Core-core interaction in spin-torque double-vortex oscillators

Owing to their ability of narrow bandwidth operation, magnetic vortex based spin-torque nano-oscillators (STNOs) are promising candidates for future on-chip microwave sources. Typically, these oscillators are nanopillars containing two stacked ferromagnetic disks, one in a vortex state, the other with quasi-homogeneous magnetization. Devices of that kind have been investigated extensively over the past years [1-3]. Only recently, a different type of vortex oscillators has attracted much interest. In these “double vortex oscillators”, both ferromagnetic disks are in a vortex state. Depending on the relative vorticity, the local alignment of the magnetic layers can be either parallel or antiparallel. Thus, the system constitutes an analogue to single domain spin valves, while also retaining the good oscillator properties of magnetic vortices, which makes this type of STNO particularly interesting for studying fundamental aspects of spin-transfer torque. However, only few studies of double-vortex oscillators exist to-date [5,6].
Here we present our results on Fe/Ag/Fe double vortex oscillators. Combining experimental and numerical methods, we address the yet open question of how the magnetostatic interaction of the vortices – their separation is typically in the order of a few nanometers –affects the spin-torque induced dynamics. Our samples are all-metallic nanopillars 150 nm in diameter, containing a Fe(30)/Ag(6)/Fe(15) pseudo spin valve (layer thicknesses given in nm). By applying d.c. currents perpendicular to the plane of the layers, we excite magnetization dynamics corresponding to gyrotropic vortex motion. The sample geometry stabilizes the magnetic vortex state in each Fe disk even if the strong Oersted fields and the vortex magnetization have opposite sense of rotations. This high degree of stability provides a yet unprecedented opportunity to investigate a more exotic class of double vortex states – those with opposed vorticities – under the high current densities necessary to enter the spin-torque precession regime.
Figure 1 displays a typical combined magnetoresistance and high frequency measurement. The magnetic field, which has an angle of 30° with the sample plane, is swept from positive values to negative saturation. For each field value, in addition to the d.c. voltage, a spectrum is also recorded. In a field interval about 100 mT wide, the sample is in a double vortex state where the vorticities of the top and bottom vortices are opposed to each other. According to the top panel of Fig. 1, this state exhibits magnetization dynamics. We vary our state preparation procedure in order to create the various vorticity and core polarity combinations. The obtained states are characterized with respect to their d.c. and high frequency behavior using the above described measuring technique where in all measurements, the electron flow is directed from the bottom to the top Fe disk. We obtain a fine structure in the modes, where the frequency splittings are in the order of hundreds of MHz.
The micromagnetic simulations are performed with our code TetraMag [7]. The simulations include the Oersted field corresponding to a sample current of 10 mA in magnitude. For a given vorticity and core polarity combination, we find the eigenmodes and frequencies of the system. Comparing the experimentally found set of frequencies to the simulated cases, we find that each measured peak matches the lowest mode of a corresponding computed spectrum in frequency. This suggests that the observed fine structure is caused by two effects. First, the Oersted field lifts the degeneracy of states with the top vortex vorticity parallel or antiparallel to the field’s sense of rotation. On top of this Zeemann-type frequency alteration, the resulting modes are split further depending on the relative alignment of the top and bottom vortex cores. This suggests that the second splitting is due to the magnetostatic interaction of the vortex cores. This remarkable result sheds light on the subtle interplay of forces governing the dynamics of double vortex oscillators, while on the other hand it allows measuring changes in relative core alignment.
References:
[1] V. S. Pribiag et al., Nature Phys. 3, 498 (2007).
[2] A. Dussaux et al., Nat. Commun. 1:8 DOI:10.1038 / ncomms1006 (2010).
[3] X. W. Yu et al., Phys. Rev. Lett. 106, 167202 (2011).
[5] A. V. Khvalkovskiy et al., Appl. Phys. Lett. 96, 212507 (2010).
[6] N. Locatelli et al., Appl. Phys. Lett. 98, 062501 (2011).
[7] A. Kákay, E. Westphal, R. Hertel, IEEE Trans. Magn. 46, 2303 (2010).