Domain Wall Segments Research Articles

An alternative understanding of the skyrmion Hall effect based on one-dimensional domain wall motion

A moving magnetic skyrmion exhibits transverse deflection. This so-called skyrmion Hall effect has been explained by the Thiele equation. Here, we provide an alternative interpretation of the skyrmion Hall effect based on the dynamics of domain walls enclosing the skyrmion. We relate the spin-torque-induced local rotation of the domain wall segments to the shift of the skyrmion core, explaining the skyrmion Hall effect at the micromagnetic level. Based on our intuitive interpretation, we also show that the skyrmion Hall effect can be suppressed by combining the spin-transfer and spin–orbit torques, thereby removing the major obstacle to utilizing skyrmions in devices.

Universal Hopping Motion Protected by Structural Topology.

A scaling law elucidates the universality in nature, presiding over many physical phenomena which seem unrelated. Thus, exploring the universality class of scaling law in a particular system enlightens its physical nature in relevance to other systems and sometimes unearths an unprecedented new dynamic phase. Here, the dynamics of weakly driven magnetic skyrmions are investigated, and its scaling law is compared with the motion of a magnetic domain wall (DW) creep. This study finds that the skyrmion does not follow the scaling law of the DW creep in 2D space but instead shows a hopping behavior similar to that of the particle-like DW in 1D confinement. In addition, the hopping law satisfies even when a topological charge of the skyrmion is removed. Therefore, the distinct scaling behavior between the magnetic skyrmion and the DW stems from a general principle beyond the topological charge. This study demonstrates that the hopping behavior of skyrmions originates from the bottleneck process induced by DW segments with diverging collective lengths, which is inevitable in any closed-shape spin structure in 2D. This work reveals that the structural topology of magnetic texture determines the universality class of its weakly driven motion, which is distinguished from the universality class of magnetic DW creep.

Giant conductivity of mobile non-oxide domain walls

Atomically sharp domain walls in ferroelectrics are considered as an ideal platform to realize easy-to-reconfigure nanoelectronic building blocks, created, manipulated and erased by external fields. However, conductive domain walls have been exclusively observed in oxides, where domain wall mobility and conductivity is largely influenced by stoichiometry and defects. Here, we report on giant conductivity of domain walls in the non-oxide ferroelectric GaV4S8. We observe conductive domain walls forming in zig-zagging structures, that are composed of head-to-head and tail-to-tail domain wall segments alternating on the nanoscale. Remarkably, both types of segments possess high conductivity, unimaginable in oxide ferroelectrics. These effectively 2D domain walls, dominating the 3D conductance, can be mobilized by magnetic fields, triggering abrupt conductance changes as large as eight orders of magnitude. These unique properties demonstrate that non-oxide ferroelectrics can be the source of novel phenomena beyond the realm of oxide electronics.

2D magnetic domain wall ratchet: The limit of submicrometric holes

The study of ratchet and crossed-ratchet effects in magnetic domain wall motion through 2D arrays of asymmetric holes is extended in this article to the submicrometric limit in hole size (small size regime). Therefore, the gap has been closed between the 2D ratchets in the range of tens-of-micrometers (large size regime) and the small size regime 1D ratchets based on nanowires. The combination of Kerr microscopy, X-ray PhotoEmission Electron Microscopy and micromagnetic simulations has allowed a full magnetic characterisation of both the domain wall (DW) propagation process over the whole array and the local DW morphology and pinning at the holes. It is found that the 2D small size limit is driven by the interplay between DW elasticity and half vortex propagation along hole edges: as hole size becomes comparable to DW width, flat DW propagation modes are favoured over kinked DW propagation due to an enhancement of DW stiffness, and pinned DW segments adopt asymmetric configurations related with Néel DW chirality. Nevertheless, both ratchet and crossed-ratchet effects have been experimentally found, and we propose a new ratchet/inverted-ratchet effect in the submicrometric range driven by magnetic fields and electrical currents respectively.

The noise of many needles: Jerky domain wall propagation in PbZrO3 and LaAlO3

Measurements of the sample length of PbZrO3 and LaAlO3 under slowly increasing force (3-30 mN/min) yield a superposition of a continuous decrease interrupted by discontinuous drops. This strain intermittency is induced by the jerky movement of ferroelastic domain walls through avalanches near the depinning threshold. At temperatures close to the domain freezing regime, the distributions of the calculated squared drop velocity maxima N(υm2) follow a power law behaviour with exponents ε=1.6±0.2. This is in good agreement with the energy exponent ε=1.8±0.2 recently found for the movement of a single needle tip in LaAlO3 [R. J. Harrison and E. K. H. Salje, Appl. Phys. Lett. 97, 021907 (2010)]. With increasing temperature, N(υm2) changes from a power law at low temperatures to an exponential law at elevated temperatures, indicating that thermal fluctuations increasingly enable domain wall segments to unpin even when the driving force is smaller than the corresponding barrier.

Local ferroelectricity at the domain walls and stripe domain heads in iron garnet films

ABSTRACTThe concept of local ferroelectricity discussed in this paper belongs to the emerging field of ultrathin multiferroics. The idea of the ferroelectric polarization associated with the domain walls in magnets proposed by V.G. Bar'yakhtar et al. more than thirty years ago has recently got experimental evidence including electric field driven magnetic domain wall motion and electric field induced Stark shift in the single molecule microscopy. The special attention is paid here to the magnetoelectric properties of dislocation in stripe domain structure (i.e. the stripe domain heads) that differ considerably from the ones of straight domain wall segments. It is shown that the electric field induced displacement of the domain wall can be increased by an order of value with external constant magnetic field.

Spin excitations of ferronematic order in underdoped cuprate superconductors.

High-temperature superconductors exhibit a characteristic hourglass-shaped spectrum of magnetic fluctuations which most likely contribute to the pairing glue in the cuprates. Recent neutron scattering experiments in strongly underdoped compounds have revealed a significant low energy anisotropy of these fluctuations which we explain by a model in which topological defects of the antiferromagnet clump to producing domain wall segments with ferronematic order. This state does not invoke global charge order but breaks C4 rotational and inversion symmetry. The incommensurability of the low doping charge-disordered state is in good agreement with experiment and interpolates smoothly with the incommensurability of the stripe phase at higher doping. Within linear spin-wave theory the dynamic structure factor is in very good agreement with inelastic neutron scattering data and can account for the observed energy dependent anisotropy.

Dynamics of domain growth driven by dipolar interactions in a perpendicularly magnetized ultrathin film

Measurements of the ac magnetic susceptibility of perpendicularly magnetized Fe/2ML Ni/W(110) ultrathin films show a clear signature of the dynamics of domain growth and domain density changes in the striped domain pattern that this system supports. The susceptibility peak measured at different constant heating rates in the range 0.20 K/s < R < 0.70 K/s shifts to higher temperature as the heating rate is increased. Analysis using a relaxation model demonstrates quantitatively that the dynamics is driven by a non-equilibrium domain density at (nearly) zero field (i.e. by dipole interactions), and that the temperature shift is due to a response time determined by the pinning of local domain wall segments by structural defects. The fundamental time scale for relaxation of the domain density driven by dipole interactions is of order 10^5 times slower than the fundamental time scale for an individual Barkhausen step driven by an applied field. The increase in the fundamental time scale reflects the relative size of dipole and Zeeman energies, and the need for the correlated motion of many local domain wall segments to affect domain growth.

A COMBINED MAGNETO-OPTIC-MAGNETIC FORCE MICROSCOPE STUDY OF AMORPHOUS AND MULTILAYER FILMS

We have combined a Magnetic Force/Atomic Force Microscope (MFM/AFM) with a Magneto-optic (MO) microscope. This instrument combines the high spatial resolution of the MFM/AFM and its capability to correlate magnetic structure with the structure of the sample surface with the real-time imaging capability and large field of view of the MO microscope. Using this instrument, we studied nucleation and displacement of domain walls (DW) in amorphous TbFe alloy films and Co/Pd multilayer films. We found that in Co/Pd multilayer film with 20 Co/Pd layer pairs and 16 nm total thickness, nucleation of domains during sample remagnetizations occurs repeatedly in the same points, and that displacement of domain walls is unidirectional. The high topographic resolution of the AFM allowed us to show that domains nucleate at small defects (1-2 nm in depth) on the sample surface. The unidirectional displacement of the domain walls was found to correlate with the anisotropic structure of the sample surface. We observed reversible bending of domain wall segments pinned to defects and irreversible, jump-like displacement of domain wall segments in an applied magnetic field. The maximum reversible displacement of domain walls was 50-100 nm and the length of the segments which reversibly curved in the field was about 150 nm. Measurement of the change in radius of curvature of a DW segment in response to an applied field allowed estimation of the DW energy density and local self-demagnetizing field of the film acting on the DW. The irreversible displacement of a DW was not a continuous process. The 200 - 400 nm long DW segments exhibited jump-like motion over distances of 100-150 nm.

Micromagnetics and hysteresis as prototypes for complex systems

Keynote remarks are made for the workshop on micromagnetics and hysteresis, mentioning magnetization patterns in both particulate and continuous media. Details on complexity in magnetic recording media are presented in a separate paper. Here the emphasis is on topology as the source of hysteresis in iron whiskers, the most well defined of all magnetic materials. It is argued that approximate methods of treating micromagnetic problems can be educational and useful for the iron whisker. The configurations discussed include the intersection of a domain wall with a surface, the intersection of two counter rotating domain wall segments and the intersection of the latter with a surface. The role of singularities in the continuum model is emphasized. Simple mathematical functions are given as starting points for complex computational modeling of the competition between local interactions including exchange and anisotropy energies, and long-range interactions including magnetostatic and magnetoelastic energies. Long-range interactions can be approximated by fictitious local energy terms in intermediate steps designed to reduce the costs in calculating six-fold magnetostatic integrals.

Domain wall displacements in amorphous films and multilayers studied with a magnetic force microscope

The magnetic force microscope (MFM) was used to study the displacement of domain walls (DW) in amorphous TbFe alloy films and Co/Pd multilayer films with high spatial resolution. The reversible bending of domain wall segments pinned to defects and irreversible, jumplike displacement of domain wall segments were imaged with the MFM in an applied magnetic field. The maximum reversible displacement of domain walls was 50–100 nm and the length of the segments which reversibly curved in the field was about 150 nm. Measurement of the change in radius of curvature of a DW segment in response to an applied field allowed estimation of the DW energy density and self-demagnetizing field of the film acting on the DW. The DW energy density for the TbFe films was about 1 erg/cm2. It was shown that the self-demagnetizing field acting on a domain wall depends on the domain structure surrounding the studied DW segment. For instance, for a film with saturation magnetization 100 G and thickness 80 nm, which exhibited a mazelike domain structure, the demagnetizing field varied from 100 G in the center of a mazelike domain to 400 G near the edge of a domain. The irreversible displacement of a DW was not a continuous process. The 200–400 nm long DW segments exhibited jumplike motion over distances of 100–150 nm.

Magnetization process in perpendicular epitaxial Cu/Ni/Cu/Si (001) (abstract)

Epitaxial Cu/Ni/Cu (001) films exhibit perpendicular anisotropy over an exceptionally wide thickness range (30 Å⩽Ni⩽145 Å).12 Magnetic force microscopy (MFM) has been used to reveal new details of the magnetization process;34 here we focus on two features. (1) the forces of attraction and repulsion between different segments of domain walls and (2) a bimodal distribution of magnetization response times to perpendicular applied fields. Domain images were taken using high-resolution scanning MFM in perpendicular fields up to 500 Oe. The following observations are explained. As high energy domains are reduced in area by a perpendicular applied field, the domain patterns (whose wall orientations in zero field have no correlation with the easy in-plane 〈110〉 directions) evolve to a serpentine pattern. Some lengths of the serpentine domains collapse completely while others shrink in width with opposite walls failing to annihilate each other even in fields up to 500 Oe. These “hard domains” show a preference for alignment with the easy 〈110〉 directions. We believe the annihilation and hard domain behavior to be due to the combination of opposing short-range exchange and long-range dipole interactions between lengths of domain wall having the same or opposite chirality; chirality along a domain wall changes at a Bloch line. The alignment of hard threadlike domains with the 〈110〉 directions is due to the magnetoelastic interaction between the misfit dislocation strain field and the in-plane magnetization of the domain wall. Films of Ni thickness up to 85 Å can be saturated and show a remanence ratio of unity by MFM, vibrating sample magnetometry and magneto-optic Kerr effect in perpendicular fields. On the other hand, for 100 Å of Ni, the remanence ratio is smaller and the MFM images at 500 Oe show a small fractional area of unreversed domains; thicker films show larger unsaturated fractions. The magnetization process in films of 75–100 Å Ni is revealed in the MFM images to have an instantaneous field response and a slower time response (in constant field) over a period of several minutes. The instantaneous response is due to the motion of glissile domain wall segments; the after effect appears to be due to the thermally activated motion of Bloch lines along the hard wall segments.

MO determination of domain wall polarity and location of VBL by spatial filtering with phase correction (abstract)

We have developed a new technique1 for direct optical observation of domain wall (DW) polarity (direction of midwall magnetization M) in order to determine the location of vertical Bloch lines (VBL) in LPE bismuth based garnet films with perpendicular anisotropy. A polarizing light microscope with slope illumination of the sample (one-side dark-field observation technique) and a quartz quarter wave plate, placed behind the objective, were used for phase corrections so that some DW (or segments) are shaded. Equations describing intensity distributions of the light diffracted by magnetic inhomogeneities were obtained from diffraction theory.1 The phase relations between complex amplitudes Ep and Es of the diffracted wave were shown to be a function of the DW polarity. According to this theory, the diffracted light from domain walls of opposite polarity will exhibit a dark light for suitable conditions of polarizer and quarter wave plate orientation. The theoretical results were experimentally verified. The proposed magneto-optic (MO) technique where the image contrast depends on the polarity of DW segments differs from that of Refs. 2 and 3 since we used the phase correction (plate λ/4) and an electronic or computer processing of the image were not needed.&amp;lt;ks&amp;gt;

The dynamics of a honeycomb array of domain walls as a network of interconnected strings

A honeycomb array of domain walls such as is found in incommensurate phases of rare-gas monolayers on graphite is shown to vibrate as an interconnected network of strings. The vibrational modes of the network are determined by the vertices, which provide the boundary conditions for the domain-wall segments. The dynamical matrix is constructed and solved for the normal modes. The krypton on graphite system is used as a test to the theory. A Hamiltonian is constructed for the domain-wall network and the amplitude of the lowest energy mode, the breathing mode, is discussed.

Renormalized model for the dynamics of the krypton-on-graphite domain-wall lattice.

The dynamics of an incommensurate monolayer with distinct domain-wall density modulations are considered, and a renormalized model is presented that accurately describes the phason-like vibrational behavior of the domain-wall network. The domain walls are shown to vibrate as strings. The string wave velocity is found to be essentially independent of the width of the walls or, in other words, of the amplitude of the substrate corrugation. For krypton on graphite it is about 600 m ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$. The vibrational modes of the network are determined by the vertices, which provide the boundary conditions for the domain-wall segments. Matching the results of the model with a normal-mode calculation for the krypton-on-graphite system [Phys. Rev. B 34, 7334 (1986)], the following parameters are determined for the vertices; (i) effective mass, (ii) moment of inertia, (iii) effective radius, (iv) vertex-vertex interaction, and (v) restoring torque exerted by the substrate when walls move away from a symmetry direction of the substrate (this torque can be weakened significantly when the domain-wall size decreases because of overcompression at the vertices). Analytic expressions are available for the first two quantities. Anharmonic effects of the adatom interaction are found to alter the vibrational-mode energies of the domain walls from those obtained by a quasiharmonic calculation for the motion of the adatoms. The limit is also taken towards very large domain size, where the solutions to the dynamical matrix become relatively simple. Thermodynamic quantities such as the specific heat, which can be calculated from the vibrational-mode spectrum, show no discontinuity at the commensurate-incommensurate transition. Near the transition the sound velocities for the domain-wall lattice have very simple expressions.

Magneto-optic observation of Bloch lines

We report the first visual observation of Bloch lines in thin garnet films without the perturbing influence of magnetic particles in suspension (Bitter solution). A second-order magneto-optic effect reveals the Bloch line position and the signs and positions of the domain wall segments lying adjacent to it. The present study is limited to Neel walls that separate in-plane domains aligned along [110] ‘‘easy’’ magnetic axes in a (100) garnet film 0.8 μm thick with large in-plane uniaxial anisotropy (Ku≪0). Images are viewed using normally incident laser illumination and crossed polarizers in a polarizing microscope also having an adjustable optical phase compensator. The contrast image for 180° walls with incident light vector E∥ polarized parallel to the wall is an adjacent pair of dark and light stripes. The usual first-order Faraday effect (magnetic circular birefringence) is excluded because all components of M are perpendicular to the beam. The quadratic dependence on M is verified, outside the wall at least, in domain contrast studies, e.g., by the lack of contrast between two opposing 180° domains. Within the wall magnetic linear birefringence would cause incident light E∥ to emerge as right- or left-handed elliptically polarized light according to the quadrants of the orientation of M wall in the E∥−E⊥ plane. Thus, the observed ordering of black/white or white/black stripes in the image reflects the sign of twist in M wall when the transmitted light is viewed through a compensator and analyser. The Bloch-line position is delineated by a discontinuous reversal in the black/white ordering.

Néel walls and line transitions in a (100) garnet film

An investigation was made of novel domain wall structures in (100) SmTmCaGe garnet films. These (100) oriented films have strong in-plane anisotropy resulting in the formation of Néel type domain walls in spite of the large thickness (∼1 μm) of the films. The dipolar nature of these walls was detected by use of a modified Bitter technique in which a bias field polarized the magnetic particles perpendicular to the film plane. Line transitions separating antiparallel domain wall segments were observed to move along the walls when appropriate polarity in-plane fields were applied. These line transitions are analogous to the Bloch point and crosstie observed in NiFe films. In the garnet films, however, anisotropy is stronger, and because the magnetization is much weaker, the crosstie does not form. Theoretical considerations suggest that the Néel wall has a width of about 1500 Å and that alternate line transitions, having different magnetization configurations, are nearly identical in width (∼600 Å) and energy. Furthermore, since the magnetization is low, there is little interaction between line transitions and they may be relatively densely packed along the Néel wall.

A study of magnetic hardening in Pt&amp;lt;inf&amp;gt;1-x&amp;lt;/inf&amp;gt;Ni&amp;lt;inf&amp;gt;x&amp;lt;/inf&amp;gt;Fe

Alloys of composition Pt <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-x</inf> Ni <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</inf> Fe with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x = 0.2, 0.3</tex> , and 0.4 can be quenched from high temperature to retain a face centred cubic disordered phase. On aging, at lower temperatures, alloys with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x = 0.2 and 0.3</tex> become magnetically hard with coercivities up to 2000 Oe at room temperature. In the hardened state the alloys have an ordered tetragonal structure with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c/a \sim 0.96</tex> and a uniaxial magnetocrystalline anisotropy of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\sim10^{7}</tex> erg cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> . Electron microscopy, of magnetically hard fully tetragonal samples, reveals a {110} lamellar structure. The <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</tex> axis of each lamella is at 90° to the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</tex> axis of the locally dominant tetragonal matrix phase in which it is embedded. Lorentz microscopy reveals domain walls, parallel to the dominant <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</tex> axis which are "kinked" where they cross lamellae. The coercive forces increase on cooling below room temperature. This increase can be attributed to the decreased probability of the thermal activation of domain wall segments, over barriers, as the temperature falls. An alloy with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x = 0.4</tex> formed a cubic ordered phase on aging but did not develop high coercivity or high remanent magnetization.

Spin-Echo and Free-Induction-Decay Measurements in Pure Fe and Fe-Rich Ferromagnetic Alloys: Domain-Wall Dynamics

Measurements were made of the free-induction-decay (FID) and spin-echo amplitudes of ${\mathrm{Fe}}^{57}$ in pure Fe and some of its alloys. Complex spectra are observed consisting of many oscillations often covering a range of many Mc/sec. The amplitudes are very dependent on the pulse length $\ensuremath{\tau}$, the applied rf field ${B}_{1}$, and the exciting frequency $\ensuremath{\omega}$. Excellent agreement is found between the experimental and calculated amplitudes when a model for domain-wall motion is used which takes into consideration the following features: 1. There is an averaging over the orientation of ${\mathbf{B}}_{1}$ with respect to the local magnetization. 2. There is a variation of the enhancement factor across the domain wall due to the spin arrangement in the wall. 3. The domain wall is considered to be composed of area segments which are immobile along their perimeters and whose motion resembles that of a vibrating drumhead. 4. These domain-wall segments have a distribution in areas. The restricted motion of the domain walls imposed by the last two features is essential in order to obtain agreement with the experimental results. This is in contrast to the usual model, which represents the domain-wall motion as given by rigid simple-harmonic-like oscillations; such a model shows great discrepancy with the experimental results presented here. In some of the spectra, asymmetries are observed in the variation of the amplitudes as a function of frequency. No satisfactory explanation for these asymmetries is known although some possible sources are suggested. Such asymmetries make it appear very doubtful that the Fe-alloy spectra obtained with this technique can be reliably unfolded to give the variation of the internal field for second- or higher-neighbor impurity atoms. FID amplitude measurements were also made on Fe in an externally applied dc field. No variation in the value of the maximum enhancement factor was observed for dc fields varying from 0 to about 5 kG.