Magnetic entropy-change in La0.67−xBixCa0.33MnO3 compound

Bi doped lanthanum manganites with the chemical composition of La_0.67−xBi_xCa_0.33MnO₃ (x=0$x=0$, 0.05, 0.1, 0.2) were prepared by the standard solid-state process. The Curie temperatures were measured to be 267 K for x=0$x=0$, 248 K for x=0.05$x=0.05$, 244 K for x=0.1$x=0.1$ and 229 K for x=0.2$x=0.2$ samples. It was found that the maximum value of the magnetic entropy change ∣ΔS_m∣ has reached the highest value of 6.08 J/kg K at 3 T for the composition with x=0.05$x=0.05$. Nearly the same maximum entropy change was observed for the x=0$x=0$ sample. A large decrease in the magnitude of the entropy change was observed for the x=0.2$x=0.2$ sample.     

Thermodynamics properties of an anisotropic Ising antiferromagnet in both external longitudinal and transverse fields

We have studied the anisotropic two-dimensional nearest-neighbor Ising model with competitive interactions in both uniform longitudinal field H$H$ and transverse magnetic field Ω$\Omega$. Using the effective-field theory (EFT) with correlation in cluster with N=1$N=1$ spin we calculate the thermodynamic properties as a function of temperature with values H$H$ and Ω$\Omega$ fixed. The model consists of ferromagnetic interaction _Jx$J_x$ in the x$x$ direction and antiferromagnetic interaction _Jy$J_y$ in the y$y$ direction, and it is found that for H/_Jy∈[0,2]$H/J_y\in [0,2]$ the system exhibits a second-order phase transition. The thermodynamic properties are obtained for the particular case of λ=_Jx/_Jy=1$\lambda =J_x/J_y=1$ (isotropic square lattice).     

A separation property for magnetic Schrödinger operators on Riemannian manifolds

We consider a Schrödinger differential expression L=_ΔA+q$L={\Delta }_A+q$ on a complete Riemannian manifold (M,g)$(M,g)$ with metric g$g$, where _ΔA${\Delta }_A$ is the magnetic Laplacian on M$M$ and q≥0$q\ge 0$ is a locally square integrable function on M$M$. In the terminology of W.N. Everitt and M. Giertz, the differential expression L$L$ is said to be separated in L²(M)$L^2\left(M\right)$ if for all u∈L²(M)$u\in L^2\left(M\right)$ such that Lu∈L²(M)$Lu\in L^2\left(M\right)$, we have qu∈L²(M)$qu\in L^2\left(M\right)$. We give sufficient conditions for L$L$ to be separated in L²(M)$L^2\left(M\right)$.     

Magnetocaloric effect of Gd5SixSn4−x Alloys

The crystal structure and magnetocaloric effect of Gd₅Si_xSn_4−x   (with x=2.4$x=2.4$, 2.6 and 2.8) alloys were studied by means of X-ray power diffraction (XRD) and magnetic measurements. From the XRD results, these alloys adopt a Gd₅Si₄-type structure for x=2.8$x=2.8$, Gd₅Si₄-type and Gd₅Si₂Ge₂-type mixed structures for x=2.4$x=2.4$ and 2.6, while some minor phases can also be found. The Curie temperatures of the Gd₅Si_xSn_4−x increases gradually when x increases from 276 K for x=2.4$x=2.4$, to 301.5 K for x=2.8$x=2.8$. Magnetic entropy changes of these alloys at a magnetic field change of 0–1.8 T are 1.88, 2.26 and 1.69 J/kg K for x=2.4$x=2.4$, 2.6 and 2.8, respectively. The temperature-dependent XRD analysis shows that there is no crystallographic transition for these alloys, which can explain their low magnetic entropy changes.     

Non-Abelian fusion rules from an Abelian system

We demonstrate the emergence of non-Abelian fusion rules for excitations of a two dimensional lattice model built out of Abelian degrees of freedom. It can be considered as an extension of the usual toric code model on a two dimensional lattice augmented with matter fields. It consists of the usual C(Z_p)$\mathbb{C}\left({\mathbb{Z}}_p\right)$ gauge degrees of freedom living on the links together with matter degrees of freedom living on the vertices. The matter part is described by a n$n$ dimensional vector space which we call H_n$H_n$. The Z_p${\mathbb{Z}}_p$ gauge particles act on the vertex particles and thus H_n$H_n$ can be thought of as a C(Z_p)$\mathbb{C}\left({\mathbb{Z}}_p\right)$ module. An exactly solvable model is built with operators acting in this Hilbert space. The vertex excitations for this model are studied and shown to obey non-Abelian fusion rules. We will show this for specific values of n$n$ and p$p$, though we believe this feature holds for all n>p$n>p$. We will see that non-Abelian anyons of the quantum double of C(S₃)$\mathbb{C}\left(S_3\right)$ are obtained as part of the vertex excitations of the model with n=6$n=6$ and p=3$p=3$. Ising anyons are obtained in the model with n=4$n=4$ and p=2$p=2$. The n=3$n=3$ and p=2$p=2$ case is also worked out as this is the simplest model exhibiting non-Abelian fusion rules. Another common feature shared by these models is that the ground states have a higher symmetry than Z_p${\mathbb{Z}}_p$. This makes them possible candidates for realizing quantum computation.     

Critical behavior of an anisotropic Ising antiferromagnet in both external longitudinal and transverse fields

In this paper we study the critical behavior of a two-sublattice Ising model on an anisotropic square lattice in both uniform longitudinal (H  ) and transverse (Ω$\Omega$) fields by using the effective-field theory. The model consists of ferromagnetic interaction J_x in the x direction and antiferromagnetic interaction J_y in the y direction in the presence of the H   and Ω$\Omega$ fields. We obtain the phase diagrams in the H–T$H–T$ and Ω–T$\Omega –T$ planes changing values of the Ω$\Omega$ and H   parameters, respectively for fixed value at λ=_Jx/_Jy=1$\lambda =J_x/J_y=1$. At null temperature, the ground state phase diagram in the Ω–H$\Omega –H$ plane for several values of λ$\lambda$ parameter is analyzed. In the particular case of λ=1$\lambda =1$ we compare our results with mean-field theory (MFT) and was not observed reentrant behavior around of the critical field _Hc/_Jy=2.0$H_c/J_y=2.0$ for Ω=0$\Omega =0$ by using EFT.     

Observation of spin reorientation in layered manganites La1.2Sr1.8(Mn1−yRuy)2O7 (0.0⩽y⩽0.2) by Lorentz transmission electron microscopy

The effect of Ru substitution for Mn in bilayered oxides La_1.2Sr_1.8(Mn_1−yRu_y)₂O₇ (0?y?0.2$0?y?0.2$) was investigated by magnetization measurements and low-temperature Lorentz transmission electron microscopy. It was found that the magnetic anisotropy is controlled by the Ru content y and temperature T. The easy axis changes from 〈1 1 0〉 for the y=0$y=0$ crystal to the c  -axis for y=0.2$y=0.2$, and it rotates away from the c-  axis for the y=0.05$y=0.05$ and y=0.07$y=0.07$ crystals with decreasing temperature. Furthermore, maze-shaped magnetic domain structures were observed in the (0 0 1) thin crystals with 0.05?y?0.2$0.05?y?0.2$. Changes in domain size and structure indicate that the uniaxial magnetic anisotropy becomes stronger as Ru content y increases.     

Three PT-symmetric Hamiltonians with completely different spectra

We discuss three Hamiltonians, each with a central-field part H₀$H_0$ and a PT-symmetric perturbation igz$igz$. When H₀$H_0$ is the isotropic Harmonic oscillator the spectrum is real for all g$g$ because H$H$ is isospectral to H₀+g²/2$H_0+g^2/2$. When H₀$H_0$ is the Hydrogen atom then infinitely many eigenvalues are complex for all g$g$. If the potential in H₀$H_0$ is linear in the radial variable r$r$ then the spectrum of H$H$ exhibits real eigenvalues for 0<g<g_c$0<g<g_c$ and a PT phase transition at g_c$g_c$.     

Tenth Peregrine breather solution to the NLS equation

In this paper we construct a particularly important solution to the focusing NLS equation, namely a Peregrine breather of the rank 10 which we call, P₁₀$P_{10}$ breather. The related explicit formula is given by the ratio of two polynomials of degree 110 with integer coefficients times trivial exponential factor. This formula drastically simplifies for the “initial values” namely for t=0$t=0$ or x=0$x=0$. This formula confirms a general conjecture saying that between all quasi-rational solutions of the rank N$N$ fixed by the condition that its absolute value tends to 1 at infinity and its highest maximum is located at the point (x=0,t=0)$(x=0,t=0)$, the P_N$P_N$ breather is distinguished by the fact that P_N(0,0)=2N+1$P_N(0,0)=2N+1$ and, in the aforementioned class of quasi-rational solutions, it is an absolute maximum. At the end we also make a few remarks concerning the rational deformations of P₁₀$P_{10}$ breather involving 2N−2$2N-2$ free real parameters chosen in a way that P_N$P_N$ breather itself corresponds to the zero values of these parameters although we have no intention to discuss the properties of these deformations here.     

Is space-time symmetry a suitable generalization of parity-time symmetry?

We discuss space-time symmetric Hamiltonian operators of the form H=H₀+igH^′$H=H_0+ig{H}^{\prime }$, where H₀$H_0$ is Hermitian and g$g$ real. H₀$H_0$ is invariant under the unitary operations of a point group G$G$ while H^′$H^{\prime }$ is invariant under transformation by elements of a subgroup G^′$G^{\prime }$ of G$G$. If G$G$ exhibits irreducible representations of dimension greater than unity, then it is possible that H$H$ has complex eigenvalues for sufficiently small nonzero values of g$g$. In the particular case that H$H$ is parity-time symmetric then it appears to exhibit real eigenvalues for all 0<g<g_c$0<g<g_c$, where g_c$g_c$ is the exceptional point closest to the origin. Point-group symmetry and perturbation theory enable one to predict whether H$H$ may exhibit real or complex eigenvalues for g>0$g>0$. We illustrate the main theoretical results and conclusions of this paper by means of two- and three-dimensional Hamiltonians exhibiting a variety of different point-group symmetries.