Micromagnetic simulation of domain wall pinning and domain wall motion

Domain wall pinning is the coercivity mechanism of permanent magnets used in high temperature applications. In SmCo based magnets domain walls get trapped at the cellular precipitation structure causing a high coercive field. The motion of domain walls and their propagation velocity are important in soft magnets as used in sensor applications. A finite element micromagnetic algorithm was developed to study the motion of domain walls in complex microstructures. The cellular microstructure of SmCo magnets or the cylindrical soft wires can be easily built using tetrahedral finite elements. The pinning of the domain walls has been studied for different material compositions. Attractive and repulsive domain wall pinning are observed and their behaviour for increasing thickness of the precipitation structure is explained. The motion of domains in magnetic nanowires was calculated using adaptive mesh refinement. The wall velocity strongly depends on the domain wall structure. Transverse and vortex walls have been observed and their velocity in wires of different thickness has been studied.     

Atomic Level 1D Structural Modulations at the Negatively Charged Domain Walls in BiFeO3 Films

Charged domain walls (CDWs) show great potentials to mediate the properties of ferroelectrics. Direct mapping of these domain walls at an atomic scale is of critical importance for understanding the domain wall dominated properties. Here, based on aberration‐corrected scanning transmission electron microscopy, tail‐to‐tail CDWs at 71°, 109°, and 180° domains in BiFeO₃ thin films have been identified. 2D mappings demonstrate 1D structural modulations with alternate lattice expansions and clockwise/counterclockwise lattice rotations at these CDWs. Such behaviors of CDWs reveal a remarkable contrast to the uncharged domain walls and imply delicate interactions between bound charges and structural compensations of domain wall. These results are expected to provide new information on domain wall structures and shed some light on the understanding of domain wall properties in ferroelectrics.     

Electron emission from ferroelectric thin films enhanced by the presence of 90 degree ferroelectric domains

In this work, a ferroelectric domain-enhanced electron emission mechanism is proposed. The polarization distribution near 90 degrees domain walls is calculated by solving a set of second order differential equations, including the Poisson's one and equations derived from an expansion of the free energy Phi(P) in power series of the polarization according to the Devonshire-Landau-Ginzburg theory. Domain walls intersecting the emitting surface cause sufficient electric fields and lower the potential barrier for electron emission. This induces centers of enhanced electron emission. Relaxing domain walls were found to excite trapped excess electrons in front of the wall.     

Intrinsic Conductance of Domain Walls in BiFeO3

Ferroelectric domain walls exhibit a number of new functionalities that are not present in their host material. One of these functional characteristics is electrical conductivity that may lead to future device applications. Although progress has been made, the intrinsic conductivity of BiFeO₃ domain walls is still elusive. Here, the intrinsic conductivity of 71° and 109° domain walls is reported by probing the local conductance over a cross section of the BiFeO₃/TbScO₃ (001) heterostructure. Through a combination of conductive atomic force microscopy, high‐resolution electron energy loss spectroscopy, and phase‐field simulations, it is found that the 71° domain wall has an inherently charged nature, while the 109° domain wall is close to neutral. Hence, the intrinsic conductivity of the 71° domain walls is an order of magnitude larger than that of the 109° domain walls associated with bound‐charge‐induced bandgap lowering. Furthermore, the interaction of adjacent 71° domain walls and domain wall curvature leads to a variation of the charge distribution inside the walls, and causes a discontinuity of potential in the [110]_p direction, which results in an alternative conductivity of the neighboring 71° domain walls, and a low conductivity of the 71° domain walls when measurement is taken from the film top surface.     

Wall clusters and domain structure conversions

The significance of wall clusters, which is a new concept in the theory of soft magnetic materials, is experimentally demonstrated in thin Permalloy configurations. The wall cluster is a collection of domain walls that have one intersection line in common. The transformation of the domain structures takes place through a coherent movement of the domain walls. The correlation between the walls is especially dominant at the intersection line of the walls, called the cluster knot. Relations for the mutual positions of the walls in the wall clusters of great practical relevance are derived explicitly and verified experimentally. The domain structure is formed by the concatenation of wall clusters. The clock sense of the rotation over the walls in the clusters determine which walls of two clusters are linked during the formation of the domain structure. The creation of new clusters takes place through the unfolding of the walls of the clusters which originally coincide with the so-called creation line. As is demonstrated fully, the application of these ideas improves the insight into the complex process of domain structure transformations.     

Electrical Tunability of Domain Wall Conductivity in LiNbO3 Thin Films

Domain wall nanoelectronics is a rapidly evolving field, which explores the diverse electronic properties of the ferroelectric domain walls for application in low‐dimensional electronic systems. One of the most prominent features of the ferroelectric domain walls is their electrical conductivity. Here, using a combination of scanning probe and scanning transmission electron microscopy, the mechanism of the tunable conducting behavior of the domain walls in the sub‐micrometer thick films of the technologically important ferroelectric LiNbO₃ is explored. It is found that the electric bias generates stable domains with strongly inclined domain boundaries with the inclination angle reaching 20° with respect to the polar axis. The head‐to‐head domain boundaries exhibit high conductance, which can be modulated by application of the sub‐coercive voltage. Electron microscopy visualization of the electrically written domains and piezoresponse force microscopy imaging of the very same domains reveals that the gradual and reversible transition between the conducting and insulating states of the domain walls results from the electrically induced wall bending near the sample surface. The observed modulation of the wall conductance is corroborated by the phase‐field modeling. The results open a possibility for exploiting the conducting domain walls as the electrically controllable functional elements in the multilevel logic nanoelectronics devices.     

Domain walls and transverse shock waves in shape-memory alloys

The martensitic phase transition in shape-memory alloys which is responsible for their ferroelastic and pseudoelastic deformation behaviour is described by a one-dimensional Landau theory. Domain walls between Martensite variants and between Austenite and Martensite are modelled as transverse shock waves. From the balance of momentum and of energy the jump of temperature across and the speed of the domain walls are calculated. The direction of motion follows from the entropy principle. Under certain conditions a moving domain wall acts like a heat engine converting free energy into mechanical work.     

Fast domain wall motion in magnetic comb structures

Modern fabrication technology has enabled the study of submicron ferromagnetic strips with a particularly simple domain structure, allowing single, well-defined domain walls to be isolated and characterized. However, these domain walls have complex field-driven dynamics. The wall velocity initially increases with field, but above a certain threshold the domain wall abruptly slows down, accompanied by periodic transformations of the domain wall structure. This behaviour is potentially detrimental to the speed and proper functioning of proposed domain-wall-based devices, and although methods for suppression of the breakdown have been demonstrated in simulations, a convincing experimental demonstration is lacking. Here, we show experimentally that a series of cross-shaped traps acts to prevent transformations of the domain wall structure and increase the domain wall velocity by a factor of four compared to the maximum velocity on a plain strip. Our results suggest a route to faster and more reliable domain wall devices for memory, logic and sensing.     

Cross-tie domain wall ground state in thin films

Cross-tie domain wall is a complex two dimensional magnetic domain wall structure, often found experimentally in this soft ferromagnetic films with thicknesses of about several exchange lengths. The structure of such a wall can roughly be imagined as a sequence of magnetic vortices and anti-vortices, arranged along a straight line. In this work, equilibrium energies of different one-dimensional magnetic domain wall configurations, existing in this soft ferromagnetic films, are calculated (fully taking into account the exchange and long range dipolar interaction), based on the various classical Ritz models. They are compared to the energy of two-dimensional cross-tie domain wall, thus, estimating the region of the film thicknesses, where the cross-tie structure is the lowest energy domain wall configuration. The upper boundary of this region is estimated here for the first time. Convenient approximate analytical energy expressions in terms of elementary functions are given here both for classical and for cross-tie domain walls.     

Domain wall types and field-induced domain wall motion in L-shaped nanowires

The formation and behavior of domain walls were studied in L-shaped nanowires via micro-magnetic simulation using the Objective Oriented Micro-Magnetic Frame program. We induced three types of domain walls by varying the thickness of the nanowire. A transverse wall, an asymmetric transverse wall, and a vortex wall were induced in 10, 20, and 40 nm-thick nanowires, respectively. The type of domain walls formed was determined by the competition between exchange and magnetostatic energy. The depinning field of the domain wall was the largest for the 20 nm-thick and the smallest for the 10 nm-thick nanowires. Domain wall behaviors were quite different from one another. The transverse wall in the 10 nm-thick nanowire was annihilated without changing its type. In the case of the 40 nm-thick nanowire, the vortex wall was not transformed to another type, but did switch its polarity throughout the depinning process. The wall in the 20 nm-thick nanowire underwent repetitions of the transformation of type and the switching of polarity until annihilation. Our results confirm that the behavior of a domain wall at a corner or a rounded part of nanowires is very complex and it originates from the different spin structures of a domain wall.     

Atomic-scale study of electric dipoles near charged and uncharged domain walls in ferroelectric films

Ferroelectrics are materials exhibiting spontaneous electric polarization due to dipoles formed by displacements of charged ions inside the crystal unit cell. Their exceptional properties are exploited in a variety of microelectronic applications. As ferroelectricity is strongly influenced by surfaces, interfaces and domain boundaries, there is great interest in exploring how the local atomic structure affects the electric properties. Here, using the negative spherical-aberration imaging technique in an aberration-corrected transmission electron microscope, we investigate the cation-oxygen dipoles near 180 degrees domain walls in epitaxial PbZr(0.2)Ti(0.8)O(3) thin films on the atomic scale. The width and dipole distortion across a transversal wall and a longitudinal wall are measured, and on this basis the local polarization is calculated. For the first time, a large difference in atomic details between charged and uncharged domain walls is reported.     

Models for I and T pattern permalloy bars based upon bitter pattern observation of domain wall movements

The magnetostatic fields of the I and T pattern Permalloy overlay bars are analyzed by proposing a model based on the Bitter pattern observation of the domain wall structure in Permalloy bars. The magnetic charges that appear on the 90° domain walls are assumed to be the sources of the magnetic fields of the bars. The model has a two-dimensional reaction to an applied rotating in-plane field due to its two-dimensional domain wall movement and the consequent two-dimensional change of magnetic domain pattern inside the bar. The magnetization of the bar is equal to Msthe saturation magnetization of the bar at every section of the bar except on the domain walls. The magnetization curve and the magnetic field well Bz(bubble drive field) under the overlay bars are calculated and compared to that of the previous models. A qualitative explanation of the rotation of the bubble around the bars is given by the three-dimensional plots of the field well obtained for different orientations of the in-plane field.     

Charged walls in thin magnetic films

Charged walls are domain walls which carry a net "magnetic charge" (div M) due to their orientation relative to the domain magnetizations. They differ from ordinary Bloch and Néel walls (which are uncharged) primarily in their much wider profile. In order to calculate such walls, a variational method was developed. It is based on the separation of that part of stray field energy which would be present even with an infinitely thin wall. The main results of the calculations are as follows. 1) Isolated charged walls do exist if exchange energy is taken into account, as opposed to the periodic solution known for the limit of negligible exchange energy. 2) Rotated, partially charged walls develop a Néel-wall-like narrow core region. Detailed results for the wall profiles, energies and widths as a function of wall angle, orientation, film thickness, and material parameters are presented. They are applied to two examples: the case of a Permalloy film in a domain tip propagation memory, and the case of the implanted layer on a contiguous disk bubble device.     

Cross-Tie Domain Wall Ground State in Thin Films

No Heading Cross-tie domain wall is a complex two dimensional magnetic domain wall structure, often found experimentally in thin soft ferromagnetic films with thicknesses of about several exchange lengths. The structure of such a wall can roughly be imagined as a sequence of magnetic vortices and anti-vortices, arranged along a straight line. In this work, equilibrium energies of different one-dimensional magnetic domain wall configurations, existing in thin soft ferromagnetic films, are calculated (fully taking into account the exchange and long range dipolar interaction), based on the various classical Ritz models. They are compared to the energy of two-dimensional cross-tie domain wall, thus, estimating the region of the film thicknesses, where the cross-tie structure is the lowest energy domain wall configuration. The upper boundary of this region is estimated here for the first time. Convenient approximate analytical energy expressions in terms of elementary functions are given here both for classical and for cross-tie domain walls.PACS numbers: 75.75.+a, 75.25.+z, 75.60.–d.     

Deformation stability of a flat domain wall in magnetic films

The forces determining the orientation of domain walls in films of magnetooptic materials with a figure of merit of order unity are studied. The behavior of small perturbations of the position of a flat domain wall in the presence of an in-plane component of the anisotropy vector is analyzed. The forces arising when the orientation of the domain wall deviates from the easy-magnetization axis and striving to return the wall to its initial state are conventionally represented as a gradient “effective magnetic field.” The forces exerted by the “effective field, ” due to the in-plane component of the anisotropy vector, on the perturbed domain wall are calculated. The orientational stability conditions for a planar domain wall are found. An explanation is given for the experimentally observed predominant orientation of striped domains. Pis’ma Zh. Tekh. Fiz. 25, 49–56 (September 12, 1999)     

Curvature of domain walls

An experiment was performed whereby domain walls were forced to bulge under the influence of an applied easy-axis fieldH. The region where the domain wall is bent appears to be approximately circular. To relate the radius of such a curved domain wall to theory, a model was chosen that takes into account magnetostatic, anisotropy, and exchange energy. The assumption was made that anisotropy and exchange energy, as well as the magnetostatic contribution due to the local magnetization distribution of a domain wall, may be summarized in a wall energy term. The energy of the entire system has been calculated under the constraint that the domain wall should be circular and that it is inscribed tangentially into a triangle. Minimizing the total energy with respect to the radius of curvatureA, the result can be expressed approximately byA propto (H - H_{c})^{-1}where Hcis the coercive force. This result fits the model of a membrane under pressure.     

Effect of magnetic anisotropy on the mobility of the boundaries in thin magnetic films

This paper discusses the effect of magnetic crystallographic anisotropy on the mobility of the domain walls in thin magnetic films with an easy axis in the plane of the film. It shows that the stable configuration of a domain wall is a single-vortex Bloch domain wall. Besides this, there are two metastable states of the domain wall—a Néel domain wall and a domain wall with two magnetic vortices along the normal to the plane of the film. It is also shown that the mobilities of the single-vortex and Néel domain walls and the domain wall with two vortices decrease as the anisotropy constant increases and tend to the same value. Pis’ma Zh. Tekh. Fiz. 24, 42–46 (January 26, 1998)     

Resonant transmission through a double domain wall in magnetic nanowires

As experimentally verified, a large magnetoresistance arises due to domain walls creation (or destruction) in Ni nanowires and in some nanostructures based on GaMnAs magnetic semiconductors. Hence the presence and structuring of magnetic domain walls have important potential applications in magnetoelectronics devices. Here, we uncover a way of controlling the conductance via resonant transmission through a double domain wall structure. This phenomenon is due to quantum interference of charge carrier wave functions in spin quantum wells, which leads to the formation of quantized energy states in the potential well created by a double domain wall. When the energy of a state in the spin quantum well is resonant with the Fermi energy in the wire, the spin–flip transmission through the domain walls becomes most effective. This gives rise to a resonance-type dependence of the conductance on the distance between the domain walls or on the Fermi energy.     

A study of coercivity in Ca-Ge substituted epitaxial garnets

This paper is an analysis of two models on the origin of coercivity in certain crystals. The first model, based upon the work of Kersten. suggested that coercivity in soft magnetic materials is due to the variation in domain wall energy throughout the crystal. The second model attributes coercivity to magnetostatic interactions between domain walls and crystal defects. Recent work on calcium and germanium substituted YIG has shown a defect structure similar to the one assumed in both of these models. Introducing the experimentally observed parameters into the models yields calculated values for the coercivity that are very close to the observed value for the magnetostatic model and very poor for the wall energy variation model.     

2∶17型烧结SmCo磁体磁畴壁钉扎机制

采用传统烧结工艺制备了一组2∶17型烧结SmCo磁体。采用综合物性测量系统(PPMS)、洛伦兹透射电镜(LTEM)和微磁学计算研究了磁体的磁性能、磁畴结构及磁化过程中磁矩的变化过程。结果表明:经慢冷工艺的样品矫顽力为2180kA/m,磁畴壁沿1∶5相分布显示出明显的畴壁钉扎特性,未经慢冷工艺的样品矫顽力很低且磁畴壁呈直线型穿过2∶17相;经慢冷工艺的样品的Cu元素在1∶5相处富集使两相交界处磁晶各向异性降低;微磁学模拟计算证明1∶5相和2∶17相界面处对磁畴壁的吸引钉扎导致慢冷样品矫顽力的提高。