Fourfold Anisotropy Research Articles

Fourfold in-plane magnetic anisotropy in epitaxial Fe(1 1 0)/Cu(0 0 1) and Fe(1 1 0)/Ni(0 0 1) bilayers

Epitaxial Fe(1 1 0) films with thicknesses of 100–800 nm on Cu(0 0 1) and Ni(0 0 1) buffer layers grown on MgO(0 0 1) substrates have been fabricated. These films contain Fe(1 1 0) crystallites which are in the Pitsch orientation relationship. Magnetization and the fourfold in-plane magnetic anisotropy constants of these films have been determined by torque measurements. All the samples under study are characterized by a fourfold magnetic anisotropy with easy axes parallel to the [1 0 0] and [0 1 0] directions of Cu(0 0 1) and Ni(0 0 1) layers. The measured values of the constant for Fe(1 1 0)/Cu(0 0 1) are found to depend on deposition temperature; a maximum value of (2.5±0.1)×10 5 erg/cm 3 is reached after annealing at 600 °С. The in-plane torque measurements on Fe(1 1 0)/Ni(0 0 1) bilayers obtained at 300 °С, on the other hand, exhibit a constant value of (2.7±0.1)×10 5 erg/cm 3. Assuming an exchange interaction between the Fe(1 1 0) crystallites, which are in the Pitsch orientation relationship, the fourfold in-plane magnetic anisotropy has been calculated as 2.8×10 5 erg/cm 3. The deviations of the experimental values from the predicted one may be explained by the formation of a polycrystalline phase within the Fe(1 1 0) layer and a partial disorientation of the epitaxial crystallites.

Anisotropic Josephson-vortex dynamics in layered organic superconductors

To study the anisotropic Josephson-vortex dynamics in the d-wave superconductors, the interplane resistance has been measured on layered organic superconductors κ ‐ ( ET ) 2 Cu ( NCS ) 2 and β ‐ ( BDA ‐ TTP ) 2 SbF 6 under magnetic fields precisely parallel to the conducting planes. For κ ‐ ( ET ) 2 Cu ( NCS ) 2 , in-plane angular dependence of the Josephson-vortex flow resistance is mainly described by the fourfold symmetry and dip structures appear when the magnetic field is applied parallel to the b- and c-axes. The obtained results have a relation to the d-wave superconducting gap symmetry. However, the absence of in-plane fourfold anisotropy was found for β ‐ ( BDA ‐ TTP ) 2 SbF 6 . The different anisotropic behavior is discussed in terms of the interlayer coupling strength.

In-plane spin reorientation transition in a two-dimensional ferromagnetic/antiferromagnetic system studied using Monte Carlo simulations

We investigated the in-plane spin reorientation transition (SRT) in a two-dimensional ferromagnetic/antiferromagnetic system by using Monte Carlo simulation based on the Heisenberg model. The temperature-driven SRT in the ferromagnetic layer is studied for the case of that the antiferromagnetic layer has an uniaxial in-plane or fourfold in-plane anisotropy. For the case of an uniaxial in-plane anisotropy in the antiferromagnetic layer, the ferromagnetic layer spin processes a $90\ifmmode^\circ\else\textdegree\fi{}$ in-plane SRT from perpendicular to parallel direction of the anisotropy. For the case of a fourfold in-plane anisotropy in the antiferromagnetic layer, the ferromagnetic layer spin processes a $45\ifmmode^\circ\else\textdegree\fi{}$ in-plane SRT. We also studied the Curie temperature of the ferromagnetic layer and find a significant reduction in the Curie temperature as the Curie temperature is close to the SRT temperature.

Exchange bias in epitaxial Fe/Ir0.2Mn0.8 bilayers grown on MgO (0 0 1)

Exchange bias has been studied in epitaxial Fe/Ir0.2Mn0.8 (IrMn) bilayers grown by molecular beam epitaxy on MgO (0 0 1) substrates. The IrMn layer has a chemically disordered fcc structure with an epitaxial relationship of MgO(0 0 1)[1 1 0]//Fe(0 0 1)[1 0 0]//IrMn(0 0 1) [1 1 0]. In this system, exchange bias is induced during growth at room temperature without post-annealing, by applying a small magnetic field, HA, along the bcc Fe [1 0 0] easy axis. The temperature dependence of the exchange bias field and the coercivity along the Fe [1 0 0] easy axis, measured up to approximately half the Néel temperature, shows an exponential decay of these parameters with increasing temperature. The magnetization measured as a function of applied field along the Fe [1 0 0] easy axis results in a negatively shifted hysteresis loop, typical for exchange bias, while when the magnetic field is applied along the Fe [0 1 0] easy axis (perpendicular to HA), a symmetric double-shifted loop is observed. In both cases, the magnetization reversal occurs through two successive events involving nucleation and propagation of domains in which the magnetic moments are perpendicular to each other. We demonstrate that due to the epitaxial growth of the IrMn layer, the unidirectional anisotropy induced by exchange bias is aligned with one of the Fe easy axis directions and, in effect, is added to the four-fold cubic anisotropy of the Fe layer.

Thermal hysteresis of ferromagnetic/antiferromagnetic compensated bilayers

We report a theoretical investigation of thermal hysteresis of fourfold anisotropy ferromagnetic FM film exchange coupled to a compensated antiferromagnetic substrate. Thermal hysteresis occurs if the temperature interval includes the reorientation transition temperature, below which the frustration of the interface exchange coupling leads to a 90° rotation of the magnetization of the ferromagnetic layer. The temperature width of the thermal hysteresis is tunable by external magnetic fields of modest magnitude, with values of 43 K for an external field of 110 Oe and of 14 K for a field of 210 Oe, for a Fe 12 nm/MnF2 110 bilayer. For a Fe 3 nm/FeF2 110 bilayer the width of the thermal hysteresis is 23 K at 110 Oe and 13 K at 300 Oe. We discuss how the thickness of the iron film affects the field tuning of the thermal hysteresis width, and also how the thermal loops may be used to identify the nature of the interface exchange energy.

Magnetic anisotropy and reversal in epitaxial Fe/MgO(001) films

We investigate the magnetization reversal in Fe/MgO(001) films with fourfold in-plane magnetic anisotropy and an additional uniaxial anisotropy whose orientation and strength are altered using different growth geometries and postgrowth treatments. The previously adopted mechanism of $180\ifmmode^\circ\else\textdegree\fi{}$ domain-wall nucleation clearly fails to explain the observed $180\ifmmode^\circ\else\textdegree\fi{}$ magnetization reversal in Fe/MgO(001) films. We introduce a reversal mechanism with two successive domain-wall nucleations to consistently predict the switching fields of Fe/MgO(001) films for all field orientations with one set of values for domain-wall nucleation energies and uniaxial anisotropy.

Strong dependence of the magnetic anisotropy on the growth temperature of [formula omitted] ( [formula omitted]) films on GaAs(1 1 3)A substrates

A strong dependence of the magnetic anisotropy on the growth temperature of Fe 3 + x Si 1 - x Heusler alloy films on GaAs(1 1 3)A substrates is reported for a composition of 17.5 at . % Si ( x = 0.34 ). This composition of Fe–Si alloy lies within the stable phase of the technologically promising Heusler alloy Fe 3 Si . The layers grown at the optimized growth temperature of 250 °C exhibit the expected four-fold magnetic anisotropy, which arises from the magnetocrystalline anisotropy and the large demagnetization energy, similar to Fe films. However, an unexpected strong uniaxial magnetic anisotropy is found for samples grown at 200 and 400 °C with the easy axes along 〈 3 3 2 ¯ 〉 and 〈 1 ¯ 1 0 〉 , respectively. The uniaxial magnetic anisotropy of these samples are shown to be related to the inferior interface quality.

Magnetic anisotropies of epitaxial Fe/MgO(001) films with varying thickness and grown under different conditions

Fe films with thickness varying between 5 and 100 nm were grown on flat MgO(001) substrates while rotating the substrates. Hysteresis loops with one step and two steps were observed and interpreted in terms of a magnetization reversal mechanism with either two successive or two separate 90° domain wall (DW) nucleations, respectively. This recently introduced, novel mechanism for 180° magnetic transitions was used to quantitatively evaluate both the uniaxial magnetic anisotropy (UMA), which accompanies the intrinsic fourfold in-plane magnetic anisotropy, and the DW nucleation energy. The strength of both the UMA and the DW nucleation energy turns out to be inversely proportional to the thickness of the Fe layers for Fe/MgO(001). This suggests that the extra UMA and the DW nucleation/propagation for Fe layers are pure interface related effects. By comparing six 15 nm thick Fe/MgO(001) films deposited under different conditions, it is found that these interface related effects originate from the presence of atomic steps due to the substrate miscut and from the presence of strain relaxation resulting from lattice mismatch.

Static and dynamic magnetic properties ofNi80Fe20square antidot arrays

We have investigated both static and dynamic magnetic properties of square antidot arrays in a ferromagnetic thin-film structure of Au (2 nm)/${\text{Ni}}_{80}{\text{Fe}}_{20}$ (27.6 nm) on a ${\text{SiO}}_{2}$ 500 nm/Si substrate using magneto-optic Kerr effect magnetometry, Brillouin light scattering (BLS), and micromagnetic simulations. The antidot patterns were $1\text{ }\ensuremath{\mu}\text{m}$ square holes arranged in two separate square lattices of dot separations $d=0.6\text{ }\ensuremath{\mu}\text{m}$ and $1.0\text{ }\ensuremath{\mu}\text{m}$. The introduction of antidots induced an in-plane fourfold magnetic anisotropy with hard axes on the two nearest-antidot-neighbor directions. The coercive field, ${H}_{c}$, was increased by the presence of antidots. Fixed-frequency modes were observed in spin-wave dispersion relations in remanent spin configurations. These modes correspond to spin-wave confinement by antidot edges, which were seen as a series of nodal lines parallel to the edges in simulated spin-wave mode spatial mappings. Domains in remanent states, some of which were responsible for the existence of dipole-exchange backward volume modes seen in BLS spectra, were also found to confine spin waves in simulations.

Anisotropy and dynamic properties of Co 2MnGe Heusler thin films

Co 2MnGe films of 30 and 50 nm in thickness were grown by RF-sputtering. Their magnetic anisotropies, dynamic properties and the different excited spin wave modes have been studied using conventional ferromagnetic resonance (FMR) and Microstrip line FMR (MS-FMR). From the in-plane and the out-of-plane resonance field values, the effective magnetization (4π M eff ) and the g-factor are deduced. These values are then used to fit the in-plane angular-dependence of the uniform precession mode and the field-dependence of the resonance frequency of the uniform mode and the first perpendicular standing spin wave to determine the in-plane uniaxial, the four-fold anisotropy fields, the exchange stiffness constant and the magnetization at saturation. The samples exhibit a clear predominant four-fold magnetic anisotropy besides a smaller uniaxial anisotropy. This uniaxial anisotropy is most probably induced by the growth conditions.

Magnetic and Structural Properties of Fully Epitaxial ${\hbox {Fe}}_{3}{\hbox {O}}_{4}/{\hbox {MgO/GaAs}}(100)$ for Spin Injection

In this paper, the authors report on the investigation on the effect of inserting an epitaxial MgO layer on the structural and magnetic properties of Fe3O4 ultrathin films grown on GaAs(100) by combined techniques of molecular beam epitaxy and postgrowth annealing in an oxygen atmosphere. The MgO films were grown with a cube-on-cube orientation to GaAs. The epitaxial Fe3O4 lattice cell was rotated by 45deg in respect to that of MgO and GaAs due to the lattice relaxation of the magnetic layer. All samples studied exhibited strong fourfold cubic magnetic anisotropy with easy axes along the lang001rang directions of GaAs. A dramatic decrease in the uniaxial anisotropy constant in the presence of the MgO barrier was observed. The existence of the uniaxial magnetic anisotropy in the Fe3O4/GaAs hybrid structure has been attributed to the interfacial contact between the magnetite film and the GaAs.

Interlayer magnetic coupling in Fe/MgO junctions characterized by vector magnetization measurements combined with polarized neutron reflectometry

Polarized neutron reflectometry has been combined with vector magnetization measurements to analyze the reversal process of antiferromagnetically coupled Fe layers through an insulating MgO spacer. We show that the use of a simple micromagnetic model applied in a field range where the reversal process is reversible allows us to determine separately the magnetic characteristics of the layers such as the anisotropy, bilinear, and biquadratic coupling constants. Using this analysis technique, we can prove that in a Fe(001)/MgO/Fe trilayer with thicknesses 35 nm/0.6 nm/6 nm, the $90\ifmmode^\circ\else\textdegree\fi{}$ configuration of the Fe layers occurring during the reversal mechanism is only related to the fourfold Fe anisotropy present in both layers without any biquadratic coupling.

Spin-Transfer Induced Dynamic Modes in Single-Crystalline Fe–Ag–Fe Nanopillars

We present measurements and simulations of spin-transfer torque (STT) induced magnetization dynamics in nanopillars containing a thin, circular, single-crystalline Fe nanomagnet with four-fold in-plane magnetocrystalline anisotropy as a free layer. The magnetocrystalline anisotropy inherent to bcc-Fe allows for a consecutive switching of the magnetization by 90deg between parallel and antiparallel alignment to the fixed layer magnetization. Additionally, the anisotropy gives rise to steady-state precession of the magnetization at low or even zero applied magnetic field as well as at large fields exceeding the coercive field. While the low-field mode is governed by the interplay between the STT and the anisotropy, the high-field dynamics result from the STT acting against the externally applied magnetic field.

Modulated multipolar structures in magnetic arrays

Electric and magnetic multipole moments are important quantities in studies of intermolecular forces, and electrostatic and magnetostatic potentials. The experimental determination of multipole moments in multipole–multipole coupling is difficult and therefore the theoretical prediction of these quantities is important. The aim of the present review is to give a general theoretical description of multipolar ordering on two-dimensional periodic and aperiodic lattices. After an introduction to the role of multipolar interactions in magnetic nanoarrays in the first part of this article, the static multipole expansions in Cartesian and spherical coordinates are outlined. Next, the established numerical approach for the calculation of multipolar ground states, i.e. Monte Carlo simulations, are summarized. Special emphasis is put on the review of ground states in multipolar systems consisting of moments of odd parity relevant for the magnetized or polarized particle ensembles. We demonstrate that higher-order interactions considerably change the dipolar ground states of in-plane magnetized arrays. While in periodic triangular, square and kagome arrays the higher-order interactions induce three- or four-fold in-plane anisotropy, on a Penrose tiling with ten-fold symmetry the multipolar terms do not seriously affect the dipolar order.

Probing Arrays of Circular Magnetic Microdots by Ferromagnetic Resonance

X-band ferromagnetic resonance (FMR) was used to characterize in-plane magnetic anisotropies in rectangular and square arrays of circular nickel and Permalloy microdots. In the case of a rectangular lattice, as interdot distances in one direction decrease, the in-plane uniaxial anisotropy field increases, in good agreement with a simple theory of magnetostatically interacting uniformly magnetized dots. In the case of a square lattice a four-fold anisotropy of the in-plane FMR field H(r) was found when the interdot distance a gets comparable to the dot diameter D. This anisotropy, not expected in the case of uniformly magnetized dots, was explained by a non-uniform magnetization m(r) in a dot in response to dipolar forces in the patterned magnetic structure. It is well described by an iterative solution of a continuous variation procedure. In the case of perpendicular magnetization multiple sharp resonance peaks were observed below the main FMR peak in all the samples, and the relative positions of these peaks were independent of the interdot separations. Quantitative description of the observed multiresonance FMR spectra was given using the dipole-exchange spin wave dispersion equation for a perpendicularly magnetized film where in-plane wave vector is quantized due to the finite dot radius, and the inhomogenetiy of the intradot static demagnetization field in the nonellipsoidal dot is taken into account. It was demonstrated that ferromagnetic resonance force microscopy (FMRFM) can be used to determine both local and global properties of patterned submicron ferromagnetic samples. Local spectroscopy together with the possibility to vary the tip-sample spacing enables the separation of those two contributions to a FMRFM spectrum. The global FMR properties of circular submicron dots determined using magnetic resonance force microscopy are in a good agreement with results obtained using conventional FMR and with theoretical descriptions.

In-plane magnetic anisotropies inFe3O4films on vicinal MgO(100)

Ferromagnetic resonance was used to study the influence of vicinal (miscut) angle and film thickness on in-plane fourfold and uniaxial magnetic anisotropies in epitaxial ${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}$ films grown on vicinal MgO(100) surfaces. The in-plane fourfold anisotropy constant ${K}_{4\ensuremath{\parallel}}$ is approximately the same for all films but the dominant in-plane uniaxial constant ${K}_{2\ensuremath{\parallel}}$ varies linearly with the inverse ${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}$ layer thickness and approximately quadratically with the vicinal angle. A second, weaker, in-plane uniaxial term is evident for the film on a larger miscut (10\ifmmode^\circ\else\textdegree\fi{}) substrate. The easy axis of the dominant in-plane uniaxial term is perpendicular to the step edges. The dominant in-plane uniaxial anisotropy has one term inversely proportional to the film thickness that is associated with anisotropy localized at the interface and a second term that is independent of film thickness; the latter may arise from the preferential alignment of antiphase boundaries with the step edges.

The interface effect of the magnetic anisotropy in ultrathin epitaxial Fe3O4 film

The magnetic anisotropy of epitaxial layered structures of Fe3O4(tFe=4nm)∕GaAs(100), MgO(3nm)∕Fe3O4(tFe=4nm)∕GaAs(100), and Fe3O4(tFe=4nm)∕MgO(3nm)∕Fe3O4(tFe=4nm)∕GaAs(100) was studied by ferromagnetic resonance. It was shown that a predominant in-plane uniaxial magnetic anisotropy and a small fourfold cubic magnetocrystalline anisotropy existed. The in-plane uniaxial anisotropy constant decreased when the MgO layer was covered on Fe3O4∕GaAs, while the cubic anisotropy increased. In the sandwich structures, two resonance peaks were observed. One is similar to that in Fe3O4∕GaAs layer, while another corresponding to Fe3O4 on MgO showed more remarkable fourfold anisotropy and lower uniaxial anisotropy due to smaller mismatch between Fe3O4 and MgO. The interface the Fe3O4 layer is deposited on has dominant effect.

Exchange bias and fourfold magnetic anisotropy in Permalloy thin film on epitaxial hematite antiferromagnet

Fourfold anisotropy was observed in NiFe films deposited on epitaxial antiferromagnet α-Fe2O3. The anisotropy was preserved despite off-axis magnetic field annealing (MFA) below the Néel temperature (TN). The cumulative effect of this fourfold anisotropy and exchange coupling due to MFA determined the exchange bias (Hex) distribution. Physically, this indicated the existence of two types of antiferromagnet domains—those that were frozen in below TN and contributed to the fourfold anisotropy and those that coupled with the annealing magnetic field and contributed to the conventional Hex distribution.

Structural and Magnetic Properties of Epitaxial Fe and Ni Thin Films Grown on n-AlGaAs(001) Using Electrodeposition

We report epitaxial growth of body-centered cubic Fe and face-centered cubic Ni thin films on n-type AlGaAs(001) substrates using electrochemical deposition with the cubic axes of Fe oriented parallel to the substrate lattice while the Ni is rotated in-plane 45°. The magnetic properties in either case are dominated by the fourfold crystalline anisotropy, a high remanence, and saturation magnetization values similar to bulk properties. The growth of such ferromagnetic contacts on AlGaAs might find applications in magneto-electronics.

Asymmetric spin-transfer torque in single-crystallineFe∕Ag∕Fenanopillars

We investigate current-perpendicular-plane giant magnetoresistance (CPP-GMR) and current-induced magnetization switching in single-crystalline $\mathrm{Fe}∕\mathrm{Ag}∕\mathrm{Fe}$ nanopillars of $70\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ diameter. The interplay between the in-plane, fourfold magnetocrystalline anisotropy of the Fe(001) layers and the spin-transfer torque (STT) gives rise to a two-step switching behavior, which allows an investigation of the angular dependences of CPP-GMR and spin-transfer torque. Both behave asymmetrically with respect to the perpendicular alignment of the two Fe layer magnetizations as theoretically predicted due to strong spin accumulation at the $\mathrm{Fe}∕\mathrm{Ag}(001)$ interfaces [M. D. Stiles and D. R. Penn, Phys. Rev. B 61, 3200 (2000)]. The asymmetry parameter determined from the STT data quantitatively agrees with calculated spin-dependent interface resistances, whereas CPP-GMR yields a smaller degree of asymmetry.