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).

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).