measurement as a field appliedat 30 degrees switches the STNO from its AP state to adroplet state at about 0.3 T, resulting in a strong signalat 8 GHz, which increases linearly with field strength; thedroplet nucleation is again accompanied by substantialmicrowave noise between 0 and 2 GHz. The precessionfrequency is deep into the SW gap of the free layer mag-netization, consistent with an essentially fully reverseddroplet.It is noteworthy that the low-frequency noise is dra-matically higher in tilted fields (inset) compared to per-pendicular fields. If the noise is generated by the dropinstability, every droplet leaving the NC generates a sim-ilar voltage spike in both cases, and the total microwavenoise power is hence a good measure of the droplet sta-bility. We are hence lead to conclude that the droplet ishighly stable in the perpendicular case.We have reproduced this general droplet behavior in FIG. 2.
Droplet nucleation and precession. ( a )Change in the resistance of a 100 nm nano-contact vs. drivecurrent showing a background of Joule heating and the nucle-ation of a droplet at a field dependent negative current. Theinset shows the same data after subtraction of the parabolicbackground. Below the resistance measurement is a plot ofthe power spectral density measured up to 0.4 GHz in a fieldof 0.35 T, showing how the resistance step is accompaniedby the appearance low-frequency microwave noise. ( b ) Field-sweep resistance measurements from 0.1 to 0.42 T at fourdifferent negative currents for the same nano-contact as in( a ). At a small negative current (-1 mA) the state switchesdirectly from AP to P at about 0.25 T. For the three largenegative currents, the AP state first switches to an interme-diate resistance state consistent with a droplet, before gradu-ally switching to the P state. The formation of the droplet isagain accompanied by substantial microwave noise. The insetshows a power spectral density measurement taken in a fieldtilted 30 degrees from the field plane clearly showing both theprecession frequency and the microwave noise of the droplet. a large number of STNOs having different nano-contactdiameters. Fig.3 shows the corresponding current den-sity/field phase diagram of the free layer magnetizationin six different STNOs with diameters ranging from 50to 150 nm, as measured by the normalized STNO re-sistance. In all STNOs the AP state either switches into FIG. 3.
Droplet nucleation phase diagram.
Field-sweepresistance measurements from 0.16 to 0.5 T at different neg-ative currents for nano-contact diameters ranging from 50 to150 nm, plotted on a color scale defined by the P and APstates. The droplet state is seen as an intermediate resis-tance state. The dashed red line marks the linear current-field droplet nucleation boundary. The inset plots the slopeof this boundary vs. nano-contact area together with a linearfit (dashed white line). the P state at low current magnitudes, or into the dropletat high current magnitudes, and the droplet nucleationboundary shows a linear dependence on current and field.The ratio of the droplet resistance vs. either the P orthe AP resistance, does not depend systematically onthe nano-contact diameter; it is rather dominated by de-vice to device variations. The linear slope of the dropletnucleation boundary is similarly independent on nano-contact diameter as the current density determines thenucleation. The inset in the bottom sub figure of Fig.3shows this slope expressed as current per field and plot-ted vs. the nano-contact area, again confirming that thecurrent density governs the nucleation.We finally turn to our scanning transmission x-ray mi-croscopy (STXM) measurements on an 80 nm NC. Fig.4ashows a spatial map of the m z component of the Ni mo-ments normalized to the up and down states well outsideof the droplet region. The left inset shows a 3D-renderedcross-section of the same data. The map reveals an es-sentially fully reversed droplet core with a well definedcircular shape. The droplet diameter is approximately150 nm, i.e. almost twice as large as the nominal NCdiameter, and the droplet perimeter width (10-90%) isabout 70 nm. Fig.4b shows the same analysis using theCo moment. As we have signal from Co moments both inthe free and the fixed layer and the normalization proce-dure switches both the free and the fixed layers, a secondnormalization step was done using the relative Co con-tent in the free and the fixed layers respectively.The spatial map of the m z component of the free layerCo moments corroborates the conclusions drawn from theNi signal, such as a fully reversed core, as well as the di-ameter and perimeter width values. In addition, we findthat the minor deviations of the perimeter from beinga perfect circle are uncorrelated between the Ni and Comaps. These deviations can therefore be ascribed to mea-surement noise and are not intrinsic to the droplet. Thedroplet is hence even more circular than what the individ-ual maps would indicate on their own. We can hence fitcircles to the ( x, y ) position of all data with a certain m z value and this way trace out the droplet perimeter withgreater accuracy. The resulting droplet envelope is shownin the right inset in Fig.4a. It is noteworthy that our di-rect measurement of the droplet diameter yields a muchlarger droplet than predicted by theory and micromag-netic simulations . However, these simulations assumea perfect cylindrical current distribution underneath theNC, whereas recent experimental and numerical resultindicate a large lateral current spread underneath theNC resulting in both spin transfer torque over an areagreater than the NC and substantial in-plane spin trans-fer torque acting on the droplet perimeter, which couldpotentially also affect its size. While it is well beyondthe scope of our study to further elucidate these effects,they highlight the need for further modelling of how a re-alistic three-dimensional current distribution underneaththe NC affects the droplet size, perimeter width, and evenstability. CONCLUSION
As any significant drift instability of the dropletwould likely have perturbed its apparent shape our re-sults indicate that droplets in all-perpendicular STNOsare both fully reversed and highly stable. The realiza-tion of stable room-temperature droplets not sufferingfrom drift instability is crucial for their further studies.In addition, the all-perpendicular geometry, in contrast M z [ C o / N i ] [ C o / P d ] C u NiCo
150 nm n m r (nm) M z -10+1 50 1501000 FIG. 4.
Direct STXM observation of a reverseddroplet.
Spatial map of the m z component of the Ni (top)and Co (bottom) moments of the free layer. Both the Ni andCo data reveal a fully reversed droplet with a diameter ofabout 150 nm. The left inset shows a 3D rendered cross sec-tion of the Ni STXM data. The right inset shows the detaileddroplet perimeter profile extracted from the Ni data assuminga circularly symmetric droplet. to the orthogonal, can be easily realized using magnetictunnel junctions (MTJs) with and without substantialDzyaloshinskiiMoriya interaction. Our demonstration ofstable droplets in all-perpendicular spin valve STNOshence represents the first step towards utilizing droplets,and potentially dynamical skyrmions , in high-outputMTJ based STNOs. METHODS
Sample Preparation
A full stack composed of aTa (4 nm)/ Cu (14 nm) / Ta (4 nm) / Pd (2 nm)seed layer and an all-perpendicular pseudo-spin valve[Co (0 .
35 nm) / Pd (0 . × .
35 nm) /Cu (5 nm) / [Co (0 .
22 nm) / Ni (0 .
68 nm)] × .
22 nm), capped by a Cu (2 nm) / Pd (2 nm) layer,was deposited on a thermally oxidized Si wafer by mag-netron sputtering technique (numbers in parentheses arethicknesses in nanometers). Using a combination of op-tical lithography and etching techniques, 8 µ m × µ mmesas were fabricated on the stack wafer and insulated bya 30-nm-thick SiO film using chemical vapor deposition(CVD). Electron beam lithography was used to patternnanocontacts, with circular sizes varying from 50 to 150nm in diameter, on top of each mesa. SiO was thenetched through by the reactive ion etching (RIE) tech-nique to open the contacts. The NC-STO device fabri-cation was completed by the deposition of Cu 500 nm/ Au 100 nm top electrode and lift-off processing. ForSTXM measurements, the similar stack deposition andprocessing were employed to fabricate NC-STOs on 300-nm-thick LPCVD silicon nitride Si wafer, then the highlyselective deep RIE was used to remove Si from backsideof the device wafer and leave nitride membranes under-neath NC-STOs for X-ray illumination. Magnetic and Electrical Characterization
Alter-nating Gradient Magnetometry was used to measure themagnetization hysteresis loops of the unpatterned ma-terial stacks. dc and microwave measurements of thefabricated STOs were carried out using our custom-builtsetup, which allows the manipulation of magnetic fieldstrength, polarity, and angle. The electromagnet cangenerate a field between -0.5 to +0.5 T and its rota-tional base easily controls the field angle between 0 and90 ◦ . The device is connected by a ground–signal–groundprobe to a dc -current source (Keithley 6221), a nano-voltmeter (Keithley 2182A), and a spectrum analyzer (R& S FSQ26). A 0–40GHz bias-tee is used to separatethe bias input and the generated microwave signal. Thelatter is amplified by a low-noise amplifier (operationalrange: 0.1–26.5 GHz) before being sent to the spectrumanalyzer. Scanning transmission x-ray microscopy
STXMmeasurements were conducted at the MPI IS operated MAXYMUS end station at the UE46-PGM2 beam lineat the BESSY II synchrotron radiation facility. The sam-ples were illuminated under normal incidence by circu-larly polarized light in an applied out-of-plane field ofup to 240 mT that was generated by a set of four ro-tatable permanent magnets . The photon energy wasset to the absorption maximum of the Ni L and Co L edge to get optimal XMCD contrast for imaging ofeach element. Intensities were locally averaged over thenominal resolution of the focusing zone plate of 18 nmusing a Gaussian filter in ImageJ . Magnetization an-gles from XMCD measurements were calibrated to thesaturation magnetization of the free layer. Both externalfield and photon polarization were flipped to compen-sate for intensity variations of the x-ray beam. The noiselevel in the reference measurements determines the un-certainty of the subsequent XMCD measurements; a spinangle larger than 160 ◦ , i.e. within 20 ◦ of full reversal, isconsidered fully reversed. A lock-in-like data acquisitionscheme based on an avalanche photo diode and a customFPGA system allows ultra low-noise measurements.This work was partially supported by the ERC Start-ing Grant 307144 “Mustang”, the Swedish Foundationfor Strategic Research (SSF) Successful Research Lead-ers program, the Swedish Research Council (VR), theGran Gustafsson foundation, and the Knut and AliceWallenberg Foundation. Helmholtz Zentrum Berlin isacknowledged for allocating beam time at the BESSYII synchrotron radiation facility. Financial support bythe Baden-Wrttemberg Stiftung in the framework of theKompetenznetz Funktionelle Nanostrukturen is grate-fully acknowledged.S.C. and T.Q.L. performed the electrical measure-ments. S.C., T.Q.L., S.J., A.H. and T.N.A.N. fabri-cated the devices. M.A., J.G, M.W. and I.B carriedout the STXM measurements. J.˚A. coordinated theproject. All authors analyzed the results and co-wrotethe manuscript. Correspondence and requests for ma-terials should be addressed to J. ˚Akerman (email: [email protected]). ∗ These two authors contributed equally H.-B. Braun, Adv. Phys. , 1 (2012). B. Ivanov and A. Kosevich, Zh. Eksp. Teor. Fiz. , 2000(1977). M. A. Hoefer, T. J. Silva, and M. W. Keller, Phys. Rev.B , 054432 (2010). E. Iacocca, R. K. Dumas, L. Bookman, M. Mohseni,S. Chung, M. A. Hoefer, and J. ˚Akerman, Phys. Rev.Lett. , 047201 (2014). S. M. Mohseni, S. R. Sani, J. Persson, T. N. A. Nguyen,S. Chung, Y. Pogoryelov, P. K. Muduli, E. Iacocca, A. Ek-lund, R. K. Dumas, S. Bonetti, A. Deac, M. a. Hoefer, andJ. Akerman, Science , 1295 (2013). F. Maci`a, D. Backes, and A. D. Kent, Nat. Nanotechnol , 992 (2014). S. Mohseni, S. Sani, R. Dumas, J. Persson, T. A. Nguyen, S. Chung, Y. Pogoryelov, P. Muduli, E. Iacocca, A. Ek-lund, and J. ˚Akerman, Physica B , 84 (2014). S. Chung, S. M. Mohseni, S. R. Sani, E. Iacocca, R. K.Dumas, T. N. Anh Nguyen, Y. Pogoryelov, P. K. Muduli,A. Eklund, M. Hoefer, and J. kerman, J. Appl. Phys. ,172612 (2014). S. Lend´ınez, N. Statuto, D. Backes, A. D. Kent, andF. Maci`a, Phys. Rev. B , 174426 (2015). S. Chung, S. Majid Mohseni, A. Eklund, P. D¨urrenfeld,M. Ranjbar, S. R. Sani, T. N. Anh Nguyen, R. K. Dumas,and J. ˚Akerman, Low Temp. Phys. , 833 (2015). S. Chung, A. Eklund, E. Iacocca, S. M. Mohseni, S. R.Sani, L. Bookman, M. A. Hoefer, R. K. Dumas, andJ. ˚Akerman, Nat. Commun. , 11209 (2016). D. Xiao, V. Tiberkevich, Y. H. Liu, Y. W. Liu, S. M.Mohseni, S. Chung, M. Ahlberg, A. N. Slavin, J. ˚Akerman, and Y. Zhou, Phys. Rev. B , 024106 (2017). S. Lend´ınez, J. Hang, S. V´elez, J. M. Hern´andez,D. Backes, A. D. Kent, and F. Maci`a, Phys. Rev. Ap-plied , 054027 (2017). D. Slobodianiuk, O. Prokopenko, and G. Melkov, J. Magn.Magn. Mater. , 144 (2017). A. Slavin and V. Tiberkevich, Phys. Rev. Lett. , 237201(2005). S. Bonetti, V. Tiberkevich, G. Consolo, G. Finocchio,P. Muduli, F. Mancoff, A. Slavin, and J. ˚Akerman, Phys.Rev. Lett. , 217204 (2010). V. E. Demidov, S. Urazhdin, and S. O. Demokritov, Nat.Mater. , 984 (2010). V. Demidov, S. Urazhdin, H. Ulrichs, V. Tiberkevich,A. Slavin, D. Baither, G. Schmitz, and S. Demokritov,Nat. Mater. , 1028 (2012). S. Bonetti, V. Puliafito, G. Consolo, V. S. Tiberkevich,A. N. Slavin, and J. ˚Akerman, Phys. Rev. B , 174427(2012). R. K. Dumas, E. Iacocca, S. Bonetti, S. R. Sani, S. M.Mohseni, A. Eklund, J. Persson, O. Heinonen, andJ. ˚Akerman, Phys. Rev. Lett. , 257202 (2013). J. C. Slonczewski, J. Magn. Magn. Mater. , L1 (1996). L. Berger, Phys. Rev. B , 9353 (1996). J. C. Slonczewski, J. Magn. Magn. Mater. , 261 (1999). J. Raabe, R. Pulwey, R. Sattler, T. Schweinbock, J. Zweck,and D. Weiss, J. Appl. Phys. , 4437 (2000). T. Shinjo, T. Okuno, R. Hassdorf, K. Shigeto, and T. Ono,Science , 930 (2000). U. K. R¨oßler, A. N. Bogdanov, and C. Pfleiderer, Nature , 797 (2006). S. Muhlbauer, B. Binz, F. Jonietz, C. Pfleiderer, A. Rosch,A. Neubauer, R. Georgii, and P. Boni, Science , 915(2009). X. Z. Yu, Y. Onose, N. Kanazawa, J. H. Park, J. H. Han,Y. Matsui, N. Nagaosa, and Y. Tokura, Nature , 901(2010). N. Romming, C. Hanneken, M. Menzel, J. E. Bickel,B. Wolter, K. von Bergmann, a. Kubetzka, and R. Wiesen-danger, Science , 636 (2013). Y. Zhou, E. Iacocca, A. A. Awad, R. K. Dumas, F. C.Zhang, H. B. Braun, and J. ˚A kerman, Nat. Commun. ,8193 (2015). R. H. Liu, W. L. Lim, and S. Urazhdin, Phys. Rev. Lett. , 137201 (2015). R. Dumas, S. Sani, S. Mohseni, E. Iacocca, Y. Pogoryelov, P. Muduli, S. Chung, P. Durrenfeld, and J. kerman, IEEETrans. Magn. , 257202 (2014). T. Chen, R. K. Dumas, A. Eklund, P. K. Muduli,A. Houshang, A. A. Awad, P. Durrenfeld, B. G. Malm,A. Rusu, and J. Akerman, Proceedings of the IEEE ,1919 (2016). M. Tsoi, A. G. M. Jansen, J. Bass, W.-C. Chiang, M. Seck,V. Tsoi, and P. Wyder, Phys. Rev. Lett. , 4281 (1998). M. Tsoi, A. G. M. Jansen, J. Bass, W.-C. Chiang, V. Tsoi,and P. Wyder, Nature , 46 (2000). W. Rippard, M. Pufall, S. Kaka, S. Russek, and T. Silva,Phys. Rev. Lett. , 027201 (2004). A. Slavin and P. Kabos, IEEE Trans. Magn. , 1264(2005). A. Slavin and V. Tiberkevich, IEEE Trans. Magn. , 1875(2009). M. Hoefer, T. Silva, and M. Stiles, Phys. Rev. B ,144401 (2008). M. Madami, E. Iacocca, S. Sani, G. Gubbiotti, S. Tacchi,R. K. Dumas, J. ˚Akerman, and G. Carlotti, Phys. Rev. B , 024403 (2015). A. Houshang, E. Iacocca, P. D¨urrenfeld, S. R. Sani,J. ˚Akerman, and R. K. Dumas, Nat. Nanotechnol. ,280 (2016). S. Kaka, M. R. Pufall, W. H. Rippard, T. J. Silva, S. E.Russek, and J. A. Katine, Nature , 389 (2005). F. B. Mancoff, N. D. Rizzo, B. N. Engel, and S. Tehrani,Nature , 393 (2005). S. Sani, J. Persson, S. M. Mohseni, Y. Pogoryelov, P. K.Muduli, A. Eklund, G. Malm, M. K¨all, A. Dmitriev, andJ. ˚Akerman, Nat. Commun. , 2731 (2013). W. H. Rippard, A. M. Deac, M. R. Pufall, J. M. Shaw,M. W. Keller, S. E. Russek, and C. Serpico, Phys. Rev. B , 014426 (2010). S. M. Mohseni, S. R. Sani, J. Persson, T. N. Anh Nguyen,S. Chung, Y. Pogoryelov, and J. ˚Akerman, Phys. StatusSolidi RRL , 432 (2011). D. Backes, F. Maci`a, S. Bonetti, R. Kukreja, H. Ohldag,and A. D. Kent, Phys. Rev. Lett. , 127205 (2015). S. A. H. Banuazizi, S. R. Sani, A. Eklund, M. M. Naiini,S. M. Mohseni, S. Chung, P. D¨urrenfeld, B. G. Malm, andJ. ˚Akerman, Nanoscale , 1896 (2017). D. Nolle, M. Weigand, P. Audehm, E. Goering, U. Wiese-mann, C. Wolter, E. Nolle, and G. Schtz, Rev. Sci. In-strum. , 046112 (2012).50