Identification and mechanical control of ferroelastic domain structure in rhombohedral CaMn7_7O12_{12}

We report on observation of ferroelastic domain structure in single crystals of multiferroic CaMn$_7$O$_{12}$ at room temperature. Two types of ferroelastic domain wall are found, consistent with the material's rhombohedral symmetry that is reduced from cubic symmetry at higher temperatures. Using Raman spectroscopy along with other measurements, we develop a systematic method to determine the microscopic domain orientation. Moreover, we find a switching behavior of the domains, which allows us to detwin the crystals conveniently at room temperature using a moderate uniaxial compression. Our result paves the way for further spectroscopic study and domain engineering in CaMn$_7$O$_{12}$.Comment: 7 pages, 4 figure

Soft vibrational mode associated with incommensurate orbital order in multiferroic CaMn7_7O12_{12}

We report inelastic light scattering measurements of lattice dynamics related to the incommensurate orbital order in $\mathrm{CaMn_7O_{12}}$. Below the ordering temperature $T_\mathrm{o} \approx 250 \,\mathrm{K}$, we observe extra phonon peaks as a result of Brillouin-zone folding, as well as a soft vibrational mode with a power-law $T$-dependent energy, $\Omega = \Omega_{0}(1 - T/T_{\mathrm{o}})^{1/2}$. This temperature dependence demonstrates the second-order nature of the transition at $T_\mathrm{o}$, and it indicates that the soft mode can be regarded as the amplitude excitation of the composite order parameter. Our result strongly suggests that the lattice degrees of freedom are actively involved in the orbital-ordering mechanism.Comment: 7 pages, 8 figure

Rational spectral methods for PDEs involving fractional Laplacian in unbounded domains

Many PDEs involving fractional Laplacian are naturally set in unbounded domains with underlying solutions decay very slowly, subject to certain power laws. Their numerical solutions are under-explored. This paper aims at developing accurate spectral methods using rational basis (or modified mapped Gegenbauer functions) for such models in unbounded domains. The main building block of the spectral algorithms is the explicit representations for the Fourier transform and fractional Laplacian of the rational basis, derived from some useful integral identites related to modified Bessel functions. With these at our disposal, we can construct rational spectral-Galerkin and direct collocation schemes by pre-computing the associated fractional differentiation matrices. We obtain optimal error estimates of rational spectral approximation in the fractional Sobolev spaces, and analyze the optimal convergence of the proposed Galerkin scheme. We also provide ample numerical results to show that the rational method outperforms the Hermite function approach

Las emociones de los profesores que enseñan alemán en las escuelas secundarias chinas

This work was supported by the Fundamental Research Funds for the Central Universities and the Funds of the Teaching Advisory Board for German majors under the Ministry of Education in China (21DYJJ06).As part of the continued effort to advocate multilingual education, China has recently included German, French, and Spanish as subjects in secondary education. Secondary teachers teaching these languages other than English (LOTEs) may confront new challenges and opportunities, potentially making their professional lives emotionally intense. We therefore take teachers teaching German in Chinese secondary schools as examples and examine their emotions, including the emotion types and the reasons behind those emotions. Using a mixed method, the study surveyed 136 Chinese German teachers nationwide, and then conducted follow-up interviews with 20 participants. The study reveals that the Chinese German teachers experienced more positive emotions than negative ones. The positive emotions were mostly associated with positive interactions in their school settings, followed by their teacher knowledge, interests, and personality, while opportunities created by the development of the German subject constituted an additional factor. Implications for how to enhance LOTE teachers’ emotional experiences are discussed.Como parte del esfuerzo continuo por promover la educación multilingüe, China ha incluido recientemente el alemán, el francés y el español como asignaturas en la educación secundaria. Los profesores de secundaria que enseñan estos idiomas distintos al inglés (LOTE) pueden enfrentarse a nuevos desafíos y oportunidades, lo que puede hacer que sus carreras profesionales sean emocionalmente intensas. Por lo tanto, tomamos como ejemplo a los profesores que enseñan alemán en las escuelas secundarias chinas y examinamos sus emociones, incluidos los tipos de emociones y las razones que subyacen a estas emociones. Utilizando un método mixto, esta investigación encuestó a 136 profesores chinos de alemán en todo el país, y luego realizó entrevistas de seguimiento con 20 participantes. El estudio revela que los profesores chinos de alemán experimentaron más emociones positivas que negativas. Las emociones positivas se asociaron en su mayoría con las interacciones positivas en sus entornos escolares, seguidas de los conocimientos, intereses y personalidad de los profesores, mientras que las oportunidades creadas por el desarrollo de la asignatura de alemán constituyeron un factor adicional. Se han discutido las implicaciones sobre cómo mejorar las experiencias emocionales de los docentes de LOTE.Fundamental Research FundsFunds of the Teaching Advisory Board (21DYJJ06

Nematic crossover in BaFe2_2As2_2 under uniaxial stress

Raman scattering can detect spontaneous point-group symmetry breaking without resorting to single-domain samples. Here we use this technique to study $\mathrm{BaFe_2As_2}$, the parent compound of the "122" Fe-based superconductors. We show that an applied compression along the Fe-Fe direction, which is commonly used to produce untwinned orthorhombic samples, changes the structural phase transition at temperature $T_{\mathrm{s}}$ into a crossover that spans a considerable temperature range above $T_{\mathrm{s}}$. Even in crystals that are not subject to any applied force, a distribution of substantial residual stress remains, which may explain phenomena that are seemingly indicative of symmetry breaking above $T_{\mathrm{s}}$. Our results are consistent with an onset of spontaneous nematicity only below $T_{\mathrm{s}}$.Comment: 4 pages, 4 figure