Scaling of Berry-curvature monopole dominated large linear positive magnetoresistance.

The linear positive magnetoresistance (LPMR) is a widely observed phenomenon in topological materials, which is promising for potential applications on topological spintronics. However, its mechanism remains ambiguous yet, and the effect is thus uncontrollable. Here, we report a quantitative scaling model that correlates the LPMR with the Berry curvature, based on a ferromagnetic Weyl semimetal CoS2 that bears the largest LPMR of over 500% at 2 K and 9 T, among known magnetic topological semimetals. In this system, masses of Weyl nodes existing near the Fermi level, revealed by theoretical calculations, serve as Berry-curvature monopoles and low-effective-mass carriers. Based on the Weyl picture, we propose a relation [Formula: see text], with B being the applied magnetic field and [Formula: see text] the average Berry curvature near the Fermi surface, and further introduce temperature factor to both MR/B slope (MR per unit field) and anomalous Hall conductivity, which establishes the connection between the model and experimental measurements. A clear picture of the linearly slowing down of carriers, i.e., the LPMR effect, is demonstrated under the cooperation of the k-space Berry curvature and real-space magnetic field. Our study not only provides experimental evidence of Berry curvature-induced LPMR but also promotes the common understanding and functional designing of the large Berry-curvature MR in topological Dirac/Weyl systems for magnetic sensing or information storage.

Teachers' learning from addressing the challenges of online teaching in a time of pandemic: a case in Shanghai.

Due to the COVID-19 pandemic in Shanghai, China, all school classes were delivered through an online environment from February 24 to May 22, 2020. To support this transition, the Shanghai Education Commission led expert teachers and specialists to develop a series of online video lessons based on the Shanghai unified curriculum, and suggested students watch the online video lessons individually from home, followed by an online synchronous lesson supported by class teachers. This study investigated what primary mathematics teachers learned from addressing these challenges through a case study. By following two purposefully selected teachers over 2 weeks during the transition, multiple data sets including online video lessons, online synchronous lessons, daily reflections, and post-online teacher interviews were collected. A fine-grained analysis of the data from the lens of the documentational approach to didactics found that teachers adaptively used online video lessons as important resources for their online synchronous lessons and virtual Teaching Research Groups as a teachers' collaboration mechanism supported them to develop online video lessons and address various technological constraints. Finally, implications of this case study for mathematics education globally are discussed. Supplementary Information: The online version contains supplementary material available at 10.1007/s10649-022-10172-2.

SnTe thermoelectric materials with low lattice thermal conductivity synthesized by a self-propagating method under a high-gravity field.

The conventional fabrication methods (for example, melting and powder metallurgy) of bulk thermoelectric materials are time- and energy-consuming, which restrict their large-scale application. In this work, ultra-fast self-propagating synthesis under a high-gravity field was used to prepare SnTe bulks, which shortened the synthesis time from several days to a few seconds. The grain growth was suppressed and some small pores were reserved in the matrix during the ultra-fast solidification process. The increased grain boundaries and pores (nanoscale to micron scale) enhanced phonon scattering, which greatly decreased the lattice thermal conductivity. The obtained minimum lattice thermal conductivity is 0.81 W m-1 K-1, and the maximum zT value is 0.5 (873 K), which is comparable to the best reported results of the undoped SnTe alloy. The ultra-fast non-equilibrium synthesis technique opens up new possibilities to prepare high-efficiency bulk thermoelectric materials with reduced time and energy consumption.

Correlation of Tunable CoSi4 Tetrahedron with the Superconducting Properties of LaCoSi.

It is known that as the FeAs4 tetrahedron in the Fe-based superconductor is close to the regular tetrahedron, critical temperature (Tc) can be greatly increased. Recently, a Co-based superconductor of LaCoSi (4 K) with "111" structure was found. In this work, we improve the Tc of LaCoSi through structural regulation. Tc can be increased by the chemical substitution of Co by Fe, while the superconductivity is suppressed by the Ni substitution. The combined analysis of neutron and synchrotron X-ray powder diffractions reveals that the change of the Si-Co-Si bond angles of the CoSi4 tetrahedron is possibly responsible for the determination of superconducting properties. The Fe chemical substitution is favorable for the formation of the regular tetrahedron of CoSi4. The present new Co-based superconductor of LaCoSi provides a possible method to enhance the superconductivity performance of the Co-based superconductors via controlling Co-based tetrahedra similar to those well established in the Fe-based superconductors.

Superconductivity in Co-Layered LaCoSi.

It is known that few Co-based superconducting compounds have been found compared with their Fe- or Ni-based counterparts. In this study, we have found superconductivity of 4 K in the LaCoSi compound for the first time. The combined analysis of neutron and synchrotron X-ray powder diffractions reveals that LaCoSi exhibits an isostructure with the known Fe-based LiFeAs superconductor, which is the first "111" Co-based superconductor. First-principles calculation shows that LaCoSi presents a quasi-two-dimensional band structure that is also similar to that of LiFeAs. The small structural distortion may be more conducive to the emergence of superconductivity in the LaCoSi compound, which provides a direction for finding new Co-based superconducting compounds.

Negative Thermal Expansion in (Hf,Ti)Fe2 Induced by the Ferromagnetic and Antiferromagnetic Phase Coexistence.

Negative thermal expansion (NTE) is an intriguing physical phenomenon that can be used in the applications of thermal expansion adjustment of materials. In this study, we report a NTE compound of (Hf,Ti)Fe2, while both end members of HfFe2 and TiFe2 show positive thermal expansion. The results reveal that phase coexistence is detected in the whole NTE zone, in which one phase is ferromagnetic (FM), while the other is antiferromagnetic (AFM). With increasing temperature, the FM phase is gradually transformed to the AFM one. The NTE phenomenon occurs in the present (Hf,Ti)Fe2 because of the fact that the unit cell volume of the AFM phase is smaller than that of the FM phase, and the mass fraction of the AFM phase increases with increasing temperature. The construction of phase coexistence can be a method to achieve NTE materials in future studies.

Adjustable Magnetic Phase Transition Inducing Unusual Zero Thermal Expansion in Cubic RCo2-Based Intermetallic Compounds (R = Rare Earth).

Metallic materials that exhibit negligible thermal expansion or zero thermal expansion (ZTE) have great merit for practical applications, but these materials are rare and their thermal expansions are difficult to control. Here, we successfully tailored the thermal expansion behaviors from strongly but abruptly negative to zero over wide temperature ranges in a series of (Gd,R)(Co,Fe)2 (R = Dy, Ho, Er) intermetallic compounds by tuning the composition to bring the first-order magnetic phase transition to second-order. Interestingly, an unusual isotropic ZTE property with a coefficient of thermal expansion of α l = 0.16(0) × 10-6 K-1 was achieved in cubic Gd0.25Dy0.75Co1.93Fe0.07 (GDCF) in the temperature range of 10-275 K. The short-wavelength neutron powder diffraction, synchrotron X-ray diffraction, and magnetic measurement studies evidence that this ZTE behavior was ascribed to the rare-earth-moment-dominated spontaneous volume magnetostriction, which can be controlled by an adjustable magnetic phase transition. The present work extends the scope of the ZTE family and provides an effective approach to exploring ZTE materials, such as by adjusting the magnetism or ferroelectricity-related phase transition in the family of functional materials.

Structure and Phase Transformation in the Giant Magnetostriction Laves-Phase SmFe2.

As one class of the most important intermetallic compounds, the binary Laves-phase is well-known for its abundant magnetic properties. Samarium-iron alloy system SmFe2 is a prototypical Laves compound that shows strong negative magnetostriction but relatively weak magnetocrystalline anisotropy. SmFe2 has been identified as a cubic Fd3̅m structure at room temperature; however, the cubic symmetry, in principle, does not match the spontaneous magnetization along the [111]cubic direction. Here we studied the crystal structure of SmFe2 by high-resolution synchrotron X-ray powder diffraction, X-ray total scattering, and selected-area electron diffraction methods. SmFe2 is found to adopt a centrosymmetric trigonal R3̅m structure at room temperature, which transforms to an orthorhombic Imma structure at 200 K. This transition is in agreement with the changes of easy magnetization direction from [111]cubic to [110]cubic direction and is further evidenced by the inflection of thermal expansion behavior, the sharp decline of the magnetic susceptibility in the field-cooling-zero field-cooling curve, and the anomaly in the specific heat capacity measurement. The revised structure and phase transformation of SmFe2 could be useful to understand the magnetostriction and related physical properties of other RM2-type pseudocubic Laves-phase intermetallic compounds.

Atomic Linkage Flexibility Tuned Isotropic Negative, Zero, and Positive Thermal Expansion in MZrF6 (M = Ca, Mn, Fe, Co, Ni, and Zn).

The controllable isotropic thermal expansion with a broad coefficient of thermal expansion (CTE) window is intriguing but remains challenge. Herein we report a cubic MZrF6 series (M = Ca, Mn, Fe, Co, Ni and Zn), which exhibit controllable thermal expansion over a wide temperature range and with a broader CTE window (-6.69 to +18.23 × 10-6/K). In particular, an isotropic zero thermal expansion (ZTE) is achieved in ZnZrF6, which is one of the rarely documented high-temperature isotropic ZTE compounds. By utilizing temperature-dependent high-energy synchrotron X-ray total scattering diffraction, it is found that the flexibility of metal···F atomic linkages in MZrF6 plays a critical role in distinct thermal expansions. The flexible metal···F atomic linkages induce negative thermal expansion (NTE) for CaZrF6, whereas the stiff ones bring positive thermal expansion (PTE) for NiZrF6. Thermal expansion could be transformed from striking negative, to zero, and finally to considerable positive though tuning the flexibility of metal···F atomic linkages by substitution with a series of cations on M sites of MZrF6. The present study not only extends the scope of NTE families and rare high-temperature isotropic ZTE compounds but also proposes a new method to design systematically controllable isotropic thermal expansion frameworks from the perspective of atomic linkage flexibility.

Cs3W3PO13: A Tungsten Phosphate with One-Dimensional Zigzag Tunnels Exhibiting Strongly Anisotropic Thermal Expansion.

A new tungsten phosphate, Cs3W3PO13, is synthesized using the high-temperature flux method. Cs3W3PO13 crystallizes in the space group Pnma and contains one-dimensional zigzag tunnels, which are found for the first time in tungsten phosphate. This highly anisotropic structural feature results in a very strong anisotropic thermal expansion, with thermal expansion coefficients of 14.15 ± 1.11 and 0.72 ± 0.22 M K(-1) along the a and b axes, respectively, over the temperature range from 13 to 270 K. In addition, thermal analysis, UV-vis-near-IR diffuse reflectance, and first-principles electronic structure calculations on Cs3W3PO13 are performed.

Effect of cobalt doping on the structural, magnetic and abnormal thermal expansion properties of NaZn13-type La(Fe1-xCox)11.4Al1.6 compounds.

Cubic NaZn13-type La(Fe1-xCox)11.4Al1.6 compounds were synthesized and extensively explored through crystal structure and magnetization analyses. By optimizing the chemical composition, the isotropic abnormal properties of excellent zero and giant negative thermal expansion in a pure form were both found at different temperature ranges through room temperature. Moreover, the temperature regions with the remarkable abnormal thermal expansion (ATE) properties have been broadened which are controlled by the dM/dT. The present study demonstrates that the ATE behavior mainly depends on special structural and magnetic properties. These diverse properties suggest the high potential of La(Fe1-xCox)11.4Al1.6 for the development of abnormal expansion materials.

Broad Negative Thermal Expansion Operation-Temperature Window Achieved by Adjusting Fe-Fe Magnetic Exchange Coupling in La(Fe,Si)13 Compounds.

Cubic La(Fe,Si)13-based compounds have been recently developed as promising negative thermal expansion(NTE) materials, but the narrow NTE operation-temperature window(∼110 K) restricts their actual applications. In this work, we demonstrate that the NTE operation-temperature window of LaFe(13-x)Si(x) can be significantly broadened by adjusting Fe-Fe magnetic exchange coupling as x ranges from 2.8 to 3.1. In particular, the NTE operation-temperature window of LaFe10.1Si2.9 is extended to 220 K. More attractively, the coefficients of thermal expansion of LaFe10.0Si3.0 and LaFe9.9Si3.1 are homogeneous in the NTE operation-temperature range of about 200 K, which is much valuable for the stability of fabricating devices. The further experimental characterizations combined with first-principles studies reveal that the tetragonal phase is gradually introduced into the cubic phase as the Si content increases, hence modifies the Fe-Fe interatomic distance. The reduction of the overall Fe-Fe magnetic exchange interactions contributes to the broadness of NTE operation-temperature window for LaFe(13-x)Si(x).

Cryogenic abnormal thermal expansion properties of carbon-doped La(Fe,Si)13 compounds.

Recently, La(Fe,Si)13-based compounds have attracted much attention due to their isotropic and tunable abnormal thermal expansion (ATE) properties as well as bright prospects for practical applications. In this research, we have prepared cubic NaZn13-type carbon-doped La(Fe,Si)13 compounds by the arc-melting method, and their ATE and magnetic properties were investigated by means of variable-temperature X-ray diffraction, strain gauge and the physical property measurement system (PPMS). The experimental results indicate that both micro and macro negative thermal expansion (NTE) behaviors gradually weaken with the increase of interstitial carbon atoms. Moreover, the temperature region with the most remarkable NTE properties has been broadened and near zero thermal expansion (NZTE) behavior occurs in the bulk carbon-doped La(Fe,Si)13 compounds.

Zero thermal expansion in NaZn13-type La(Fe,Si)13 compounds.

A zero thermal expansion material in a pure form of NaZn13-type La(Fe,Si)13 was fabricated. Through optimizing the chemical composition, an isotropic zero thermal expansion material is achieved. The obtained materials exhibit a low expansion of |α| < 1.0 × 10(-6) K(-1) (α is the coefficient of linear thermal expansion) over a broad temperature range (15-150 K). The present study indicates that the thermal expansion behavior of the NaZn13-type La(Fe,Si)13 compounds depends mainly on the content of Si element. This new material is desirable in many fields of industry as a reliable and low-cost zero thermal expansion material.

Abnormal thermal expansion properties of cubic NaZn13-type La(Fe,Al)13 compounds.

The cubic NaZn13-type La(Fe,Al)13 compounds were synthesized, and their linear thermal expansion properties were investigated in the temperature range of 4.2-300 K. It was found that these compounds exhibit abnormal thermal expansion behavior, i.e., pronounced negative thermal expansion (NTE) or zero thermal expansion (ZTE) behavior, below the Curie temperature due to the magnetovolume effect (MVE). Moreover, in the La(Fe,Al)13 compounds, the modification of the coefficient of thermal expansion (CTE) as well as the abnormal thermal expansion (ATE) temperature-window is achieved through optimizing the proportion of Fe and Al. Typically, the average CTE of the LaFe13-xAlx compounds with x = 1.8 reaches as large as -10.47 × 10(-6) K(-1) between 100 and 225 K (ΔT = 125 K). Also, the ZTE temperature-window of the LaFe13-xAlx compounds with x = 2.5 and x = 2.7 could be broadened to 245 K (from 5 to 250 K). Besides, the magnetic properties of these compounds were measured and correlated with the abnormal thermal expansion behavior. The present results highlight the potential application of such La(Fe,Al)13 compounds with abnormal thermal expansion properties in cryogenic engineering.

Enhanced negative thermal expansion in La(1-x)Pr(x)Fe10.7Co0.8Si1.5 compounds by doping the magnetic rare-earth element praseodymium.

Experiments have been performed to enhance negative thermal expansion (NTE) in the La(Fe,Co,Si)13-based compounds by optimizing the chemical composition, i.e., proper substitution of La by magnetic element Pr. It is found that increasing the absolute value of the average coefficient of thermal expansion (CTE) in the NTE temperature region (200-300 K) attributes to enhancement of the spontaneous magnetization and its growth rate with increasing Pr content. Typically, the average CTE of La(1-x)Pr(x)Fe10.7Co0.8Si1.5 with x = 0.5 reaches as large as -38.5 × 10(-6) K(-1) between 200 and 300 K (ΔT = 100 K), which is 18.5% larger than that of x = 0. The present results highlight the potential applications of La(Fe,Co,Si)13-based compounds with a larger NTE coefficient.

Giant negative thermal expansion in NaZn13-type La(Fe, Si, Co)13 compounds.

La(Fe, Si)13-based compounds are well-known magnetocaloric materials, which show a pronounced negative thermal expansion (NTE) around the Curie temperature but have not been considered as NTE materials for industrial applications. The NaZn13-type LaFe13-xSix and LaFe11.5-xCoxSi1.5 compounds were synthesized, and their linear NTE properties were investigated. By optimizing the chemical composition, the sharp volume change in La(Fe, Si)13-based compounds was successfully modified into continuous expansion. By increasing the amount of Co dopant in LaFe11.5-xCoxSi1.5, the NTE shifts toward a higher temperature region, and also the NTE operation-temperature window becomes broader. Typically, the linear NTE coefficient identified in the LaFe10.5Co1.0Si1.5 compound reaches as much as -26.1 × 10(-6) K(-1), with an operation-temperature window of 110 K from 240 to 350 K, which includes room temperature. Such control of the specific composition and the NTE properties of La(Fe, Si)13-based compounds suggests their potential application as NTE materials.

Self-Stacked 3D Anisotropic BNNS Network Guided by Para-Aramid Nanofibers for Highly Thermal Conductive Dielectric Nanocomposites.

The enhancement of the heat-dissipation property of polymer-based composites is of great practical interest in modern electronics. Recently, the construction of a three-dimensional (3D) thermal pathway network structure for composites has become an attractive way. However, for most reported high thermal conductive composites, excellent properties are achieved at a high filler loading and the building of a 3D network structure usually requires complex steps, which greatly restrict the large-scale preparation and application of high thermal conductive polymer-based materials. Herein, utilizing the framework-forming characteristic of polymerization-induced para-aramid nanofibers (PANF) and the high thermal conductivity of hexagonal boron nitride nanosheets (BNNS), a 3D-laminated PANF-supported BNNS aerogel was successfully prepared via a simple vacuum-assisted self-stacking method, which could be used as a thermal conductive skeleton for epoxy resin (EP). The obtained PANF-BNNS/EP nanocomposite exhibits a high thermal conductivity of 3.66 W m-1 K-1 at only 13.2 vol % BNNS loading. The effectiveness of the heat conduction path was proved by finite element analysis. The PANF-BNNS/EP nanocomposite shows outstanding practical thermal management capability, excellent thermal stability, low dielectric constant, and dielectric loss, making it a reliable material for electronic packaging applications. This work also offers a potential and promotable strategy for the easy manufacture of 3D anisotropic high-efficiency thermal conductive network structures.

Magnetic-field modulation of topological electronic state and emergent magneto-transport in a magnetic Weyl semimetal.

The modulation of topological electronic state by an external magnetic field is highly desired for condensed-matter physics. Schemes to achieve this have been proposed theoretically, but few can be realized experimentally. Here, combining transverse transport, theoretical calculations, and scanning tunneling microscopy/spectroscopy (STM/S) investigations, we provide an observation that the topological electronic state, accompanied by an emergent magneto-transport phenomenon, was modulated by applying magnetic field through induced non-collinear magnetism in the magnetic Weyl semimetal EuB6. A giant unconventional anomalous Hall effect (UAHE) is found during the magnetization re-orientation from easy axes to hard ones in magnetic field, with a UAHE peak around the low field of 5 kOe. Under the reasonable spin-canting effect, the folding of the topological anti-crossing bands occurs, generating a strong Berry curvature that accounts for the observed UAHE. Field-dependent STM/S reveals a highly synchronous evolution of electronic density of states, with a dI/dV peak around the same field of 5 kOe, which provides evidence to the folded bands and excited UAHE by external magnetic fields. This finding elucidates the connection between the real-space non-collinear magnetism and the k-space topological electronic state and establishes a novel manner to engineer the magneto-transport behaviors of correlated electrons for future topological spintronics.

Teachers' changes when addressing the challenges in unexpected migration to online mathematics teaching during the COVID-19 pandemic: a case study in Shanghai.

In the research reported in this paper we investigated teachers' changes when adopting and adapting to emergency online teaching during the COVID-19 pandemic, from the perspective of the Interconnected Model of Professional Growth (IMPG). By adapting complementary accounts methodology to research into teachers' changes when addressing the unexpected migration to online teaching, an integrated data set, including online teaching videos, teacher daily reflections, and teacher interviews from two purposefully selected teachers over two weeks of online teaching, was collected and analyzed qualitatively. Both teachers encountered different difficulties and thus had different knowledge changes displayed in different change routes. For the experienced teacher, students' mistakes in homework and her online teaching practice triggered her knowledge changes. For the young teacher, the online video lessons, relevant resources on the Internet and students' performance were her primary sources that triggered the changes of her knowledge for teaching. These differences between the experienced teacher and young teacher provide evidence of the complexity of teacher's professional growth, which is related to a variety of external and internal factors. This study demonstrates how the IMPG model helps uncover teachers' changes in such an unprecedented virtual-teaching environment. Finally, the implications of this study for teacher professional development in general are discussed. Supplementary Information: The online version contains supplementary material available at 10.1007/s11858-022-01378-y.