Angle Dependent Ferromagnetic Resonance Research Articles

Giant anisotropic Gilbert damping and spin wave propagations in single-crystal magnetic insulator

Gilbert damping in magnetic systems describes the relaxation of magnetization. This term was phenomenologically introduced into the Landau–Lifschitz–Gilbert (LLG) equation to describe spin dynamics. In most studies, such as magnetic random access memory, spin-wave propagations, and microwave devices, it has been assumed that the Gilbert damping is an isotropic constant. In this study, we uncover a giant anisotropic Gilbert damping parameter of up to 431% in single-crystal thin films of epitaxial [100]-oriented yttrium iron garnet (YIG) using angle-dependent ferromagnetic resonance. In contrast, the Gilbert damping parameter of a [111]-oriented YIG film is almost isotropic. The observed anisotropic damping is shown to have a similar fourfold symmetry with magneto-crystalline anisotropy. The anisotropic spin-wave group velocity (vg), relaxation time (τ), and decay length (ld) were also experimentally evaluated through spin-wave spectra of [100]-oriented YIG thin film. We developed the LLG equation with the introduction of an anisotropic orbital Gilbert damping term. This anisotropic orbital damping originates from the crystal-field dominated anisotropic spin–orbit coupling and orbital-related magnon–phonon coupling. Our results extend the understanding of the mechanism of anisotropic Gilbert damping in single-crystal magnetic insulators with strong magneto-crystalline anisotropy.

Field angle dependent resonant dynamics of artificial spin ice lattices

Artificial spin ice structures which are networks of coupled nanomagnets arranged on different lattices that exhibit a number of interesting phenomena are promising for future information processing. We report reconfigurable microwave properties in artificial spin ice structures with three different lattice symmetries namely square, kagome, and triangle. Magnetization dynamics are systematically investigated using field angle dependent ferromagnetic resonance spectroscopy. Two distinct ferromagnetic resonance modes are observed in square spin ice structures in contrast with the three well-separated modes in kagome and triangular spin ice structures that are spatially localized at the center of the individual nanomagnets. A simple rotation of the sample placed in magnetic field results in the merging and splitting of the modes due to the different orientations of the nanomagnets with respect to the applied magnetic field. Magnetostatic interactions are found to shift the mode positions after comparing the microwave responses from the array of nanomagnets with control simulations with isolated nanomagnets. Moreover, the extent of the mode splitting has been studied by varying the thickness of the lattice structures. The results have potential implications for microwave filter-type applications which can be operated for a wide range of frequencies with ease of tunability.

Nanometer-Thick Yttrium Iron Garnet Films with Perpendicular Anisotropy and Low Damping

${\mathrm{Y}}_{3}{\mathrm{Fe}}_{5}{\mathrm{O}}_{12}$ ($\mathrm{YIG}$) thin films having a thickness of several nanometers and showing both strong perpendicular magnetic anisotropy (PMA) and low magnetic damping are reported. The films are deposited by magnetron sputtering at room temperature first and then annealed in ${\mathrm{O}}_{2}$ at high temperature. The substrates are ${\mathrm{Gd}}_{3}({\mathrm{Sc}}_{2}{\mathrm{Ga}}_{3}){\mathrm{O}}_{12}$, which share the same crystalline structure as $\mathrm{YIG}$, but have a lattice constant slightly larger than that of $\mathrm{YIG}$; the lattice mismatching gives rise to an out-of-plane compressive strain and PMA in the $\mathrm{YIG}$ films. The PMA is confirmed by vibrating sample magnetometer, magneto-optical Kerr effect, anomalous Hall effect, and angle-dependent ferromagnetic resonance (FMR) measurements. The damping of the films is analyzed through frequency-dependent FMR measurements. As an example, an 8-nm-thick $\mathrm{YIG}$ film shows an effective PMA field of about 2800 Oe, a nearly square hysteresis loop, and a damping constant of only $4.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$. As an illustration of possible applications of such films in spintronic devices, current-induced switching of the magnetization of the PMA $\mathrm{YIG}$ films is demonstrated by the use of $\mathrm{YIG}$/$\mathrm{Pt}$ bilayered Hall bar devices.

Unidirectional and uniaxial anisotropies in the MnN/CoFeB exchange bias system

Abstract We report on broadband and in-plane angle dependent ferromagnetic resonance measurements of MnN (30 nm)/CoFeB ( t CoFeB ) exchange bias bilayer systems with CoFeB thicknesses ranging from 5 to 20 nm. We find that the strong unidirectional anisotropy in this system is accompanied by a strong uniaxial in-plane anisotropy and a small interfacial perpendicular anisotropy ( K ⊥ , i = 0.043 ± 0.001 erg / cm 2 ). The strength of the interfacial exchange bias coupling in this system Δ σ eb = 0.193 ± 0.005 erg / cm 2 is only 2.5 times larger than the interfacial uniaxial coupling strength Δ σ u = 0.076 ± 0.003 erg / cm 2 . The relaxation in this system also shows a strong unidirectional and uniaxial in-plane anisotropy. While the observed thickness dependence of the uniaxial anisotropy of the relaxation is consistent with an interfacial two-magnon scattering contribution, we find that this is not the case for the unidirectional relaxation.

Study of anisotropy, magnetization reversal and damping in ultrathin Co films on MgO (0 0 1) substrate

Ultrathin Co films of 3nm thickness have been prepared on MgO (001) substrate in presence or absence of substrate pre-annealing. Uniaxial anisotropy is induced in the samples due to the deposition under oblique angle of incidence. Along with the oblique deposition induced anisotropy, another uniaxial anisotropy contribution has been observed due to pre-annealing. However, no cubic anisotropy has been observed here as compared to the thicker films. Angle dependent ferromagnetic resonance (FMR) measurement confirms the presence of two anisotropies in the pre-annealed sample with ∼18° misalignment with each other. The two anisotropy constants were calculated from both superconducting quantum interference device (SQUID) magnetometry and FMR spectroscopy. The magnetization reversal is governed by nucleation dominated aftereffect followed by domain wall motion for the pre-annealed sample. Branched domains are observed for the sample prepared without pre-annealing which indicates grain disorientation of Co. However, in the thicker (25nm) Co films ripple domains were observed in contrary to ultrathin (3nm) films.

Effects of field annealing on Gilbert damping of polycrystalline CoFe thin films

The effects of annealing and magnetic field annealing on the Gilbert damping constant of polycrystalline CoFe thin films were investigated. Angle dependent ferromagnetic resonance (FMR) demonstrates that an in-plane (IP) anisotropy is developed by field annealing which dramatically reduces the effective Gilbert damping constant. An inverse relation between effective IP anisotropic field and effective damping is shown by FMR measurement in cryogenic environment. This relation is further confirmed in bilayer films of IrMn/CoFe where a strong in-plane unidirectional anisotropy is developed. A large effective IP anisotropic field is possibly associated with a smaller distribution of local fields which reduces the FMR linewidths and subsequently effective damping.

Magnetic anisotropy and relaxation of single Fe/FexOy core/shell- nanocubes: A ferromagnetic resonance investigation

In this work a full angle dependent Ferromagnetic Resonance (FMR) investigation on a system of 20 separated Fe/FexOy nanocubes without dipolar coupling is reported. The angular magnetic field dependence of FMR spectra of 20 single particles and 2 dimers were recorded using a microresonator setup with a sensitivity of 106 μB at X-band frequencies. We determine an effective magnetocrystalline anisotropy field of 2K4,eff/M = 50 mT ± 5 mT for selected particles, which is smaller than the one of bulk Fe due to the core shell morphology of the particles. The FMR resonances have a linewidth of 4 mT ± 1 mT, corresponding to a magnetic effective damping parameter α = 0.0045 ± 0.0005 matching the values of high quality iron thin films. Numerical calculations taking into account the different angular orientations of the 24 particles with respect to the external magnetic field yield a good agreement to the experiment.

Ferromagnetic resonance measurements of GaP epilayers with embedded MnP nanoclusters grown on GaP(001)

The relation between crystallographic texture and magnetic properties of GaP epilayers with embedded MnP nanoclusters grown by metal-organic vapor phase epitaxy is investigated with angle-dependent ferromagnetic resonance (FMR) measurements. A systematic methodology entirely based on magnetic characterization identifies all the crystallographic orientations of the MnP nanoclusters relative to the GaP matrix as well as the volume fraction of MnP in each orientation. For all 18 crystallographic orientations of the MnP nanoclusters that were determined for samples grown at 650 ◦C, the MnP c axis is oriented along GaP 〈110〉. Our approach also reveals that approximately 90% of the clusters have their b axis oriented along GaP 〈111〉, while the remaining clusters have their b axis oriented along GaP 〈100〉. In addition, FMR indicates that the ratio of the anisotropy field along the intermediate magnetic axis over that of the hard magnetic axis of the embedded MnP clusters is increased by more than 20% compared to bulk MnP. Calculations suggest that a magnetoelastic and/or a surface contribution to the magnetic anisotropy of the nanoclusters is required to explain the observed difference. The methodology presented in this work is particularly suited for semiconducting epilayers with embedded nanomagnets but could be easily applied to other similar systems.

Evolution of ferromagnetic and spin-wave resonances with crystalline order in thin films of full-Heusler alloy Co2MnSi

We report the evolution of magnetic moment as well as magnetic anisotropy with crystalline order in Co2MnSi thin films grown on (100) MgO by pulsed laser deposition. The films become more ordered as the annealing temperature (TA) increases from 400 to 600 °C. The extent of L21 ordering in the films annealed at 600 °C is ≈96%. The static magnetization measurements by vibrating sample magnetometry shows a maximum moment of 4.95 μB per formula unit with low coercivity (HC ≈ 65 Oe) in the films annealed at 600 °C. A rigorous analysis of the azimuthal and polar angle dependent ferromagnetic resonance (FMR) measured at several temperatures allows determination of various anisotropy fields relevant to our system as a function of TA. Finally, we have evaluated the exchange stiffness constant down to 100 K using spin wave modes in FMR spectra. We have also estimated the exchange energies as well as stiffness constant by ab initio calculations using the Korringa-Kohn-Rostoker method.

Magnetostrictive effect in single crystal Fe1−xGax thin films

The magnetic properties of single crystal Fe1−xGax thin films deposited on ZnSe/GaAs(001) and MgO(001) substrates by molecular beam epitaxy were investigated by vibrating sample magnetometry and angle dependent ferromagnetic resonance. Depositions on the ZnSe buffer layer feature a strong uniaxial anisotropy that scales with the thin film magnetostriction of the samples, while depositions on MgO(001) substrates result in a purely cubic anisotropy whose cubic anisotropy constant, K1, switches sign at a lower Ga concentration than is seen in bulk.

Adjusting the magnetic properties of semiconductor epilayers by the crystallographic orientation of embedded highly anisotropic magnetic nanoclusters

GaP:MnP samples, which consist of GaP(001) epilayers with embedded MnP nanoclusters occupying approximately 7% of the epilayer volume, were grown at three different substrate temperatures (600, 650, and 700 °C) using metal-organic vapor phase epitaxy. Angle dependent ferromagnetic resonance (FMR) spectroscopy indicates that, in all samples, MnP clusters are crystallographically oriented along specific GaP directions and possess high magnetic anisotropy fields. FMR results also suggest that the growth temperature significantly modifies the distribution of clusters among the possible orientations. This is verified from the measured angular dependence of the remanent magnetization, which shows a different crystallographic orientation of the GaP:MnP effective magnetic easy axis for each growth temperature. Modeling of the remanent magnetization allowed the determination of the relative volume fraction of clusters corresponding to each MnP c-axis orientation at a given growth temperature. These results support our assumption that the clusters are monodomains and suggest that the growth temperature could eventually be used to adjust the magnetic properties of these GaP:MnP structures.

Magnetic anisotropy in GaP(001) epilayers containing MnP nanoclusters observed by angle dependent ferromagnetic resonance measurements

We report on the angular dependence of ferromagnetic resonance (FMR) of GaP(001) epilayers with embedded MnP nanoclusters (GaP:MnP) grown on a GaP(001) substrate using metal-organic vapor phase epitaxy (MOVPE). Angle dependent FMR spectra obtained at 292K show several peaks and indicate a strong magnetic anisotropy. The measured angular dependence of resonance fields can be modeled assuming that the MnP clusters possess a strong biaxial magnetocrystalline anisotropy whose axes are oriented along specific GaP crystallographic directions. Dominant populations of MnP clusters have their b-axis along GaP [111] and [111¯] directions, while a smaller population has the b-axis along the GaP [001] direction. In comparison, angle dependent FMR spectra of a polycrystalline MnP thin film grown on a GaP(001) substrate using MOVPE suggest that the crystals b-axis is oriented favorably along the GaP [001] direction.

Spin dynamics in ferromagnets: Gilbert damping and two-magnon scattering

The magnetic relaxation processes following the dynamical excitation of the spin system of ferromagnets are investigated by ferromagnetic resonance (FMR) between 1 and $70\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}$ using epitaxial ${\mathrm{Fe}}_{3}\mathrm{Si}$ films as a prototype system. Two relaxation channels, i.e., dissipative, isotropic Gilbert damping $G$ as well as anisotropic two-magnon scattering $\ensuremath{\Gamma}$, are simultaneously identified by frequency and angle dependent FMR and quantitatively analyzed. The scattering rates due to two-magnon scattering at crystallographic defects for spin waves propagating in ⟨100⟩ and ⟨110⟩ directions, $\ensuremath{\gamma}{\ensuremath{\Gamma}}_{⟨100⟩}=0.25(2)\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}$ and $\ensuremath{\gamma}{\ensuremath{\Gamma}}_{⟨110⟩}=0.04(2)\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}$, and the Gilbert damping term $G=0.051(1)\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}$ are determined. We show that changing the film thickness from $8\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}40\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ and slightly modifying the Fe concentration influence the relaxation channels. Our results, which reveal the contributions of longitudinal and transverse relaxation processes may be of general importance for the understanding of spin-wave dynamics in magnetic structures.

Strong uniaxial anisotropies of iron grown on UHV cleaved InAs(110) investigated by correlated scanning tunneling microscopy and ferromagnetic resonance

The magnetic properties of iron films grown under UHV condition are governed by the deposition condition and the substrate preparation. One way of producing almost perfect surface conditions with large terrace width and exact orientation is cleaving. With this method no additional cleaning process of the surface is needed. Here we present our investigations of iron films (thickness: 0.1–30nm) grown on UHV cleaved InAs substrates using in situ scanning tunnel microscopy (STM) investigations combined with in situ magneto-optical Kerr effect (MOKE) and ex situ angle and frequency dependent conventional ferromagnetic resonance (FMR). The (110) InAs surface allows the investigation of three magnetic axes: in-plane easy (001), hard (111), and intermediate (110) axes of the iron layer. The (110) symmetry of the magnetic cubic crystalline anisotropy should lead to angles of 110° and 70° between the hard axes, respectively. STM images of the clean InAs(110) show 500nm wide terraces with mono atomic steps predominately oriented parallel to the (001) direction. MOKE hysteresis loops were measured during the Fe deposition to prove the ferromagnetic state. The angle dependent in-plane FMR measurement revealed unexpected 90° symmetry. Deducing the anisotropy constants from the FMR resonance position, one finds a slightly increased bulk crystalline anisotropy and a uniaxial anisotropy of the same order of magnitude. This strong uniaxial anisotropy distorts the 110° symmetry to 90° symmetry. The correlation of frequency and angle dependent FMR and STM measurements evidences that the uniaxial anisotropy is due to the dislocations caused by the orientation of the terraces.

Anisotropic FMR-linewidth of triple-domain Fe layers on hexagonal GaN(0001)

We present a ferromagnetic resonance (FMR) study of Fe films with thicknesses between 5 and 70 nm prepared by electron-beam evaporation on top of hexagonal GaN(0001). X-ray diffraction (XRD) and low-energy electron diffraction (LEED) suggest the growth in crystallographic Fe(110) domains with three different orientations. The magnetic properties have been investigated by in-plane angle-dependent FMR at frequencies between 4.5 to 24 GHz. All samples show a hexagonal in-plane anisotropy with the easy axes oriented parallel to the Fe [001] directions. The anisotropy field strength of about 8 mT reveals a bulk-like thickness dependence. Therefore, we can exclude the following origins of anisotropy: (i) interface effects because of the bulk-like thickness dependence and (ii) averaged first order cubic or uniaxial anisotropies arising from the three grain orientations because of the relative strengths. We qualitatively explain the sixfold anisotropy by spin relaxation inside the grains. The FMR linewidth versus frequency curves are linear with almost no zero-frequency offset indicating a good homogeneity of the magnetic properties over the sample area. However, the effective damping parameter a shows pronounced anisotropy and thickness dependence, with enhanced damping along the hard axes and for thicker layers. We suggest that the additional damping can be explained by two-magnon scattering at defects which are due to the triple domain structure.