PHYSICAL REVIEW B 96, 174402 (2017) Tunable magnetic vortex resonance in a potential well P. Warnicke, 1 , * P. Wohlhüter, 1, 2 A. K. Suszka, 1, 2 S. E. Stevenson, 1 L. J. Heyderman, 1, 2 and J. Raabe 1 1 Paul Scherrer Institute, 5232 Villigen PSI, Switzerland 2 Laboratory for Mesoscopic Systems, Department of Materials, ETH Zurich, 8093 Zurich, Switzerland (Received 5 April 2017; revised manuscript received 23 September 2017; published 3 November 2017) We use frequency-resolved x-ray microscopy to fully characterize the potential well of a magnetic vortex in a soft ferromagnetic permalloy square. The vortex core is excited with magnetic broadband pulses and simultaneously displaced with a static magnetic field. We observe a frequency increase (blueshift) in the gyrotropic mode of the vortex core with increasing bias field. Supported by micromagnetic simulations, we show that this frequency increase is accompanied by internal deformation of the vortex core. The ability to modify the inner structure of the vortex core provides a mechanism to control the dynamics of magnetic vortices. DOI: 10.1103/PhysRevB.96.174402 I. INTRODUCTION The magnetic vortex [1,2] has generated wide interest due to the rich physics associated with its complex nature and promising functionality in spin-based technology. Although a range of applications has been suggested such as information storage [3], magnetic logic [4,5], and oscillators [6–8], the fundamental properties of the vortex that govern its high- frequency behavior are not fully understood. In a ferromagnetic square, a well-known low-energy- domain configuration is the Landau state, where spins circulate around an out-of-plane vortex core to minimize magnetic stray fields. The magnetostatic energy, which depends on the position of the vortex core, can be summed up into an effective potential, and displacing the core from its equilibrium position creates magnetic charges along the edges of the square and increases the magnetostatic energy. Inside the potential, the lowest energy excitation is the gyrotropic mode [9,10]. Experimental attempts to determine the potential of a magnetic vortex using high-frequency excitations have so far led to different conclusions. While the resonance frequency is expected to remain largely unchanged in a harmonic potential [11], observations of both a redshift [12] and a blueshift [13] in the resonance frequency have been attributed to an anharmonicity of the potential well. Among methods to investigate the dynamic behavior of the vortex, spectroscopic techniques [11,14] have been employed to measure its characteristic frequency. Impedance spectroscopy [11], for example, is usually performed on a large number of structures due to its limited sensitivity and thereby provides an average of the dynamic behavior. Anisotropic magnetoresistance measurements [14] have been performed on a single structure, thus avoiding the problem of averaging over multiple structures with different spin configurations. However, the high current densities required for effective spin transfer induce thermal loads and Oersted fields within the vortex that obscure a straightforward analysis. Magnetic microscopy techniques making use of, for example, the magneto-optic Kerr effect [15] or photoemission [16], provide a direct measure of the spin configuration of the vortex, thus * peter.warnicke@psi.ch allowing for direct determination of the vortex-core position. However, up to now there has been no successful attempt to quantify the potential well using magnetic imaging. In this study, we map out the energy potential of the confined vortex using spatially resolved broadband spectroscopy, which allows the resonance frequency and displacement to be determined with the same technique. This extended frequency- resolved mode of scanning transmission x-ray microscopy (STXM) was implemented at the X07DA/PolLux beamline [17] at the Swiss Light Source using x-ray magnetic circular dichroism (XMCD) as a contrast mechanism. II. EXPERIMENT Thin-film permalloy squares with a side length of b = 6 μm were prepared by electron-beam lithography and lift-off pro- cessing. Polycrystalline permalloy (Ni 80 Fe 20 ) with a thickness of h = 50 nm was sputtered onto 100-nm-thick silicon nitride membranes and capped with 1 nm of Al to prevent rapid oxida- tion. A stripline consisting of Ti(5 nm)/Cu(200 nm)/Ti(5 nm) was subsequently patterned on top of the squares, and magnetic microwave field excitations were generated in the sample with currents transmitted through the stripline. An upper limit of the magnetic field intensity in the sample was estimated from the field μ 0 J/2w generated by a planar conductor where w = 10 μm is the width of the stripline and J is the transmitted current. The transmitted currents are measured at the output of the stripline with a real-time oscilloscope. To allow for XMCD measurements of the in-plane magnetization, the sample normal is tilted 30° away from the incoming x-ray beam. Temporal evolution of the magnetization is imaged via time-resolved XMCD in a pump-probe scheme at the Ni L 3 absorption edge (852.7 eV). Timing signals from the synchrotron are used to lock an arbitrary function generator with the data acquisition system [see Fig. 1(a)]. Current signals from the generator are amplified and passed through the stripline shown in Fig. 1(a), where the resulting magnetic fields inductively excite the sample. The magnetic field excitation is synchronized with the probing photon pulses from the synchrotron. An acquisition system based on a field-programmable gate array sorts the detector signal into N time channels. Ultimately, the time resolution in this experiment is limited by the width of the photon bunches of 2469-9950/2017/96(17)/174402(5) 174402-1 ©2017 American Physical Society