Analytic theory of wall configuration and depinning mechanism in magnetic nanostructure with perpendicular magnetic anisotropy

We present an analytic theory of the domain wall depinning in magnetic nanostructure with perpendicular magnetic anisotropy. The variational principle reveals that the wall is bent in the form of a circular arc which intersects the structure boundaries perpendicularly. The radius is inversely proportional to the magnetic field. With increasing the field the radius shrinks, followed by depinning from the constriction when the arc is not geometrically allowed. The depinning field is proportional to the sine of the constriction angle and the inverse of the constriction width. The validity of the theory is confirmed by comparison with the micromagnetic simulation.     

Domain wall dynamics near the limit velocity in a cubic ferromagnet with induced magnetic anisotropy

A research has been conducted into the dynamics of the 180° domain wall in a cubic ferromagnet with induced magnetic anisotropy, this domain wall moving at a velocity close to the limit one. The Landau–Lifshits equation has been reduced to a modified double Sine–Gordon equation with the highest dispersion. A solution has been found which corresponds to the moving 180° domain wall. This paper has determined the dependencies of the velocity of the domain wall's stationary movement on the quality factor and on the ratio of the induced and the cubic magnetic anisotropy constants in slabs with the developed (0 0 1) and (0 1 1) surfaces.     

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.     

Micromagnetic investigation of the sub-nanosecond magnetic pulse driven domain wall motion in CoFeB nanowire

We report our micromagnetic simulations based on Landau-Lifshitz-Gilbert (LLG) equation for CoFeB nanowire which was exposed by sub-nanosecond magnetic pulse with varied pulse width between 100 and 1000 ps. It is found that the Walker Breakdown field (H_WB) shifted as the field pulse duration decreased and reached at the highest value in case of 100 ps pulse width, then decreased steeply with respect to the pulse width up to 400 ps. H_WB values are not significantly dependent for pulses longer than 500 ps. It is observed that, below the H_WB, the exchange energy is larger than the demagnetization energy in the wider nanowire. By energy density analysis, it is understood that the increase of H_WB values in the cases of narrower pulse width was to compensate the energy needed to move the DW.     

Magnetic properties of co-sputtered Tb-Co2FeAl films with perpendicular anisotropy

We present a systematic study on magnetic properties of co-sputtered Tb-Co₂FeAl (TCFA) films. The TCFA films with suitable Tb content have perpendicular magnetic anisotropy (PMA). The PMA deteriorates with both decreasing film thickness and high temperature annealing. Under a certain thickness, the perpendicular coercivity of the TCFA films with PMA can be reduced down to 60 Oe, which is comparable with normal soft ferromagnets. After annealing at 100 °C, a large remanence squareness of 0.95 is observed in the TCFA film with 33% Tb and a thickness of 30 nm.     

Faster 360° domain wall motion in nanostrip induced by spin-polarized current with out-of-plane magnetic field

By micromagnetic simulation, we show that faster propagation of 360° domain wall in magnetic nanostrips under spin-polarized currents in conjunction with out-of-plane magnetic fields can be obtained. Without magnetic field, the annihilation process of 360° domain wall is irreversible when spin-polarized current velocity above about 220 m/s. The annihilation of 360° domain wall can be suppressed by an out-of -plane magnetic field and domain wall speed can exceed 1500 m/s at large current density. This is different from the case exhibited in 180° domain wall. The underlying mechanism is investigated by changing the state of 360° domain wall and the direction of out-of-plane field.     

Origin of perpendicular magnetic anisotropy and evolution of magnetic domain structure of amorphous Pr-TM-B (TM=Fe, Co) films

In this study, the deposition pressure dependence of the compositional ratio, magnetic domain structure, and perpendicular magnetic anisotropy (PMA) of B-containing PrFe- and PrCo-based films, which are rare-earth-transition-metal (RE-TM) films, was investigated. PrFe- and PrCo-based films were fabricated by magnetron sputtering. The film compositions were controlled in a wide range by varying the deposition pressure. On the basis of experimental results, the residual stress of the films was considered to be the possible origin of their PMA. The films showed strong magneto-optical effects over the entire wavelength range of 300-750 nm. Because of the excellent magnetic and magneto-optical (MO) properties of the films, they have high potential for MO applications at wavelengths of red and blue lasers.     

Detection of domain wall propagation in a mesoscopic wire

Extraordinary Hall effect was used to detect the propagation of a domain wall in magnetic devices patterned in sputter grown Pt/Co(1 nm)/Pt sandwiches with perpendicular easy magnetization axis. In such films, domain walls propagate as coherent 1D nano-object in a 2D medium with weak fluctuation energy density. In a patterned device, the competition between global wall energy and Zeeman energy strongly influences the wall propagation.     

Dynamics of sandwich domain structure in Co-based amorphous ribbons with helical magnetic anisotropy: Part I

The distribution of axes of easy magnetization close to a homogeneous distribution is revealed in each half-thickness of a ribbon after annealing it in a helical magnetic field. The transition from magnetic reversal of a ribbon by the displacement of two domain walls formed near a middle plane of a ribbon to magnetic reversal of a ribbon by displacement of two domain walls formed near to the main surfaces of a ribbon is found out during each half-period of a magnetic reversal.     

Temperature and bias voltage dependence of Co/Pd multilayer-based magnetic tunnel junctions with perpendicular magnetic anisotropy

Temperature- and bias voltage-dependent transport measurements of magnetic tunnel junctions (MTJs) with perpendicularly magnetized Co/Pd electrodes are presented. Magnetization measurements of the Co/Pd multilayers are performed to characterize the electrodes. The effects of the Co layer thickness in the Co/Pd bilayers, the annealing temperature, the Co thickness at the MgO barrier interface, and the number of bilayers on the tunneling magneto resistance (TMR) effect are investigated. TMR-ratios of about 11% at room temperature and 18.5% at 13 K are measured and two well-defined switching fields are observed. The results are compared to measurements of MTJs with Co-Fe-B electrodes and in-plane anisotropy.     

Spin-dependent thermoelectric effect in Co2Fe0.4Mn0.6Si thin film with perpendicular magnetic anisotropy

We report the anomalous Nernst effect in trilayers containing a thin film of the half-metallic ferromagnetic Heusler alloy Co₂Fe_0.4Mn_0.6Si with perpendicular magnetic anisotropy. The structure is MgO/CFMS/Pd and we have studied the variation of anomalous Hall and Nernst effects as a function of CFMS and Pd thickness. The anomalous Nernst coefficient reaches 0.5 μV/K at room temperature and we have observed a strong dependence of the anomalous Nernst coefficient on the thickness of both layers. Our results indicate that inducing perpendicular magnetic anisotropy in a strongly spin-polarising Heusler alloy such as CFMS is very promising for new thermoelectric devices based on exploiting the anomalous Nernst effect.     

Role of anisotropy on the domain wall properties of ferromagnetic nanotubes

In this paper we investigate the role of magneto-crystalline anisotropy on the domain wall (DW) properties of tubular magnetic nanostructures. Based on a theoretical model and micromagnetic simulations, we show that either cubic or uniaxial magneto-crystalline anisotropies have some influence on the domain wall properties (wall size, propagation velocity and energy barrier) and then on the overall magnetization reversal mechanism. Besides the characterization of the transverse and vortex domain wall sizes for different anisotropies, we predict an anisotropy dependent transition between the occurrence of transverse and vortex domain walls in tubular nanowires. We also discuss the dynamics of the vortex DW propagation gradually increasing the uniaxial anisotropy constant and we found that the average velocity is considerably reduced. Our results show that different anisotropies can be considered in real samples in order to manipulate the domain wall behavior and the magnetization reversal process.     

Compressed exponential form for disordered domain wall motion in ultra-thin Au/Co/Au ferromagnetic films

Magnetization reversal in ultra-thin Au/Co/Au films deposited on single crystal silicon (1 0 0) was investigated using Kerr microscopy. In the considered ultra-thin Co films, with a thickness between 0.7 and 1 nm, the coercivity and magnetic anisotropy decrease with decrease in cobalt layer thickness and the magnetization reversal dynamics is dominated by disordered domain wall motion. An analysis of the observed magnetization reversal dynamics is proposed, starting from the Fatuzzo-Labrune model. We show that the relaxation curves of these samples are well described by a function obtained by a technical transformation of Fatuzzo-Labrune model in the regime dominated by domain wall motion.     

Nonmonotonic effects of perpendicular magnetic anisotropy on current-driven vortex wall motions in magnetic nanostripes

In a magnetic nanostripe, the effects of perpendicular magnetic anisotropy(PMA) on the current-driven horizontal motion of vortex wall along the stripe and the vertical motion of the vortex core are studied by micromagnetic simulations.The results show that the horizontal and vertical motion can generally be monotonously enhanced by PMA. However, when the current is small, a nonmonotonic phenomenon for the horizontal motion is found. Namely, the velocity of the horizontal motion firstly decreases and then increases with the increase of the PMA. We find that the reason for this is that the PMA can firstly increase and then decrease the confining force induced by the confining potential energy. In addition, the PMA always enhances the driving force induced by the current.     

Influence of exchange coupling on current-driven domain wall motion in a nanowire

In this study, the effect of exchange stiffness constant on current-driven domain wall motion in nanowires with in-plane magnetic anisotropy (IMA) and perpendicular magnetic anisotropy (PMA) has been investigated using micromagnetic simulation. The critical current density in a nanowire with IMA decreases as the exchange stiffness constant decreases because the domain wall width at the upper edge of the nanowire narrows according to the decrease of the exchange stiffness constant. On the other hand, the critical current density in a nanowire with PMA slightly decreases contrary to that of IMA although the domain wall width reasonably decreases as the exchange stiffness constant decreases. The slight reduction rate of the critical current density is due to the increase of the effective hard-axis anisotropy of PMA nanowire.     

Micromagnetic study of domain wall depinning driven by nanosecond current pulse in notched Permalloy nanowires

The complete understanding of domain wall (DW) dynamics is important in the design of future spintronic devices. The characteristics of faster time-scale and lower current amplitude to move DW along nanowire are crucial in fabrication upgrade. In this study, we have investigated depinning behavior of magnetic domain wall triggered by nanosecond current pulse in notched Permalloy nanowires by means of micromagnetic simulation. We introduced double-triangular notch as the constrictions in the nanowire. The non-adiabaticity of the spin-transfer-torque is considered in simulation by varying the non-adiabatic constant (β) value. We observed that the depinning current density (J_d) was not significantly affected by β for notch size (s) < 50 nm. Interestingly, we found that the depinning time (t_d) for β ≥ 0.04 was slightly constant for all the cases with s > 70 nm, where the DW structure was kept to be a transverse structure during the depinning process. The broadly applicable depinning behavior is considered to contribute to the development of high-speed memory storage devices based on magnetic domain wall.     

Control of the magnetic domain wall propagation in Pt/Co/Pt ultra thin films using direct mechanical AFM lithography

We create mesoscopic point and line defects by scanning probe lithography to control the magnetization reversal process in Pt/Co/Pt ultra thin film devices. The domain wall propagation near the defects is studied by the Kerr microscopy and extraordinary Hall effect measurements. The observed domain wall pinning is used to block and channel the domain expansion and to create artificial domain patterns.     

Hard layer demagnetization by soft layer cycling in a MgO-based perpendicular magnetic tunnel junction

We report here that in perpendicular tunnel junction the hard layer demagnetizes when the soft layer is cycled. This happens faster when the cycling field is closer to the reversal field of the hard layer. Magnetic force microscopy imaging done at different stages of the cycle after several loops show compact demagnetized areas surrounded by large saturated zones in the hard layer. A mechanism based on interlayer magnetostatic coupling induced by the stray field created by domain wall in the soft layer is presented.     

Thickness-dependent magnetic properties in Pt/[Co/Ni]n multilayers with perpendicular magnetic anisotropy

We systematically investigated the Ni and Co thickness-dependent perpendicular magnetic anisotropy (PMA) coefficient, magnetic domain structures, and magnetization dynamics of Pt(5 nm)/[Co($t_{\rm Co}$)/Ni($t_{\rm Ni}$)]$_{5}$/Pt(1 nm) multilayers by combining the four standard magnetic characterization techniques. The magnetic-related hysteresis loops obtained from the field-dependent magnetization $M$ and anomalous Hall resistivity (AHR) $\rho_{{xy}}$ showed that the two serial multilayers with $t_{\rm Co} = 0.2$ nm and 0.3 nm have the optimum PMA coefficient $K_{\rm U}$ as well as the highest coercivity $H_{\rm C}$ at the Ni thickness $t_{\rm Ni}= 0.6 $ nm. Additionally, the magnetic domain structures obtained by magneto-optic Kerr effect (MOKE) microscopy also significantly depend on the thickness and $K_{\rm U}$ of the films. Furthermore, the thickness-dependent linewidth of ferromagnetic resonance is inversely proportional to $K_{\rm U}$ and $H_{\rm C}$, indicating that inhomogeneous magnetic properties dominate the linewidth. However, the intrinsic Gilbert damping constant determined by a linear fitting of the frequency-dependent linewidth does not depend on the Ni thickness and $K_{\rm U}$. Our results could help promote the PMA [Co/Ni] multilayer applications in various spintronic and spin-orbitronic devices.     

The 50 nm-thick yttrium iron garnet films with perpendicular magnetic anisotropy

Yttrium iron garnet (YIG) films possessing both perpendicular magnetic anisotropy (PMA) and low damping would serve as ideal candidates for high-speed energy-efficient spintronic and magnonic devices. However, it is still challenging to achieve PMA in YIG films thicker than 20 nm, which is a major bottleneck for their development. In this work, we demonstrate that this problem can be solved by using substrates with moderate lattice mismatch with YIG so as to suppress the excessive strain-induced stress release as increasing the YIG thickness. After carefully optimizing the growth and annealing conditions, we have achieved out-of-plane spontaneous magnetization in YIG films grown on sGGG substrates, even when they are as thick as 50 nm. Furthermore, ferromagnetic resonance and spin pumping induced inverse spin Hall effect measurements further verify the good spin transparency at the surface of our YIG films.