Linear Domain Walls Research Articles

Hybrid Dry and Wet Etching of LiNbO3 Domain-Wall Memory Devices with 90° Etching Angles and Excellent Electrical Properties.

Ferroelectric domain walls, agile nanoscale interfaces of polar order, can be selectively controlled by electric fields for their position, conformation, and function, which is ultimately the key to realizing novel low-energy memory and computing structures. LiNbO3 single-crystal domain wall memory has the advantages of high operational speed, high integration density, and virtually unlimited endurance cycles, appearing as a good solution for the next generation of highly miniaturized low-energy memories. However, the etching process poses significant challenges in the nanofabrication and high-density integration of LiNbO3 domain-wall memories. Here, we employed a hybrid etching technique to achieve smooth sidewalls with a 90° inclined angle, leading to a 24% reduction in the coercive field and a 2.5-fold increase in the linear domain wall current density with a retention time of more than 106 seconds and endurance of over 105 writing cycles. Combined with the results of X-ray diffraction patterns and X-ray photoelectric spectra, it is concluded that the excellent electrical performance is related to the formation of an oxygen-deficient LiNbO3-x layer on the sidewall surface during the wet chemical etching process, which is a conductive layer that reduces the thickness of the "dead" layer between the side electrodes and the LiNbO3 cell and rectifies the diode-like wall currents with an onset voltage reduced from 1.23 to 0.28 V. These results prove the high-density integration of ferroelectric domain-wall memories at the nanoscale and provide a new strategy applicable to the development of LiNbO3 photonic devices.

Asymmetric transport computations in Dirac models of topological insulators

This paper presents a fast algorithm for computing transport properties of two-dimensional Dirac operators with linear domain walls, which model the macroscopic behavior of the robust and asymmetric transport observed at an interface separating two two-dimensional topological insulators. Our method is based on reformulating the partial differential equation as a corresponding volume integral equation, which we solve via a spectral discretization scheme.We demonstrate the accuracy of our method by confirming the quantization of an appropriate interface conductivity modeling transport asymmetry along the interface, and moreover, confirm that this quantity is immune to local perturbations. We also compute the far-field scattering matrix generated by such perturbations and verify that while asymmetric transport is topologically protected the absence of back-scattering is not.

Asymmetric Transport Computations in Dirac Models of Topological Insulators

This paper presents a fast algorithm for computing transport properties of two-dimensional Dirac operators with linear domain walls, which model the macroscopic behavior of the robust and asymmetric transport observed at an interface separating two two-dimensional topological insulators. Our method is based on reformulating the partial differential equation as a corresponding volume integral equation, which we solve via a spectral discretization scheme. We demonstrate the accuracy of our method by confirming the quantization of an appropriate interface conductivity modeling transport asymmetry along the interface, and moreover confirm that this quantity is immune to local perturbations. We also compute the far-field scattering matrix generated by such perturbations and verify that while asymmetric transport is topologically protected the absence of back-scattering is not.

Highly Anisotropic Magnetic Domain Wall Behavior in In-Plane Magnetic Films.

We have studied the nucleation of magnetic domains and propagation of magnetic domain walls (DWs) induced by pulsed magnetic field in a ferromagnetic film with in-plane uniaxial anisotropy. In contrast to observed behavior in films with out-of-plane anisotropy, the nucleated domains have a rectangular shape in which a pair of the opposite sides are perfectly linear DWs, while the other pair present zigzags. The field induced propagation of these two DW types are found to be different. The linear ones follow a creep law identical to what is usually observed in out-of-plane films, while the velocity of zigzag DWs depends linearly on the applied field amplitude down to very low field. This unexpected feature can be explained by the shape of the DW, and these results provide first experimental evidence of the applicability of the 1D model in two-dimensional ferromagnetic thin films.

Charge and spin textures of Ising quantum Hall ferromagnet domain walls

We investigate the charge and spin structures associated with arbitrary smooth polarization textures in Ising (integer) quantum Hall ferromagnets. We consider the case where the two polarizations (denoted "pseudospin" up and down) correspond to states with opposite physical spin and different Landau level indices, $n\uparrow$ and $m\downarrow$. We derive analytic expressions for the charge and spin densities, as functions of the underlying pseudospin texture, and use these results to investigate different types of linear domain walls, both analytically and numerically. We find that any smooth domain wall between two oppositely polarized domains carries a universal quantized charge dipole density proportional to the difference of Landau level indices, $n-m$. Additionally, non-uniformities in the domain wall may give rise to excess net charge localized at the domain wall. Interestingly, the physical spin density associated with the domain wall generally exhibits a much more complex multipolar structure than that of the pseudospin texture. These results should for example help to elucidate the mechanisms underlying nuclear electric resonance and nuclear polarization oscillations in Ising quantum Hall systems.

Superior room-temperature magnetic field-dependent magnetoelectric effect in BiFeO3-based multiferroic

Multiferroics that exhibit simultaneous electric and magnetic orders have attracted a great deal of interests both in fundamental science and practical applications. In general, high-performance single-phase multiferroics are extremely rare, owing to the incompatibility between ferroelectricity and magnetism. The most interesting property that makes multiferroics useful in device applications is the direct and significant magnetoelectric coupling at room temperature, resulting in a hysteretic magnetoelectric response. However, it still remains a great challenge to realize such a cross-coupling hysteresis loop between the ferroelectric and magnetic orders, i.e. an effective magnetic command of polarization, or an electric-field command of magnetization in a single-phase bulk material. Here we report the multiferroic behavior of chemically modified bismuth ferrite, Bi0.88Dy0.12Fe0.97Ti0.03O3+δ, which exhibits simultaneous (weak) ferromagnetism and ferroelectricity. More interestingly, this solid solution shows an evident magnetoelectric effect at a low magnetic field by demonstrating a hysteretic loop that characterizes the electric voltage signal as a function of bias magnetic field. Moreover, the room-temperature magnetoelectric effect with the saturated magnetoelectric coefficient up to ±0.23 mV/cm•Oe at ±250 Oe is obtained. The observed properties are attributed to the combination of linear magnetoelectric effect and domain wall motion. This result points to potential new applications of single-phase multiferroic materials in spintronic devices in which electric dipoles can be effectively tuned by a magnetic field.

Asymptotics of quasi-classical localized states in 2D system of charged hard-core bosons

The continuous quasi-classical two-sublattice approximation is constructed for the 2D system of charged hard-core bosons to explore metastable inhomogeneous states analogous to inhomogeneous localized excitations in magnetic systems. The types of localized excitations are determined by asymptotic analysis and compared with numerical results. Depending on the homogeneous ground state, the excitations are the ferro and antiferro type vortices, the skyrmion-like topological excitations or linear domain walls.

Quasi-classical localized states in the 2D ferrimagnet

We consider highly anisotropic 2D quantum s = 1/2 (pseudo)magnetic system which is equivalent to the frequently used system of charged hard-core bosons on a square lattice. In the continuous quasi-classical approximation, the types of localized excitations are determined by asymptotic analysis and compared with numerical results. Depending on the homogeneous ground state, the excitations are the ferro and antiferro type vortices, the skyrmion-like topological excitations or linear domain walls.

Anisotropic Friedel oscillations inside the domain wall

The influence of the non-collinear magnetic configuration on Friedel oscillations is investigated theoretically. Specifically the influence of the magnetic configuration on the induced electric charge in a Néel type domain wall (DW) has been obtained. The well-known Levy and Zhang eigenstates for a linear DW have been employed. Then the dielectric function of this magnetic system has been obtained within the random phase approximation. Results of the current work demonstrate that magnetic configuration of the system manifests itself in the electric properties such as induced charge distribution. Meanwhile the anisotropy of the induced charge distribution in the real space provides a measurable way for the determination of the DW orientation. In addition anisotropy of the dielectric function in k-space arises as a result of the anisotropy of the magnetic configuration. Therefore the orientation of the magnetic DW could also be captured by full optical measurements.

Fast magnetization switching in Fe-rich amorphous microwires: Effect of magnetoelastic anisotropy and role of defects

We studied effect of magnetoelastic anisotropy and role of defects on domain wall (DW) dynamics and remagnetization process of magnetically-bistable Fe-rich microwires. We manipulated the magnetoelastic anisotropy applying the tensile stresses. Application of stresses resulted in decrease of the DW velocity v, and DW mobility S. Consequently, we observed certain correlation between the magnetoelastic energy and DW dynamics in microwires: decreasing the magnetoelastic energy, Kme, DW velocity can be increased. We are trying to reveal contribution of local defects on DW propagation in amorphous microwires. Below some critical magnetic field, Hn, determined by the microwires inhomogeneities, almost linear DW velocity, v on magnetic field, H, dependence is found. When the applied magnetic field exceeds Hn, new reverse domains can be nucleated and consequently tandem remagnetization mechanism can be realized. The role of defects existing in magnetically bistable microwires is related with nucleation of new reversed domains. Abrupt jumps on v(H) dependences correlate with defects existing in microwires. Magnetic field value, corresponding to such jump on v(H) dependences, correlates with the minimum nucleation field, which determines threshold between single and multiple domain wall propagation regimes. In the latter case, under the action of the magnetic field, a new domain can be spontaneously nucleated in front of the propagating head-to-head closure domain. In this way real structure of microwires limits single DW propagation regime.

Spin-flip and domain wall magnetoresistance in quantum magnetic nanocontacts

The theory of nanosize point contacts made of ferromagnetic metals is developed. A general quantum scattering theory is applied to calculate magnetoresistance of a nanocontact with a domain wall located in the constriction. The exact solution of the electron motion in a potential of the linear domain wall is used as a zero-order approximation. Spin-flip and spin-conserving quantized conductances of the nanocontact are calculated by the perturbation theory by the difference between the model and the Cabrera–Falicov potentials of the domain wall. It is explicitly shown that spin-flip conductance imposes natural limitation on magnetoresistance of the point contact, which otherwise diverges in the regime of complete spin-rectified conductance through the contact.

Domain wall properties of FePt: From Bloch to linear walls

An investigation of the orientation and temperature dependence of domain wall properties in FePt is presented. We use a microscopic, atomic model for the magnetic interactions within an effective, classical spin Hamiltonian constructed on the basis of spin density functional theory. We find a significant dependence of the domain wall width and the domain wall energy on the orientation of the wall with respect to the crystal lattice. Investigating the temperature dependence, we demonstrate the existence of elliptical as well as linear domain walls in FePt. The calculation and further analysis of the domain wall free energy results in the evaluation of a thermodynamic exchange stiffness and anisotropy constant.

Influence of Rashba coupling on the magnetoresistance of a smooth domain wall

The effect of the Rashba-type spin-orbit interaction on the domain-wall (DW) magnetoresistance (MR) is investigated for a smooth linear DW within the semiclassical approach. Results of this study are indicative of a negative MR for current-in-wall geometry for some ranges of the impurity densities and the chirality dependence of the DW MR. The increase of the Rashba coupling strength can effectively increase the MR of the DW in the samples with low impurity concentrations.

Giant magnetoresistance in nanoscale ferromagnetic heterocontacts

A quasi-classical theory of giant magnetoresistance (GMR) in nanoscale point contactsbetween different ferromagnetic metals is developed. The contacts were sorted by threetypes of mutual positions of the conduction spin-subband bottoms which are shifted oneagainst another by the exchange interaction. A model of a linear domain wall has been usedto account for the finite contact length. The magnetoresistance is plotted against the size ofthe nanocontact. In heterocontacts the magnetoresistance effect not only turnsout to be negative, as usual, but it can be positive as well. The relevance of theresults to existing experiments on GMR in point heterocontacts is discussed.

Transition to Linear Domain Walls in Nanoconstrictions

Domain walls in nanoconstrictions are investigated with a focus on thermal properties. In general, the magnetization component perpendicular to the easy axis which in a domain wall usually occurs has a value different from the easy-axis bulk magnetization value with a separate phase transition at a critical temperature below the Curie temperature. Since this effect is the more pronounced the smaller the domain wall width is, we investigate it especially in domain walls with a confined geometry, using analytical arguments, mean-field theory, and Monte Carlo simulations. Our findings may contribute to the understanding of magnetoresistive effects in domain walls with sizes of only a few atomic layers, as, e.g., in nanocontacts or nanoconstrictions.

Interacting fermions and domain wall defects in 2+1 dimensions

We consider a Dirac field in 2+1 dimensions with a domain wall like defect in its mass, minimally coupled to a dynamical Abelian vector field. The mass of the fermionic field is assumed to have just one linear domain wall, which is externally fixed and unaffected by the dynamics. We show that, under some general conditions on the parameters, the localized zero modes predicted by the Callan and Harvey mechanism are stable under the electromagnetic interaction of the fermions.

Fermionic determinant with a linear domain wall in 2+1 dimensions

We consider a Dirac field in 2+1 Euclidean dimensions, in the presence of a linear domain wall defect in its mass, and a constant electromagnetic field. We evaluate the exact fermionic determinant for the situation where the defect is assumed to be rectilinear, static, and the gauge field is minimally coupled to the fermions. We discuss the dependence of the result on the (unique) independent geometrical parameter of this system, namely, the relative orientation of the wall and the direction of the external field. We apply the result for the determinant to the evaluation of the vacuum energy.

Bloch wall phase transition in the anisotropic spherical model (abstract)

The temperature-induced second-order phase transition from Bloch to linear (Ising-like) domain walls in uniaxial ferromagnets was predicted theoretically1 within the mean-field approximation and observed in the dynamic susceptibility experiments on Sr hexaferrite.2 Here the fluctuational effects at this phase transition are investigated for the exactly solvable anisotropic model of D-component classical spin vectors in the limit D→∞. This anisotropic spherical model is equivalent to the common spherical model in the homogeneous case, but deviates from it and is free from nonphysical behavior in a general inhomogeneous situation. It is shown that the thermal fluctuations of the transverse magnetization in the wall (the Bloch wall order parameter) result in the diminishing of the domain wall transition temperature TB in comparison to its mean-field value, thus favoring the existence of linear walls. For ensuring finite values of TB, an additional anisotropy in the basal plane x, y is required: In purely uniaxial ferromagnets a domain wall behaves like a two-dimensional system with a continuous spin symmetry and does not order into the Bloch wall at any nonzero temperature. The theory qualitatively explains the fact that the value TB=0.99Tc measured on the Sr hexaferrite2 is substantially more remote from Tc than the mean-field estimation TB=0.996Tc, as well as some other characteristics of domain wall relaxation in the critical region.

Bloch-wall phase transition in the spherical model

The temperature-induced second-order phase transition from Bloch to linear (Ising-like) domain walls in uniaxial ferromagnets is investigated for the model of D-component classical spin vectors in the limit D \to \infty. This exactly soluble model is equivalent to the standard spherical model in the homogeneous case, but deviates from it and is free from unphysical behavior in a general inhomogeneous situation. It is shown that the thermal fluctuations of the transverse magnetization in the wall (the Bloch-wall order parameter) result in the diminishing of the wall transition temperature T_B in comparison to its mean-field value, thus favouring the existence of linear walls. For finite values of T_B an additional anisotropy in the basis plane x,y is required; in purely uniaxial ferromagnets a domain wall behaves like a 2-dimensional system with a continuous spin symmetry and does not order into the Bloch one.

Strong critical fluctuations in domain walls in Sr hexaferrite: Effect of magnetic fields

The domain wall (DW) relaxation rate Γw of the uniaxial Sr hexaferrite in the region 0.9TC ≤ TC = 740 K, displays a deep minimum at T = 0.99TC due to a continuous 2D phase transition from Bloch to linear domain walls. In fields parallel to the easy axis, Γw is reduced by the increase of the DW spacing d, whereas a perpendicular field increases Γw. This feature is associated with the increase of the DW order parameter mB with the field near the transition.