This analytical and numerical work builds on our previous experimental demonstration of magnetic droplet solitons [Science 339, 1295 (2013)] where we confirmed the predictions by Ivanov and Kosevich from over 35 years ago [Zh. Eksp. Teor. Fiz. 72, 2000 (1977)] and the more recent predictions by Hoefer, Silva and Keller [Phys. Rev. B 82, 054432 (2010)].

Droplets form naturally in systems with attractive forces. Water droplets are e.g. formed from the attractive polar interactions between water molecules. In ultrathin magnetic films the so-called perpendicular magnetic anisotropy (PMA) can create an attraction between spin wave excitations (magnons) and if a sufficient number of magnons are present in a region (analogous to a sufficient number of water molecules) they can condense into a magnetic droplet soliton.

Much like water on extended surfaces, droplets are easily formed in extended PMA layers. However, the nucleation in a narrow channel is not easily predicted. In this paper, we show by numerical simulations that magnetic droplets can indeed be excited in nanowires and in doing so can acquire two novel forms: an edge and a quasi-one-dimensional (Q1D) nanowire mode. The edge mode arises as the physical boundaries attract the droplet the same way as a water drop would be attracted by a neighboring polar surface, e.g. a piece of glass. On the other hand, the Q1D exists in very narrow wires, where both boundaries attract the droplet. As a result, the Q1D acquires an additional property known as chirality which is a well-defined magnetic state that makes it especially resistant to disturbances. Due to these characteristics, such novel droplet modes can be identified by their intrinsically different frequency. Our simulations suggest means to experimentally prepare and observe these modes for their detailed physical study and in the prospect of nanoscopic applications for data storage.

E. Iacocca, R.K. Dumas, L. Bookman, S.M. Mohseni, S. Chung, M. Hoefer, and J. Åkerman, Confined dissipative droplet solitons in spin-valve nanowires with perpendicular magnetic anisotropy, Phys. Rev. Lett. 112, 047201 (2014).

Spin torque oscillators (STOs) often exhibit multiple modes, leading to complex behavior. One example is mode hopping between different eigenmodes of a magnetic tunnel junction (MTJ) STO. This mode hopping is a strong function of current and angle between the magnetization in the free and fixed layers, and away from anti-parallel configuration, mode hopping can be the dominant decoherence process. Another example is the linewidth of a nanocontact STO that can be a complex non-monotonic function of temperature in regions where two or more modes are excited by the oscillators. These phenomena require a generalization of the single-mode nonlinear STO theory to include mode coupling. We derive equations describing the slow time evolution of the coupled system and show they describe a dynamically driven system, similar to other systems that exhibit mode hopping in the presence of thermal fluctuations. In our description, mode coupling also leads to additional coupling between power and phase fluctuations, which can in certain limited cases lead to longer relaxation times for power fluctuations, and consequently to larger linewidths through the nonlinear frequency shift.

O. Heinonen, P. Muduli, E. Iacocca, and Johan Åkerman, Decoherence, Mode Hopping, and Mode Coupling in Spin Torque Oscillators, IEEE Trans. Magn. 49, 4398 (2013).

We have observed distinct temperature-dependent magnetization reversal modes in a perpendicular (Co/Pd)4/Co/Cu/(Co/Ni)4/Co pseudo-spin-valve, which are correlated with spin-transport properties. At 300 K, magnetization reversal occurs by vertically correlated domains. Below 200 K the hysteresis loop becomes bifurcated due to laterally correlated reversal of the individual stacks. The magnetic configuration change also leads to higher spin disorders and a significant increase in the giant magnetoresistance effect. First order reversal curve measurements reveal that the coupled state can be re-established through field cycling and allow direct determination of the interlayer coupling strength as a function of temperature.

J. E. Davies, D. A. Gilbert, S. M. Mohseni, R. K. Dumas, J. Åkerman, and Kai Liu, APL 103, 022409 (2013).

Theory predicts that a strongly injection-locked spin-torque oscillator (STO) should show a characteristic ringing frequency both on its approach to the locked state and under the influence of thermal noise. While experiments have so far failed to detect such ringing, we here show numerically and analytically how current modulation of injection-locked STOs can excite the ringing frequency in a resonant manner, and hence increase the experimental sensitivity. The complexity of such dynamics leads to a nonlinear resonance, which can even unlock the STO as a function of the modulation strength. The results presented here offer a plausible method for experimentally measuring the ringing frequency of STOs. Moreover, the onset of unlocking also provides a measure for the maximum modulation strength that can be applied to phase-locked STOs.

Ezio Iacocca and Johan Åkerman, Resonant excitation of injection-locked spin-torque oscillators, PRB 87, 214428 (2013).

It has been argued that if multiple spin wave modes are competing for the same centrally located energy source, as in a nanocontact spin torque oscillator, that only one mode should survive in the steady state. Here, the experimental conditions necessary for mode coexistence are explored. Mode coexistence is facilitated by the local field asymmetries induced by the spatially inhomogeneous Oersted field, which leads to a physical separation of the modes, and is further promoted by spin wave localization at reduced applied field angles. Finally, both simulation and experiment reveal a low frequency signal consistent with the intermodulation of two coexistent modes.

Randy K. Dumas, E. Iacocca, S. Bonetti, S. R. Sani, S. M. Mohseni, A. Eklund, J. Persson, O. Heinonen, and Johan Åkerman, Spin-Wave-Mode Coexistence on the Nanoscale: A Consequence of the Oersted-Field-Induced Asymmetric Energy Landscape, PRL 110, 257202 (2013).

Anh Nguyen, Randy Dumas and Johan Åkerman have published a paper in Phys. Rev. B on Brillouin Light Scattering measurements of fundamental spin wave modes in tilted exchange springs [1]. These results are part of an ongoing collaboration with the University of Perugia, Italy, and also involved collaborators from Florence, Italy, and NIST Gaithersburg, USA.

[1] S. Tacchi, T. N. Anh Nguyen, G. Carlotti, G. Gubbiotti, M. Madami, R. K. Dumas, J. W. Lau, Johan Åkerman, A. Rettori, and M. G. Pini, "Spin wave excitations in exchange-coupled [Co/Pd]-NiFe films with tunable tilting of the magnetization", Phys. Rev. B 87, 144426 (2013)

Drops are natural objects in systems with attractive forces. Water drops are e.g. formed from the attractive polar interaction between the H atoms in one H2O molecule and the O atom in another.  In ultrathin magnetic films the so-called perpendicular magnetic anisotropy (PMA) can create an attraction between spin wave excitations (magnons) and if a sufficient number of magnons are present in a region (analogous to a sufficient number of water molecules) they can condense into a magnon drop where all spins in the drop precess in-phase on a single magnon frequency.

Magnon drops were predicted theoretically by Ivanov and Kosevich over 35 years ago [Zh. Eksp. Teor. Fiz. 72, 2000 (1977)]. More recently, Hoefer, Silva and Keller demonstrated analytically and numerically that nano-contact spin torque oscillators (NC-STOs) with PMA free layers should be able to nucleate and sustain the dissipative (= lossy and actively driven) analogue of magnon drops; they called this new potential soliton object a magnetic droplet [Phys. Rev. B 82, 054432 (2010)].

In this work, we present the first experimental demonstration of magnetic droplets. Our devices consist of NC-STOs with a Co fixed layer and a [Co/Ni] multilayer free layer. The creation of a magnetic droplet is experimentally observed as a dramatic 10 GHz drop in the measured microwave frequency, accompanied with a sharp increase in the device resistance. The droplet displays a wide range of additional magnetodynamic phenomena, experimentally observed as a number of sidebands at different frequencies. Our work both brings closure to a long-standing theoretical prediction and provides the nanomagnetic and spintronic community with a novel dynamic nanomagnetic object, which joins the magnetic domain wall and magnetic vortex with similar potential for rich science.

S. M. Mohseni, S. R. Sani, J. Persson, T. N. Anh Nguyen, S. Chung, Ye. Pogoryelov, P. K. Muduli, E. Iacocca, A. Eklund, R. K. Dumas, S. Bonetti, A. Deac, M. A. Hoefer, and J. Åkerman, Spin Torque–Generated Magnetic Droplet Solitons, Science 339, 1295 (2013).