Multidomain State Research Articles

Influence of crystallite size on the magnetic properties of Fe3O4 nanoparticles

Structural and magnetic properties of chemically synthesized magnetite nanoparticles have been studied using X-ray diffraction, Transmission Electron Microscopy and Vibrating Sample Magnetometer. Magnetically the synthesized nanoparticles are ranging from superparamagnetic to multi domain state. Average crystallite size of the synthesized magnetite nanoparticles were determined using X-ray line broadening and are found to be in the range of 9–53 nm. On the other hand, the TEM images show that the size is ranging between 7.9 and 200 nm with the transition from spherical superparamagnetic particles to faceted cubic multi domain particles. Magnetic parameters of the samples show a strong dependence on average crystallite size. The ratio of coercive field at 20 K to that at 300 K (Hc (20 K)/Hc (300 K)) increased sharply with decrease in crystallite size. A critical crystallite diameter of order 36 nm may be inferred as boundary between single domain to multi domain transition. Zero-field-cooled (ZFC) and field-cooled (FC) measurements at 10 Oe field validate the same for smallest and largest size samples, confirming that the anisotropy energy is greater than thermal energy upto 300 K temperature. For 9 nm sample broad ZFC curve with overlapping of FC curve is observed just at 300 K, indicating the effect of strong dipolar field in superparamagnetic system.

Growth, mechanical, and magnetic study of SmFeO3 single crystal grown by optical floating zone technique

Single crystals of Samarium orthoferrite (SmFeO3) have been grown by the optical floating zone technique. The growth parameters to yield good quality crystals are 5 mm/h for pulling and 30–40 rpm for rotation. The mechanical behavior of the grown crystal has been investigated. Rosette pattern has been observed around the indentation and the microhardness has been found to decreases non-linearly with the applied load. For load higher than 1.96 N there is a transition from palmqvist to median crack due to plastic deformation of the crystal. The hardness parameters like fracture toughness, brittleness index, and yield strength have also been calculated for palmqvist and median cracks occurring on the crystal surface. The magnetic investigations revealed that a magnetic transition in the range of 300–180 K. Above 180 K, the magnetization decreases as Sm and Fe sublattices have opposite spins. At high temperature, two anomalies are observed, one due to near spin reorientation (TSR = 480 K) and the other is AFM to paramagnetic transitions (TN = 670 K). The M–H curves exhibit a shape change with temperature due to the emergence and enlargement of multi-domain state of the SmFeO3 crystals. Bloch parameter (3.28 × 10−5 K−3/2) has also been evaluated.

A(2+) Cation Control of Chiral Domain Formation in A(TiO)Cu4(PO4)4 (A = Ba, Sr).

Single crystals of two novel tetragonal chiral materials, A(TiO)Cu4(PO4)4 (A = Ba, Sr), were grown from Na2Mo2O7 flux, and their crystal and chiral domain structures were characterized. Polarized-light microscopy studies of the chiral domain structures in the crystals show that Ba(TiO)Cu4(PO4)4 mostly hosts a multidomain state, while a monodomain state predominantly appears in Sr(TiO)Cu4(PO4)4. To explain this striking difference, we quantified the chirality strength of these materials by comparing atomic positions in the chiral and nearest-achiral crystal structures, revealing larger chirality strength in Sr(TiO)Cu4(PO4)4 than in Ba(TiO)Cu4(PO4)4. Our proposed mechanisms linking the chirality strength and domain formation can account for the different occurrence frequency of chiral domains in this system.

新物質<i>A</i>（TiO）Cu<sub>4</sub>（PO<sub>4</sub>）<sub>4</sub>（<i>A</i>＝Ba, Sr）における結晶カイラリティの強度とドメイン構造の相関

Crystal chirality, a label defining the handedness of a system without improper symmetry, has long been an intensive subject in a variety of research fields such as chemistry, biology, and solid-state physics. Its great importance in solid-state physics lies in the potential unique functionalities of chiral materials such as optical activity, piezoelectricity, and recently discovered unconventional magnetism and associated magneto-transport and magnetoelectric phenomena. An important step toward further development of the chirality research would be a quantification of chirality and a clarification of its relationship to physical properties. Here, we report the discovery of two novel chiral materials, A(TiO)Cu4(PO4)4 (A＝Ba, Sr), and the detailed characterization of their crystal and chiral domain structures. We identify that the chiral crystal structure of this system can be characterized by an antiferrorotative distortion of structural units, indicating that the rotation angle is a good quantitative measure of the chirality strength. Interestingly, the rotation angle and thus the chirality strength can be tuned by changing A site cations. We observe striking differences in the occurrence frequency of chiral domains in the two materials：weakly chiral Ba(TiO)Cu4(PO4)4 mostly hosts a multidomain state, while strongly chiral Sr(TiO)Cu4(PO4)4 predominantly shows monodomain state. On the basis of these results, we discuss the relationship between the chirality strength and the occurrence frequency of chiral domains in this system.

Structural Domain Switching by Magnetic Fields in RAl3C3 (R = Rare Earth)

Hexagonal-to-orthorhombic structural transitions in RAl$_3$C$_3$ have been studied by X-ray diffraction for R=Yb, Tm, Er, Dy, and Lu. We report how orthorhombic domains are controlled by adjusting external magnetic fields. It is shown that orthorhombic domains in RAl$_3$C$_3$ can be aligned by the field when the R ion is magnetic. It is also shown that a single-domain state can be switched to another single-domain state by the field even in paramagnetic states with small induced moments. For R=Lu, however, it was not possible to change the multidomain state by a field of up to 70 kOe. We discuss that domain selection and switching are caused by magnetic anisotropies in the orthorhombic phase of RAl$_3$C$_3$. We also propose an idea to explain the field-induced antiferromagnetism revealed by Khalyavin et al. [Phys. Rev. B \textbf{87}, 220406 (2013)].

Domain control of carrier density at a semiconductor-ferroelectric interface.

Control of charge carrier distribution in a gated channel via a dielectric layer is currently the state of the art in the design of integrated circuits such as field effect transistors. Replacing linear dielectrics with ferroelectrics would ultimately lead to more energy efficient devices as well as the added advantage of the memory function of the gate. Here, we report that the channel-off/channel-on states in a metal/ferroelectric/semiconductor stack are actually transitions from a multi domain state to a single domain state of the ferroelectric under bias. In our approach, there is no a priori assumption on the single or multi-domain nature of the ferroelectric layer that is often neglected in works discussing the ferroelectric-gate effect on channel conductivity interfacing a ferroelectric. We also predict that semiconductor/ferroelectric/semiconductor stacks can function at even lower gate voltages than metal/ferroelectric/semiconductor stacks when an n-type semiconductor is placed between the ferroelectric and the gate metal. Our results suggest the ultimate stability of the multidomain state whenever it interfaces a semiconductor electrode and that a switchable single domain state may not be necessary to achieve effective control of conductivity in a p-type channel. Finally, we discuss some experimental results in the literature in light of our findings.

Low-voltage ferroelectric–paraelectric superlattices as gate materials for field-effect transistors

The demand for new materials to be used in field-effect transistors and similar devices with low energy loss is more than ever before as integrated circuits have become a considerable source of energy consumption. One of the challenges in designing such energy efficient logic devices is finding suitable dielectric materials systems for the gate that controls the drain current in a p-type channel. A fundamental limit for energy efficiency exists in such devices imposed by the polarizability of conventional linear gate dielectrics. Generating on/off states in the channel that differ by at least a million times in the magnitude of the drain current near saturation requires several volts of gate bias for the case of a linear dielectric material in a submicron device. In this study, we demonstrate that ferroelectric–paraelectric superlattice heterostructures can generate the same effect in a p-type channel for bias voltages much lower than in a linear high dielectric constant gate. We consider a metal/superlattice/p-type semiconductor stack for this purpose. Using a thermodynamic model, we show that the multi-domain state of the ferroelectric layers can be tailored and distinct on/off states of the channel are possible for gate bias voltages below 1 V. The origins of such functionality of ferroelectric–paraelectric superlattices are discussed with respect to material characteristics such as the phase transition temperature of the ferroelectric, total polarization, and the dielectric response.

Reversible temperature-driven domain transition in bistable Fe magnetic nanostrips grown on Ru(0001)

High-aspect-ratio Fe nanostrips are studied with real-space micromagnetic imaging methods. We experimentally demonstrate reversible switching from essentially homogeneous single-domain states at room temperature to multidomain diamond states at elevated temperature. This temperature-dependent magnetic bistability can be understood and modeled by accounting for the temperature dependence of the magnetocrystalline, shape, and magnetoelastic anisotropies. These results show how the transition temperature between two magnetic domain states can be tailored by controlling epitaxial strain and particle geometry, which may generate new opportunities for magnetic memory and logic device design.

Wide Compositional RangeIn SituElectric Field Investigations on Lead-FreeBa(Zr0.2Ti0.8)O3−x(Ba0.7Ca0.3)TiO3Piezoceramic

Applications ranging from microphones to AFM transducers exploit the interplay between mechanical stress and electric field arising from structural transitions in certain perovskite oxides. The classic material contains lead, however, and efficient, environmentally friendly alternatives have long been sought. The authors use a challenging technique to visualize the real-time microstructural evolution of a lead-free ferroelectric system, and the multidomain states and transitions they find are expected to inform the search for additional systems, as well as the applications that will rely on them.

Tuning magnetic fingerprints of FeNi nanowire arrays by varying length and diameter

Magnetic nanowires (NWs) electrodeposited into solid templates are of high interest due to their tunable properties which are required for magnetic recording media and spintronic devices. Here, highly ordered arrays of FeNi NWs with varied lengths (ranging from 2.5 to 12 μm) and diameters (between 45 and 75 nm) were fabricated into anodic aluminum oxide templates using a pulsed ac electrodeposition technique. X-ray diffraction patterns along with energy dispersive spectroscopy indicated the formation of Fe70Ni30 NWs with fcc and bcc alloy phases, being highly textured along the bcc [110] direction. Magnetic properties were studied by hysteresis loop measurements at room temperature and they showed reductions in coercivity and squareness values by increasing length and diameter. Further, magnetic fingerprints of the NWs were characterized using the first-order reversal curve (FORC) analysis. FORC measurements revealed that, with increasing length and diameter from 2.5 to 10 μm and 45–55 nm, respectively, besides an increase in inter-wire magnetostatic interactions, a transition from a single domain (SD) state to a pseudo SD state occurred. Moreover, a multi-domain (MD) state was found for the longest length and diameter. While the irreversible magnetization component of the SD NWs was approximately 100%, the reversible component of MD NWs increased up to 20%.

Spontaneous domain nucleation under in-plane fields in ultrathin films with Dzyaloshinskii-Moriya interaction

In this paper, we show that applying a hard axis field reduces the energy barrier for the spontaneous formation of a multi-domain state in magnetic ultrathin films sandwiched between a heavy metal and an oxide. This provides a simple technique to generate a metastable multi-domain state in magnetic films where the ground state is uniform. This approach could be particularly interesting in materials with strong Dzyaloshinskii-Moriya interaction as a means to realize metastable chiral textures.

Curvature-induced lipid segregation**Project supported by the Hundred-Talent Program of the Chinese Academy of Sciences (FY) and the National Science Foundation of USA via Grant DMR-1106014 (RLBS, JVS).

We investigate how an externally imposed curvature influences lipid segregation on two-phase-coexistent membranes. We show that the bending-modulus contrast of the two phases and the curvature act together to yield a reduced effective line tension. On largely curved membranes, a state of multiple domains (or rafts) forms due to a mechanism analogous to that causing magnetic-vortex formation in type-II superconductors. We determine the criterion for such a multi-domain state to occur; we then calculate respectively the size of the domains formed on cylindrically and spherically curved membranes.

Magnetic single-domain state of the monochiral helimagnet MnSi in the zero-field limit: Magnetic properties study

Attention is drawn to a possibility to obtain the monochiral helimagnet MnSi in a magnetic single domain state (SDS) in zero magnetic field limit. It is shown that this metastable zero field magnetic SDS can be achieved by gradual decrease of the field down to zero after initial transformation of MnSi to a spin-polarized state in high fields $H$. This can be achieved only for $\bf{H}\parallel$ [111]. Investigations of MnSi in magnetic SDS give us a possibility to determine the two components of low field magnetic susceptibility of this compound, $\chi_{\perp}(T)$ and $\chi_{\parallel}(T)$ [$\chi_{\perp}$ and $\chi_{\parallel}$ correspond to $\bf{H}\perp$, and $\bf{H}\parallel$ (111)-plane containing magnetic moments in helically ordered state]. These results are compared with macroscopic magnetic susceptibility of MnSi earlier determined for this compound only in magnetic multi domain state (MDS). In addition our results are compared with the data reported for some non-monochiral helimagnets. Characteristic features of monochiral helimagnets are elucidated.

Templates as Shadow Masks to Tune the Magnetic Anisotropy in Nanostructured CoCrPt/Ti Bilayer Films

Off‐axis deposition of Ti and CoCrPt films onto lithographically patterned templates has been used to make nanostructures with a lateral thickness variation that allows the tuning of the magnetic anisotropy. CoCrPt rectangles of 1 μm × 725 nm without a thickness variation show an out‐of‐plane easy axis and a single‐domain configuration after demagnetization. On the other hand, rectangles with a thickness variation along their longer dimension show an out‐of‐plane multidomain state, but an in‐plane vortex configuration occurs when the thickness variation is along the shorter dimension. The evolution of the magnetic behavior is understood from the change in both Ti and CoCrPt thicknesses and their effects on the magnetic anisotropy, and provides a simple method for controlling the magnetic state and reversal process of patterned nanostructures.

Influence of quenching conditions on the kinetics of formation of a domain structure of ferroelectrics

The kinetics of the formation and growth of 180° domains in a weak quasi-stationary external electric field has been investigated theoretically in the framework of the Ginzburg-Landau model within the statistical approach for proper ferroelectrics used as an example. The influence of the temperature quenching and the strength of an external electric field applied after quenching on the subsequent evolution of the system toward the thermodynamic equilibrium has been analyzed. It has been shown that, despite the polarizing role of the external electric field, in the case of a weak field the formation of a multi-domain structure is more preferable than the direct transition to a single-domain state of ordering. It has been established that the formation of nonequilibrium (“virtual”) multi-domain states is possible under the given initial conditions for specific quenching temperatures of the sample and at particular strengths of the electric field applied to the ferroelectric after quenching. It has been found that, for all depths of quenching, there is a time delay (incubation period) in the formation of a multi-domain structure of the ferroelectric. This situation occurs when, immediately after the quenching of the sample, the dispersion of the polarization is sufficiently large and the initial size of quenched polarization inhomogeneities is relatively small.

Variation of skyrmion forms and their stability in MnSi thin plates

By systematic real-space observations using Lorentz transmission electron microscopy, we report here various forms of skyrmions (and related spin textures) for a prototype of cubic helimagnet MnSi as well as their stability that depends on crystalline-orientation and crystal-plate thickness. Below a crossover thickness $({t}_{\mathrm{c}}\ensuremath{\sim}75\phantom{\rule{0.16em}{0ex}}\mathrm{nm})$ of a sample, the robust two-dimensional hexagonal skyrmion crystal (SkX) appears over a wide window of temperature and magnetic field, regardless of crystal orientation, while the SkX phase region shrinks to a small pocket near the helical transition temperature ${T}_{\mathrm{N}}$ in a (111) plate with the thickness above ${t}_{\mathrm{c}}$, in contrast to the stable SkX in (110) and (001) plates. This observation indicates the importance of the magnetic anisotropy and thermal fluctuation effects for the skyrmion stability. Furthermore, the forms of skyrmions have been found to change from multidomain state of SkX to skyrmion glass structure via single domain state of SkX with increasing magnetic field.

Low-temperature resistivity, magnetoresistance, and domain-wall resistance of highly pure single- and polycrystalline iron

On a set of 12 bulk and highly pure [residual resistance ratio (RRR) up to 6000] iron single crystals with different crystallographic orientation and on polycrystalline material the ``hidden'' basic resistivity $\ensuremath{\rho}(T,B\ensuremath{\rightarrow}0)$ and magnetoresistive effects (anisotropic magnetoresistance, longitudinal and transverse Lorentz resistance) are quantitatively disentangled. The temperature-dependent basic resistivity for $T\ensuremath{\le}30\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ follows a $\ensuremath{\Delta}\ensuremath{\rho}(T,B\ensuremath{\rightarrow}0)=a{T}^{2}+b{T}^{5}$ law, proving that electron-electron and electron-phonon scattering (with a resistive Debye temperature ${\ensuremath{\Theta}}_{\mathrm{R}}\ensuremath{\cong}450\phantom{\rule{0.28em}{0ex}}\mathrm{K}$) are dominant also in iron, similar to nonferromagnetic transition metals. Here the crystal-orientation dependence of the intrinsic longitudinal magnetoresistance in the single-domain state could be quantitatively evaluated in accordance with the symmetry of the Fermi surface. The transverse magnetoresistance (TMR) turns out to be the sum of the so-called ``two-band conduction term'' and the unboundedly growing TMR term in compensated metals. It is proven that the second term is not restricted to the high-field limit (as usually discussed up to now) but acts down to lowest TMR or ${\ensuremath{\omega}}_{\mathrm{C}}\ensuremath{\tau}$ values. This conclusion is verified by TMR measurements on highly pure molybdenum single crystals (RRR \ensuremath{\cong} 100 000). Supported by Kerr microscopy, a small positive domain wall resistance (DWR) could be isolated from the dominating negative DWR in the multidomain state of iron, resulting in a relation of larger than 5:1 for the electrons to pass a domain wall with spin tracking compared to scattering with spin conservation.

Reversal-mechanism of perpendicular switching induced by an in-plane current

We propose a magnetization reversal model to explain the perpendicular switching of a single ferromagnetic layer induced by an in-plane current. Contrary to previously proposed reversal mechanisms that such magnetic switching is directly from the Rashba or spin Hall effects, we suggest that this type of switching arises from the current-induced chirality dependent domain wall motion. By measuring the field dependent switching behaviors, we show that such switching can also be achieved between any two multidomain states, and all of these switching behaviors can be well explained by this model. This model indicates that the spin Hall angle in such structures may be overestimated and also predicts similar switching behaviors in other ferromagnetic structures with chiral domain walls or skyrmions.

Domain Structure and Magnetoresistance in Co2MnGe Zigzag Structures

We report a clear manifestation of the negative contribution to the magnetoresistance due to domain walls in Co2MnGe-Heusler submicron zigzag wires in which the domain structure, domain size and domain wall density can be well controlled. The magnetic behavior of these systems results from the interplay between the intrinsic magneto-crystalline (K4) anisotropy, growth induced uniaxial (KU = 4.7x103 J/m3) anisotropy and shape anisotropy (KS), as observed by magnetic-force microscopy (MFM) and longitudinal Kerr hysteresis loop measurements. Magnetoresistance measurements were performed by the four-point method under a field applied in the plane of the wires at a temperature of 300K. In these structures, domain wall-creation and annihilation occur in a coherent way. As a result, clear jumps of the resistance are detected during the transition from single-domain- to multi-domain states. At room temperature a value RDW = -2.5 mΩ was obtained; this result is the same order of magnitude as other experimental and theoretical findings. The negative resistive contribution due to the domain wall is also discussed and compared with the existing theoretical models.

Stress-induced magnetic textures and fluctuating chiral phase in MnGe chiral magnet

We have studied the MnGe chiral magnet below ${T}_{\text{N}}=170$ K, by magnetic measurements, M\"ossbauer spectroscopy, and by neutron diffraction at ambient and under nonhydrostatic pressure. At ambient pressure, we observe the coexistence of two magnetic phases belonging to the same crystal phase in a large temperature range (down to 100 K) below ${T}_{\mathrm{N}}$: ferromagnetically correlated rapidly fluctuating spins coexist with frozen spins involved in the helical order. Applying a uniaxial pressure component induces a strong magnetic texture, where most of the helical axes reorient along the stress axis. The magnetic texture persists in the fluctuating chiral state up to ${T}_{\mathrm{N}}$. Our results suggest that the zero field ground state at ambient pressure is a multidomain state consisting of helical domains with random orientations rather than a three-dimensional skyrmion lattice. They show the presence of an unusually broad transition to paramagnetism with a dynamical phase separation triggered by temperature.