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We study the stochastic Leray-{\alpha} model of Euler equations with transport noise. We first use weak convergence approach to show the large deviations of the stochastic Leray-{\alpha} model of Euler equations in a suitable scaling limit. Then, we establish the quantitative convergence rate by semigroup approach. Moreover, we obtain a central limit theorem with strong convergence and get the explicit rate., Comment: there was an error

MnMX (M = Co or Ni, X = Si or Ge) alloys, experiencing structural transformation between Ni2In-type hexagonal and TiNiSi-type orthorhombic phases, attract considerable attention due to their potential applications as room-temperature solid refrigerants. Although lots of studies have been carried out on how to tune this transformation and obtain large entropy change in a wide temperature region, the crystallography of this martensitic transformation is still unknown. The biggest obstacle for crystallography investigation is to obtain a bulk sample, in which hexagonal and orthorhombic phases coexist, because the MnMX alloys will fragment into powders after experiencing the transformation. For this reason, we carefully tune the transformation temperature to be slightly below 300 K. In that case, a bulk sample with small amounts of orthorhombic phases distributed in hexagonal matrix is obtained. Most importantly, there are no cracks between the two phases. It facilities us to investigate the microstructure using electron microscope. The obtained results indicate that the orientation relationship between hexagonal and orthorhombic structures is [4-2-23]h//[120]o & (01-10)h//(001)o and the habit plane is {-2113.26}h. WLR theory is also adopted to calculate the habit plane. The calculated result agrees well with the measured one. Our work reveals the crystallography of hexagonal-orthorhombic transformation for the first time and is helpful for understanding the transformation-associated physical effects in MnMX alloys., Comment: 22 pages, 5 figures, 2 tables

Giant magnetocaloric effect is widely achieved in hexagonal MnMX-based (M = Co or Ni, X = Si or Ge) ferromagnets at their first-order magnetostructural transition. However, the thermal hysteresis and the low sensitivity of the magnetostructural transition to the magnetic field inevitably lead to a sizeable irreversibility of the low-field magnetocaloric effect. In this work, we show an alternative way to realize a reversible low-field magnetocaloric effect in MnMX-based alloys by taking advantage of the second-order phase transition. With introducing Cu into Co in MnCoGe alloy, the martensitic transition is stabilized at high temperature, while the Curie temperature of the orthorhombic phase is reduced to room temperature. As a result, a second-order magnetic transition with negligible thermal hysteresis and a large magnetization change can be observed, enabling a large reversible magnetocaloric effect. By both calorimetric and direct measurements, a reversible adiabatic temperature change of about 1 K is obtained under a field change of 0-1 T at 304 K, which is larger than that obtained in a first-order magnetostructural transition. To get a better insight into the origin of these experimental results, first-principles calculations are carried out to characterize the chemical bonds and the magnetic exchange interaction. Our work provides a new understanding of the MnCoGe alloy and indicates a feasible route to improve the reversibility of the low-field magnetocaloric effect in the MnMX system., Comment: 21 pages, 9 figures

In this work, we reported the observation of a novel planar topological Hall effect (PTHE) in single crystal of Fe3GeTe2, a paradigmatic two-dimensional ferromagnet with strong uniaxial anisotropy. The Hall effect and magnetoresistance varied periodically when the external magnetic field rotated in the ac (or bc) plane, while the PTHE emerged and maintained robust with field swept across the hard-magnetized ab plane. The PTHE covers the whole temperature region below Tc (~150 K) and a comparatively large value is observed at 100 K. Emergence of an internal gauge field was proposed to explain the origin of this large PTHE, which is either generated by the possible topological domain structure of uniaxial Fe3GeTe2 or the non-coplanar spin structure formed during the in-plane magnetization. Our results promisingly provide an alternative detection method to the in-plane skyrmion formation and may bring brand-new prospective to magneto-transport studies in condensed matter physics., Comment: 15 pages, 4 figures

Hexagonal D019-type Mn3Z alloys that possess large anomalous and topological-like Hall effects have attracted much attention due to their great potential in the antiferromagnetic spintronic devices. Here, we report the preparation of Mn3Ga film in both tetragonal and hexagonal phases with a tuned Ta/Ru seed layer on the thermally oxidized Si substrate. A large coercivity together with a large anomalous Hall resistivity is found in the Ta-only sample with mixed tetragonal phase. By increasing the thickness of Ru layer, the tetragonal phase gradually disappears and a relatively pure hexagonal phase is obtained in the Ta(5)/Ru(30) buffered sample. Further magnetic and transport measurements revealed that the anomalous Hall conductivity nearly vanishes in the pure hexagonal sample, while an abnormal asymmetric hump structure emerges in the low field region. The extracted additional Hall term is robust in a large temperature range and presents a sign reversal above 200K. The abnormal Hall properties are proposed to be closely related with the frustrated spin structure of D019 Mn3Ga.