Sample Preparation, Micromagnetic Simulations, Circular-Rotational Currents, Parasitic Oersted Fields and Clover Samples (Magnetic Antivortex-Core Reversal by Circular-Rotational Spin Currents) Thomas Kamionka, 1, Michael Martens, 1, Kang Wei Chou, 2 Michael Curcic, 3 André Drews, 4 Gisela Schütz, 3 Tolek Tyliszczak, 2 Hermann Stoll, 3 Bartel Van Waeyenberge, 5 and Guido Meier 1 1 Institut für Angewandte Physik und Zentrum für Mikrostrukturforschung, Universität Hamburg, 20355 Hamburg, Germany 2 Advanced Light Source, LBNL, 94720 Berkeley, California, USA 3 Max-Planck-Institut für Metallforschung, 70569 Stuttgart, Germany 4 Arbeitsbereich Technische Informatiksysteme, Universität Hamburg, 22527 Hamburg, Germany 5 Department of Solid State Sciences, Ghent University, 9000 Ghent, Belgium 1
SAMPLE PREPARATION The sample was prepared by means of electron-beam lithography in combination with lift-off processing. The permalloy microstructure was deposited first by thermal evaporation on a 100 nm thick Si 3 N 4 membrane. We carried out atomic-force microscopy to determine the thickness t = (53 ± 1) nm and the edge length of the inner square l = (903 ± 22) nm. In a second step the leads were added by sputter deposition of 90 nm gold subsequently to a short in-situ argonplasma etching process. The latter process removes oxide at the contact areas and improves the conductivity of the sample. MICROMAGNETIC SIMULATIONS Preceding the experiment we performed micromagnetic simulations with the OOMMF code to estimate the order of magnitude of the resonance frequency. Only the center part (1900 nm 1900 nm) of the structure is simulated and discretized by simulation cells of 4 nm in x- and y-direction, which is below the exchange length of permalloy. The shape anisotropy of the missing outer parts is replaced by a strong unidirectional anisotropy to stabilize the ground state. The antivortex is displaced by a short field pulse, and the subsequent spiral trajectory is fitted with the trajectory of a weakly damped harmonic oscillator. A saturation magnetization M S = 8.0 10 5 Am 1, an exchange constant A = 13 10 12 Jm 1, and a Gilbert-damping constant α = 0.01 are assumed [1]. The simulation yields a resonance frequency ω/2π = 127 MHz and a damping constant Γ = 2.3 10 7 s 1. CIRCULAR-ROTATIONAL CURRENTS Balanced-to-unbalanced transformers or baluns in front of the x- and y-electrodes prevent any leakage current away from the respective electrode pair. A circular-rotational current is generated by the superposition of mutually orthogonal alternating currents with a phase-shift of ±π/2. The sample resistance was increased to 50 Ω by connecting additional resistors in series. Due to the impedance matching, the total current through the sample can be calculated from the power transmitted to a powermeter which is in place of the sample during the calibration. The ratio between the total current and the current density in the center of the structure is determined by numerical calculations with the finite-element solver COMSOL multiphysics (see Fig. 1). 2
FIG. 1: Numerically calculated current distribution due to a total current of 6.32 ma through the horizontal electrodes. The magnitude of the current density is color-coded. In the center the current-density vector has a magnitude of 8.1 10 10 A/m 2 and only a slight tilt angle of 8.3 due to the small current through the loops of the structure. These parameters vary less than 3 % or less than 2.0 within a radius of 100 nm, i.e. larger than the observed gyration amplitudes. The three-dimensional structure is modeled in accordance with atomic-force micrographs. As material parameters electrical conductivities of permalloy σ Py = 2.9 10 6 Ω 1 m 1 and gold σ Au = 5.0 10 7 Ω 1 m 1 are assumed, respectively. PARASITIC OERSTED FIELDS With parameters corresponding to the micromagnetic simulations (see above), a resonance amplitude of 100 nm requires a minimum current density (fully spin-polarized current) of 3.3 10 10 A/m 2 according to Eq. 2 of the main Letter. The same resonance amplitude is already effected by small fields of 73 A/m in the case of field coupling. In the experiment we injected current densities of 8.1 10 10 A/m 2 (and more) which generate much higher in-plane Oersted fields within the thin-film structure. To get a quantitative image, we consider a thin layer with the thickness of the sample (53 nm) and a homogeneous in-plane current flow of 8.1 10 10 A/m 2 in x-direction. Within the layer in-plane fields in y-direction are generated. The magnitude of the 3
field increases linearly in z-direction and reaches a maximal value of 2000 A/m at the surface. In spite of this high value, the averaged field would vanish because the fields in the upper half and in the lower half of the layer are directly opposed. We want to name reasons why the current flow may vary in the real sample in z-direction leading to an unbalanced situation and a non-vanishing field torque, respectively. The conductivity of the gold contacts on top of the structure is by a factor of 20 higher than the conductivity of permalloy. This leads to a higher current density at the upper surface of the structure, which is illustrated in Ref. [2]. Another possible reason is that the conductivity of the permalloy may vary in z-direction due to fluctuations of process parameters (temperature, chamber pressure...) during the evaporation process. In the end there is an out-ofplane current flow (up and down) at the gold contacts because of the different conductivities which also generates in-plane Oersted fields nearby the antivortex. The unbalance of in-plane fields is considered as a parasitic rotating Oersted field in the main Letter. CLOVER SAMPLES At first the analyzed switching behavior was verified for two identically prepared infinity samples. Within the next measurement period, we reproduced the results for another replica and for two additional structures with the geometry of four-leaved clover [3, 4]. The infinity structure was extended by two additional curved parts to an axially symmetric structure (see Fig. 2). These clover samples are invariant to a rotation of 90 including the electrodes. The increased symmetry is another legitimation of our essential assumption that a possible Oersted field has the same sense of rotation as the circular-rotational current in the experiments. Electronic address: tkamionk@physnet.uni-hamburg.de Electronic address: michael.martens@physnet.uni-hamburg.de [1] B. Krüger et al., Phys. Rev. B 76, 224426 (2007). [2] L. Bocklage et al., Phys. Rev. B 78, 180405(R) (2008). [3] K. Shigeto et al., Appl. Phys. Lett. 80, 4190 (2002). [4] A. Drews et al., Phys. Rev. B 77, 094413 (2008). 4
FIG. 2: Overview of investigated sample types. All prepared samples were characterized by atomic-force microscopy (AFM) and scanning transmission X-ray microscopy (STXM) with sensitivity to the in-plane magnetization. 5