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We study the effect of depolarization field related with inhomogeneous polarization distribution, strain and surface energy parameters on a domain wall profile near the surface of a ferroelectric film within the framework of Landau-Ginzburg-Devonshire phenomenology. Both inhomogeneous elastic stress and positive surface energy lead to the wall broadening at electrically screened surface. For ferroelectrics with weak piezoelectric coupling, the extrapolation length that defines surface energy parameter, affects the wall broadening more strongly than inhomogeneous elastic stress. Unexpectedly, the domain wall profile follows a long-range power law when approaching the surface, while it saturates exponentially in the bulk. In materials with high piezoelectric coupling and negligibly small surface energy (i.e. high extrapolation length) inhomogeneous elastic stress effect dominates.
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Using a Ginzburg--Landau--Devonshire model that includes the coupling of polarization to strain, we calculate the fluctuation spectra of ferroelectric domain walls. The influence of the strain coupling differs between 180 degree and 90 degree walls due to the different strain profiles of the two configurations. The finite speed of acoustic phonons, $v_s$, retards the response of the strain to polarization fluctuations, and the results depend on $v_s$. For $v_s to infty$, the strain mediates an instantaneous electrostrictive interaction, which is long-range in the 90 degree wall case. For finite $v_s$, acoustic phonons damp the wall excitations, producing a continuum in the spectral function. As $v_s to 0$, a gapped mode emerges, which corresponds to the polarization oscillating in a fixed strain potential.
A phenomenological treatment of domain walls based on the Ginzburg-Landau-Devonshire theory is developed for uniaxial, trigonal ferroelectrics lithium niobate and lithium tantalate. The contributions to the domain wall energy from polarization and strain as a function of orientation are considered. Analytical expressions are developed which are analyzed numerically to determine the minimum polarization, strain, and energy configurations of domain walls. It is found that hexagonal y-walls are preferred over x-walls in both materials. This agrees well with experimental observation of domain geometries in stoichiometric composition crystals.
It was found that high current density needed for the current-driven domain wall motion results in the Joule heating of the sample. The sample temperature, when the current-driven domain wall motion occurred, was estimated by measuring the sample resistance during the application of a pulsed-current. The sample temperature was 750 K for the threshold current density of 6.7 x 10^11 A/m2 in a 10 nm-thick Ni81Fe19 wire with a width of 240 nm. The temperature was raised to 830 K for the current density of 7.5 x 10^11 A/m2, which is very close to the Curie temperature of bulk Ni81Fe19. When the current density exceeded 7.5 x 10^11 A/m2, an appearance of a multi-domain structure in the wire was observed by magnetic force microscopy, suggesting that the sample temperature exceeded the Curie temperature.
Domains and domain walls are among the key factors that determine the performance of ferroelectric materials. In recent years, a unique type of domain walls, i.e., the sawtooth-shaped domain walls, has been observed in BiFeO$_{3}$ and PbTiO$_{3}$. Here, we build a minimal model to reveal the origin of these sawtooth-shaped domain walls. Incorporating this model into Monte-Carlo simulations shows that (i) the competition between the long-range Coulomb interaction (due to bound charges) and short-range interaction (due to opposite dipoles) is responsible for the formation of these peculiar domain walls and (ii) their relative strength is critical in determining the periodicity of these sawtooth-shaped domain walls. Necessary conditions to form such domain walls are also discussed.
Perpendicularly magnetized materials have attracted tremendous interest due to their high anisotropy, which results in extremely narrow, nano-sized domain walls. As a result, the recently studied current-induced domain wall motion (CIDWM) in these materials promises to enable a novel class of data, memory, and logic devices. In this letter, we propose the spin Hall effect as a radically new mechanism for CIDWM. We are able to carefully tune the net spin Hall current in depinning experiments on Pt/Co/Pt nanowires, offering unique control over CIDWM. Furthermore, we determine that the depinning efficiency is intimately related to the internal structure of the domain wall, which we control by small fields along the nanowire. This new manifestation of CIDWM offers a very attractive new degree of freedom for manipulating domain wall motion by charge currents, and sheds light on the existence of contradicting reports on CIDWM in perpendicularly magnetized materials.
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