Magnetic soft x-ray microscopy of the domain wall depinning process in permalloy magnetic nanowires

Full-field magnetic transmission x-ray microscopy at high spatial resolution down to 20 nm is used to directly observe field-driven domain wall motion in notch-patterned permalloy nanowires. The depinning process of a domain wall around a notch exhibits a stochastic nature in most nanowires. The stochasticity of the domain wall depinning sensitively depends on the geometry of the nanowire such as the wire thickness, the wire width, and the notch depth. We propose an optimized design of the nanowire for deterministic domain wall depinning field at a notch.     

Unique depinning fields at symmetric double notches in a ferromagnetic permalloy nanowire

Ferromagnetic domain-wall pinning and depinning mechanisms were investigated at permalloy nanowire notches using a micromagnetic calculation. A unique depinning field originated from the symmetric double notches irrespective of the wall polarity or the propagation direction, whereas several distinct pinning mechanisms appeared from single or asymmetric notches. The depinning field was principally determined by the exiting notch slope due to the dynamic narrowing of the domain wall thickness.     

Electric current effect on the energy barrier of magnetic domain wall depinning: origin of the quadratic contribution

The energy barrier of a magnetic domain wall trapped at a defect is measured experimentally. When the domain wall is pushed by an electric current and/or a magnetic field, the depinning time from the barrier exhibits perfect exponential distribution, indicating that a single energy barrier governs the depinning. The electric current is found to generate linear and quadratic contributions to the energy barrier, which are attributed to the nonadiabatic and adiabatic spin-transfer torques, respectively. The adiabatic spin-transfer torque reduces the energy barrier and, consequently, causes depinning at lower current densities, promising a way toward low-power current-controlled magnetic applications.     

Energy landscape study by telegraph noise of domain wall motion

The energy barrier landscape in-between two adjacent pinning sites of magnetic domain wall was investigated by telegraph noise of domain wall motion. The telegraph noise provided numerous depinning times for each pinning site, from which the depinning energy barrier characteristics were extracted. By generating the telegraph noise under application of magnetic field and electric current, the energy barrier landscape could be reconstructed with the barrier height and lateral size of the adjacent pinning sites. The lateral size fits well with other independent estimation based on the signal level with the focused laser beam, providing the validity of the present approach.     

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.     

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.     

Dependence of current and field driven depinning of domain walls on their structure and chirality in permalloy nanowires

A magnetic domain wall (DW) injected and pinned at a notch in a permalloy nanowire is shown to exhibit four well-defined magnetic states, vortex and transverse, each with two chiralities. These states, imaged using magnetic force microscopy, are readily detected from their different resistance values arising from the anisotropic magnetoresistance effect. Whereas distinct depinning fields and critical depinning currents in the presence of magnetic fields are found, the critical depinning currents are surprisingly similar for all four DW states in low magnetic fields. We observe current-induced transformations between these DW states below the critical depinning current which may account for the similar depinning currents.     

Explicit solutions to phenomenological models of magnetization reversal of thin ferromagnetic films in the presence of a sawtooth magnetic field

Explicit solutions are derived for several phenomenological models of magnetization reversal in thin ferromagnetic films driven by a sawtooth magnetic field. For a domain wall velocity that is linear in the magnetic field, it is found that the dynamic coercive field follows a square-root power-law in the slope of the magnetic field, shifted by the depinning field. For a more general domain wall velocity different power-law exponents are found, yet the overall form for the scaling of the area of the hysteresis loop remains a power-law shifted by the depinning field. This shifted power-law could be interpreted to be a crossover between adiabatic and dynamic regimes.     

The influence of wire width on the charge distribution of transverse domain walls and their stray field interactions

We present here a numerical study of the magnetostatic charge distribution of transverse Néel type domain wall in permalloy nanowires. The calculations indicate that not only is the distribution highly non-uniform within a given transverse wall but it also varies dramatically with respect to the wire width. The implications of this for magnetostatic domain wall pinning are analyzed by considering the stray field interaction between a wall and another extended magnetic body for a particular domain wall chirality, where two distinct depinning mechanisms are observed depending on the wire width.     

Thermally activated depinning of a narrow domain wall from a single defect

We describe the field induced depinning process of a magnetic domain wall (DW) from a single bidimensional nanometric defect. The DW propagates in a wire lithographed on a film with strong perpendicular anisotropy. We observe a statistical distribution of the relaxation time consistent with a Néel-Brown picture of magnetization reversal. This indicates that the nanometric DW can be considered as an ideal monodomain particle switching over a single energy barrier. Such a stochastic character of DW depinning has to be taken into account for spintronic applications.     

Depinning of a domain wall in the 2d random-field Ising model

We report studies of the behaviour of a single driven domain wall in the 2-dimensional non-equilibrium zero temperature random-field Ising model, closely above the depinning threshold. It is found that even for very weak disorder, the domain wall moves through the system in percolative fashion. At depinning, the fraction of spins that are flipped by the proceeding avalanche vanishes with the same exponent as the infinite percolation cluster in percolation theory. With decreasing disorder strength, however, the size of the critical region decreases. Our numerical simulation data appear to reflect a crossover behaviour to an exponent at zero disorder strength. The conclusions of this paper strongly rely on analytical arguments. A scaling theory in terms of the disorder strength and the magnetic field is presented that gives the values of all critical exponent except for one, the value of which is estimated from scaling arguments. Received: 13 February 1998 / Accepted: 30 March 1998     

Controlled pinning and depinning of domain walls in nanowires with perpendicular magnetic anisotropy

We investigate switching and field-driven domain wall motion in nanowires with perpendicular magnetic anisotropy comprising local modifications of the material parameters. Intentional nucleation and pinning sites with various geometries inside the nanowires are realized via a local reduction of the anisotropy constant. Micromagnetic simulations and analytical calculations are employed to determine the switching fields and to characterize the pinning potentials and the depinning fields. Nucleation sites in the simulations cause a significant reduction of the switching field and are in excellent agreement with analytical calculations. Pinning potentials and depinning fields caused by the pinning sites strongly depend on their shapes and are well explained by analytical calculations.     

烧结Nd-Fe-B永磁合金矫顽力机制的理论与实验研究

从理论和实验上研究了烧结Ｎｄ－Ｆｅ－Ｂ永磁合金的矫顽力随取向磁场的变化规律。指出磁体反磁化过程主要是晶粒边界软磁性区的反磁化成核以及反磁化核长大成畴并向晶粒内部不可逆畴壁位移的过程。比较了成核场与退钉扎场的大小及其随磁场方向的变化，并得出结论：退钉扎场是决定烧结Ｎｄ－Ｆｅ－Ｂ磁体矫顽力的主要机制。 关键词：     

Domain wall pinning by defects and the C-I transition

The influence of randomly distributed defects on domain wall fluctuations is investigated. These fluctuations lead to the long-range repulsion between domain walls resulting in the experimentally observed n;～ √z.sfnc;T;? T_cz.sfnc; behaviour of the domain wall density near the C-I transition. The impossibility of thermal depinning of one domain wall in the impurity potential is also shown.     

Measurement of the nucleation and domain depinning field in a single Co/Pt multilayer dot by Anomalous Hall effect

Co/Pt multilayer dots with perpendicular anisotropy and with diameters of 250 and 350 nm were fabricated on top of a Hall cross configuration. The angular dependence of the magnetic reversal of the individual dot was investigated by Anomalous Hall effect measurements. At near in-plane angles (85° with the magnetic easy axis) the dot switches partially into a stable two-domain state. This allows for separate analysis of the angular dependence of both the field required for nucleation of a reversed domain, and the field required for depinning of the domain wall. The angular dependence of the depinning field fits accurately to a 1/cos(θ) behavior, whereas the angular dependence of the nucleation field shows a minimum close to 45°. The latter dependency can be accurately fitted to the modified Kondorsky model proposed by Schumacher [1].     

Influence of three-dimensional inhomogeneities of the magnetic parameters on the dynamics of vortex-like domain walls

The interaction of a vortex-like domain wall moving in an external magnetic field with a three-dimensional periodic chain of cubic volumes with high values of the saturation magnetization and magnetic anisotropy constant has been investigated theoretically. It has been found that the result of the interaction depends on the initial distance between the wall and the region of inhomogeneity of magnetic parameters at the moment of turning on the external magnetic field. The pinning of domain walls near the regions with high values of the saturation magnetization and magnetic anisotropy constant has been investigated, and the anisotropy of the corresponding depinning fields has been revealed. The method of investigation is the numerical micromagnetic simulation.     

The stochastic nature of the domain wall motion along high perpendicular anisotropy strips with surface roughness

The domain wall dynamics along thin ferromagnetic strips with high perpendicular magnetocrystalline anisotropy driven by either magnetic fields or spin-polarized currents is theoretically analyzed by means of full micromagnetic simulations and a one-dimensional model, including both surface roughness and thermal effects. At finite temperature, the results show a field dependence of the domain wall velocity in good qualitative agreement with available experimental measurements, indicating a low field, low velocity creep regime, and a high field, linear regime separated by a smeared depinning region. Similar behaviors were also observed under applied currents. In the low current creep regime the velocity-current characteristic does not depend significantly on the non-adiabaticity. At high currents, where the domain wall velocity becomes insensitive to surface pinning, the domain wall shows a precessional behavior even when the non-adiabatic parameter is equal to the Gilbert damping. These analyses confirm the relevance of both thermal fluctuations and surface roughness for the domain wall dynamics, and that complete micromagnetic modeling and one-dimensional studies taking into account these effects are required to interpret the experimental measurements in order to get a better understanding of the origin, the role and the magnitude of the non-adiabaticity.     

Numerical approaches on driven elastic interfaces in random media

We discuss the universal dynamics of elastic interfaces in quenched random media. We focus on the relation between the rough geometry and collective transport properties in driven steady-states. Specially devised numerical algorithms allow us to analyze the equilibrium, creep, and depinning regimes of motion in minimal models. The relevance of our results for understanding domain wall experiments is outlined.     

Quantum mechanisms of density wave transport

We report on new developments in the quantum picture of correlated electron transport in charge and spin density waves. The model treats the condensate as a quantum fluid in which charge soliton domain wall pairs nucleate above a Coulomb blockade threshold field. We employ a time-correlated soliton tunneling model, analogous to the theory of time-correlated single electron tunneling, to interpret the voltage oscillations and nonlinear current-voltage characteristics above threshold. An inverse scaling relationship between threshold field and dielectric response, originally proposed by Grüner, emerges naturally from the model. Flat dielectric and other ac responses below threshold in NbSe₃ and TaS₃, as well as small density wave phase displacements, indicate that the measured threshold is often much smaller than the classical depinning field. In some materials, the existence of two distinct threshold fields suggests that both soliton nucleation and classical depinning may occur. In our model, the ratio of electrostatic charging to pinning energy helps determine whether soliton nucleation or classical depinning dominates.     

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.