Magnetic Nanoelements Research Articles

Shape and Proximity Effect of Magnetic Nanoelements Used as Biomolecular Labels for Magnetic Notched Nanowire Biosensors

Three magnetic nanoelements of different shapes and sizes were investigated as potential candidates for biological magnetic labels to be used on a biosensor, which incorporates magnetoresistive nanowires. Circular, square, and triangular nanoelements were positioned at varying distances from a Permalloy, single notched, nanowire to determine how the shape and proximity of the nanoelements affected the domain wall structure of the nanowire. All results were simulated using micro-magnetic simulations by the object oriented micro-magnetic framework. It is shown that both the proximity and the shape of each of the nanoelements produce changes in the domain structure that are specific to the nanoelement and could potentially generate measurable magnetoresistive changes. The 200 nm diameter circularly shaped nanoelement had the greatest proximity effect on the nanowire. It also had a closed, circular domain structure when isolated, which is potentially useful since this is likely to reduce the tendency of biologically labeled material in solution to form agglomerations.

Magnetic force microscopy study of shape engineered FEBID iron nanostructures

The capability to control matter down to the nanoscale level in combination with the novel magnetic properties of nanomaterials have attracted increasing attention in the last few decades due to their applications in magnetic sensing, hard disc data storage and logic devices. Therefore, many efforts have been devoted to the implementation of both nanofabrication methods as well as characterization of magnetic nanoelements. In this study, Fe‐based nanostructures have been synthesized on Si(100) by focused electron beam induced deposition (FEBID) utilizing iron pentacarbonyl as precursor. The so obtained nanostructures exhibit a remarkably high iron content (Fe > 80 at.%), expected to give rise to a ferromagnetic behaviour. For that reason, magnetic force microscopy (MFM) analyses were performed on the obtained FEBID Fe nanostructures. Moreover, object oriented micromagnetic framework (OOMMF) magnetic simulations have been executed to study the influence of the geometry on the magnetic properties of iron single‐domain nanowires. FEBID is a mask‐less nanofabrication method based on the injection of precursor gas molecules in proximity of the deposition area where their decomposition is locally induced by a focused electron beam.

Size-dependent magnetization switching characteristics and spin wave modes of FePt nanostructures

We present a comprehensive investigation of the size-dependent switching characteristics and spin wave modes of FePt nanoelements. Curved nanomagnets (“caps”) are compared to flat disks of identical diameter and volume over a size range of 100 to 300 nm. Quasi-static magnetization reversal analysis using first-order reversal curves shows that spherical caps have lower vortex nucleation and annihilation fields than the flat disks. As the element diameter decreases, the reversal mechanism in the caps crosses over sooner to coherent rotation than in the disks. The magnetization dynamics are studied using optically induced small angle precession and reveal a strong size dependence that differs for the two shapes. Flat disks exhibit well-known center and edge modes at all sizes, but as the diameter of the caps increases from 100 to 300 nm, additional oscillation modes appear in agreement with dynamic micromagnetic simulations. In addition, we show that the three-dimensional curvature of the cap causes a much greater sensitivity to the applied field angle, which provides an additional way for controlling the ultrafast response of nanomagnetic elements.

Role of boundaries in micromagnetic calculations of magnonic spectra of arrays of magnetic nanoelements

We have used micromagnetic simulations performed with open and periodic boundary conditions to study the influence of the presence of array boundaries on the spectra and spatial profiles of collective spin-wave excitations in arrays of magnetic nanoelements. The spectra and spatial profiles of collective spin waves excited in isolated arrays of nanoelements and those forming a part of quasi-infinite arrays are qualitatively different even if the same excitation field is used in the simulations. In particular, the use of periodic boundary conditions suppresses the excitation of nonuniform collective modes by uniform excitation fields. However, the use of nonuniform excitation fields in combination with periodic boundary conditions is shown to enable investigation of the structure of magnonic dispersion curves for quasi-infinite arrays (magnonic crystals) in different directions in the reciprocal space and for different magnonic bands. The results obtained in the latter case show a perfect agreement with those obtained with the dynamical matrix method for infinite arrays of nanoelements of the same geometry and magnetic properties.

Magnetic nanostructures for non-volatile memories

In this work we present two fabrication approaches for patterning submicron Pacman-like (PL) magnetic nanoelements, the additive and subtractive process. Within the first process, PL structures are revealed using a standard lift-off technique. The second one is based on argon ion milling through titanium mask patterns. In the PL magnet the missing sector itself represents a dipole, which together with the external field, controls the chirality of the nucleated vortex. In order to determine the chirality of the vortex ground state, an array of PL nanomagnets of the diameter 200nm prepared by the subtractive process, is mapped by the magnetic force microscopy. The experimental results are in good agreement with the results achieved by the micromagnetic simulations.

Energy barriers to magnetization reversal in perpendicularly magnetized thin film nanomagnets

Understanding the stability of thin film nanomagnets with perpendicular magnetic anisotropy (PMA) against thermally induced magnetization reversal is important when designing perpendicularly magnetized patterned media and magnetic random access memories. The magnetization reversal rate depends primarily on the energy barrier the system needs to surmount in order for reversal to proceed. In this paper, we study the reversal dynamics of these systems and compute the relevant barriers using the string method of E, Vanden-Eijnden, and Ren. We find the reversal to be often spatially incoherent; that is, rather than all parts of the element switching simultaneously, reversal proceeds instead through a soliton-like domain wall sweeping through the system. We show that for square nanomagnetic elements, the energy barrier increases with element size up to a critical length scale, beyond which the energy barrier is constant. For circular elements, the energy barrier continues to increase indefinitely, albeit more slowly beyond a critical size. In both cases, the energy barriers are smaller than those expected for coherent magnetization reversal.

Synthesis of Individually Tuned Nanomagnets for Nanomagnet Logic by Direct Write Focused Electron Beam Induced Deposition

Nanomagnet Logic (NML) is a promising new technology for future logic which exploits interactions among magnetic nanoelements in order to encode and compute binary information. This approach overcomes the well-known limits of CMOS-based microelectronics by drastically reducing the power consumption of computational systems and by offering nonvolatility. An actual key challenge is the nanofabrication of such systems that, up to date, are prepared by complex multistep processes in planar technology. Here, we report the single-step synthesis of NML key elements by focused electron beam induced deposition (FEBID) using iron pentacarbonyl as a gas precursor. The resulting nanomagnets feature an inner iron part and a 3 nm iron oxide cover (core-shell structure). Full functionality of conventional NML gates from FEBID-nanowires was achieved. An advanced structure maintaining the gate functionality based on bended nanowires was realized. The unique design obtained by direct-writing reduces the error probability and may merge several NWs in future NML elements.

Shape Effect of Magnetic Nanoelements as Biomolecular Labels for Magnetic Biosensors

Four magnetic nanoelements of different shapes were investigated at varying distances from a permalloy nanowire to see how the shape of the nanoelements affected the resultant demagnetizing field from the nanoelements onto the nanowire. All results were simulated using micromagnetic simulations by Object Oriented Micromagnetic Framework (OOMMF). It is shown that the square nanoelements performed the best and that the shape anisotropy has an important role in determining the external demagnetizing field for nanoelements.

Spin Torque Diode Spectroscopy of Quantized Spin Wave Excited in a Magnetic Tunnel Junction

We systematically measured the spin torque diode spectra of a magnetic tunnel junction nanoelement as a function of external magnetic field and field angle using a homemade quasi-omnidirectional broadband electrical spectrometer. The electrical spectroscopies reveal a significant higher-order spin wave modes excited in the free layer, which is substantiated by an analytical model.

Spin-wave excitations of domain walls in bubble-state magnetic nanoelements

Domain wall (DW) excitation spectrum for a bubble-state element has been investigated using three-dimensional micromagnetic simulations within a wide frequency range (0.1--100 GHz). Multiple DW resonance lines have been identified; localized modes at the DW in the low-frequency part of the spectrum and a set of high-frequency DW excitations above the frequency gap of domains spreading into the adjacent domains. In the last case, various DW modes with and without rotational symmetry coupled to multinodal domain modes are revealed. Due to the geometrical confinement leading to a strongly nonuniform static effective field, high-frequency DW modes with the same number of nodes but different localizations and frequencies exist, which prevents the use of a mode indexation with independent quantization numbers. The effects of the size of the element and a longitudinal polarizing magnetic field on the DW spectrum are then analyzed. In particular, the softening of the fundamental DW mode is evidenced at the first-order phase transitions between the bubble state and the saturated states. These numerical findings are discussed in light of theoretical models.

Dispersion of collective magnonic modes in stacks of nanoscale magnetic elements

We report a numerical study of the dispersion of collective magnonic modes in magnonic crystals formed by stacks of magnetostatically coupled magnetic nanoelements. The calculations reveal that the sign of the magnonic dispersion is determined by the spatial character and ellipticity of precession for the eigenmodes of the isolated elements that give rise to the magnonic bands. We identify a critical value of the ellipticity at which the dispersion of the collective magnonic modes changes sign. The critical value is independent of the magnetic parameters and shape of the elements but is a characteristic of their arrangement (superstructure).

짧은 전류 펄스를 이용한 전류 유도 자화 반전에서 에너지 장벽 분포의 효과

본 논문에서는 짧은 전류 펄스를 이용한 미소자기 소자에서의 전류 유도 자화 반전에 대한 매크로 스핀 시뮬레이션 연구를 수행하였다. 자화 반전 전류 분포에 있어서 에너지 장벽이 미치는 효과에 특별히 주목하였다. 자화 반전 전류의 크기 및 분포는 전류 펄스 폭의 감소에 따라 증가했다. 여기서 긴 전류 펄스 폭 영역에서는 에너지 장벽과 자화 반전 전류 분포 사이의 관계가 아레니우스-닐 법칙에 의해 서술된다. 하지만 짧은 전류 펄스 폭의 영역에서는 이 관계가 풀리지 않은 채로 남아있다. 이는 짧은 전류 펄스로 인한 자화 반전이 열적 활성화에 의해서가 아닌 세차 운동에 의해 좌우되기 때문이며, 이를 해결하는 데에 있어서 어려움이 발생한다. 그러므로 포커-플랑크 방정식을 풀어서 짧은 전류 펄스 영역에서의 자화 반전에 대한 정확한 공식을 얻어내는 것이 필요하며 이를 통해 짧은 전류 펄스 영역에서의 자화 반전 양상을 이해 할 수 있을 것으로 본다. We performed macro-spin simulation studies of the current-induced magnetization reversal of nanomagnetic elements with short current pulses. A special attention was paid to the effect of the energy barrier on the switching current distribution. The switching current and its distribution increase with decreasing the current pulse-width. The relationship between the energy barrier and switching current distribution is described by the Arrhenius-N<TEX>$\'{e}$</TEX>el law at a long pulse-width regime. At a regime of short pulse-width, however, the relationship is left unaddressed. The difficulty to address this issue arises because the magnetization switching with a short current pulse is governed not by the thermal activation but by the precession motion. Therefore, an exact formulation for the short pulse regime by solving the Fokker-Plank equation is needed to understand the result.

Collective magnonic modes of pairs of closely spaced magnetic nano-elements

We report upon a theoretical study of collective magnonic modes in pairs of magnetic nano-elements with quasi-uniform magnetization. The mode spectrum and character are numerically computed for an individual isolated nano-element and then used to analytically calculate the splitting of the modes due to the inter-element magneto-dipole interaction. The results are compared with those obtained using direct simulations for the pairs of elements, yielding a generally good agreement. For the edge mode the interaction between the edges of the neighboring elements can exceed that between the edges of the same element, leading to softening of the mode profile and hence to the violation of the assumptions of the analytical approach. The softening has to be taken into account in the interpretation of dynamical studies of closely packed arrays of magnetic elements (magnonic crystals).

Imaging Collective Magnonic Modes in 2D Arrays of Magnetic Nanoelements

We have used time resolved scanning Kerr microscopy to image collective spin wave modes within a 2D array of magnetic nanoelements. Long wavelength spin waves are confined within the array as if it was a continuous element of the same size but with effective material properties determined by the structure of the array and its constituent nanoelements. The array is an example of a magnonic metamaterial, the demonstration of which provides new opportunities within the emerging field of magnonics.

The influence of interfaces on the properties of magnetic nanoelements and wires

The influence of interfaces on the properties of magnetic nanoelements and wires

Magnetodipolar interlayer interaction effect on the magnetization dynamics of a trilayer square element with the Landau domain structure

We present a detailed numerical simulation study of the effects caused by the magnetodipolar interaction between ferromagnetic (FM) layers of a trilayer magnetic nanoelement on its magnetization dynamics. As an example, we use a Co∕Cu∕Ni80Fe20 element with a square lateral shape where the magnetization of FM layers forms a closed Landau-like domain pattern. First, we show that when the thickness of the nonmagnetic (NM) spacer is in the technology relevant region h∼10nm, magnetodipolar interaction between 90° Neel domain walls in FM layers qualitatively changes the equilibrium magnetization state of these layers. In the main part of the paper, we compare the magnetization dynamics induced by a sub-nsec field pulse in a single-layer Ni80Fe20 (Py) element and in the Co∕Cu∕Py trilayer element. Here, we show that (i) due to the spontaneous symmetry breaking of the Landau state in the FM/NM/FM trilayer, its domains and domain walls oscillate with different frequencies and have different spatial oscillation patterns; (ii) magnetization oscillations of the trilayer domains are strongly suppressed due to different oscillation frequencies of domains in Co and Py; (iii) magnetization dynamics qualitatively depends on the relative rotation sense of magnetization states in Co and Py layers and on the magnetocrystalline anisotropy kind of Co crystallites. Finally, we discuss the relation of our findings with experimental observations of magnetization dynamics in magnetic trilayers, performed using the element-specific time-resolved x-ray microscopy.

Tunable magnetic landscape

By using micro-magnetic simulations we demonstrate how the shape of magnetic nano-elements affects the out-of-plane component of the magnetization in magnetic dots and rings. We show that by removing the highly energetic out-of-plane magnetic vortex core we fundamentally alter the magnetic states in nanomagnets. In addition, we explore the nucleation and annihilation of the domain walls as a function of external magnetic field. We demonstrate that the annihilation of the domain walls lead to formation of the vortex state in magnetic ring structures.

Patterning of permalloy thin films by means of electron-beam lithography and focused ion-beam milling

Focused ion-beam milling has been employed to structure magnetic nanoelements from 20 nm thick films of permalloy (Ni 81Fe 19). Rectangles are patterned into permalloy thin films grown on Si substrates by means of electron-beam lithography and focused ion-beam (FIB) milling down to 100 nm dimensions. In this study, we analyse the effect of the FIB milling parameters (ion current, spot size, dose) on the resulting magnetic domain structures. The ion currents have been varied between 10 pA and 10 000 pA; the dose of the ion beam used for milling was varied in order to achieve the best definition for the milled areas. The resulting edges of the permalloy structures are characterized by means of AFM. We find that a small ion dose does not affect the resulting magnetic domain patterns in the structures, so FIB milling can be applied to create high-quality permalloy nanostructures.

Reliable low-power control of ultrafast vortex-core switching with the selectivity in an array of vortex states by in-plane circular-rotational magnetic fields and spin-polarized currents

The authors investigated the technological utility of counterclockwise (CCW) and clockwise (CW) circular-rotating fields (HCCW and HCW) and spin-polarized currents with an angular frequency ωH close to the vortex eigenfrequency ωD, for the reliable, low-power, and selective switching of the bistate magnetization (M) orientations of a vortex core (VC) in an array of soft magnetic nanoelements. CCW and CW circular gyrotropic motions in response to HCCW and HCW, respectively, show remarkably contrasting resonant behaviors, (i.e., extremely large-amplitude resonance versus small-amplitude nonresonance), depending on the M orientation of a given VC. Owing to this asymmetric resonance characteristics, the HCCW(HCW) with ωH∼ωD can be used to effectively switch only the up (down) core to its downward (upward) M orientation, selectively, by sufficiently low field (∼10Oe) and current density (∼107A∕cm2). This work provides a reliable, low power, effective means of information storage, information recording, and information readout in vortex-based random access memory, simply called VRAM.

Micro-Brillouin Light Scattering Spectroscopy of Magnetic Nanostructures

We describe a new technique, micro-Brillouin light scattering spectroscopy, for investigation of spin wave dynamics in magnetic nanostructures. The technique offers advantages for studies of small magnetic squares with closure domain structure and magnetic nanoelements similar to those used in magnetic random access memory. The technique is particularly effective in two-dimensional mapping of spin waves excited by a single nanocontact due to the spin torque transfer effect.