Effective Uniaxial Anisotropy Research Articles

Spin transfer torque and field driven 360° domain wall to bimeron conversion

In this work, using micromagnetic simulations we study the mechanism involved in the conversion of a 360° domain wall into stable pairs of bimeron (Q = +1) and antibimeron (Q = -1) in a ferromagnetic background when it is subjected to Zhang Li type of spin transfer torque. We show that the time scales associated with the conversion process can be significantly reduced by applying out of plane bias field. In particular, choosing a constant inclination angle and increasing the intensity of bias field aids in reducing the energy barrier required to stabilize the spin textures. Similarly, for a constant bias field intensity, varying the inclination angle between 0° to 40° reveals that the time required to stabilize the first bimeron is reduced by ∼ 3 ns. Further, tailoring the strength of in-plane current density as well as effective uniaxial anisotropy leads to faster conversion of domain wall to bimerons.

Magnetic anisotropy and ferromagnetic resonance in inhomogeneous demagnetizing fields near edges of thin magnetic films

Using local ferromagnetic resonance spectroscopy, we have studied the magnetic properties near edges of thin tangentially magnetized permalloy films, in which a well-defined uniaxial magnetic anisotropy was induced perpendicular to one of the edges. In the experiment, two samples with thicknesses of 90 and 300 nm and with slightly different compositions were examined. To explain the magnetization dynamics near edges, we propose a simple yet effective model of a film in the form of a rectangular prism, which yields the modified Kittel formula for the resonance frequency. In this formula, the locally averaged distance-dependent demagnetizing field that emerges near the edges is included as an additional uniaxial anisotropy term. The measurements reveal that at a certain distance from the edge, the resulting (apparent) anisotropy, determined from the angular dependencies of the resonance field, almost vanishes. Moreover, its easy axis reorients to become parallel to the edge. The model predictions agree well with these results, proving that the main resonance mode behavior near the film edges can be accurately described by introducing additional effective uniaxial anisotropy, provided the measuring area is relatively large. However, for the thick (300 nm) sample, additional precession modes are also observed. These modes distort the angular dependence of the main mode, thus demonstrating the limitations of the model.

Temperature-dependent magnetic properties of the room-temperature ferromagnetic Janus monolayer Fe2XY (X, Y = I, Br, Cl; X ≠ Y).

Excellent magnetic properties at room temperature are crucial for the application of ferromagnets in spintronic and topological quantum devices. Using first-principles calculations and atomistic spin model simulations, we investigate the temperature-dependent magnetic properties of the Janus monolayer Fe2XY (X, Y = I, Br, Cl; X ≠ Y), as well as the effects of different magnetic interactions within the next-nearest-neighbor shell on the Curie temperature (TC). A large isotropic exchange interaction between one Fe atom and its next-nearest-neighbor counterparts can significantly increase the TC, while an antisymmetric exchange interaction decreases it. More importantly, we employ the temperature rescaling method, which can obtain temperature-dependent magnetic properties quantitatively consistent with experimental values, and find that the effective uniaxial anisotropy constant and coercive field decrease with increasing temperature. Moreover, at room temperature, Fe2IY is a rectangular-loop magnetic material with a giant coercive field up to ∼8 T, demonstrating its potential for application in room-temperature memory devices. Our findings can advance the application of these Janus monolayers in room-temperature spintronic devices and through heat-assisted techniques.

Structural characterization and electronic properties of Ni/rubrene bilayers with alternative stacking sequences.

Recent progress in organic electronics has attracted interest due to their excellent characteristics that include photovoltaic, light emission, and semiconducting behaviours. Spin-induced properties play important roles in organic electronics, while introducing spin into an organic layer in which spin responses, such as a weak spin-orbital coupling and long spin-relaxation time, allows a variety of spintronic applications to be achieved. However, such spin responses are rapidly attenuated by misalignment in the electronic structure of hybrid structures. We report herein on the energy level diagrams of Ni/rubrene bilayers that can be tuned by an alternating stacking. The band edges of the highest occupied molecular orbital (HOMO) levels were determined to be 1.24 and 0.48 eV relative to the Fermi level for Ni/rubrene/Si and rubrene/Ni/Si bilayers, respectively. This raises a possibility of accumulating electric dipoles at the ferromagnetic/organic semiconductor (FM/OSC) interface, which would inhibit the transfer of spin in the OSC layer. This phenomenon is caused by the formation of a Schottky-like barrier in the rubrene/Ni heterostructures. According to the information about the band edges of the HOMO levels, schematic plots of the HOMO shift in the electronic structure of the bilayers are presented. Based on the lower value of the effective uniaxial anisotropy for Ni/rubrene/Si, the uniaxial anisotropy was suppressed compared to that of rubrene/Ni/Si. The characteristics of the formation of Schottky barriers at the FM/OSC interface have an impact on the temperature-dependent spin states in the bilayers.

Interface change of Pr-Fe-B thin films with different ferromagnetic compositions

The thin film structure of the Si3N4/Pr-Fe-B/Si3N4/glass substrate was fabricated by the sputtering process followed by an in-situ annealing process at 650 °C. The changes at the interface of magnetic layer/underlayer were investigated with simultaneous addition of Fe content in the range of 68.9 to 76.61 at.% during the sputtering process. With ferromagnetic properties and more reactive and movable capacity of Fe, the addition of Fe created significant changes in the crystal structure, surface morphology, microstructure, and magnetic properties in Pr-Fe-B thin films. X-ray diffraction results confirmed the presence of two Pr2Fe14B and Pr2Fe23B3 magnetic phases in the thin films. The surface morphology of the thin films observed through SEM pictures and AFM images showed the blossom phenomenon with various grain sizes and surface roughness, respectively. The microstructure of the thin films through HR-TEM pictures revealed the discernable change at the interface of the Pr-Fe-B layer/Si3N4 underlayer. The new Fe3Si underlayer formed different thicknesses at the interface corresponding to various Fe contents. The stacking of (100) and (010) planes of Pr2Fe14B phase with different d-spacings was observed at higher magnification of HR-TEM. Results of magnetic measurement showed that the thin film at 73.32 at.% Fe content had the better growth potential of perpendicular magnetic anisotropy (PMA) and obtained a higher coercivity of approximately 4.5 kOe. MFM images through magnetic domain observation showed that the thin films had the same magnetic domain pattern but varied in magnetic domain size. Analysis of saturation magnetization and effective uniaxial anisotropy of the thin films showed the contribution of the interface magnetic anisotropy (to the PMA with the value of Ki = 122.25 × 106 erg/m2.

Anomalous Hall Effect in Epitaxial Thin Films of the Hexagonal Heusler MnPtGa Noncollinear Hard Magnet

AbstractMaterials hosting noncollinear magnetic ordering and sizeable spin‐orbit coupling can manifest perpendicular magnetic anisotropy and a Berry curvature‐driven intrinsic anomalous Hall effect. In this work, the structural, magnetic, and magnetotransport properties of crystalline hexagonal Heusler MnPtGa epitaxial thin films are reported. The centrosymmetric MnPtGa films (P63/mmc space group) crystallize with a preferred c‐axis (0001) crystal orientation. Along this crystallographic direction, the MnPtGa films exhibit preferential perpendicular magnetic anisotropy, below the Curie temperature TC = 263 K, with a large effective uniaxial magnetic anisotropy Keff = 0.735 MJ m−3, at 150 K. In addition, the MnPtGa system undergoes a thermally induced spin reorientation transition below Tsr = 160 K, which marks the onset of a noncollinear spin‐canted state. The anomalous Hall conductivity (AHC) of MnPtGa films exhibits a nonmonotonic behavior as a function of temperature, which changes sign at T* = 110 K. Concurrently with the reported unusual dependence of the AHC on the longitudinal conductivity in MnPtGa crystalline thin films, these findings strongly suggest an anomalous Hall effect of intrinsic origin, driven by a momentum‐space Berry curvature mechanism, as supported by first‐principle calculations.

Controlled Switching of the Number of Skyrmions in a Magnetic Nanodot by Electric Fields.

Magnetic skyrmions are topological swirling spin configurations that hold promise for building future magnetic memories and logic circuits. Skyrmionic devices typically rely on the electrical manipulation of a single skyrmion, but controllably manipulating a group of skyrmions can lead to more compact and memory-efficient devices. Here, an electric-field-driven cascading transition of skyrmion clusters in a nanostructured ferromagnetic/ferroelectric multiferroic heterostructure is reported, which allows a continuous multilevel transition of the number of skyrmions in a one-by-one manner. Most notably, the transition is non-volatile and reversible, which is crucial for multi-bit memory applications. Combined experiments and theoretical simulations reveal that the switching of skyrmion clusters is induced by the strain-mediated modification of both the interfacial Dzyaloshinskii-Moriya interaction and effective uniaxial anisotropy. The results not only open up a new direction for constructing low-power-consuming, non-volatile, and multi-bit skyrmionic devices, but also offer valuable insights into the fundamental physics underlying the voltage manipulation of skyrmion clusters.

Twofold and fourfold anisotropies in zinc ferrite thin films investigated by ferromagnetic resonance

By means of the ferromagnetic resonance (FMR) technique (at the $X$ band) we investigated the magnetic properties of ${\mathrm{ZnFe}}_{2}{\mathrm{O}}_{4}$ (ZFO) films grown on different substrates. Angular dependence of the FMR field showed the existence of twofold and fourfold anisotropies for the same material, grown on Si(111), MgO(100), and STO(100), respectively. By using a model that takes into consideration the relevant contributions to the energy, we were able to extract the following parameters: effective magnetization ${M}_{\mathrm{eff}}$, cubic magnetocrystalline anisotropy field, in-plane and out of plane uniaxial anisotropy fields, and the $g$ factor. The samples deposited on Si showed a twofold in-plane anisotropy while a fourfold magnetic anisotropy was observed for the ZFO/MgO and ZFO/${\mathrm{SrTiO}}_{3}$ samples. All samples showed a strong perpendicular uniaxial anisotropy above 1 kOe and low in-plane uniaxial and cubic anisotropy field, on the order of tens of oersteds. The FMR linewidth ($\mathrm{\ensuremath{\Delta}}H$) fitted from FMR data shows $\mathrm{\ensuremath{\Delta}}H$ values above 190 Oe for all samples, indicating high damping of this material to be $\ensuremath{\sim}{10}^{\ensuremath{-}2}$ for the ZFO/MgO. The present analysis compared the FMR data obtained for the in-plane and out of plane measurements. Likewise, the effective magnetization and perpendicular uniaxial anisotropy field by FMR were compared with the magnetic response obtained by a vibrating sample magnetometer.

Critical behavior in the van der Waals itinerant ferromagnet Fe4GeTe2

The critical phenomenon of the magnetic phase transition in the van der Waals itinerant ferromagnet ${\mathrm{Fe}}_{4}{\mathrm{GeTe}}_{2}$ has been investigated by measuring the dc magnetization. The compound undergoes a continuous paramagnetic to ferromagnetic phase transition at the Curie temperature ${T}_{C}=270.0\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. A detailed analysis of magnetization isotherms measured in the vicinity of ${T}_{C}$ with magnetic field $H$ applied parallel to the $ab$ plane yields the asymptotic critical exponents $\ensuremath{\beta}=0.37, \ensuremath{\gamma}=1.20$, and $\ensuremath{\delta}=4.21$, whereas the magnetization isotherms for $H\ensuremath{\parallel}c$ yield $\ensuremath{\beta}=0.34, \ensuremath{\gamma}=1.20$, and $\ensuremath{\delta}=4.52$. Both sets of the critical exponents obey the scaling relation and scaling equation of the magnetic state predicted by the scaling theory. The renormalization group theory analysis for the critical exponents and the analysis based on the self-consistent renormalization theory of spin fluctuations manifest a quasi-two-dimensional itinerant magnetism in the ${\mathrm{Fe}}_{4}{\mathrm{GeTe}}_{2}$ single crystal where the magnetic exchange coupling $J(r)$ is the long-range type that decreases spatially slower than ${r}^{\ensuremath{-}4.76}$. Moreover, a small reduction in the value of $\ensuremath{\beta}$ for $H\ensuremath{\parallel}c$ attests to the observed weak effective uniaxial magnetic anisotropy of ${\mathrm{Fe}}_{4}{\mathrm{GeTe}}_{2}$.

Multiscale modelling of magnetostatic effects on magnetic nanoparticles with application to hyperthermia

We extend a renormalization group-based (RG) coarse-graining method for micromagnetic simulations to include properly scaled magnetostatic interactions. We apply the method in simulations of dynamic hysteresis loops at clinically relevant sweep rates and at 310 K of iron oxide nanoparticles (NPs) of the kind that have been used in preclinical studies of magnetic hyperthermia. The coarse-graining method, along with a time scaling involving sweep rate and Gilbert damping parameter, allow us to span length scales from the unit cell to NPs approximately 50 nm in diameter with reasonable simulation times. For both NPs and the nanorods composing them, we report effective uniaxial anisotropy strengths and saturation magnetizations, which differ from those of the bulk materials magnetite and maghemite of which they are made, on account of the combined non-trivial effects of temperature, inter-rod exchange, magnetostatic interactions and the degree of orientational order within the nanorod composites. The effective parameters allow treating the NPs as single macrospins, and we find for the test case of calculating loops for two aligned NPs that using the dipole approximation is sufficient for distances beyond 1.5 times the NP diameter. We also present a study on relating integration time step to micromagnetic cell size, finding that the optimal time step size scales approximately linearly with cell volume.

Properties of assembly of superparamagnetic nanoparticles in viscous liquid

Detailed calculations of the specific absorption rate (SAR) of a dilute assembly of iron oxide nanoparticles with effective uniaxial anisotropy dispersed in a liquid are performed depending on the particle diameters, the alternating (ac) magnetic field amplitude H0 and the liquid viscosity. For small and moderate H0 values with respect to particle anisotropy field Hk the SAR of the assembly as a function of the particle diameter passes through a characteristic maximum and then reaches a plateau, whereas for sufficiently large amplitudes, H0 ~ Hk, the SAR increases monotonically as a function of diameter. The realization of viscous and magnetic oscillation modes for particle unit magnetization vector and director for moderate and sufficiently large H0 values, respectively, explains this behavior. It is found that the SAR of the assembly changes inversely with the viscosity only in a viscous mode, for nanoparticles of sufficiently large diameters. In the magnetic mode the SAR of the assembly is practically independent of the viscosity, since in this case the nanoparticle director only weakly oscillates around the ac magnetic field direction. The conditions for the validity of the linear response theory have been clarified by comparison with the numerical simulation data.

Ferromagnetic Resonance and Elastic Vibrations in Epitaxial Yttrium Iron Garnet Films

The ferromagnetic resonance (FMR) spectra of epitaxial yttrium iron garnet films are experimentally studied. The field dependences of the FR frequency are used to determine the effective fields induced by the first and second anisotropy constants and the effective uniaxial anisotropy field. The FMR frequency and linewidth are found to increase in the fields lower than 8 Oe applied in the bismuth-containing film plane. This increase is related to the formation of a nonuniform magnetization distribution, which is supported by a direct magnetooptical observation. The FMR spectra are found to be modulated by a set of narrow lines, the amplitude of which is proportional to the FMR signal intensity. The frequency position of the lines is independent of the magnitude and direction of a dc magnetic field. This modulation is shown to be associated with the resonance excitation of transverse elastic vibration modes. The effective magnetoelastic coupling parameter and the linewidth of the elastic vibrations excited by resonance pumping are estimated.

Thickness dependence of interfacial Dzyaloshinskii-Moriya interaction, magnetic anisotropy and spin waves damping in Pt/Co/Ir and Ir/Co/Pt trilayers

Asymmetric Ir/Co/Pt and Pt/Co/Ir trilayers with a wedged Co layer (Co thickness d = 0 ÷ 3.6 nm) were deposited by magnetron sputtering on naturally oxidized Si substrates with a Ta/Au buffer. Their magnetic properties have been investigated using magneto-optical polar Kerr effect and Brillouin light scattering (BLS) technique in the Damon-Eshbach geometry. The BLS measurements shows a frequency asymmetry between Stokes and anti-Stokes peaks position, exploited to determine interfacial Dzyaloshinskii-Moriya interaction energy density DS. DS was nearly two times larger for the Ir/Co/Pt trilayer than for the Pt/Co/Ir with opposite chirality. The effective uniaxial magnetic anisotropy and Ds depend non-monotonically on d with a maximum at d ≈ 1.2 nm. The asymmetry in linewidth for Stokes and anti-Stokes peaks is observed for both Ir/Co/Pt and Pt/Co/Ir trilayers for d < 1.6 nm, and it is increasing with decrease of Co thickness.

Stabilization of the skyrmion crystal phase and transport in thin-film antiferromagnets

We investigate the formation and stability of the skyrmion crystal phase in antiferromagnetic thin films subjected to fieldlike torques such as, e.g., those induced by an electric current in CuMnAs and Mn$_{2}$Au via the inverse spin-galvanic effect. We show that the skyrmion lattice represents the ground state of the antiferromagnet in a substantial area of the phase diagram, parametrized by the staggered field and the (effective) uniaxial anisotropy constant. Skyrmion motion can be driven in the crystal phase by the spin transfer effect. In the metallic scenario, itinerant electrons experience an emergent SU$(2)$-electromagnetic field associated with the (N\'{e}el) skyrmion background, leading to a topological spin-Hall response. Experimental signatures of the skyrmion crystal phase and readout schemes based on topological transport are discussed.

Fine-tuning of canted magnetization in stepped Fe films through thickness variation, Au capping, and quantum confinement

Author(s): Daobrowski, M; Cinal, M; Schmid, AK; Kirschner, J; Przybylski, M | Abstract: We present a joint experimental and theoretical study that demonstrates how to efficiently control a canted state of magnetization in Fe films grown on Ag(001) vicinal surface and precisely characterize it with the magneto-optical Kerr effect. It is shown that by employing different mechanisms to tune the magnetization tilting angle, any magnetization orientation within the plane perpendicular to the step edges can be achieved. In particular, increasing the Fe film thickness leads to continuous rotation of the magnetization easy axis toward the film surface and the sense of this rotation in uncovered films is opposite to that in films covered with Au. Another tuning mechanism is provided by oscillatory changes of the tilting angle at low temperatures due to formation of quantum well states in Fe films. The observed canting of magnetization is explained within a phenomenological model by an interplay of the shape anisotropy and two magnetocrystalline anisotropy terms, perpendicular and step-induced anisotropies, which results in an effective uniaxial magnetic anisotropy. The fitted thickness dependencies of the anisotropy constants accurately reproduce experimental variations of the tilting angle with both Fe and Au thicknesses as well as transient changes of the magnetization orientation in ultrathin Fe films upon submonolayer Au coverage, observed with spin-polarized low-energy electron microscopy.

Coupling dependent reversal in Co/Pt based mixed anisotropy multilayer stacks

Abstract A series of multilayers [Co(6)/Pt(15)]4/(Pt(s))/[Co(10)/Pt(15)]4 (thicknesses in A) consisting from a perpendicular magnetic anisotropy [Cο(6)/Pt(15)]4-stack (PA) coupled to an in-plane anisotropy [Cο(10)/Pt(15)]4-stack (IPA) through the variable Pt interlayer (with s = 0–45 A), is studied as a model mixed-anisotropy system. Vector vibrating sample magnetometry and polarized neutron reflectometry show that, at remanence, the magnetization of each stack relaxes to its own easy axis, with the exception of the s = 0. For the s = 0 sample, the strong coupling between the two different anisotropy stacks results in a collective reversal of both stacks. This process corresponds to an averaged effective uniaxial anisotropy, which suppresses the PA characteristics. For the rest of the samples the stacks are weakly coupled and separate reversal of the two stacks occurs. The PA stack reverses by rapid domain wall motion under the influence of the IPA which has relaxed to its own easy plane. The remaining coupling, despite being weak, influences the values and angular dependence of the reversal fields as well as the positions of positive/negative and doublets on the First Order Reversal Curve (FORC) distributions.

Permalloy (NiFe) nanometer square-antidot arrays: Dynamic modes and use as a monolithic microwave band-pass filter

Abstract Nanometer sized Permalloy antidot arrays with different square hole sizes have been fabricated using field emission scanning electron microscopy technique. The dynamic properties of the antidot arrays are measured at GHz frequencies using a Vector Network Analyzer. For a given applied magnetic field, we observe three resonance frequencies – one corresponds to that of a uniform mode in an infinitely extended film, and the other two (above and below this mode in frequency) correspond to modes associated with finite structures. These two modes exhibit an effective uniaxial in-plane anisotropy. The static behavior of the antidot arrays are simulated using a micromagnetic model and the electromagnetic signal transmission is analyzed using an analytical model. The results show that the three different resonance frequencies are due to the different localized shape anisotropies created by the nonmagnetic holes in the antidot array. Possible application as a magnetically tunable local band-pass filter at 5G frequency band is also studied.

Magnetoresistance of a single polycrystalline nickel nanowire

We report the magnetoresistance study of an individual polycrystalline nickel nanowire at temperature T=10K. Transport measurements have indicated a large coercive field of the nanowire, justified by the polycrystalline structure of the studied sample, where both magnetocrystalline anisotropy of randomly oriented grains and effective uniaxial anisotropy at the grain boundaries enhance the coercive field. Magnetization reversal studied with micromagnetic simulations occurs via the curling mode when vortices are nucleated and propagate along the nanowire, and propagation is inhibited at grain boundaries. The applicability of micromagnetic simulations is confirmed by a good agreement between experimental and simulated magnetoresistance curves.

Evidence of substrate roughness surface induced magnetic anisotropy in Ni80Fe20 flexible thin films

Experimental and computational evidence of a surface roughness induced magnetic anisotropy in NiFe thin films coated onto substrates of various surface roughnesses is reported. Magnetic coercive fields of 15 nm NiFe thin films coated on substrates with approximately 7 nm average roughness were remarkably 233% larger than identical thin films coated onto smooth substrates with < 1 nm average roughness. The NiFe films coated onto rough substrates developed hard and easy axes, normally non-existent in NiFe Permalloy. A linear correlation of the incline angles of the hard axis hysteresis loops to the average roughness values of the individual substrates was observed, with 99% correlation level. Using a modified micromagnetics theory that incorporates the effects of surface roughness, it is shown the observed magnetic anisotropy arises due to the spatial anisotropy of the surface roughness, resulting in an effective in-plane uniaxial magnetic anisotropy with energy density up to 15 kJ/m3.

Unexpected Development of Perpendicular Magnetic Anisotropy in Ni/NiO Multilayers After Mild Thermal Annealing

We report on the significant enhancement of perpendicular magnetic anisotropy of Ni/NiO multilayers after mild annealing up to 90 min at 250 °C. Transmission electron microscopy shows that after annealing, a partial crystallization of the initially amorphous NiO layers occurs. This turns out to be the source of the anisotropy enhancement. Magnetic measurements reveal that even multilayers with Ni layers as thick as 7 nm, which in the as-deposited state showed in-plane anisotropy with square hysteresis loops, show reduced in-plane remanence after thermal treatment. Hysteresis loops recorded with the field in the normal-to-film-plane direction provide evidence for perpendicular magnetic anisotropy with up and down magnetic domains at remanence. A plot of effective uniaxial magnetic anisotropy constant times individual Ni layer thickness as a function of individual Ni layer thickness shows a large change in the slope of the data attributed to a drastic change of volume anisotropy. Surface anisotropy showed a small decrease because of some layer roughening introduced by annealing.