Intrinsic Domain Wall Research Articles

Real-time probing technique of domain wall dynamic in perpendicularly magnetized film

We present the study of a rarely mentioned method for measuring the magnetic domain wall velocity, which makes it possible to have a real-time probing of the domain wall movement in the perpendicularly magnetized thin film. We have compared this technique in detail with the most common Kerr imaging method. The comparison results show interesting differences if the spot size is too small. It can be explained by the dendritic shape of the domain wall. By changing the size spot, we propose a basic model that describes quite well the transit time in the laser spot as a function of its size and makes it possible to extract the velocity and depth of the dendrites. By generalizing our method, it helps people to understand magnetic domain wall dynamics from the temporal dimension and helps the academic community to obtain intrinsic domain wall motion characteristics in the film sample, ultimately promoting the development of spintronic devices.

Scaling of intrinsic domain wall magnetoresistance with confinement in electromigrated nanocontacts

In this work we study the evolution of intrinsic domain wall magnetoresistance (DWMR) with domain wall confinement. Clean permalloy notched half-ring nanocontacts are fabricated using a special ultra-high vacuum electromigration procedure to tailor the size of the wire in-situ and through the resulting domain wall confinement we tailor the domain wall width from a few tens of nm down to a few nm. Through measurements of the dependence of the resistance with respect to the applied field direction we extract the contribution of a single domain wall to the MR of the device, as a function of the domain wall width in the confining potential at the notch. In this size range, an intrinsic positive MR is found, which dominates over anisotropic MR, as confirmed by comparison to micromagnetic simulations. Moreover, the MR is found to scale monotonically with the size of the domain wall, $\delta_{DW}$, as 1/$\delta_{DW}^b$, with $b=2.31\pm 0.39 $. The experimental result is supported by quantum-mechanical transport simulations based on ab-initio density functional theory calculations.

Low-Temperature Dielectric Anisotropy Driven by an Antiferroelectric Mode in SrTiO_{3}.

Strontium titanate (SrTiO_{3}) is the quintessential material for oxide electronics. One of its hallmark features is the transition, driven by antiferrodistortive (AFD) lattice modes, from a cubic to a ferroelastic low-temperature phase. Here we investigate the evolution of the ferroelastic twin walls upon application of an electric field. Remarkably, we find that the dielectric anisotropy of tetragonal SrTiO_{3}, rather than the intrinsic domain wall polarity, is the main driving force for the motion of the twins. Based on a combined first-principles and Landau-theory analysis, we show that such anisotropy is dominated by a trilinear coupling between the polarization, the AFD lattice tilts, and a previously overlooked antiferroelectric (AFE) mode. We identify the latter AFE phonon with the so-called "R mode" at ∼440 cm^{-1}, which was previously detected in IR experiments, but whose microscopic nature was unknown.

Stability of Polar Vortex Lattice in Ferroelectric Superlattices.

A novel mesoscale state comprising of an ordered polar vortex lattice has been demonstrated in ferroelectric superlattices of PbTiO3/SrTiO3. Here, we employ phase-field simulations, analytical theory, and experimental observations to evaluate thermodynamic conditions and geometric length scales that are critical for the formation of such exotic vortex states. We show that the stability of these vortex lattices involves an intimate competition between long-range electrostatic, long-range elastic, and short-range polarization gradient-related interactions leading to both an upper and a lower bound to the length scale at which these states can be observed. We found that the critical length is related to the intrinsic domain wall width, which could serve as a simple intuitive design rule for the discovery of novel ultrafine topological structures in ferroic systems.

Skyrmions at the Edge: Confinement Effects in Fe/Ir(111).

We have employed spin-polarized scanning tunneling microscopy and MonteCarlo simulations to investigate the effect of lateral confinement onto the nano-Skyrmion lattice in Fe/Ir(111). We find a strong coupling of one diagonal of the square magnetic unit cell to the close-packed edges of Fe nanostructures. In triangular islands this coupling in combination with the mismatching symmetries of the islands and of the square nano-Skyrmion lattice leads to frustration and triple-domain states. In direct vicinity to ferromagnetic NiFe islands, the surrounding Skyrmion lattice forms additional domains. In this case a side of the square magnetic unit cell prefers a parallel orientation to the ferromagnetic edge. These experimental findings can be reproduced and explained by MonteCarlo simulations. Here, the single-domain state of a triangular island is lower in energy, but nevertheless multidomain states occur due to the combined effect of entropy and an intrinsic domain wall pinning arising from the skyrmionic character of the spin texture.

Achieving Both High d 33 and High Q m for the Pb(Zr0.26Sn0.26Ti0.48)1−x Fe x O3−x/2 Ternary System for Use in High-Power Ultrasonic Transducers

For applications in high power ultrasonic transducers, both high piezoelectric coefficients d 33 and high mechanical quality factor Q m are essential. In this work, acceptor-doped Pb(Zr0.26Sn0.26Ti0.48)1−x Fe x O3−x/2 ferroelectric ceramics with compositions near the morphotropic phase boundary were prepared by routine solid-state reaction. By introducing Fe3+ ion into the perovskite crystal lattices, defect dipoles resulting from Fe3+ ions and oxygen vacancies are formed, pinning extrinsic domain wall motion, and hence increasing Q m but reducing d 33. It was found that substitution with 0.5 mol% Fe3+ resulted in high d 33 (390 pC/N) and high Q m (540). The nonlinear dielectric responses of these ceramics were evaluated on the basis of the Rayleigh law. Both Rayleigh coefficients, $$\alpha$$ and $$\kappa_{\rm{init}},$$ are reduced by doping with the acceptor ion Fe3+, indicating that the intrinsic contribution and reversible domain wall mobility are both reduced.

Intrinsic domain-wall resistivity in half-metallic manganite thin films

Deciphering the intrinsic magnetic domain-wall (DW) resistivity of manganite materials by typical low-field magnetoresistance measurement is flawed due to the addition of different galvanomagnetic effects such as, colossal magnetoresistance, Lorentz force magnetoresistance, and anisotropic magnetoresistance (AMR). In this paper, by taking the advantage of rotational anisotropy and the stable rotation of the DW planes in half-metallic manganite La${}_{0.7}$Sr${}_{0.3}$MnO${}_{3}$ film, we deploy a remanent state resistance measurement technique to exclude all the field-dependent spurious effects from the intrinsic DW resistivity. To further refine its magnitude, we calculate the remanent state DW AMR by exploiting the three-dimensional micromagnetic simulation, which reveals a comparable but opposite contribution to the positive DW resistivity. From these results, we estimate the intrinsic DW resistance-area product in La${}_{0.7}$Sr${}_{0.3}$MnO${}_{3}$ to be $1.9\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}\phantom{\rule{0.16em}{0ex}}\ensuremath{\Omega}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{m}}^{2}$.

Dynamic Oscillations of Coupled Domain Walls

In domain wall (DW) excitation experiments, nonlinearity (NL) intrinsic to the DW dynamics is often hard to distinguish from perturbation due to the confining potential or DW distortion. Here we numerically investigate the dynamic oscillations of magnetostatically coupled DWs: a system well understood in the quasistatic limit. NL is observed, even for a harmonic potential, due to the intrinsic DW motion. This behavior is principally dependent on terms normally associated with the DW canonical momentum and is in contrast with a NL restoring potential. This NL is not observable in quasistatic measurements, relatively insensitive to the confining potential, and may be tuned by the nanowire parameters. The shown NLs are present in any DW restoring potential and must be accounted for when probing DW potential landscapes.

Tunable Resistivity of Individual Magnetic Domain Walls

Despite the relevance of current-induced magnetic domain wall (DW) motion for new spintronics applications, the exact details of the current-domain wall interaction are not yet understood. A property intimately related to this interaction is the intrinsic DW resistivity. Here, we investigate experimentally how the resistivity inside a DW depends on the wall width Δ, which is tuned using focused ion beam irradiation of Pt/Co/Pt strips. We observe the nucleation of individual DWs with Kerr microscopy, and measure resistance changes in real time. A 1/Δ(2) dependence of DW resistivity is found, compatible with Levy-Zhang theory. Also quantitative agreement with theory is found by taking full account of the current flowing through each individual layer inside the multilayer stack.

Measurements of Nanoscale Domain Wall Flexing in a Ferromagnetic Thin Film

We use the high spatial sensitivity of the anomalous Hall effect in the ferromagnetic semiconductor Ga(1-x)Mn(x)As, combined with the magneto-optical Kerr effect, to probe the nanoscale elastic flexing behavior of a single magnetic domain wall in a ferromagnetic thin film. Our technique allows position sensitive characterization of the pinning site density, which we estimate to be ∼10(14) cm(-3). Analysis of single site depinning events and their temperature dependence yields estimates of pinning site forces (10 pN range) as well as the thermal deactivation energy. Our data provide evidence for a much higher intrinsic domain wall mobility for flexing than previously observed in optically probed μm scale measurements.

Domain wall resistance in epitaxial Fe wires

We studied the magnetoresistance behavior of epitaxial Fe wires grown on GaAs(110) with varying widths at room temperature. Single nanowires show a wire width (w) dependence of the coercive field, which increases with 1/w for decreasing wire widths. This enables the pinning of a single domain wall in the connection area of two wires with different widths. Magnetoresistance measurements of such wire structures clearly reveal resistance contributions arising from a domain wall. The presence of the domain wall is proven by photoemission electron-microscopy with synchrotron radiation. Moreover, micromagnetic simulations are performed to determine the spin orientations, especially within the domain wall. This permits us to calculate the anisotropic magnetoresistance caused by the domain wall. Taking this into account, we determine the intrinsic domain wall resistance, for which we found a positive value of 0.2%, in agreement with theoretical predictions.

Domain wall resistance in perpendicular (Ga,Mn)As: Dependence on pinning

We have investigated the domain wall resistance for two types of domain walls in a (Ga,Mn)As Hall bar with perpendicular magnetization. A sizeable positive intrinsic DWR is inferred for domain walls that are pinned at an etching step, which is quite consistent with earlier observations. However, much lower intrinsic domain wall resistance is obtained when domain walls are formed by pinning lines in unetched material. This indicates that the spin transport across a domain wall is strongly influenced by the nature of the pinning.

Thermodynamics of nanodomain formation and breakdown in scanning probe microscopy: Landau-Ginzburg-Devonshire approach

Thermodynamics of tip-induced nanodomain formation in scanning probe microscopy of ferroelectric films and crystals is studied using the Landau-Ginzburg-Devonshire phenomenological approach. The local redistribution of polarization induced by the biased probe apex is analyzed including the effects of polarization gradients, field dependence of dielectric properties, intrinsic domain wall width, and film thickness. The polarization distribution inside subcritical nucleus of the domain preceding the nucleation event is very smooth and localized below the probe, and the electrostatic field distribution is dominated by the tip. In contrast, polarization distribution inside the stable domain is rectangular-like, and the associated electrostatic fields clearly illustrate the presence of tip-induced and depolarization field components. The calculated coercive biases of domain formation are in a good agreement with available experimental results for typical ferroelectric materials. The microscopic origin of the observed domain tip elongation in the region where the probe electric field is much smaller than the intrinsic coercive field is the positive depolarization field in front of the moving counter domain wall. For infinitely thin domain walls local domain breakdown through the sample depth appears. The results obtained here are complementary to the Landauer-Molotskii energetic approach.

Resistance of domain walls created by means of a magnetic force microscope in transversally magnetized epitaxial Fe wires

Magnetic domain walls are created in a controllable way in transversally magnetized epitaxial Fe wires on GaAs(110) by approaching a magnetic force microscope (MFM) tip. The electrical resistance-change due to the addition of these domain walls is measured. The anisotropic magnetoresistance as well as the intrinsic domain wall resistance contribute to the resistance-change. The efficiency of this procedure is proven by MFM images, which are obtained subsequent to the domain wall creation at a larger sample-to-probe distance. The contribution of the anisotropic magnetoresistance is calculated using micromagnetic calculations, thus making it possible to quantify the intrinsic domain wall resistance.

The intrinsic domain wall resistance of Fe films with a periodic domain pattern

The intrinsic domain wall resistance (DWR) of 180° Néel walls in a polycrystalline Fe film is determined by creating a periodic domain pattern, obtained by locally inducing exchange bias. After field cooling, the coercivity is spatially modulated, resulting in periodic 180° domain walls. To determine the intrinsic DWR, a rotating magnetic field is used to reversibly create and annihilate the domain walls. After correcting for the anisotropic magnetoresistance, the extracted DWR is positive.

Domain structure formation by using Scanning Probe Microscopy: equilibrium polarization distribution and effective piezoelectric response calculations

In the paper we adopt the analytical Landau-Ginzburg-Devonshire theory to describe the ferroelectric domain structure formation using Scanning Probe Microscopy. We calculate the effective local piezoresponse of the domain structure within the decoupling approximation using the conventional relation between piezoelectric tensor components and the spontaneous polarization vector. The depth profile of the polarization distribution was derived from the nonlinear Landau-Ginzburg-Devonshire equation. We demonstrate that depending on the material parameters such as the intrinsic domain wall width and probe apex geometry, the shape of the nucleating nanodomains induced by the probe can be either oblate or prolate. The derived analytical expressions for the polarization redistribution caused by the biased probe are valid for both first and second order ferroelectrics.

Effects of Surface Abrasion on Magnetization of VITROVAC 6025Z Ribbons

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> The effects of abrading with sandpaper the surface of VITROVAC 6025Z ribbons on the parameters of their <formula formulatype="inline"><tex Notation="TeX">$M$</tex> </formula>-<formula formulatype="inline"><tex Notation="TeX">$H$</tex></formula> loops (the coercive field <formula formulatype="inline"><tex Notation="TeX">$H_{c}$</tex> </formula>, the position of the center <formula formulatype="inline"><tex Notation="TeX">$C$</tex></formula>, etc.) have been investigated. The application of surface fields <formula formulatype="inline"><tex Notation="TeX">$H_{P}$</tex> </formula> (generated by core currents) enabled us to single out the effects of surface domains (surface domain structure (SDS) pinning) and surface irregularities (intrinsic pinning) on domain wall (DW) pinning in abraded and unabraded ribbons. The abrasion enhances the intrinsic DW pinning (increases <formula formulatype="inline"> <tex Notation="TeX">$H_{c}$</tex></formula>) and strongly modifies the SDS pinning which shows up in specific variations of <formula formulatype="inline"> <tex Notation="TeX">$H_{c}$</tex></formula> and <formula formulatype="inline"> <tex Notation="TeX">$C$</tex></formula> with <formula formulatype="inline"> <tex Notation="TeX">$H_{P}$</tex></formula>. In particular, the effect of <formula formulatype="inline"><tex Notation="TeX">$H_{P}$</tex></formula> on surface domain structure (SDS) pinning, which was symmetrical in unabraded ribbon becomes asymmetrical upon abrasion (i.e., different on opposite surfaces). A simple model for the influence of <formula formulatype="inline"><tex Notation="TeX">$H_{P}$</tex> </formula> on magnetization processes in soft magnetic ribbons describes the observed variations of <formula formulatype="inline"><tex Notation="TeX">$H_{c}$</tex> </formula> and <formula formulatype="inline"><tex Notation="TeX">$C$</tex> </formula> with <formula formulatype="inline"><tex Notation="TeX">$H_{P}$</tex> </formula> in both abraded and unabraded ribbons</para>

Effect of the intrinsic width on the piezoelectric force microscopy of a single ferroelectric domain wall

Intrinsic domain wall width is a fundamental parameter that reflects bulk ferroelectric properties and governs the performance of ferroelectric memory devices. We present closed-form analytical expressions for vertical and lateral piezoelectric force microscopy (PFM) profiles of a single ferroelectric domain wall for the conical and disk models of the tip, beyond point charge and sphere approximations. The analysis takes into account the finite intrinsic width of the domain wall and dielectric anisotropy of the material. These analytical expressions provide insight into the mechanisms of PFM image formation and can be used for a quantitative analysis of the PFM domain wall profiles. The PFM profile of a realistic domain wall is shown to be the convolution of its intrinsic profile and the resolution function of PFM.

Angular Dependence of Domain Wall Resistivity in Artificial Magnetic Domain Structures

We exploit the ability to precisely control the magnetic domain structure of perpendicularly magnetized Pt/Co/Pt trilayers to fabricate artificial domain wall arrays and study their transport properties. The scaling behavior of this model system confirms the intrinsic domain wall origin of the magnetoresistance, and systematic studies using domains patterned at various angles to the current flow are excellently described by an angular-dependent resistivity tensor containing perpendicular and parallel domain wall resistivities. We find that the latter are fully consistent with Levy-Zhang theory, which allows us to estimate the ratio of minority to majority spin carrier resistivities, rho downward arrow/rho upward arrow approximately 5.5, in good agreement with thin film band structure calculations.

Intrinsic Domain-Wall Resistance in Ferromagnetic Semiconductors

Transport through zinc blende magnetic semiconductors with magnetic domain walls is studied theoretically. We show that these magnetic domain walls have an intrinsic resistance due to the effective hole spin-orbit interaction. The intrinsic resistance is independent of the domain-wall shape and width and survives the adiabatic limit. For typical parameters, the intrinsic domain-wall resistance is comparable to the Sharvin resistance and should be experimentally measurable.