Micromagnetic modal analysis of spin-transfer-driven ferromagnetic resonance of individual nanomagnets (original) (raw)
Ferromagnetic Resonance Studies in Magnetic Nanosystems
Magnetochemistry
Ferromagnetic resonance is a powerful method for the study of all classes of magnetic materials. The experimental technique has been used for many decades and is based on the excitation of a magnetic spin system via a microwave (or rf) field. While earlier methods were based on the use of a microwave spectrometer, more recent developments have seen the widespread use of the vector network analyzer (VNA), which provides a more versatile measurement system at almost comparable sensitivity. While the former is based on a fixed frequency of excitation, the VNA enables frequency-dependent measurements, allowing more in-depth analysis. We have applied this technique to the study of nanostructured thin films or nanodots and coupled magnetic layer systems comprised of exchange-coupled ferromagnetic layers with in-plane and perpendicular magnetic anisotropies. In the first system, we have investigated the magnetization dynamics in Co/Ag bilayers and nanodots. In the second system, we have st...
Journal of Applied Physics, 2008
A full micromagnetic study of the spin-transfer-driven self-oscillations of individual ellipsoidal PyCu nanomagnets as small as 30ϫ 90ϫ 5.5 nm 3 is presented. The magnetic parameters have been computed by fitting static magnetoresistance measurements. The main mode found in the experiments by Sankey et al. ͓Phys. Rev. Lett. 96, 227601 ͑2006͔͒ is analyzed. The full width at half maximum is calculated without taking into account the effect of thermal activation. The full width is found to decrease from 6.5 to 3.3 MHz when increasing the current in the self-oscillation region. These narrow widths are mainly produced by the nonuniformities of the magnetization and since they are computed at zero temperature mark a limit for the spectral purity of the self-oscillations in those nanomagnets.
Micromagnetic study of spin-transfer driven ferromagnetic resonance: Equivalent circuit
Journal of Applied Physics, 2009
Micromagnetic computations are used to describe spin-transfer driven ferromagnetic resonance in a nanopillar spin-valve with elliptical cross section. Nonuniform magnetization resonance is found. With the aim of describing the resonance phenomena, an equivalent electrical circuit is proposed, and its electrical parameters are deduced from micromagnetic simulations. Comparisons of spin-torque nano-oscillators with conventional voltage-controlled oscillators are also provided.
Ferromagnetic Resonance in Nanometric Magnetic Systems
Encyclopedia of Materials: Science and Technology, 2008
Nanometric magnetic systems are of growing importance, displaying novel magnetic properties which are of both fundamental scientific interest as well as of practical importance. There are several types of system which can be classified as nanometric, which depend on the fabrication process, for example, amorphous / nanocrystalline alloys, immiscible alloys (e. g. Co -Cu), nanostructured films and discontinuous multilayer systems. In whatever case, magnetic confinement effects and the interactions between magnetic particles, via an intervening phase, give rise to the particular magnetic behaviour and properties of the system in question. Ferromagnetic resonance (FMR) is a powerful technique for the study of magnetic properties and has been applied to many different types of magnetic system. FMR essentially measures the internal effective field to which a spin system is subject and as such can reveal useful information on fundamental magnetic properties such as the g -factor, magnetisation, magnetocrystalline anisotropies and shape effects. In the present paper we present experimental results of FMR studies of FeZrCuB amorphous/nanocrystalline alloy, FeAl cluster systems and the discontinuous multilayer system Al 2 O 3 [CoFe(t)/Al 2 O 3 ] 10 , where t is the effective thickness, ranging from 7 to 13 Å.
Magnetic anisotropy in nanoscaled materials probed by ferromagnetic resonance
Phase Transitions, 2006
Ferromagnetic resonance measurements probe the dynamical response of magnetic systems due to an excitation within the microwave regime. Offering high sensitivity and energy resolution in the meV range of ferromagnetic resonance this technique is well suited for the investigation of magnetic anisotropy in nanoscale systems. Ferromagnetic Resonance experiments give direct and quantitative access to magnetic anisotropy based on an analysis that uses the Landau-Lifshitz equation of motion. This will be demonstrated for the case of ultrathin magnetic 5-20ML thick Fe films on {4 Â 6}GaAs(001) (2D system) which have been grown and measured in situ in ultra high vacuum, magnetic MnAs stripes (1D system) grown on GaAs(001) as well as for arrays of highly monodisperse FePt nanoparticles (quasi 0D system).
Element-Specific Detection of Sub-Nanosecond Spin-Transfer Torque in a Nanomagnet Ensemble
Spin currents can exert spin-transfer torques on magnetic systems even in the limit of vanishingly small net magnetization, as is the case for antiferromagnets. Here, we experimentally show that a spin-transfer torque is operative in a material with weak, shortrange magnetic ordernamely, a macroscopic ensemble of superparamagnetic-like Co nanomagnets. We employ element-and time-resolved X-ray ferromagnetic resonance (XFMR) spectroscopy to directly detect sub-ns dynamics of the Co nanomagnets, excited into precession with cone angle ≥0.003 o by an oscillating spin current. XFMR measurements reveal that as the net moment of the ensemble decreases, the strength of the spin-transfer torque increases relative to those of magnetic field torques. Our findings point to spin-transfer torque as an effective way to manipulate the state of nanomagnet ensembles at sub-ns timescales. A flow of spin angular momentum, or spin current, injected into a thin-film magnetic medium can exert a spin-transfer torque (STT) on the magnetization 1-3. STT enables a variety of scalable and energy-efficient nanoscale ferromagnetic devices for computing and communications applications 4-7. Furthermore, STT can efficiently rotate the magnetic order of materials with zero net moment. For instance, STT (in particular, spin-orbit torque) allows for Néel vector switching 8,9 and auto-oscillations 10,11 in antiferromagnets. STT therefore may permit nanoscale information-technology devices based on antiferromagnets, which are insensitive to stray magnetic fields (e.g., of up to ~10 T) due to the strong inter-sublattice exchange coupling. The net magnetization also averages to zero in a thermally disordered ensemble of weakly interacting ferromagnetic or superparamagnetic nanoparticles (e.g., often used in biomedical applications 12), particularly in the absence of an applied magnetic field. These nanomagnets are not exchange-coupled to each other, such that a large fraction of the
Spin-wave spectroscopy of individual ferromagnetic nanodisks
Nanoscale
An original spatially resolved approach is demonstrated for spin-wave spectroscopy of individual circular magnetic elements. It allows for the deduction of the saturation magnetization and the exchange stiffness of the material with high precision.
Angular dependent ferromagnetic resonance analysis in a single micron sized cobalt stripe
Journal of Applied Physics, 2014
We demonstrate how planar microresonators (PMRs) can be utilized to investigate the angular dependent magnetic resonance response of single magnetic nanostructures. In contrast to alternative detection schemes like electrical or optical detection, the PMR approach provides a classical means of investigating the high frequency dynamics of single magnetic entities, enabling the use of well-established analysis methods of ferromagnetic resonance (FMR) spectroscopy. To demonstrate the performance of the PMR-based FMR setup for angular dependent measurements, we investigate the microwave excited magnons in a single Co stripe of 5 Â 1 Â 0.02 lm 3 and compare the results to micromagnetic simulations. The evolution of excited magnons under rotation of one individual stripe with respect to a static magnetic field is investigated. Besides quasi uniform excitations, we observe magneto-static as well as localized excitations. We find a strong influence of inhomogeneous dynamic and static demagnetizing fields for all modes. V
Coupling of spin-transfer torque to microwave magnetic field: A micromagnetic modal analysis
Journal of Applied Physics, 2007
Micromagnetic computational spectral mapping technique is applied to analyze the magnetic oscillation modes excited by either a microwave circularly polarized magnetic field or a spin polarized current flowing through Permalloy ͑Py͒ spin valves. A complete study has been carried out on multilayers Py͑10 nm͒ /Cu͑5 nm͒ /Py͑2.5 nm͒ with rectangular cross section ͑60ϫ 20 nm 2 ͒. The magnetic normal modes obtained agree with recent analytical spin wave models in patterned nanostructures. When both excitations, microwave field and spin polarized current, are applied at the same time a complex coupling process is observed. The detailed micromagnetic analysis of the coupling shows three different stages: ͑i͒ The initial stage in which the magnetic normal modes are dominant, ͑ii͒ an intermediate stage showing an incoherent behavior, and ͑iii͒ the final stage where a persistent domain wall oscillation is present. Micromagnetic spectral mapping technique is shown to be an adequate tool for describing the temporal evolution of the magnetization spatial patterns in nanostructures.
Physical Review B, 2018
We develop an analytical approach for studying the FMR frequency shift due to dipolar interactions and surface effects in two-dimensional arrays of nanomagnets with (effective) uniaxial anisotropy along the magnetic field. For this we build a general formalism on the basis of perturbation theory that applies to dilute assemblies but which goes beyond the point-dipole approximation as it takes account of the size and shape of the nano-elements, in addition to their separation and spatial arrangement. The contribution to the frequency shift due to the shape and size of the nanoelements has been obtained in terms of their aspect ratio, their separation and the lattice geometry. We have also varied the size of the array itself and compared the results with a semi-analytical model and reached an agreement that improves as the size of the array increases. We find that the red-shift of the ferromagnetic resonance due to dipolar interactions decreases for smaller arrays. Surface effects may induce either a blue-shift or a red-shift of the FMR frequency, depending on the crystal and magnetic properties of the nano-elements themselves. In particular, some configurations of the nano-elements assemblies may lead to a full compensation between surface effects and dipole interactions.
Visualization of spin dynamics in single nanosized magnetic elements
Nanotechnology, 2011
The design of future spintronic devices requires a quantitative understanding of the microscopic linear and nonlinear spin relaxation processes governing the magnetization reversal in nanometer-scale ferromagnetic systems. Ferromagnetic resonance is the method of choice for a quantitative analysis of relaxation rates, magnetic anisotropy and susceptibility in a single experiment. The approach offers the possibility of coherent control and manipulation of nanoscaled structures by microwave irradiation. Here, we analyze the different excitation modes in a single nanometer-sized ferromagnetic stripe. Measurements are performed using a microresonator setup which offers a sensitivity to quantitatively analyze the dynamic and static magnetic properties of single nanomagnets with volumes of (100 nm) 3. Uniform as well as non-uniform volume modes of the spin wave excitation spectrum are identified and found to be in excellent agreement with the results of micromagnetic simulations which allow the visualization of the spatial distribution of these modes in the nanostructures.
Comparison of frequency, field, and time domain ferromagnetic resonance methods
Journal of Magnetism and Magnetic Materials, 2006
We present vector network analyzer ferromagnetic resonance measurements of epitaxial Fe films having a thickness of 16 monolayers. Our objective is to test the reliability of this novel frequency domain technique with respect to frequency and damping. For this purpose we compare vector network analyzer ferromagnetic resonance to pulsed inductive microwave magnetometry, time resolved magnetooptic Kerr effect (both methods in the time domain), and conventional ferromagnetic resonance (measured in the field domain) in terms of position and width of the ferromagnetic resonance. In addition, we compare the various techniques with respect to the signal to noise ratio of the raw data. All data is obtained using the same well characterized ultrathin magnetic Fe/GaAs (0 0 1) film. Finally, we demonstrate the potential of the vector network analyzer ferromagnetic resonance technique for the investigation of nano-structured magnetic elements having nonuniform magnetization configuration. The absorption spectrum of Permalloy disks with a diameter of 200 nm and a thickness of 15 nm shows up to eight distinct resonance peaks. The spatial structure of the corresponding modes was derived from numerical calculations and reveals that azimuthal modes up to the fifth order have been observed inductively.
This work provides a detailed investigation of the measured in-plane field-swept homodyne-detected ferromagnetic resonance (FMR) spectra of an extended Co/Cu/NiFe pseudo-spin-valve stack using a nanocontact (NC) geometry. The magnetodynamics are generated by a pulse-modulated microwave current, and the resulting rectified dc mixing voltage, which appears across the NC at resonance, is detected using a lock-in amplifier. Most notably, we find that the measured spectra of the NiFe layer are composite in nature and highly asymmetric, consistent with the broadband excitation of multiple modes. Additionally, the data must be fit with two Lorentzian functions in order to extract a reasonable value for the Gilbert damping of the NiFe. Aided by micromagnetic simulations, we conclude that (i) for in-plane fields the rf Oersted field in the vicinity of the NC plays the dominant role in generating the observed spectra, (ii) in addition to the FMR mode, exchange-dominated spin waves are also generated, and (iii) the NC diameter sets the mean wave vector of the exchange-dominated spin wave, in good agreement with the dispersion relation.
An analytical study of the spectral line shape of ferromagnetic resonance (FMR) detected by spin rectification effect and driven by the combined action of spin-transfer torque (STT) and voltage-controlled magnetic anisotropy (VCMA) is developed. The system under consideration consists of a magnetic tunnel junction (MTJ). Explicit expressions for the symmetric and asymmetric components of the rectified voltage are derived, where the role of the VCMA, in-plane STT, and field-like torque is clearly identified and discussed. Typical geometrical configurations are particularly analyzed and compared with recent experimental results. The analytical findings show that the change of sign in the FMR response upon reversal of the magnetization is completely due to VCMA. By distinguishing in-plane, out-of-plane, and full magnetization reversal processes, it is shown that the VCMA induces a change of sign in the symmetric part for the in-plane and out-of-plane magnetization reversal, while the asymmetric part change its sign under a full and in-plane reversion of the magnetization. Explicit expressions of the symmetric and asymmetric contributions of the spectral line shape allow us to detect under what conditions the STT and VCMA can increase or decrease the FMR spectral line shape. The proposed theory allows access to a better understanding of the physics behind ferromagnetic resonance phenomena, promoting potential applications in STT+VCMA-based MTJs.
Magnetic susceptibility measurements as a probe of spin transfer driven magnetization dynamics
Applied Physics Letters, 2010
An experimental technique has been developed to characterize spin-transfer driven magnetization dynamics. It was tested on a nanopillar spin valve with perpendicular anisotropy by measuring the nanopillar voltage under ac injected current ͑dV / dI͒, and ac magnetic field ͑dV / dH͒. Both the amplitude and the sign of the signals are different which reveals the different influences of the current and the field on the magnetization dynamics. Comparison between experiments and macrospin simulation shows that dV / dH measurements reveal the presence of a "canted state" demonstrating that dV / dH and dV / dI measurements are complementary techniques to probe magnetic states and their dynamics.
Applied Physics Letters, 2006
We demonstrate on-chip resonant driving of large cone-angle magnetization precession of an individual nanoscale permalloy element. Strong driving is realized by locating the element in close proximity to the shorted end of a coplanar strip waveguide, which generates a microwave magnetic field. We used a microwave frequency modulation method to accurately measure resonant changes of the dc anisotropic magnetoresistance. Precession cone angles up to 9 0 are determined with better than one degree of resolution. The resonance peak shape is well-described by the Landau-Lifshitz-Gilbert equation.
Electrically detected ferromagnetic resonance
Applied Physics Letters, 2007
We study the magnetoresistance properties of thin ferromagnetic CrO 2 and Fe 3 O 4 films under microwave irradiation. Both the sheet resistance and the Hall voltage V Hall characteristically change when a ferromagnetic resonance ͑FMR͒ occurs in the film. The electrically detected ferromagnetic resonance ͑EDFMR͒ signals closely match the conventional FMR, measured simultaneously, in both resonance fields and line shapes. The sign and the magnitude of the resonant changes ⌬ / and ⌬V Hall / V Hall can be consistently described in terms of a Joule heating effect. Bolometric EDFMR thus is a powerful tool for the investigation of magnetic anisotropy and magnetoresistive phenomena in ferromagnetic micro-or nanostructures.
Study of magnetic correlations in nanostructured ferromagnets by correlation magnetometry
Journal of Experimental and Theoretical Physics Letters, 2003
We propose a theoretically justified experimental magnetometric technique for determining the size of stochastic domains spontaneously formed in the spin system of nanostructured ferromagnets and for evaluating the effective anisotropy in these magnetically correlated regions. The method is based on monitoring the ∆ M ~ H-2 relationship in the low-field part of the integral magnetization curve.
2012
We analyze the effects of lateral device size and magnetic material parameters on the ferromagnetic resonance (FMR) response. Results presented are directly relevant to widely used FMR experimental techniques for extracting magnetic parameters from thin films, the results of which are often assumed to carry over to corresponding nanometer-sized patterned devices. We show that there can be significant variation in the FMR response with device size, and that the extent of the variation depends on the magnetic material properties. This explains, for example, why different experiments along these lines have yielded different size-dependent trends from damping measurements. Observed trends with increasing size and different material parameters are explained through the evolution of three distinct eigen-modes, demonstrating the respective roles of demagnetization and exchange. It is also shown that there is a crossover of dominant eigen-modes in the response signal, accompanied by conjugating edge-type modes, leading to evident effects in measured linewidth and damping. Among the sizes considered, in higher saturation magnetization, we observe as much as a 40% increase in apparent damping, due solely to device size variation.