Harmonic oscillator model for current- and field-driven magnetic vortices

Abstract

In experiments the distinction between spin-torque and Oersted-field driven magnetization dynamics is still an open problem. Here, the gyroscopic motion of current-and field-driven magnetic vortices in small thinfilm elements is investigated by analytical calculations and by numerical simulations. It is found that for small harmonic excitations the vortex core performs an elliptical rotation around its equilibrium position. The global phase of the rotation and the ratio between the semi-axes are determined by the frequency and the amplitude of the Oersted field and the spin torque. PACS numbers: 75.60.Ch, 72.25.Ba Recently it has been found that a spin-polarized current flowing through a magnetic sample interacts with the magnetization and exerts a torque on the local magnetization. 1,2 A promising system for the investigation of the spin-torque effect is a vortex in a micro-or nanostructured magnetic thinfilm element. Vortices are formed when the in-plane magnetization curls around a center region. In this few nanometer large center region 3 , called the vortex core, the magnetization turns out-of-plane to minimize the exchange energy. 4 It is known that these vortices precess around their equilibrium position when excited by magnetic field pulses 5,6 and it was predicted that spin-polarized electric currents can do the same. 7 The spacial restriction of the vortex core as well as its periodic motion around its ground state yield an especially accessible system for space-and time-resolved measurements with scanning probe and time-integrative techniques such as soft X-ray microscopy or X-ray photoemission electron microscopy. 5,6,8,9,10 Magnetic vortices also occur in vortex domain walls. The motion of such walls has recently been investigated intensively. 11,12 Understanding the dynamics of confined vortices can give deeper insight in the mechanism of vortex-wall motion. 13 An in-plane Oersted field accompanying the current flow also influences the motion of the vortex core. For the interpretation of experimental data it is crucial to distinguish between the influence of the spin torque and of the Oersted field. 14 (a) l X (b) FIG. 1: (a) Scheme of the magnetization in a square magnetic thinfilm element with a vortex that is deflected to the right. (b) Magnetization of a vortex in its static ground state. The height denotes the z-component while the gray scale corresponds to the direction of the in-plane magnetization.In this paper we investigate the current-and field-driven gyroscopic motion of magnetic vortices in square thin-film elements of size l and thickness t as shown in Fig. 1 and present a method to distinguish between spin torque and Oersted field driven magnetization dynamics. In the presence of a spinpolarized current the time evolution of the magnetization is given by the extended Landau-Lifshitz-Gilbert equationwith the coupling constant b j = P µ B /[eM s (1 + ξ 2 )] between the current and the magnetization where P is the spin polarization, M S the saturation magnetization, and ξ the degree o...

Direct dynamic imaging of non-adiabatic spin torque effects

“…Figure 2 displays the response of the vortex core with CCW chirality to AC currents of varying frequency with a step size of 2.5 MHz. The theoretical amplitudes based on a harmonic oscillator model 15,17,20 match the experimental measurements well (Fig. 2c).…”

“…Phenomenological descriptions of the vortex motion predict that the size of the orbit at resonance will depend not only on the magnitude of the excitation current but also on the chirality of the vortex if Oersted fields contribute to the excitation 15,17 . The Oersted field h o is perpendicular to the direction of current flow, which provides a force on the vortex core parallel or antiparallel to the current ( j o ) depending on the chirality and the nature of the current imbalance within the sample, typically attributed to higher current density near the top or bottom surface of the sample.…”

“…It is difficult, however, to discriminate between the effects of spin-transfer torques and the Oersted fields in experiments involving electrical currents [15][16][17] , which complicates the determination of β. To date, the lowest reported relative error estimates of the nonadiabatic spin torque are based on X-ray imaging measurements of the position of a vortex core displaced by pulsed DC currents 6 .…”

Limits for the vortex state spin torque oscillator in magnetic nanopillars: Micromagnetic simulations for a thin free layer

“…The vortex magnetization distribution stability as well as the vortex excitations were studied in Refs. [5][6][7][8][9][10][11][12][13][14][15].…”

Time-resolved scanning electron microscopy with polarization analysis

“…Since its first experimental observation in 1984 15 the vortex gyration has been extensively studied, both theoretically 16,17 as well as experimentally. [18][19][20] The sample investigated here consists of a series of FeCoSiB squares with a side length of 3.5 lm, structured from 60 nm thick Fe 70 Co 8 Si 12 B 10 on top of a gold microstrip on sapphire (see Fig.…”