Figure 1 Phase diagram of the resonant switching of the vortex core by rf pulses. Applying a short picoJoule pulse at the eigen-frequency of the gyrotropic mode allows a deterministic writing of the memory state.
Magnetization dynamics in individual vortex-state nanodots has been investigated using the spectroscopic technique of magnetic resonance force microscopy (MRFM) developed in the LNO. It has led to the discovery of future potential magnetic memories based on the resonant switching of the vortex core
A magnetic vortex corresponds to a curling in-plane magnetization distribution leaving a small core region (a few nanometers wide, the size of the exchange length) at the center of the dot, where the magnetization is pointing out-of-plane, either up (polarity p=+1) or down (p=-1). Its lowest energy mode corresponds to a gyrotropic motion of the vortex core about its equilibrium position. This mode has recently attracted practical interest for future magnetic memories and microwave devices by allowing the engineering of the spin-wave excitation spectrum of isolated nanodots and large array of dipolarly coupled nanodots (magnonic crystals).
We have first demonstrated that the frequency degeneracy corresponding to the gyrotropic modes with opposite polarities in zero field can be lifted by applying a magnetic field perpendicular to the disk plane  This Zeeman-like splitting can be used for a simple reading of the polarity state in an individual nanodisk. In order to discriminate the resonant frequencies f- and f+ associated respectively to the core polarities p=-1 and p=+1, it is necessary to choose the static magnetic field in such a way that the field-induced gyrotropic frequency splitting exceeds the linewidth of the gyrotropic mode. In our experiment, a bias field as small as µ0H=13 mT is sufficient to fulfill this condition.
We have proposed to take advantage of this frequency discrimination in order to reverse deterministically the vortex core polarity, as shown in references . Starting with the vortex core polarity in, say, the p=+1 state, a single microwave field pulse whose carrier frequency is tuned at f+ and with sufficient amplitude will resonantly excite the gyrotropic motion of the core until it reaches a critical threshold for reversal (see Figure 1). Once it has been reversed, the final state p=-1 is out-of-resonance with the writing pulse so that it cannot be switched back to p=+1. Similarly, it is possible to write the state p=+1 starting from the p=-1 state using the appropriate pulse. This writing process has been shown to be very robust, as no mistake could be recorded out of several hundred attempts with our experimental parameters.
Figure 2 MRFM studies on the vortex dynamics in individual nanodots have led to the discovery of a frequency controlled magnetic memory where the binary information is stored in the polarity of the vortex core.
In sum, our frequency-controlled magnetic vortex memory prototype has two main advantages  Owing to the resonant switching, the writing is very efficient in energy: a picoJoule pulse is sufficient to change the state of the memory. Moreover, deterministic and local addressing in a large array of memory cells can be easily obtained by using very small bias in bit and word lines (see Figure 2). Indeed the selectivity is not set by the coercitivity field but by the linewidth of the resonance, which is 2-3 orders of magnitude smaller.
 Bistability of vortex core dynamics in a single perpendicularly magnetized nanodisk
G. de Loubens, A. Riegler, B. Pigeau, F. Lochner, F. Boust, K. Y. Guslienko, H. Hurdequint, L. W. Molenkamp, G. Schmidt, A. N. Slavin, V. S. Tiberkevich, N. Vukadinovic, and O. Klein, Phys. Rev. Lett. 102 177602 (2009)
 “A frequency-controlled magnetic vortex memory”
B. Pigeau, G. de Loubens, O. Klein, A. Riegler, F. Lochner, G. Schmidt, L. W. Molenkamp, V. S. Tiberkevich and A. N. Slavin, Appl. Phys. Lett. 96 (2010) 132506.
“Optimal control of vortex-core polarity by resonant microwave pulses”
B. Pigeau, G. de Loubens, O. Klein, A. Riegler, F.Lochner, G. Schmidt & L.W. Molenkamp, Nature Physics 7 (2011) 26.
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