Spin-wave excitation by direct current in obliquely magnetized nanostructures

The magnetization dynamics of magnetic nanostructures magnetized at an arbitrary out-of-plane angle is investigated with the spin-wave formalism. The magnetic excitations driven by a spin-polarized direct current are considered to be standing spin-wave modes appropriate for nanopillar structures. The spin waves grow exponentially above a certain critical value of the current density and their post-threshold nonlinear dynamics leads to magnetization oscillations in the microwave range. Due to demagnetizing fields, the current-driven excitation strongly depends on the direction of the applied external magnetic field. In order to calculate the microwave oscillation frequency we derive an equation of motion for the spin-wave amplitude as a function of the out-of-plane angle of the applied field. The results are compared with recent experimental data as well as with another theoretical approach.     

Domain wall dynamics driven by spin transfer torque and the spin-orbit field

We have studied current-driven dynamics of domain walls when an in-plane magnetic field is present in perpendicularly magnetized nanowires using an analytical model and micromagnetic simulations. We model an experimentally studied system, ultrathin magnetic nanowires with perpendicular anisotropy, where an effective in-plane magnetic field is developed when current is passed along the nanowire due to the Rashba-like spin-orbit coupling. Using a one-dimensional model of a domain wall together with micromagnetic simulations, we show that the existence of such in-plane magnetic fields can either lower or raise the threshold current needed to cause domain wall motion. In the presence of the in-plane field, the threshold current differs for positive and negative currents for a given wall chirality, and the wall motion becomes sensitive to out-of-plane magnetic fields. We show that large non-adiabatic spin torque can counteract the effect of the in-plane field.     

AC-current-induced magnetization switching in amorphous microwires

We studied the influence of AC current flowing through microwires, on magnetization dynamics. We used a previously developed Sixtus-Tonks modified setup to evaluate the domain wall (DW) velocity within the microwire. However, instead of a magnetizing solenoid, we used a current flowing through the microwire. We observed that the AC current flowing through the annealed Co-rich microwire leads to remagnetization by fast domain wall propagation. The estimated DW velocity was approximately 4.5 km/s, which is similar to and even higher than that reported for the magnetic-field-driven domain wall propagation in Fe- and Co-rich microwires. We measured the DW velocity under tensile stress, and found that the DW velocity decreases under applied stress. An observed DW propagation induced by the current flowing through the microwire is explained considering the influence of an Oersted magnetic field on the outer domain shell. This field has a circular easy magnetization direction and magnetostatic interaction between the outer circumferentially magnetized shell and the inner axially magnetized core.     

Simultaneous observation of atomic step and domain wall structure of ultrathin Co films by magnetic force microscopy in ultrahigh vacuum

We have applied magnetic force microscopy in ultrahigh vacuum to study the correlation between the atomic step and magnetic domain wall structure of ultrathin Co films prepared in situ on Au(111) substrates. For the first time we were able to achieve high-resolution images showing simultaneously a clear domain wall contrast and the underlying atomic step structure. Although for in-plane magnetized Co films the domain walls were found to run preferentially in a direction perpendicular to the steps, no such correlation could be observed for out-of-plane magnetized Co films. Received: 3 June 1999 / Accepted: 4 June 1999 / Published online: 29 July 1999     

Current-driven magnetization switching and domain wall motion in nanostructures—Survey of recent experiments

An overview of recent experimental studies and new routes in the field of current-driven magnetization dynamics in nanostructured materials is given. The review introduces the basic concepts (Landau–Lifshitz phenomenology, critical current, spin currents in relation to spin accumulation, adiabatic/non-adiabatic spin-torque) and describes the main results of recent experiments on current-driven magnetization reversal within vertical pillar-like nanostructures and current-driven domain wall motion within laterally confined specimens. While for the pillar systems a discussion is provided of how the introduction of layers with perpendicular magnetic anisotropy, tunnel barriers and exchange bias and(or) oxide layers can be used to reduce the critical current densities for current-induced switching, the role of perpendicular anisotropy, use of spin valve structures, diluted magnetic semiconductors and epitaxial materials to increase the domain wall velocities are reviewed in the case of current-driven domain wall movement within lateral systems.     

Concept of the field-driven domain wall motion memory

In this paper, the concept of field-driven domain wall motion memory is presented. It is confirmed that a domain is shifted with a carefully designed non-uniform field by micromagnetic simulations. The shift of a domain—a bit—can be established by the motion of two domain walls to the same direction and the same distance. In order to get a better understanding of the domain wall motion under the non-uniform transverse magnetic field, we investigate the motion of the transverse Néel-type domain wall by micromagnetic simulations and the collective coordinate approach. The validity of the equation of motion for the domain wall is confirmed by the micromagnetic simulations as functions of the gradient of the non-uniform field, the saturation magnetization, and the Gilbert damping parameter α.     

Controlled domain wall motion by current into patterned-U Ni80Fe20 wires

The current-induced domain wall motion was observed experimentally in the case of the domain wall trapped at the semicircular arc within the U shape Ni₈₀Fe₂₀ wire. The measurement of the current-induced domain wall motion was achieved by adding a biased field before switching field and a critical current density was measured. We found two magnetic domain structures in the U pattern. At zero fields, the vortex domain wall nucleated at the semicircular arc of the U pattern. Continuous magnetic state without wall was investigated in near-switching field.     

In-plane current-induced magnetization reversal of Pd/CoZr/MgO magnetic multilayers

High critical current density ($> 10^{6}$ A/cm$^{2})$ is one of major obstacles to realize practical applications of the current-driven magnetization reversal devices. In this work, we successfully prepared Pd/CoZr(3.5 nm)/MgO thin films with large perpendicular magnetic anisotropy and demonstrated a way of reducing the critical current density with a low out-of-plane magnetic field in the Pd/CoZr/MgO stack. Under the assistance of an out-of-plane magnetic field, the magnetization can be fully reversed with a current density of about 10$^{4}$ A/cm$^{2}$. The magnetization reversal is attributed to the combined effect of the out-of-plane magnetic field and the current-induced spin-orbital torque. It is found that the current-driven magnetization reversal is highly relevant to the temperature owing to the varied spin-orbital torque, and the current-driven magnetization reversal will be more efficient in low-temperature range, while the magnetic field is helpful for the magnetization reversal in high-temperature range.     

Dynamics of magnetization in ferromagnet with spin-transfer torque

We review our recent works on dynamics of magnetization in ferromagnet with spin-transfer torque. Driven by constant spin-polarized current, the spin-transfer torque counteracts both the precession driven by the effective field and the Gilbert damping term different from the common understanding. When the spin current exceeds the critical value, the conjunctive action of Gilbert damping and spin-transfer torque leads naturally the novel screw-pitch effect characterized by the temporal oscillation of domain wall velocity and width. Driven by space- and time-dependent spin-polarized current and magnetic field, we expatiate the formation of domain wall velocity in ferromagnetic nanowire. We discuss the properties of dynamic magnetic soliton in uniaxial anisotropic ferromagnetic nanowire driven by spin-transfer torque, and analyze the modulation instability and dark soliton on the spin wave background, which shows the characteristic breather behavior of the soliton as it propagates along the ferromagnetic nanowire. With stronger breather character, we get the novel magnetic rogue wave and clarify its formation mechanism. The generation of magnetic rogue wave mainly arises from the accumulation of energy and magnons toward to its central part. We also observe that the spin-polarized current can control the exchange rate of magnons between the envelope soliton and the background, and the critical current condition is obtained analytically. At last, we have theoretically investigated the current-excited and frequency-adjusted ferromagnetic resonance in magnetic trilayers. A particular case of the perpendicular analyzer reveals that the ferromagnetic resonance curves, including the resonant location and the resonant linewidth, can be adjusted by changing the pinned magnetization direction and the direct current. Under the control of the current and external magnetic field, several magnetic states, such as quasi-parallel and quasi-antiparallel stable states, out-of-plane precession, and bistable states can be realized. Th     

Magnetization switching modes in nanopillar spin valve under the external field

The current-induced magnetic switching is studied in Co/Cu/Co nanopillar with an in-plane magnetization traversed under the perpendicular-to-plane external field.Magnetization switching is found to take place when the current density exceeds a threshold.By analyzing precessional trajectories,evolutions of domain walls and magnetization switching times under the perpendicular magnetic field,there are two different magnetization switching modes:nucleation and domain wall motion reversal;uniform magnetization ...     

Giant current-driven domain wall mobility in (Ga,Mn)As

We study theoretically hole current-driven domain wall dynamics in (Ga,Mn)As. We show that the spin-orbit coupling causes significant hole reflection at the domain wall, even in the adiabatic limit when the wall is much thicker than the Fermi wavelength, resulting in spin accumulation and mistracking between current-carrying spins and the domain wall magnetization. This increases the out-of-plane nonadiabatic spin-transfer torque and consequently the current-driven domain wall mobility by 3 to 4 orders of magnitude. Trends and magnitude of the calculated domain wall current mobilities agree with experimental findings.     

Magnetic field dependence of asymmetry in the magnetization reversal of ultrathin Co films and Co/Pt multilayers with perpendicular anisotropy

We studied the magnetization reversal in ultrathin [Co/Pt]_n films (n=1, 2, and 4) using magneto-optical Kerr microscopy. These materials demonstrate unusual asymmetries in the activity of nucleation centers and domain wall motion. It was found that application of very high holding magnetic field prior to magnetization reversal, exceeding some critical value much larger than the apparent saturation field, suppresses the subsequent ‘asymmetric’ nucleation centers, activity. We revealed that the ‘asymmetric’ nucleation centers become active again after subsequent reversal cycles coming from a smaller holding field and studied how the asymmetry returns with the decrease of applied holding field. It was found that in low-coercivity ultrathin Co films, the asymmetry in domain wall velocity decreased sharply with the applied field increase and disappeared when the reversal field is greater than μ₀H=1.5 mT.     

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.     

Magnetic structure and mechanisms of magnetic reversal of a quick-quenched ferromagnetic wire core

Mechanisms of motion of the domain top separating oppositely magnetized domains through an amorphous ferromagnetic wire core are investigated in an external magnetic field. The equilibrium parameters of the domain in the wire core are determined. It is established that the character of motion of the domain top trough the wire core depends on the mutual orientation of the external magnetic field and the domain magnetization. It is demonstrated that amorphous ferromagnetic wires based on transition metals possess the magnetic diode effect. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 64–69, February, 2008.     

Domain structure and magnetization processes in permalloy propagation elements

A review of domain structures and magnetization processes in permalloy overlays is given, together with some new results. The simplest domain structure for a given element consists of a loop of magnetic flux, but in elements with irregular geometry the circulating flux is not constant. More complex structures arise when an element contains internal closure domains. In-plane anisotropy in permalloy affects the distribution of closure domains but with decreasing bar width the influence of anisotropy is reduced. Reversible wall motion in weak fields gives way to hysteresis effects when the applied field exceeds a certain level, H_s. In particular magnetization buckling may occur. Some details of buckling in asymmetric chevrons and half-discs are given and compared with the behaviour in an I-bar. The proximity of a bubble medium containing stripe domains is shown to reduce considerably the applied fields needed for buckling in overlay components. Following saturation, changes in the demagnetized state are usually apparent. On a simple level, the spin structure and polarity of Bloch walls is altered. More noticeably the wall pattern itself can change when closure domains are created or annihilated in pairs. The significance of these fluctuations for bubble propagation is assessed by considering the intrinsic stray field profile of a Bloch wall segment. A simple wall model is employed. It is demonstrated that a curved domain wall provides a reasonable basis for modelling the field of a magnetized bar up to saturation. Calculated values of H_s agree qualitatively with experiment. The external field of the bar is rather insensitive to the exact distribution of free-pole density. Together with the observed complexities of domain behabiour this reaffirms the validity of the continuum approach to modelling.     

Anomalous magnetization processes and non-symmetrical domain wall displacements in L10 FePt particulate films

Anomalous magnetization processes and non-symmetrical domain wall displacements in the minor loop of L1₀ FePt particulate films were investigated by magnetization measurements and in situ magnetic force microscopy. Magnetization (M) decreases dramatically on increasing the magnetic field to ∼3 kOe after which M becomes small and constant in the range of 5–20 kOe as observed in the successive measurement of minor loops. The domain wall displacement is non-symmetrical with respect to the field direction. The anomalous magnetization behavior was attributed to the non-symmetrical domain wall displacement and large magnetic field required for domain wall nucleation. Energy calculations from modeling suggest that non-symmetrical domain wall displacement is caused by the existence of metastable domains in which the domain edges are stuck to the particle boundaries.     

Nanometer scale observation of high efficiency thermally assisted current-driven domain wall depinning

Nanometer scale observation of the depinning of a narrow domain wall (DW) under a spin current is reported. We studied approximately 12 nm wide 1D Bloch DWs created in thin films exhibiting perpendicular magnetic anisotropy. Magnetotransport measurements reveal thermally assisted current-driven DW motion between pinning sites separated by as little as 20 nm. The efficiency of current-driven DW motion assisted by thermal fluctuations is measured to be orders of magnitude higher than has been found for in-plane magnetized films, allowing us to control DW motion on a nanometer scale at low current densities.     

Instantons and solitons in a monolayer film of ferromagnetic grains with biaxial anisotropy

We investigate domain wall and domain structure in a monolyer film consisting of ferromagnetic grains with biaxial anisotropy, which are seen to be the static versions of instanton and soliton, respectively. The equation of motion of the magnetization vector is reduced to the (1 + 2)-dimensional sine-Gordon field equation in strong anisotropy limit and the instanton and soliton configurations are obtained analytically. Various new domain structures in the ferromagnetic film are found.     

Spatial distribution of magnetic field and persistent currents in Condon domain phase

The distributions of magnetic field above the surface of the sample due to existence of the diamagnetic domain structure are found. It is shown, that the constant magnetic induction splitting inside of a sample is caused by the magnetization current density, localised in the boundaries between adjacent domains, close to the sample surface. The properties of this current are studied. The influence of the domain wall thickness on the spatial distribution of magnetic field and magnetization current density is present. A possibility of detection of the changes in the magnetic field distribution in vacuum, close to the surface of the sample, by means of Hall probes, is discussed. The measurement of the spatial distribution of magnetic field can give lacking information about characteristic sizes of magnetic domain formation at the conditions of the strong de Haas van Alphen effect.     

Experimental evidence for intra-atomic noncollinear magnetism at thin film probe tips

The energy-dependent spin-density orientation (SDO) at the apex of thin magnetic film tips is studied by spin-polarized scanning tunneling spectroscopy (SP-STS) at different bias voltages. At most energies the SDO is collinear with the tip magnetization resulting in a domain or domain-wall contrast in SP-STS images of out-of-plane magnetized samples measured with Gd or Fe coated tips, respectively. For some bias voltages, however, the SDO of the tip is found to be almost perpendicular to its magnetization. This result is explained in terms of intra-atomic noncollinear magnetism.