Micromagnetic analysis of current-driven DW dynamics along rough strips with high perpendicular anisotropy at room temperature

Domain-wall motion along thin ferromagnetic strips with high perpendicular magnetocrystalline anisotropy driven by spin-polarized currents is theoretically analyzed by means of full micromagnetic simulations and one-dimensional model, both including surface roughness and thermal effects. At finite temperature, the results show a current dependence of the domain wall velocity in good qualitative agreement with available experimental observations, depicting a low-current, low velocity creep regime, and a high-current, linear regime separated by a smeared depinning region. The analysis points out the relevance of both thermal fluctuations and surface roughness on the domain wall dynamics, and confirms that these effects are essential to get a better understanding on the origin, the role and the magnitude of the non-adiabaticity by direct comparison with experiments.     

Magnetisation reversal in media with perpendicular anisotropy

In this paper, we discuss two key aspects of magnetisation reversal in magnetic thin films with perpendicular anisotropy. Firstly, a study has been made of the additional field required to erase data written perpendicular to a thin film recording disk as the linear data density is increased. It has been found that an increase in data density from 40 to 360 kfci results in an increase of 1.25 kOe in the field required to erase the data. Secondly, the effect of varying the level of exchange coupling by co-sputtering CoCrPt samples with SiO₂ has been studied using a characterisation technique that is independent of the self-demagnetising field. It has been found that the samples are fully exchange de-coupled when the film contains >9.8% SiO₂ and the activation volume of reversal remains constant for higher levels of SiO₂.     

Compensation of nonlinear phase noise in an in-plane-magnetized anisotropic spin-torque oscillator

A theory of generation linewidth of a spin-torque oscillator (STO) based on an in-plane-magnetized nano-pillar with an anisotropic “free” magnetic layer has been developed. It is predicted that by choosing the direction of the in-plane bias magnetic field H₀ along the “hard” anisotropy axis of the STO “free” layer and the magnitude of this field to be four times larger than the anisotropy field H_A (H₀=4H_A) it would be possible to compensate the nonlinear phase noise and to achieve the minimum value of the generation linewidth, characteristic for an auto-oscillator without a nonlinear frequency shift.     

Antisymmetric magnetoresistance in magnetic multilayers with perpendicular anisotropy

While magnetoresistance (MR) has generally been found to be symmetric in applied field in nonmagnetic or magnetic metals, we have observed antisymmetric MR in Co/Pt multilayers. Simultaneous domain imaging and transport measurements show that the antisymmetric MR is due to the appearance of domain walls that run perpendicular to both the magnetization and the current, a geometry existing only in materials with perpendicular magnetic anisotropy. As a result, the extraordinary Hall effect gives rise to circulating currents in the vicinity of the domain walls that contributes to the MR. The antisymmetric MR and extraordinary Hall effect have been quantitatively accounted for by a theoretical model.     

Shape-induced anisotropy in epitaxial Fe3O4 nanopillars

Fe₃O₄ nanopillars with remarkably high uniformity and crystallinity are grown on (100)-oriented magnesium aluminate substrates by pulsed laser deposition with a simple anodic-aluminum-oxide template method. Compared with Fe₃O₄ full film, the nanopillars exhibit higher in-plane magnetic saturation field and lower out-of-plane saturation field. The angular-dependent ferromagnetic resonance, investigated by electron spin resonance spectroscopy, confirms the shape-induced anisotropy change in Fe₃O₄ nanopillars. High Gilbert damping parameter of 0.23 is obtained by measuring the resonance field at different microwave frequencies.     

Micromagnetic structure in multilayer films with moderate perpendicular anisotropy

Micromagnetic simulations have been performed in order to obtain deeper insight into the domain structures within multilayer films, as they are expected to differ from those of single films. These 2D calculations have been done in the case of multilayers exhibiting a moderate perpendicular anisotropy, with no indirect exchange coupling between the magnetic layers, where a “weak stripe" domain structure develops. First, these results are compared quantitatively to the very detailed experimental data available in the literature on the (Co/Au)_N system. More generally, the nucleation of a stripe pattern in multilayers is discussed as a function of the magnetic parameters and the number of magnetic layers in the stack. Compared to a single film, two main differences appear in the equilibrium domain period and the magnetization profiles. The physical origin of these effects is discussed. Received 12 January 2001 and Received in final form 15 May 2001     

Tunneling magnetoresistance in small dot arrays with perpendicular anisotropy

The tunneling magnetoresistance (TMR) of a small magnetic dot array with perpendicular anisotropy, is studied by using a resistor network model. Because of the competition between dipolar interaction and perpendicular anisotropy, the TMR ratio can be up to a maximum value (~26%) as predicted by a theoretical model. At moderate dipolar interaction strength, the perpendicular TMR ratio exhibits abrupt jumps due to the switching of magnetic moments in the array when the applied field (normal to the array plane) decreases from a saturation field. This novel character does not occur if the dipolar interaction between particles is quite strong. Furthermore, the effect of the array size N on TMR is also studied and the result shows that TMR ratio fluctuates when N increases for a moderate dipolar interaction strength. When the applied field h_e is parallel to the array plane, the in-plane TMR curve seems insensitive to the dipolar interaction strength, but the maximum TMR ratio (~26%) can also be obtained at h_e=0.     

Domain wall motion in perpendicular anisotropy nanowires with edge roughness

We study field-driven domain wall (DW) motion in nanowires with perpendicular magnetic anisotropy using finite element micromagnetic simulations. Edge roughness is introduced by deforming the finite element mesh, and we vary the correlation length and magnitude of the roughness deformation separately. We observe the Walker breakdown both with and without roughness, with steady DW motion for applied fields below the critical Walker field H(c), and oscillatory motion for larger fields. The value of H(c) is not altered in the presence of roughness. The edge roughness introduces a depinning field. During the transient process of depinning, from the initial configuration to steady DW motion, the DW velocity is significantly reduced in comparison to that for a wire without roughness. The asymptotic DW velocity, on the other hand, is virtually unaffected by the roughness, even though the magnetization reacts to the edge distortions during the entire course of motion, both above and below the Walker breakdown. A moving DW can become pinned again at some later point ('dynamic pinning'). Dynamic pinning is a stochastic process and is observed both for small fields below H(c) and for fields of any strength above H(c). In the latter case, where the DW shows oscillatory motion and the magnetization in the DW rotates in the film plane, pinning can only occur at positions where the DW reverses direction and the instantaneous velocity is zero, i.e., at the beginning or in the middle of a positional oscillation cycle. In our simulations pinning was only observed at the beginnings of cycles, where the magnetization is pointing along the wire. The depinning field depends linearly on the magnitude of the edge roughness. The strongest pinning fields are observed for roughness correlation lengths that match the domain wall width.     

Permalloy-copper-Permalloy sandwiches with perpendicular anisotropy axes in the magnetic layers

Layerd FeNi-Cu-FeNi structures with a mutually perpendicular orientation of the easy axes in the FeNi layers are fabricated in ultrahigh vacuum, and the physical properties of these structures are investigated: ferromagnetic resonance, quasistatic magnetization reversal, and the Faraday rotation of the plane of polarization of a light wave. Zh. Tekh. Fiz. 67, 45–48 (November 1997)     

Dynamic susceptibility of thin films with perpendicular magnetic anisotropy

We investigate the spin dynamics related to the Gilbert damping constant in infinite continuous thin films with perpendicular magnetic anisotropy (PMA), based on numerical and analytic approaches. We obtain the dynamic susceptibility of the infinite continuous thin films with various PMA energies by using micromagnetic simulations with periodic boundary conditions. These results are compared with the analytic solution that we derived from the Landau–Lifshitz–Gilbert equation. Based on our numerical and analytic studies, we support the physical analysis for results in the experimental determination of the Gilbert damping constant for PMA materials.     

Current induced domain wall motion in nanostripes with perpendicular magnetic anisotropy

We report micromagnetic modeling results of current induced domain wall (DW) motion in magnetic devices with perpendicular magnetic anisotropy by solving the Landau-Lifschitz-Gilbert equation including adiabatic and non-adiabatic terms. A nanostripe model system with dimensions of 500 nm (L)×25 nm (W)×5 nm (H) was selected for calculating the DW motion and its width, as a function of various parameters such as non-adiabatic contribution, anisotropy constant (K_u), saturation magnetization (M_s), and temperature (T). The DW velocity was found to increase when the values of K_u and T were increased and the M_s value decreased. In addition, a reduction of the domain wall width could be achieved by increasing K_u and lowering M_s values regardless of the non-adiabatic constant value.     

Phase segregation and exchange biasing in TbFeCo films with perpendicular anisotropy

A TbFeCo film was deposited by DC magnetron sputtering and studied by transmission electron microscopy, polar and longitudinal magneto-optical Kerr effect, and magnetometry measurements. Transmission electron microscopy has shown the existence of lateral compositional inhomogeneity. Magneto-optical measurements have shown that the initial layer at the bottom consists of only magnetic perpendicular component and the top surface layer has a compositional inhomogeneity and consists of in-plane components and perpendicular one. The perpendicular components in the bottom and the surface layers have identical composition. Two in-plane components have been shown by magnetometry measurements. It is shown that phase segregation exists in the TbFeCo film and possible form of compositional inhomogeneity has been discussed. The two in-plane components are exchange coupled with a magnetization off-alignment of 35°. For the soft in-plane component, the in-plane and out-of-plane angular dependence of the exchange biasing is similar to those of the conventional one. Within temperatures from 100 to 300 K, the exchange field and the coercivity are both linear functions of temperature.     

Dynamic self-organization of magnetic domains in amorphous films with perpendicular anisotropy

Dynamic self-organization of magnetic domains is observed in amorphous gadolinium-cobalt films in narrow temperature intervals on both sides of the magnetic compensation point. Spiral dynamic domains form in a limited range of ac magnetic field amplitudes and frequencies. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 11, 688–692 (10 December 1997)     

Magnetic properties of Pr-Fe-B/Mn films with perpendicular anisotropy

The influence of a Mn layer on the magnetic properties of sputtered Pr-Fe-B/Mn films with Cu spacer layer has been investigated for various Mn layer thicknesses. The Pr-Fe-B/Mn films all possess perpendicular anisotropy. An enhancement of the intrinsic coercivity _iH_c is observed for suitable Mn layer thickness and _iH_c exhibits an oscillatory dependence on the thickness of the Mn layer with a period of about 60 nm. The average size of the columnar Pr₂Fe₁₄B grains is about 100 nm. A highest _iH_c value of 22.1 kOe and an optimal (BH)_max value of 18.2 MGOe are reported for these Pr-Fe-B/Mn films.     

Critical magnetization and hysteresis of nanogranular films with perpendicular anisotropy

The magnetic-field dependences of the stability boundaries of the nonequilibrium magnetic states that exist in a nanogranular film with perpendicular anisotropy in tilted magnetic fields are theoretically described, and the corresponding critical magnetization is calculated. The field dependences of the critical magnetization of the film are analyzed at various ratios of the anisotropy field of particles to the maximum possible demagnetizing field of the film. In a tilted magnetic field, the magnetization reversal curves, which include hysteresis loops, are shown to consist of segments of the following three types: equilibrium stable magnetization, nonequilibrium stable magnetization, and critical type of magnetization.     

Patterned media with composite in-plane and perpendicular anisotropy recording layers

Magnetization reversal mechanism in nanostructures composed of exchange coupled bi-layers with in-plane and perpendicular anisotropy was investigated. Micromagnetic simulation was carried out for bit-patterned media with areal density of 5 Tb/in², as example. Magnetization of thermally stable recorded bit using a single layer may not switch under write field. However, a complete and fast switching is possible with an exchange coupling to a layer with in-plane anisotropy. By adjusting the thicknesses and intrinsic properties of the two layers, the composite recording layer still can retain perpendicular anisotropy. The exchange coupled structure with dual-anisotropy can be extended to magnetic memories.     

Hysteresis of two interacting magnetic pairs with inequivalent perpendicular anisotropy

We consider a model for magnetic memory that consists of strongly coupled dipolar or antiferromagnetic (AF) pairs with inequivalent perpendicular anisotropy _K1$K_1$ and _K2$K_2$. For appropriate parameter values, determined in this work, they have two inequivalent storage states with zero net magnetic moment. Both analytical and numerical calculations are performed, in some cases yielding different results because of relaxation effects (i.e., a dependence on the damping parameter α$\alpha$). Hysteresis loops for a wide variety of parameter values are obtained, both for the AF case and the dipole case. An Appendix gives analytic results for slightly non-collinear spins in an applied field, which were used to test the numerical results.     

Dirac oscillator in perpendicular magnetic and transverse electric fields

We study (2+1)$(2+1)$ dimensional massless Dirac oscillator in the presence of perpendicular magnetic and transverse electric fields. Exact solutions are obtained and it is shown that there exists a critical magnetic field B_c$B_c$ such that the spectrum is different in the two regions B>B_c$B>B_c$ and B<B_c$B<B_c$. The situation is also analyzed for the case B=B_c$B=B_c$.