Magnetic field dependence of quantized and localized spin wave modes in thin rectangular magnetic dots

Gubbiotti, G.; Conti, M.; Carlotti, G.; Candeloro, Patrizio; Fabrizio, E. Di; Guslienko, K. Yu.; André, A.; Bayer, Christian; Slavin, A. N.

doi:10.1088/0953-8984/16/43/011

Cited by 82 publications

(64 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For example, the nonuniform demagnetizing field may lead to the spatial confinement and quantization of spin-wave modes on the nanometer length scale. [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] For thin-film elements where the magnetization lies in plane, the magnitude of the static in-plane demagnetizing field and the nonuniformity of the total effective field acting upon the magnetization increase when the element aspect ratio ͑size to thickness͒ is reduced. This results in a richer mode spectrum and hence in a less uniform magnetic response to a pulsed magnetic field, which can be directly imaged in the case of micrometer sized magnetic elements.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Time-resolved investigation of magnetization dynamics of arrays of nonellipsoidal nanomagnets with nonuniform ground states

et al. 2008

View full text Add to dashboard Cite

Time-resolved scanning Kerr microscopy measurements have been performed upon arrays of square ferromagnetic nanoelements of different sizes and for a range of bias fields. The experimental results were compared to micromagnetic simulations of model arrays in order to understand the nonuniform precessional dynamics within the elements. In the experimental spectra acquired from an element of length of 236 nm and thickness of 13.6 nm, two branches of excited modes were observed to coexist above a particular bias field. Below this so-called crossover field, the higher frequency branch was observed to vanish. Micromagnetic simulations and Fourier imaging revealed that modes from the higher frequency branch had large amplitude at the center of the element where the effective field was parallel to the bias field and the static magnetization. Modes from the lower frequency branch had large amplitude near the edges of the element perpendicular to the bias field. The simulations revealed significant canting of the static magnetization and effective field away from the direction of the bias field in the edge regions. For the smallest element sizes and/or at low bias field values, the effective field was found to become antiparallel to the static magnetization. The simulations revealed that the majority of the modes were delocalized with finite amplitude throughout the element while the spatial character of a mode was found to be correlated with the spatial variation in the total effective field and the static magnetization state. The simulations also revealed that the frequencies of the edge modes are strongly affected by the spatial distribution of the static magnetization state both within an element and within its nearest neighbors. Furthermore, the simulations suggest that collective modes may be supported in arrays of interacting nanomagnets, which act as magnonic crystals.

show abstract

Section: Introductionmentioning

confidence: 99%

“…There have been many reports on the excitation of similar modes in micrometer sized elements. 11,12,14,17,20 In Ref. 24 the evolution of the mode character was studied for noninteracting nanoscale elements in which the static magnetization was assumed to be uniform.…”

Section: Introductionmentioning

confidence: 99%

Time-resolved investigation of magnetization dynamics of arrays of nonellipsoidal nanomagnets with nonuniform ground states

et al. 2008

View full text Add to dashboard Cite

show abstract

“…The lack of nanoscale spatial resolution has been circumvented by measuring the frequency [16][17][18][19][20][21] or time 22,23 domain response from sufficiently large arrays of nanomagnets and comparing the measured signals with analytical theories [18][19][20] and/or micromagnetic simulations. 16,17,[21][22][23][24][25][26][27][28][29] In particular, this approach has led to the discovery of a crossover from a center to edge localized mode as the magnetic element size is reduced to less than 220 nm.…”

Section: Introductionmentioning

confidence: 99%

Time resolved studies of edge modes in magnetic nanoelements (invited)

Kruglyak

Keatley

Hicken

et al. 2006

Journal of Applied Physics

View full text Add to dashboard Cite

Micromagnetic simulations have been performed to investigate the frequencies and relative amplitudes of resonant magnetic modes within nanomagnetic elements of varying size that have been previously studied by time resolved Kerr magnetometry. The magnetic response of a nanoscale element generally consists of the edge and center localized modes. For 2.5 nm thick elements, a crossover from center to edge mode excitation occurs as the element size is reduced to less than 220 nm. Additional modes appear in the spin wave spectrum as the thickness of the element is increased. The frequency of the edge mode is particularly sensitive to the strength of the exchange interaction, dipolar interactions with nearest neighbor elements, and rounding of the corners of the element. Simulations with in-plane pulsed fields show that the edge mode becomes dominant in elements of somewhat larger size, emphasizing the importance of the edge mode in technological applications.

show abstract

“…This transfer function form is convenient as it directly reveals information about the natural frequency of the system, its stability and state of damping, independent of the input field. The spin-resonance frequency in (26) is given by: (27) From the Laplace transform of (25c), the solution for the perturbed z-component of the magnetisation is m z (t) = m z (0) = 0, and hence…”

Section: Y-directed Field (Point A)mentioning

confidence: 99%

Sub-Nanosecond Electromagnetic-Micromagnetic Dynamic Simulations Using the Finite-Difference Time-Domain Method

Aziz¹

2009

PIER B

View full text Add to dashboard Cite

Abstract-This paper presents an efficient and simple approach of implementing the Landau-Lifshitz-Gilbert (LLG) equation of magnetisation motion within the Finite-difference Time-domain (FDTD) method. This combined electromagnetic-micromagnetic simulation technique is particularly important for modeling electromagnetic interaction with lossy magnetic material in the presence of current and magnetic sources, particularly at very high frequencies. The efficient implementation involves simple two-point spatial interpolations that are applicable to two and three-dimensional FDTD grids, and uses a stable iterative algorithm for the time integration of the LLG equation. A ferromagnetic resonance numerical experiment on a rectangular Permalloy prism excited through its cross-section by a non-uniform pulse field from a transmission line was carried out for the purpose of verifying the combined FDTD-LLG computations. The numerical results were in good agreement with linearised analytical solutions of the LLG equation for uniform and non-uniform precession modes. This paper also presents a brief investigation on the use of non-staggered FDTD grid schemes to model magnetic material using the LLG equation, and indicates that the classical FDTD staggered scheme offers simplicity in implementation and more accuracy for modeling wave interaction with lossy magnetic material than the non-staggered schemes based on Maxwell's equations formulation.

show abstract

Magnetic field dependence of quantized and localized spin wave modes in thin rectangular magnetic dots

Cited by 82 publications

References 21 publications

Time-resolved investigation of magnetization dynamics of arrays of nonellipsoidal nanomagnets with nonuniform ground states

Time-resolved investigation of magnetization dynamics of arrays of nonellipsoidal nanomagnets with nonuniform ground states

Time resolved studies of edge modes in magnetic nanoelements (invited)

Sub-Nanosecond Electromagnetic-Micromagnetic Dynamic Simulations Using the Finite-Difference Time-Domain Method

Contact Info

Product

Resources

About