Anisotropic magnetic coupling of permalloy micron dots forming a square lattice (original) (raw)
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Origin of fourfold anisotropy in square lattices of circular ferromagnetic dots
Physical Review B, 2006
We discuss the four-fold anisotropy of in-plane ferromagnetic resonance (FMR) field Hr, found in a square lattice of circular Permalloy dots when the interdot distance a gets comparable to the dot diameter d. The minimum Hr, along the lattice 11 axes, and the maximum, along the 10 axes, differ by ∼ 50 Oe at a/d = 1.1. This anisotropy, not expected in uniformly magnetized dots, is explained by a non-uniform magnetization m(r) in a dot in response to dipolar forces in the patterned magnetic structure. It is well described by an iterative solution of a continuous variational procedure.
Static and dynamic properties of patterned magnetic permalloy films
Journal of Magnetism and Magnetic Materials, 1997
Static magnetic and spin wave properties of square lattices of permalloy micron dots with thicknesses of 500 Å and 1000 Å and with varying dot separations have been investigated. The spin wave frequencies can be well described taking into account the demagnetization factor of each single dot. A magnetic fourfold anisotropy was found for the lattice with dot diameters of 1 µm and a dot separation of 0.1 µm. The anisotropy is attributed to an anisotropic dipole-dipole interaction between magnetically unsaturated parts of the dots. The anisotropy strength (order of 10 5 erg/cm 3) decreases with increasing in-plane applied magnetic field.
Magnetic properties of submicron circular permalloy dots
IEEE Transactions on Magnetics, 2002
Both the static and the dynamical magnetic properties of a square array of circular permalloy dots, characterized by a magnetic vortex configuration of the magnetization, have been investigated by means of magneto-optical Kerr effect and of Brillouin light scattering (BLS) from thermally excited spin waves. The measured hysteresis loop can be satisfactorily reproduced by micromagnetic simulations, showing that the vortex configuration is stable over a wide range of applied field. The high frequency response of the dots was analyzed by BLS measurements performed under external magnetic field intensity large enough to uniformly magnetize the dots. Evidence is given of a marked discretization of the spin wave spectrum with respect to the case of the continuous permalloy film, where only one peak, corresponding to the Damon-Eshbach mode, was detected. The experimental frequencies have been compared to those calculated using a recently developed analytical model for a flat uniformly magnetized cylindrical dot.
Interactions and switching behavior of anisotropic magnetic dots
Journal of Applied Physics, 2004
The magnetic properties of collections of three soft magnetic nanodots with various aspect ratios are investigated. Permalloy films are first produced by dc magnetron sputtering. Focused ion beam milling is then used to mill dots, each with different shape anisotropy. We find that each of the three dots in the system has a unique switching field, and that there is significant magnetostatic coupling. Micromagnetic simulations suggest that for dot separations of less than 50 nm there exists strong interdot interaction, leading to the possibility of controlled switching of neighboring dots. This switching behavior is of interest in magnetic information processing.
Effect of interdot dipolar coupling on the magnetic properties of permalloy nano-cylinders
Surface Science, 2006
Square arrays of nanometric cylindrical dots (radius 100 nm), with interdot spacing variable in the range 50-800 nm, have been patterned by e-beam lithography, starting from a 50 nm thick permalloy film. A detailed magneto-optical Kerr effect study revealed that on reducing the interdot separation below 200 nm, there is a marked decrease of the vortex nucleation and annihilation fields, as well as an increase of the susceptibility. These results are interpreted in terms of the influence of interdot dipolar coupling, on the basis of micromagnetic simulations with either open or periodic boundary conditions. The coupling also affects the high-frequency magnetic properties, as seen by the modification of the spin-wave spectrum measured by Brillouin light scattering. In particular, a broadening of the discrete resonance modes and a shift to higher frequency for some of them is evident for the specimens with small interdot spacings.
Journal of Physics: Condensed Matter, 2004
The magnetic field dependences of the frequencies of standing spin-wave modes in a tangentially magnetized array of thin rectangular permalloy dots (800 × 550 nm) were measured experimentally by a Brillouin light scattering technique and calculated theoretically using an approximate size-dependent quantization of the spin-wavevector components in the dipole-exchange dispersion equation for spin waves propagating in a continuous magnetic film. It was found that the inhomogeneous internal bias magnetic field of the dot has a strong influence on the profiles of the lowest spin-wave standing modes. In addition, the dynamic magnetization distributions found for both longitudinally and transversely magnetized long magnetic stripes gives a good approximation for mode distributions in a rectangular dot magnetized along one of its inplane sides. An approximate analytic theory of exchange-dominated spin-wave modes, strongly localized along the dot edge that is perpendicular to the bias magnetic field, is developed. A good quantitative agreement with the results of the BLS experiment is found.
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We have studied the magnetization of Ni dot with 50 to 70 nanometer diameter and 12 nanometer thickness using a magnetic force microscopy with an in-plane magnetic field. The Ni dots were prepared using self-assembled dot patterns with poly (styrene-b-methyl mathacrylate) diblock copolymers on Ni film and ion etching. It was found that the remanent magnetization direction of the dot was perpendicular to the plane as prepared. From the vibrating sample magnetometer measurement, a hysteresis loop was found in the perpendicular magnetization. When an in-plane external magnetic field was applied, the magnetization was rotated into a horizontal direction with low coercivity along the field direction.
Spin-wave quantization and dynamic coupling in micron-size circular magnetic dots
Applied Physics Letters, 1999
We report on the observation of spin wave quantization in square arrays of micron size circular magnetic Ni 80 Fe 20 dots by means of Brillouin light scattering spectroscopy. For a large wavevector interval several discrete, dispersionless modes with a frequency splitting of up to 2.5 GHz were observed. The modes are identified as magnetostatic surface spin waves laterally quantized due to in-plane confinement in each single dot. The frequencies of the lowest observed modes decrease with increasing distance between the dots, thus indicating an essential dynamic magnetic dipole interaction between the dots with small interdot distances.
Collective spin modes in chains of dipolarly interacting rectangular magnetic dots
Physical Review B, 2011
We present a combined experimental and micromagnetic study of spin excitations in chains of dense magnetic dots. The samples consist of long chains of rectangular dots with rounded corners having lateral dimensions of 715 × 450 nm 2 and 1025 × 450 nm 2 , respectively. Chains are composed of magnetic elements put side by side along either their major or minor axis with edge-to-edge separation below 100 nm. The frequency dispersion of the spin-wave excitations was measured by Brillouin light-scattering technique as a function of the transferred wave vector directed along the chains of dots and for an external magnetic field applied perpendicularly to the transferred wave vector in the dots plane. Evidence is given of collective excitations in the form of Bloch waves propagating through the chains characterized by magnonic energy bands. Micromagnetic calculations, performed by using the dynamical matrix method, enable us to satisfactorily reproduce the frequency dispersion of collective spin modes as well as to visualize the spatial profile of the dynamic magnetization inside the dots. We also propose a general rule to understand the frequency dispersion of collective modes starting from the relative phase of dynamic magnetization in the facing sides of adjacent dots.