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Recently, Kittel’s theory of ferromagnetic domains in thin films in one dimension, i. e. with the domains extended infinitely over one in-plane direction and with the anisotropy axis oriented perpendicular to the film was revisited by considering the film thickness and unbalanced domains with up and down magnetization, yielding to the computation of magnetic hysteresis [C. M. Teodorescu, Res. Phys. 46 (2023) 106287]. In this work, the above study is extended to samples featuring two-dimensional domain landscapes, for materials with strong magnetic anisotropy, typically characterized by a superunitary ratio between the anisotropy energy and the stray field energy densities. This allows one to compute the most stable structures for vanishing average magnetization 〈M〉 together with hysteresis curves for thin films with perpendicular magnetic anisotropy and two-dimensional rectangular domains and also for thin films with in-plane magnetic anisotropy. For two-dimensional films with perpendicular magnetic anisotropy, the most stable structure for 〈M〉 = 0 is found to be that with domains infinitely elongated along one in-plane direction, i. e. the one-dimensional case treated in the preceding work. For thin stripes with in-plane magnetization, the domain size l is approximately linear with the stripe lateral size d for low film thickness, while for large film thicknesses it follows a Kittel-like law, but as function of the stripe size l ∼ d1/2. For in-plane magnetized thin films of infinite lateral extent, the most stable structure is the single domain. As for hysteresis curves, the two-dimensional case with perpendicular magnetic anisotropy is shown to evolve from a 2D landscape derived from the checkerboard structure, but with unbalanced domains for magnetization near saturation, towards one-dimensional domain structures for lower magnetization. In some cases and depending also on the demagnetization factor, the one-dimensional case is not reached, and the film exhibit 2D structures on the whole range of the magnetization curve. The hysteresis obtained for thin magnetic stripes with in-plane magnetization also can exhibit a rich structure, with minor cycles on the wings of the magnetization curves evolving towards „normal” hysteresis (again, depending on the film thickness, stripe lateral size and demagnetization factor). An infinite thin film with in-plane anisotropy features a steplike magnetization dependence on the applied field.

In 1946 and 1949, Charles Kittel proposed a simple model for the size of ferromagnetic domains that is still widely used nowadays [C. Kittel, Phys. Rev. 70 (1946) 965–971 and Rev. Mod. Phys. 21 (1949) 541–583], including for other ferroic systems, such as ferroelectrics and multiferroics. Kittel’s theory is revisited in this work, with a more detailed demonstration and emphasizing the main assumptions utilized, by using SI units instead of CGS units, as in the original Kittel’s works. The validity limits of the Kittel’s scaling law where the domain width varies with the square root of the sample thickness towards low thicknesses is derived, with the possibility of evolution towards large domains for ultralow thicknesses. Further, Kittel’s model is extended to the case where the sample has a non-vanishing net magnetization and it is shown how magnetization curves at zero temperature can be obtained. This is discussed by supposing constant width of a pair of neighboring domains with opposed magnetization, or by allowing this width to vary as function on the net magnetization of the sample. Though this latter assumption seems to be more reasonable from the point of view of the evolution towards a single domain state at saturation, it seems that the model able to yield most accurate vales of the coercive field is the domain with fixed width of the pair of domains, which justifies the assumption of „domain wall pinning”. The introduction of the demagnetization factor associated with the finite size of the film yields a maximum thickness up to which the films present hysteresis curves. The validity of this theory for ferrelectric domains is also briefly discussed.

Among the magnetocaloric materials featuring first-order phase transitions (FOPT), FeRh is considered as a reference system to study the FOPT because it is a "simple" binary system with a CsCl structure exhibiting a large adiabatic temperature change. Recently, ab initio theory predicted that changes in the Fe/Rh stoichiometry in the vicinity of equiatomic composition strongly influence the FOPT characteristics. However, this theoretical prediction was not clearly verified experimentally. Here, we investigated the composition dependence of the transitional hysteresis in FeRh. It is shown that a Fe excess of only 1 at. % induces a ferromagnetic state in the whole temperature range (from 5 K up to T ) for a minor portion of the sample (≈10%), while 5 at. % is enough to completely eliminate the FOPT. Element-specific X-ray magnetic circular dichroism (XMCD) measurements suggest that this ferromagnetic contribution arises from residual FeRh ferromagnetic regions. We attribute the formation of such domains to Fe antisite defects, as Mössbauer spectroscopy demonstrates the presence of Fe atoms located at the 1b (Rh) sites in the CsCl-type structure. As a consequence, compared with the equiatomic composition, the slightly Fe-rich sample exhibits completely different FOPT properties, influencing the magnetocaloric performances. Thus, our study sheds light on the origin of the remarkable stoichiometric sensitivity of the FOPT behavior in FeRh. These insights have broader implications for understanding FOPT dynamics and the role of residual ferromagnetic domains.c ) for a minor portion of the sample (≈10%), while 5 at. % is enough to completely eliminate the FOPT. Element-specific X-ray magnetic circular dichroism (XMCD) measurements suggest that this ferromagnetic contribution arises from residual FeRh ferromagnetic regions. We attribute the formation of such domains to Fe antisite defects, as Mössbauer spectroscopy demonstrates the presence of Fe atoms located at the 1b (Rh) sites in the CsCl-type structure. As a consequence, compared with the equiatomic composition, the slightly Fe-rich sample exhibits completely different FOPT properties, influencing the magnetocaloric performances. Thus, our study sheds light on the origin of the remarkable stoichiometric sensitivity of the FOPT behavior in FeRh. These insights have broader implications for understanding FOPT dynamics and the role of residual ferromagnetic domains.

Multiferroic materials, characterized by the coexistence of ferroelectric and ferromagnetic properties, have garnered considerable attention in recent years due to their potential for revolutionizing various technological applications. A crucial aspect of multiferroics is the domain structure, which plays a pivotal role in their properties and functionalities. This abstract provides an overview of multiferroic domain structures in oxide materials with multiferroic properties. Multiferroic domain structures represent a complex interplay of ferroelectric and ferromagnetic domains, giving rise to intriguing phenomena such as magnetoelectric coupling and unique optical responses. Understanding and manipulating these domain structures are essential for harnessing the full potential of multiferroic materials. In this context, we explore the fundamental principles governing the formation, stability, and dynamics of multiferroic domains. We delve into the various characterization techniques, including advanced microscopy and spectroscopy methods, used to probe and manipulate these domains at nanoscale dimensions. we discuss the role of domain engineering in tailoring multiferroic properties for specific applications, ranging from data storage and sensors to energy harvesting and spintronics. The potential of domain wall engineering for creating novel devices with enhanced functionalities is also highlighted. [ABSTRACT FROM AUTHOR]

• 1D landscape favored for perpendicular anisotropy for null average magnetization. • Checkerboard 2D landscape favored for perpendicular anisotropy near saturation. • Minor hysteresis loops occur on the wings of the magnetization curve. • Lower demagnetization factors promote the onset of rectangular hysteresis. • Low coercive fields are obtained by using small deviation of demagnetization factors. Recently, Kittel's theory of ferromagnetic domains in thin films in one dimension, i. e. with the domains extended infinitely over one in-plane direction and with the anisotropy axis oriented perpendicular to the film was revisited by considering the film thickness and unbalanced domains with up and down magnetization, yielding to the computation of magnetic hysteresis [C. M. Teodorescu, Res. Phys. 46 (2023) 106287]. In this work, the above study is extended to samples featuring two-dimensional domain landscapes, for materials with strong magnetic anisotropy, typically characterized by a superunitary ratio between the anisotropy energy and the stray field energy densities. This allows one to compute the most stable structures for vanishing average magnetization 〈 M 〉 together with hysteresis curves for thin films with perpendicular magnetic anisotropy and two-dimensional rectangular domains and also for thin films with in-plane magnetic anisotropy. For two-dimensional films with perpendicular magnetic anisotropy, the most stable structure for 〈 M 〉 = 0 is found to be that with domains infinitely elongated along one in-plane direction, i. e. the one-dimensional case treated in the preceding work. For thin stripes with in-plane magnetization, the domain size l is approximately linear with the stripe lateral size d for low film thickness, while for large film thicknesses it follows a Kittel-like law, but as function of the stripe size l ∼ d 1/2. For in-plane magnetized thin films of infinite lateral extent, the most stable structure is the single domain. As for hysteresis curves, the two-dimensional case with perpendicular magnetic anisotropy is shown to evolve from a 2D landscape derived from the checkerboard structure, but with unbalanced domains for magnetization near saturation, towards one-dimensional domain structures for lower magnetization. In some cases and depending also on the demagnetization factor, the one-dimensional case is not reached, and the film exhibit 2D structures on the whole range of the magnetization curve. The hysteresis obtained for thin magnetic stripes with in-plane magnetization also can exhibit a rich structure, with minor cycles on the wings of the magnetization curves evolving towards „normal" hysteresis (again, depending on the film thickness, stripe lateral size and demagnetization factor). An infinite thin film with in-plane anisotropy features a steplike magnetization dependence on the applied field. [ABSTRACT FROM AUTHOR]

Fe-containing oxide coatings fabricated by the plasma-electrolytic oxidation (PEO) method have been studied by means of scanning electron and magnetic force microscopy. The data comparison has demonstrated that ferromagnetic properties of the coatings are mainly associated with concentrating of iron in specific pores. A scheme has been suggested that would explain iron distribution in the course of the coating growth. [ABSTRACT FROM AUTHOR]

• Kittel's theory of ferromagnetic domains, revised, presented in detail, in SI units. • Kittel's scaling law (power 1/2) is retrieved for high sample thickness. • For low sample thickness, the domain width becomes very large. • Domain wall migration is integrated into a theory of magnetic hysteresis. • Low coercive fields may be obtained in the hypothesis of pinned domain walls. In 1946 and 1949, Charles Kittel proposed a simple model for the size of ferromagnetic domains that is still widely used nowadays [C. Kittel, Phys. Rev. 70 (1946) 965–971 and Rev. Mod. Phys. 21 (1949) 541–583], including for other ferroic systems, such as ferroelectrics and multiferroics. Kittel's theory is revisited in this work, with a more detailed demonstration and emphasizing the main assumptions utilized, by using SI units instead of CGS units, as in the original Kittel's works. The validity limits of the Kittel's scaling law where the domain width varies with the square root of the sample thickness towards low thicknesses is derived, with the possibility of evolution towards large domains for ultralow thicknesses. Further, Kittel's model is extended to the case where the sample has a non-vanishing net magnetization and it is shown how magnetization curves at zero temperature can be obtained. This is discussed by supposing constant width of a pair of neighboring domains with opposed magnetization, or by allowing this width to vary as function on the net magnetization of the sample. Though this latter assumption seems to be more reasonable from the point of view of the evolution towards a single domain state at saturation, it seems that the model able to yield most accurate vales of the coercive field is the domain with fixed width of the pair of domains, which justifies the assumption of „domain wall pinning". The introduction of the demagnetization factor associated with the finite size of the film yields a maximum thickness up to which the films present hysteresis curves. The validity of this theory for ferrelectric domains is also briefly discussed. [ABSTRACT FROM AUTHOR]

Abstract: We have studied the structure, the surface morphology, the magnetic domains and the magnetization of ferromagnetic BaFeO3−δ (BFO) thin films deposited on single-crystal MgO (001) substrate. The BFO film is ferromagnetic-insulating at room temperature and shows a growth of self organized symmetric square-shaped structures of various length-scales on the surface. The film, after oxygen annealing, shows several pronounced modifications: (i) in addition to square structures, the pyramid-shaped structures also manifest on the surface, (ii) the lattice parameter decreases indicating a change in the structure, (iii) the magnetization isotherms show magnetic anisotropy with a five-fold increase in magnetic coercivity and two-fold increase in magnetic moment, and (iv) a larger growth of the magnetic domains. These results demonstrate a strong influence of oxygen annealing on structural and magnetic properties of BFO films. Our results suggest that the structural and the magnetic properties are strongly correlated in BFO films, albeit with unaltered insulating state. [Copyright &y& Elsevier]

In this article, we present results of field cooled (FC) and zero field cooled (ZFC) magnetization measurements and investigation of aging and memory effect in bismuth ferrite (BFO) multiferroic micro-cubes obtained by means of simple microwave synthesis procedure. It is found that difference between FC and ZFC magnetizations appear at the temperature of freezing of ferromagnetic domain walls. The decay of the magnetic momentversustime described by power-law relation and the absence of memory effect are caused by domain growth mechanism rather than by the spin-glass phase. The negligible value of remnant magnetic moment indicates that BFO compound exhibits low concentration of ferromagnetic domains and can be close to ferromagnetic to spin-glass transition. [ABSTRACT FROM PUBLISHER]

Abstract: Ferromagnetic property of Co1.5Fe1.5O4 ferrite has been studied in a wide range of measurement temperature and magnetic field. Grain size effect on the ferromagnetic parameters has been examined by annealing the chemical routed sample at different temperatures up to 1150°C. The evolution from hard to soft ferromagnetism of the material has been correlated with undergoing changes of crystal structure, grain morphology, crystalline anisotropy, and transformation of the ferromagnetic grains from single domain to multi-domain structure during annealing process. The present ferrite samples also showed some interesting low temperature features, e.g., blocking of ferromagnetic grains that started above 300K and its control by varying magnetic field intensity, competition of the crystalline anisotropy between uniaxial and cubic character, large magnetic squareness and variable coercivity as the function of annealing temperature of the samples. The material seems to be technologically interesting for its high squareness value. [Copyright &y& Elsevier]

The Andreev current and the subgap conductance in a superconductor/insulator/ferromagnet (SIF) structure in the presence of a small spin-splitting field show novel interesting features (Ozaeta et al. in Phys. Rev. B 86:060509(R), ). For example, the Andreev current at zero temperature can be enhanced by a spin-splitting field h, smaller than the superconducting gap Δ, as has been recently reported by the authors. Also at finite temperatures, the Andreev current has a peak for values of the spin-splitting field close to the superconducting gap, h≈Δ. Finally, the differential subgap conductance at low temperatures shows a peak at the bias voltage eV= h. In this paper, we investigate the Andreev current and the subgap conductance in SFF structures with arbitrary direction of magnetization of the F layers. We show that all the aforementioned features occur now at the value of the 'effective field', which is the field acting on the Cooper pairs in the multi-domain ferromagnetic region, averaged over the decay length of the superconducting condensate into a ferromagnet. We also briefly discuss the heat transport and electron cooling in the considered structures. [ABSTRACT FROM AUTHOR]

Abstract: We present a magneto-optical study of the magnetization dynamics in ferromagnetic quantum wells in the time range down to 20ns. We use a small electromagnet coil to produce short pulses of magnetic field. The magnetization relaxation after the pulse (observed through PL polarization) is faster than 20ns in the paramagnetic state. Decreasing the temperature below the Curie temperature results in an increase of the relaxation time up to . This relaxation corresponds to the dynamics of the ferromagnetic domains. The mobility of the domains increases with temperature. [Copyright &y& Elsevier]

Abstract: Magnetisation reversal has been investigated in 2μm diameter epitaxial Fe(100) disks using scanning Hall probe microscopy. The high spatial resolution (∼200nm) and non-invasiveness of our Hall sensors has allowed the domain structure, which is governed by biaxial in-plane anisotropy, to be resolved in the disks. We find that most disks appear to exhibit a double vortex magnetisation reversal mechanism, in agreement with the results of micromagnetic simulations with the OOMMF code. Although the switching dynamics tend to be influenced by domain wall pinning sites within our Fe samples, we find a strong correlation between most of our measured images and the results of simulations. Additional confirmation for the double vortex reversal mechanism is drawn from local measurements of out-of-plane magnetic induction loops. [Copyright &y& Elsevier]

Abstract: The magnetic and electronic ground states of the polycrystalline perovskite compound La0.7Sr0.3Co0.9Mn0.1O3 have been studied using AC susceptibility, resistivity and neutron depolarization techniques. Results of neutron depolarization study establish the existence of ferromagnetic domains of ∼3μm size below 180K. The substitution of 10at% Mn ions at the Co site in the compound La0.7Sr0.3CoO3 reduces the effective eg electron transfer and suppresses the double exchange interaction. The competition between the reduced ferromagnetic double exchange interaction and the coexisting antiferromagnetic interaction along with the random nature of substitution leads to a randomly canted ferromagnetic ground state for the substituted compound. Resistivity study confirms that the randomly canted ferromagnetic ground state is insulating. [Copyright &y& Elsevier]

GaAs/AlGaAs two-dimensional electron gas (GaAs-2DEG) Hall probes are impractical for sub-micron room-temperature scanning Hall microscopy (RT-SHPM), due to surface depletion effects that limit the Hall driving current and magnetic sensitivity (Bmin). Nano and micro Hall-effect sensors were fabricated using Bi and InSb thin films and shown to be practical alternatives to GaAs-2DEG probes for high resolution RT-SHPM. The GaAs-2DEG and InSb probes were fabricated using photolithography and the Bi probes by optical and focused ion beam lithography. Surface depletion effects limited the minimum feature size of GaAs-2DEG probes to ∼1.5 μm2 with a maximum drive current Imax of ∼3 μA and Bmin∼0.2 G/√ of Hz. The Bmin of 1.5 μm2 InSb Hall probes was 6 × 10-3 G/√ of Hz at Imax of 100 μA. Further, 200 nm × 200 nm Bi probes yielded good RT-SHPM images of garnet films, with Imax and sensitivity of 40 μA and ∼0.80 G/√ of Hz, respectively. [Copyright &y& Elsevier]

A room temperature scanning Hall probe microscope system utilizing GaAs/AlGaAs and bismuth micro-Hall probes was used for magnetic imaging of ferromagnetic domain structures on the surfaces of crystalline thin film garnets and permanent magnets. The Bi micro-Hall probes had dimensions ranging between 0.25 and 2.8 μm2 and were fabricated using a combination of optical lithography and focused ion beam milling. The use of bismuth was found to overcome surface depletion effects associated with semiconducting micro-Hall probes. Our experiments demonstrated that Bi is a practical choice of material for fabricating sub-micron sized Hall sensors. [Copyright &y& Elsevier]

Abstract: Three-dimensional neutron depolarization measurements have been carried out on single-crystalline UGe at ambient pressure between 4 and 80K in order to determine the average ferromagnetic domain size d. It is found that below K uniaxial ferromagnetic domains are formed with an estimated magnetic domain size of m. The domain wall thickness is estimated to be only a few percent of the domain size. These results clearly indicate the microscopic nature of the ferromagnetic domains. [Copyright &y& Elsevier]