A. Pyatakov 1,2 ; A. Sergeev 1 , D. Sechin 1 , G. Meshkov 1 , E. Nikolaeva 1 , A. Nikolaev 1 ,

1. Magnetic domain wall motion induced by electric field ; ; 1Physics Department, M.V. Lomonosov Moscow State University, Leninskie gory, Moscow, 119992, Russia 2 A.M. Prokhorov General Physics Institute, 38, Vavilova st., Moscow, 119991, Russia We propose the new approach to the problem of electrically controlled magnetic state: the electric field driven domain wall motion.This effect is observed in epitaxial iron garnet films grown on (210) and (110) gadolinium-gallium garnet substrates. The displacement of the domain wall changes to the opposite at the reversal of electric field polarity, and it is independent of the magnetic polarity of the domains. Dynamic observation of the domain wall motion in 400 V electric pulses gives the domain wall velocity about 50 m/s. The same velocity is achieved in magnetic field pulse about 50 Oe. This type of magnetoelectric effect is implemented in single phase material at room temperature. The theoretical model based on inhomogenous magnetoelectric interaction provides with the necessary criteria of the effect and the way to maximize it. Introduction Theory and discussion The conventional means of magnetic data writing put the limit for increasing storagedensity. The inductive coils and conducting lines that are used to generate magnetic field suffer from energy losses, that cause the progressive damage of the metalconductors [1]. The alternative approach of magnetic writing such as spin-current induced domain wall motion was proposed [2]. However the spin transfer also requires large current densities of 106-107A/cm2. We propose the new approach to the problem of electrically controlled magneticstate: the electric field driven domain wall motion [3,4]. The characteristic features of the effect evidenced for its magnetoelectric nature [3]. This effect was predicted theoreticallyin [5] as electric polarization associated with magnetic inhomogeneities. Magnetic domain wall motion triggered by electric field was implemented in epitaxially grown single crystal iron garnet films at room temperature. The influence of electric field on micromagnetic structure was predicted theoretically in the work [5]. This theoretical model tooks into account the so-called inhomogeneous magnetoelectric interaction that gives rise to electric polarization associated with magnetic inhomogeneities. The inhomogeneous magnetoelectric contribution into thermodynamic potential for the bulk crystal of ferrite garnets with cubic symmetry takes the following highly symmetric form: (1) where M is magnetization vector,  is differential operator vector, E is electric field,  is inhomogeneous magnetoelectric interaction constant. One can learn immediately from Eq. (1) that the effect is odd with respect to electric field E and does not change the sign with magnetization M reversal, which agrees with experiment. The electric polarization induced by magnetic inhomogeneity can be found in the following way: Experiment Epitaxial films of iron garnets are the model object to study micromagnetism. The electromagnetooptical effect observed in iron garnet films [6] served as an indirect proof for their salient magnetoelectric properties.In our experiments we used iron garnet films (BiLu)3(FeGa)5O12, grown by liquid-phase epitaxy on (111), (110), and (210) Gd3Ga5O12 substrate.The parameters of the samples are listed in the Table. (2) To account for the enhancement of the effect observed at stripe domain heads in magnetic film let us consider the special features of the boundary between domains with tilted magnetization. This magnetization lies in yz plane and is directed at angle  with respect to the z-axis normal to the surface (fig.5 a). However the plane of magnetization rotation is not the same for different point of domain heads. The intersection of the rotation plane and film surface changes its direction from point to point (see tangent to the domain boundary marked with dotted line and symbol “ x′ ” in figure 5 b). So it is more convenient to use the coordinate system (x′,y′) rotated at angle  with respect to the (x,y), where x′– axis is directed along the intersection line and y’ axis along the direction of spin modulation. In this case the rotation of the magnetization in domain wall is expressed by the dependence (y′) where  is the angle with respect to the direction of magnetization in the domain M0(fig.5c). The orientation of M0in the plane of magnetization rotation is determined by angle 0 (fig.5 c), that can be found from the relation between the coordinate systems (see fig. 5 a,b,c): (3) To produce a high-strength electric field in the dielectric iron garnet film, we used a 50 μm-diameter copper wire with a pointed tip, which touched the surface of the sample in the vicinity of the domain wall (Fig. 1 a). The tip curvature radius of the copper “needle” was about 5 μm. This allowed us to obtain electric field strength up to 1000 kV/cm near the tip by supplying a voltage up to 500 V to the needle. The absence of the possible leakage currents between the tip and the grounding electrode (e.g., on along the sample surface) was verified by milliamperemeter. The magnetooptical technique in Faraday geometry was used to observe the micromagnetic structure through a pinhole of the diameter ~ 0.3 mm that was made in the grounding electrode. A. Pyatakov1,2; A. Sergeev1, D. Sechin1, G. Meshkov1, E. Nikolaeva1, A. Nikolaev1, A. Logginov1, A. Zvezdin2 Fig. 5 a) b) c) 1 – tip electrode 2 – ground electrode 3 –(BiLu)3(FeGa)5O12 film The magnetization components in terms of angles ,, and 0 can be written in the following way: Assuming for (y′) the conventional law [7]: where ∆ is the width of the domain wall one can obtain from (2) and (4): 4 – substrate 5 – objective lens Fig.1 (4) Static measurements We register the magnetization distribution in initial state, and the position of domain wall in static electric field applied. Typical magnetooptical images are shown in figures 2. In the left column there are initial position of the domain boundaries with respect to the tip electrode (large black area 1). In the right column one can see the transformation of micromagnetic structure at the positive potential of the tip with respect to the substrate. As soon as the dc voltage was switched off the domain walls 2 usually came back to the equilibrium position.Such reversible domain wall displacements were detected up to 5 μm. At higher values of the displacement the modification of the micromagnetic structure had irreversible character (Fig. 2, the right bottom). (5) (6) Fig.2 Dynamic measurements The high speed photography technique was used: the pulses of electric field (pulse width ~ 300 ns, the rise time ~20 ns) were followed by pulses of laser illumination (duration ~10 ns) to get an instantaneous image of the structure under the influence of electric field. Varying the time delay between field and laser pulses enabled us to observe the consecutive positions of domain wall and thus investigate its dynamics. In response to the applied electric field domain wall steadily moves until it reaches the equilibrium position corresponding to the field applied (the consecutive positions of stripe domain head are shown in fig. 3 a). Both the values of domain wall velocity and the ultimate displacement of domain wall increase with the value of electric field (fig.3 b) To compare the velocities achieved in electric field with typical velocities of domain wall in magnetic field we carried out the measurements in magnetic field pulses. The velocity of 50 m/s similar to that one obtained in voltage pulse of 400 V (electric field at the tip E=400 V/5 µm=800 kV/cm) was achieved in pulse magnetic field about 50 Oe. • , Δ is the width of the domain wall. and One can readily see from (6) that the film polarization is zero at =0, that explains the absence of the effect in (111) films. Nonvanishing effect should be observed in the case of (210) and (110), and it should be more pronounced in the films with larger angles , i.e. (210) films (see the Table). Furthermore, effect is maximum at those domain wall segments where (=90,0=0), i.e. at the domain head, while at the segments of the wall parallel to the projection of magnetization on film surface (=0,0=) the polarization should be zero. a) Conclusion Summarizing, the theoretical model of the electric field induced magnetic domain wall motion based on inhomogeneous magnetoelectric mechanism explains the basic features of the effect (the dependence on the electric polarity of the tip electrode and independence on the magnetic polarity of the domains). It also predicts the maximum value of the effect for stripe domain heads in (210) films that corresponds to the results of experimental study. References b) Fig.3 • The characteristic features of the effect: • The direction of the domain wall displacement depends on the polarity of the voltage: in the case of positive polarity, the wall was attracted to the needle (marked with red in the figure 4), and, in the case of negative polarity, it was repelled (marked with blue). • The direction of the wall displacement did not depend on the magnetic polarity of the domain over which the tip was located. • The effect was observed in films with considerable in-plane anisotropy (the films with (210) and (110) substrate orientations) and was not observed in highly symmetrical (111) films. C. Chappert, Fert A., F. N. van Dau, Nature Mater.6 813 (2007) M. Tsoi, R. E. Fontana, S. S. P. Parkin, Appl. Phys. Lett. 83 2617(2003) A. S. Logginov, G. A. Meshkov, A. V. Nikolaev, E.P. Nikolaeva, A. P. Pyatakov, A.K. Zvezdin, Room Temperature Magnetoelectric Control of micromagnetic structure in Iron Garnet Films, Appl. Phys. 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