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In this paper, crystallized core–shell Co@CoO nanocluster assembled thin films with different thicknesses were prepared by magnetron sputtering. A large zero-field-cooled exchange bias (ZEB) around...

Three distorted tetrahedral Dy(iii) aryloxide complexes, [Na(THF)6][Dy(OArAd2tBu)2Cl2] (1) (OArAd2tBu = OC6H2Adamantyl2-2,6-tBu-4) and [Na(THF)6][Dy(OMes*)3X] (X = Cl, 2; BH4, 3), (OMes* = OC6H2tBu3-2,4,6) exhibit easy axis magnetic anisotropy and slow magnetic relaxation at zero field, with relaxation rates 1 < 2 < 3., Magnetostructural correlations: The magnetic relaxation dynamics of three distorted tetrahedral dysprosium aryloxide complexes are shown to vary according to their local coordination environments.

A mononuclear Ni(II) complex, [NiL2]·2H2O, was prepared by the reaction of a N2O2 donor monocondensed Schiff base ligand, 2-((3-aminopropylimino)methyl)-6-methoxyphenol (HL), with NiCl2·6H2O. The reaction of this complex with NiCl2·6H2O and LnCl3·6H2O (Ln = Gd, Tb, Dy, Ho) in a 1:1:1 molar ratio leads to four hexanuclear Ni4Ln2 complexes formulated as [{(NiL)2Gd}2(μ2-Cl)2(μ3-OH)4(OH2)4]Cl4·CH3CN·H2O (1), [{(NiL)2Tb}2(μ2-Cl)2Cl2(μ3-OH)4(OH2)2]Cl2·12H2O (2), [{(NiL)2Dy}2(μ2-Cl)2Cl2(μ3-OH)4(OH2)2]Cl2·16H2O (3), and [{(NiL)2Ho}2(μ2-Cl)2(μ3-OH)4(OH2)4]Cl4·CH3CN·1.8H2O (4). The Ln(III) centers are octacoordinated with a triangular-dodecahedral geometry, and the geometries around the Ni(II) centers are distorted octahedral in all four complexes. The temperature-dependent DC magnetic measurements reveal the existence of ferromagnetic interactions in all four complexes (1–4). The AC susceptibility measurements performed with and without an applied DC field show SMM behavior in complexes 2–4 with a single slow relaxation process in 2 (SR) but slow (SR) and fast (FR) relaxation processes in 3 and 4. The energy barriers of the relaxation times for the SR processes are ca. 13, 20, and 19 K in 2–4, respectively.

In this work, we describe a new way to measure spin dependent charge capture events at MOSFET interfaces called near-zero-field spin dependent charge pumping (NZF SDCP) which yields similar information as conventional electron paramagnetic resonance. We find that NO anneals have a significant effect on the spectra obtained from 4H-SiC MOSFETs. We also likely resolve hyperfine interactions which are important for defect identification. Finally, we fully integrate a NZF SDCP measurement system into a wafer prober for high throughput applications.

It was shown that 40-min exposure of peritoneal neutrophils to hypomagnetic conditions (with a residual field of 0.01 μT) caused a significant (25%) decrease in the intensity of intracellular dichlorofluorescein fluorescence. This effect of the weak magnetic field persisted if the constant magnetic field was increased to 1 μT. Upon further increase of the field to 2.5 μT, the effect of the field disappeared and reappeared at 5 μT in a reduced form, reaching a maximum at 7 μT. There was an equally pronounced and stable inhibitory effect under a sequential increase in the induction of a constant magnetic field (9, 15, and 19.5 μT), the degree of manifestation of which was significantly reduced only at 30 μT. Fluorescence intensity of the 2,7-dichlorodydrofluorescein oxidation products did not differ from the control values at a constant magnetic field of 45 μT. There was no observed effect on these processes under further increase of the field to 74 and 100 μT.

Magnetic properties of ${A}_{2}{BB}^{\ensuremath{'}}{\mathrm{O}}_{6}$ ($A=\mathrm{rare}$ or alkaline-earth ions; $B,{B}^{\ensuremath{'}}=\mathrm{transition}\text{\ensuremath{-}}\mathrm{metal}$ ions) double perovskites are of great interest due to their potential spintronic applications. Particularly fascinating is the zero-field-cooled exchange bias effect observed for the hole-doped ${\mathrm{La}}_{2\ensuremath{-}x}{A}_{x}{\mathrm{CoMnO}}_{6}$ polycrystalline samples. In this paper we synthesize ${\mathrm{La}}_{2}{\mathrm{CoMnO}}_{6},\phantom{\rule{0.28em}{0ex}}{\mathrm{La}}_{1.5}{\mathrm{Ca}}_{0.5}{\mathrm{CoMnO}}_{6}$, and ${\mathrm{La}}_{1.5}{\mathrm{Sr}}_{0.5}{\mathrm{CoMnO}}_{6}$ single crystals by the floating zone method and study their magnetic behavior. The three materials are ferromagnetic. Surprisingly, we observe no zero or even conventional exchange bias effect for the Ca- and Sr-doped single crystals, in sharp contrast to polycrystalline samples. This absence indicates that the lack of grain boundaries and spin-glass-like behavior, not observed in our samples, might be key ingredients for the spontaneous exchange bias phenomena seen in polycrystalline samples.

We investigate the Goos-Hanchen (GH) shifts of a laser for V-type three-level atoms with a fourth auxiliary level in a constant cavity structure. In the presence of interference mechanisms induced by spontaneous emission and incoherent pumping, the lateral shifts of the reflected and transmitted laser field switch from positive to negative just by the rates of direct and indirect incoherent pump fields. In the presence of quantum interference, the maximum lateral shifts of the reflected laser field appear. In this case, the sensitivity is $$9.39 \times 10^{6} \lambda$$ . Also, maximum lateral shifts of the reflected and transmitted laser field reach in zero field detuning.

A novel lanthanide double-decker complex with nickel metallacrowns (MCs) as coordinating ligands has been synthesized. In the 3d/4f metallacrown complex TbIII[12-MCNiIIN(shi)-4]2, the central lanthanide ion is sandwiched between two [12-MC-4] units, forming an almost ideal square-antiprismatic coordination sphere. The resulting zenithal angles at the central lanthanide ion are smaller than those for previously reported sandwich compounds. Magnetic measurements reveal an energy barrier of 346 K under zero field and up to 585 K under 3200 Oe, the highest reported for metallacrowns with D4d symmetry.

Magnetic skyrmions are twirling spin structures observed in bulk, thin films, and multilayers with several features for both fundamental physics understanding and spintronic applications, i.e., nanoscale size, efficient transport under electrical current, and topological protection against defects. However, most magnetic skyrmions have been observed under the assistance of an out-of-plane magnetic field, which may limit their use in magnetic memory technologies. In this chapter, we review and present two recent mechanisms to create zero-field skyrmions at room-temperature in ferromagnetic multilayers. First, by tuning the perpendicular magnetic anisotropy (PMA) and remnant magnetization (near magnetization saturation) in unpatterned symmetric multilayer systems, it was achieved a transition from worm-like domains to isolated skyrmions. Besides, we present how to find stable zero-field skyrmions in arrays of ferrimagnetic discs by tailoring their diameter. Both methods demonstrate a robust route to stabilize zero-field skyrmions at room temperature, thus providing an important contribution to possible applications of these textures in the next generation of skyrmionics devices.

Two mononuclear tetrahedral Co(II) complexes (HNEt3)2[Co(L1)2]·H2O (1) and (Bu4N)2[Co(L2)2]·H2O (2) (H2L1 = N,N′-bis(p-toluenesulfony1)oxamide, H2L2 = N,N′-diphenyloxamide) have been synthesized, a...

Photoexcited pentacene, upon arriving via intersystem crossing into its lowest triplet state, has been extensively studied due to the large and relatively long-lived spin polarization that it exhibits. However, the spin dynamics of these triplets has not hitherto been accurately determined, with glaring inconsistencies between published values. Using zero-field transient electron paramagnetic resonance (ZF-trEPR), we here report the determination of a complete set of depopulation and spin–lattice relaxation rates for the lowest triplet state of pentacene doped at 0.1% into a p-terphenyl host crystal at room temperature in zero applied magnetic field. The rates of spin–lattice relaxation between the triplet’s sublevels are found to be highly anisotropic (i.e., transition-specific) and not negligible compared to the rates of depopulation from the same three sublevels back to pentacene’s ground state. The spin dynamics, as well as the ZF-trEPR technique reported here, can aid the rational, quantitative engineering of applications such as room-temperature masers and triplet dynamic nuclear polarization.

We have performed 59Co zero field nuclear magnetic resonance (NMR) experiment at 4 K on Co x Cu 1 - x (x = 0.10, 0.32 and 0.76) nanogranular alloys. The NMR signal arises from Co rich ferromagnetic clusters formed within the Cu matrix. The analysis of NMR spectra shows that the resonance peaks arise from both fcc and hcp phases of Co. However, Co nuclei experience magnetic hyperfine field from Co only environment as well as other environments in which nearest-neighbor (NN) Co atoms are replaced by Cu. Assuming that these two environments constitute the core and the shell of the Co clusters, it is estimated using previous magnetization measurements that the contribution of core dominates in the ferromagnetism of the particles though it occupies only about 20% of the volume of Co clusters even for high Co containing alloys.

Two dysprosium complexes bearing unsupported Dy–Ge/Sn metal–metal bonds are reported here, wherein the Dy–Ge and Dy–Sn bonds both contain relatively large covalency. The complexes exhibit slow relaxation of magnetization at zero field with energy barriers of 485 and 620 K, respectively, and the blocking temperature of 6 K.

Two dinuclear lanthanide complexes (Gd and Dy) were prepared and characterized by X-ray, magnetic and computational methods. The Dy analogue shows SMM behavior with an energy barrier of 98.4 K in the absence of an applied dc field. Theoretical calculations were performed on model complexes which support the hypothesis that the energy barrier will increase if the soft-donor atoms S and Se are used in lieu of an O donor.

A detailed zero-field and transverse-field muon spin relaxation/rotation ($\ensuremath{\mu}\mathrm{SR}$) experiments have been carried out on the recently discovered noncentrosymmetric superconductor ${\mathrm{W}}_{3}{\mathrm{Al}}_{2}\mathrm{C}$ to speculate about its superconducting ground state. Bulk nature of superconductivity below 7.6 K is confirmed through magnetization and specific heat measurements. No change in the zero field $\ensuremath{\mu}\mathrm{SR}$ spectra collected above and below ${T}_{c}$ is visible, ruling out the possibility of spontaneous magnetic field below ${T}_{c}$. This confirms that time-reversal symmetry is preserved for ${\mathrm{W}}_{3}{\mathrm{Al}}_{2}\mathrm{C}$ upon entering in the superconducting ground state. Temperature-dependent superfluid density [${\ensuremath{\rho}}_{s}(T)$], which directly reflects the superconducting gap symmetry is obtained by the analysis of spectra obtained from the transverse-field $\ensuremath{\mu}\mathrm{SR}$ experiments. Despite a noncentrosymmetric structure, ${\mathrm{W}}_{3}{\mathrm{Al}}_{2}\mathrm{C}$ adopts a fully gapped spin-singlet superconducting ground state as confirmed through the analysis of ${\ensuremath{\rho}}_{s}(T)$ and ${C}_{e}(T)$. The zero-temperature value of gap is ${\mathrm{\ensuremath{\Delta}}}_{0}$ = 1.139(5) meV with gap-to-${T}_{c}$ ratio $2{\mathrm{\ensuremath{\Delta}}}_{0}/{k}_{B}{T}_{c}\ensuremath{\approx}3.48$, classifying this material as a weakly coupled superconductors. We have also revealed that the ratio ${T}_{c}/{\ensuremath{\lambda}}_{\mathrm{eff}}^{\ensuremath{-}2}$ is comparable to the class of unconventional superconductors, which points towards an unconventional pairing mechanism in ${\mathrm{W}}_{3}{\mathrm{Al}}_{2}\mathrm{C}$.

We performed high-magnetic-field ultrasonic experiments on YbB$_{12}$ up to 59 T to investigate the valence fluctuations in Yb ions. In zero field, the longitudinal elastic constant $C_{11}$, the transverse elastic constants $C_{44}$ and $\left( C_{11} - C_{12} \right)/2$, and the bulk modulus $C_\mathrm{B}$ show a hardening with a change of curvature at around 35 K indicating a small contribution of valence fluctuations to the elastic constants. When high magnetic fields are applied at low temperatures, $C_\mathrm{B}$ exhibits a softening above a field-induced insulator-metal transition signaling field-induced valence fluctuations. Furthermore, at elevated temperatures, the field-induced softening of $C_\mathrm{B}$ takes place at even lower fields and $C_\mathrm{B}$ decreases continuously with field. Our analysis using the multipole susceptibility based on a two-band model reveals that the softening of $C_\mathrm{B}$ originates from the enhancement of multipole-strain interaction in addition to the decrease of the insulator energy gap. This analysis indicates that field-induced valence fluctuations of Yb cause the instability of the bulk modulus $C_\mathrm{B}$., 15 pages, 11 figures

Layered trigonal ${\mathrm{EuMg}}_{2}{\mathrm{Bi}}_{2}$ is reported to be a topological semimetal that hosts multiple Dirac points that may be gapped or split by the onset of magnetic order. Here, we report zero-field single-crystal neutron-diffraction and bulk magnetic susceptibility measurements versus temperature $\ensuremath{\chi}(T)$ of ${\mathrm{EuMg}}_{2}{\mathrm{Bi}}_{2}$ that show the intraplane ordering is ferromagnetic (${\mathrm{Eu}}^{2+},\phantom{\rule{0.16em}{0ex}}S=7/2$) with the moments aligned in the $ab$ plane while adjacent layers are aligned antiferromagnetically (i.e., A-type antiferromagnetism) below the N\'eel temperature.

Metamagnetic off-stoichiometric Heusler alloys are actively being investigated because of their great potential as magnetocaloric materials. These properties are intimately related to the nanoscale homogeneity of their magnetic properties, mainly due to a strong influence of the nature of the exchange interactions between Mn atoms on the magnetism of the alloys. In this work, a spontaneous exchange bias phenomenon on a Ni–Co–Mn–Sn metamagnetic Heusler sputtered film is presented and studied in detail. More particularly, a series of DC magnetization curves measured as a function of the temperature demonstrates that the system exhibits canonical spin glass-like features. After a careful study of the field-cooling and zero-field-cooling curves measured on this system, the existence of magnetic inhomogeneities is inferred, as a consequence of the competition between ferromagnetic and antiferromagnetic exchange interactions between Mn atoms. Further AC susceptibility measurements on this system demonstrate that the underlying exchange bias phenomenon can be attributed to a magnetic clusters model based on superferromagnetic-like interactions present in the film. These findings suggest that the spontaneous exchange bias exhibited by the studied system is a consequence of the formation of this superferromagnetic-like state. This research was funded by the Hellenic Foundation of Research and Innovation (HFRI) and the General Secretariat for Research and Innovation (GSRI) of Greece (grant M.M.ME.H.A., no. 2530); by the H2020 Excellent Science-Marie Skłodowska-Curie Actions with the individual fellow no.753025; and the Spanish Government under grant no. RTI2018 094683-B-C5.

Let $\Bbbk$ be a field of characteristic 0. Let $X$ be a smooth complete intersection over $k$ of dimension $n-k$ in the projective space $\mathbf{P}^n_{k}$, for given positive integers $n$ and $k$. When $k=\mathbb{C}$, Terasoma (\cite{Ter90}) and Konno (\cite{Ko91}) provided an explicit representative (in terms of differential forms) of a basis for the primitive middle-dimensional algebraic de Rham cohomology $H_{dR,\operatorname{prim}}^{n-k}(X;\mathbb{C})$. Later Dimca constructed another explicit representative of a basis of $H_{dR,\operatorname{prim}}^{n-k}(X;\mathbb{C})$ in \cite{Dim95}. Moreover, he proved that his representative gives the same cohomology class as the previous representative of Terasoma and Konno. The goal of this article is to examine the above two different approaches without assuming that $k=\mathbb{C}$ and provide a similar comparison result for any field $k$. Dimca's argument depends heavily on the condition $k=\mathbb{C}$ and our idea is to find appropriate Cech-de Rham complexes and spectral sequences corresponding to those two approaches, which work without restrictions on $k$., Comment: 13 pages

The interfacial Dzyaloshinskii-Moriya interaction (iDMI) was investigated in Co thin-films with different combinations of seeding and capping layers in previous works. The variations in the local magnetic out-of-plane (oop) anisotropy K as a function of film thickness t lead to additional contributions that make the quantification of the iDMI more challenging. These additional contributions were specifically attributed to the transition of fcc Co to hcp Co at a critical thickness tcr. In this work we clarify this issue by investigating the local structure and local magnetic stiffness and their contribution to the oop anisotropy K in two Pt/Co(t)/Ir film stacks with t = 10 nm and t = 25 nm. Zero-field nuclear magnetic resonance spectroscopy (ZF NMR) is the method of choice as it is a non-destructive and sensitive probe to examine structure and magnetic properties of nano-sized samples. We describe the evolution of the Co allotropes (fcc & hcp) and stacking fault disorder with the increase of t and illustrate the structure-property relationship between the local environments of Co and their respective magnetic stiffness.

We study resonant dipole-dipole coupling and the associated van der Waals energy shifts in Rydberg excited atomic rubidium and potassium and investigate F\"orster resonances between interspecies pair states. A comprehensive survey over experimentally accessible pair state combinations reveals multiple candidates with small F\"orster defects. We crucially identify the existence of an ultrastrong, "low" electric field K-Rb F\"orster resonance with a extremely large zero-field crossover distance exceeding 100 $\mu$m between the van der Waals regime and the resonant regime. This resonance allows for a strong interaction over a wide range of distances and by investigating its dependence on the strength and orientation of external fields we show this to be largely isotropic. As a result, the resonance offers a highly favorable setting for studying long-range resonant excitation transfer and entanglement generation between atomic ensembles in a flexible geometry. The two-species K-Rb system establishes a unique way of realizing a Rydberg single-photon optical transistor with a high-input photon rate and we specifically investigate an experimental scheme with two separate ensembles.

We present a study of the Nernst effect in an iron-based superconductor with a nontrivial band topology ${\mathrm{Fe}}_{1+y}{\mathrm{Te}}_{1\ensuremath{-}x}{\mathrm{Se}}_{x}$. A nonzero Nernst signal is observed in a narrow temperature region around the superconducting transition temperature ${T}_{c}$ at a zero field. This anomalous Nernst signal shows symmetric dependence on the external magnetic field and indicates an unconventional vortex contribution in an $s$-wave superconductor with a strong spin-orbit coupling, which is originated from the local magnetic moments of the interstitial Fe atoms. Our experiments also provide the first evidence of a locally broken time-reversal symmetry in bulk ${\mathrm{Fe}}_{1+y}{\mathrm{Te}}_{1\ensuremath{-}x}{\mathrm{Se}}_{x}$ single crystals.

Recently, a new transition-metal dichalcogenide (TMD) material $2M$-phase ${\mathrm{WS}}_{2}$ was synthesized. The material $2M\text{\ensuremath{-}}{\mathrm{WS}}_{2}$ not only exhibits superconductivity, with the highest ${T}_{\text{c}}$ being 8.8 K at ambient pressure among TMDs, but also hosts a topological surface state. Here we report the low-temperature thermal conductivity measurements on $2M\text{\ensuremath{-}}{\mathrm{WS}}_{2}$ single crystals to investigate its superconducting gap structure. A negligible residual linear term ${\ensuremath{\kappa}}_{0}/T$ in zero field shows that $2M\text{\ensuremath{-}}{\mathrm{WS}}_{2}$ has a fully superconducting gap with all electrons paired. The field dependence of ${\ensuremath{\kappa}}_{0}/T$ suggests an anisotropic superconducting gap or multiple nodeless superconducting gaps in $2M\text{\ensuremath{-}}{\mathrm{WS}}_{2}$. Such a fully gapped superconducting state is compatible with $2M\text{\ensuremath{-}}{\mathrm{WS}}_{2}$ being a topological superconductor candidate.

Zero- to ultralow-field (ZULF) nuclear magnetic resonance (NMR) is an emerging tool for precision chemical analysis. In this work, we study dynamic processes and investigate the influence of chemical exchange on ZULF NMR J-spectra. We develop a computational approach that allows quantitative calculation of J-spectra in the presence of chemical exchange and apply it to study aqueous solutions of [15N]ammonium (15N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{H}}_4^ +$$\end{document}H4+) as a model system. We show that pH-dependent chemical exchange substantially affects the J-spectra and, in some cases, can lead to degradation and complete disappearance of the spectral features. To demonstrate potential applications of ZULF NMR for chemistry and biomedicine, we show a ZULF NMR spectrum of [2-13C]pyruvic acid hyperpolarized via dissolution dynamic nuclear polarization (dDNP). We foresee applications of affordable and scalable ZULF NMR coupled with hyperpolarization to study chemical exchange phenomena in vivo and in situations where high-field NMR detection is not possible to implement., Zero-field nuclear magnetic resonance can identify species and collective behaviors in mixtures without applied magnetic fields. Here the authors demonstrate its use for resolving proton exchange in ammonium and for the detection of hyperpolarized pyruvic acid, an important imaging biomarker.

We perform a microscopic study on the redistribution of electric charge near the surface of a model $d$-wave superconductor cut along the [110] direction, with a Fermi surface appropriate for cuprate superconductors, using the augmented quasiclassical equations. We identify two possible mechanisms for the redistribution of charged particles different from the well-known magnetic Hall effect, namely; the pair potential gradient (PPG) force due to surface effects on the pair potential and the pressure difference between the normal and superconducting regions arising from the slope of the density of states (SDOS) in the normal states at the Fermi level. Our present results show that in spite of the absence of supercurrents, electric charge is induced around the surface. Moreover, the charging effect due to the SDOS pressure dominates over that due to the PPG force for all the realistic electron-fillings $n=0.8$, $0.9$, and $1.15$, at all temperatures. In addition, for the filling $n=1.15$, the PPG force and the SDOS pressure contributions have the same negative signs, which gives a larger total surface charge i.e., both the sign and amount of the surface charge depends greatly on the Fermi-surface curvature. We have also calculated the local density of states (LDOS) within the augmented quasiclassical theory. Spatially varying local particle-hole asymmetry appears in the LDOS, which suggests the presence of electric charge., 9 pages, 11 figures

The promise of magnetic skyrmions in future spintronic devices hinges on their topologically enhanced stability and the ability to be manipulated by external fields. The technological advantages of nonvolatile zero-field skyrmion lattice (SkL) are significant if their stability and reliability can be demonstrated over a broad temperature range. Here, we study the relaxation dynamics including the evolution and lifetime of zero-field skyrmions generated from field cooling (FC) in an FeGe single-crystal plate via in situ Lorentz transmission electron microscopy (L-TEM). Three types of dynamic switching between zero-field skyrmions and stripes are identified and distinguished. Moreover, the generation and annihilation of these metastable skyrmions can be tailored during and after FC by varying the magnetic fields and the temperature. This dynamic relaxation behavior under the external fields provides a new understanding of zero-field skyrmions for their stability and reliability in spintronic applications and also raises new questions for theoretical models of skyrmion systems.

If for a vector space V of dimension g over a characteristic zero field we denote by ∧ i V ∧ i V its alternating powers, and by V ∨ V ∨ its linear dual, then there are natural Poincare isomorphisms: ∧ i V ∨ ≅∧ g−i V. ∧ i V ∨ ≅ ∧ g − i V . We describe an analogous result for objects in rigid pseudo-abelian Q Q -linear ACU tensor categories.

Two structurally intriguing dysprosium(III)-substituted polyoxometalates, [Dy6(ampH)4(H2O)23(ampH2)(PW11O39)2] (1) and [Dy9(CO3)3(ampH)2(H2O)12(PW10O37)6]35– (2), are assembled by the same precursor under different pH conditions. The structure of 1 contains an octahedral {Dy6(ampH)4} core, and a unique windmill-type {Dy9(CO3)3(ampH)2} for 2. Single-molecule magnet behavior is observed for 2 with a thermally activated energy barrier of 56 K and no appreciable quantum tunneling of magnetization under zero field.

Using combinatorial methods we study the structural coefficients of the formal homogeneous universal enveloping algebra $$\widehat{U}_h({\mathfrak {sl}}_2) $$ of the special linear algebra $$ {\mathfrak {sl}}_2$$ over a characteristic zero field. We provide explicit formulae for the product of generic elements in $$ \widehat{U}_h({\mathfrak {sl}}_2),$$ and construct combinatorial objects giving flesh to these formulae; in particular, we provide explicit formulae and combinatorial interpretations for the structural coefficients of divided power Poincare–Birkhoff–Witt basis.

The temperature depolarization process has been studied in [001]-cut lead magnesium niobate-lead titanate single crystals with 33% lead titanate content by in situ visualization of as-grown domain ...

Interesting magnetic behaviors, including negative magnetization, zero field fooled and field cooled exchange bias effects, have been observed in Eu0.9Pr0.1CrO3. The negative magnetization at low temperature results from the antiparallel coupling between the Pr3+ moment and the canted moment of Cr3+ sublattice. Left shift of zero field cooled M-H loops, and right shift of field cooled M-H loops have been observed, due to the growth and competition of two types of magnetic structures with GxFz (EuCrO3) and GzFx (PrCrO3) orderings under magnetic field. When the cooling field is high enough, the Pr3+ moment is frozen antiparallel with the applied field during the cooling process, giving rise to a positive exchange bias (right shift of M-H). However, when the cooling field is near zero, magnetic clusters with GxFz (EuCrO3) or GzFx (PrCrO3) orderings are formed and distribute randomly during the cooling process, and the net Pr3+ moment get aligned along the applied field during the initial magnetization process to lower the Zeeman energy, and then negative exchange bias (left shift of M-H) appears.