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.     

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$g_c$.     

Effect of La doping on magnetotransport and magnetic properties of double perovskite Sr2FeMoO6 system

We have investigated the magnetotransport and magnetic properties on polycrystalline samples of Sr_2−xLa_xFeMoO₆ (x=0$x=0$, 0.2, 0.4, 0.6, 0.8 and 1.0). The magnitude of intergrain tunneling magnetoresistance with low magnetic field of 0.88 T for x=0.2$x=0.2$ and 0.4$0.4$ samples are as large as 5% and 7% at room temperature and 13% and 10% at 10 K, respectively. The increase of coercivity (_Hc$H_{\mathrm{c}}$), ratio of remanent magnetization with respect to saturation magnetization (_Mr/_Ms$M_{\mathrm{r}}/M_{\mathrm{s}}$), high saturation fields, and reduction of the saturation magnetization indicate that random disorder of spin orientation is mainly responsible for enhancement of the low-field magnetoresistance for samples with x?0.4$x?0.4$. Whereas rapid drop of _Hc$H_{\mathrm{c}}$, _Mr/_Ms$M_{\mathrm{r}}/M_{\mathrm{s}}$, _Mr$M_{\mathrm{r}}$, and saturation fields for samples with x>0.4$x>0.4$ signifies the growth of antiphase boundary, which gives rise to lower values of low-field MR.     

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).     

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.     

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.     

On m-accretive Schrödinger-type operators with singular potentials on Riemannian manifolds

We consider a Schrödinger-type differential expression _HV=∇^∗∇+V$H_V={\nabla }^{\ast }\nabla +V$, where ∇$\nabla$ is a Hermitian connection on a Hermitian vector bundle E$E$ over a complete Riemannian manifold (M,g)$(M,g)$ with metric g$g$ and positive smooth measure dμ$d\mu$, and V$V$ is a locally integrable section of the bundle of endomorphisms of E$E$. We give a sufficient condition for m$m$-accretivity of a realization of _HV$H_V$ in L²(E)$L^2\left(E\right)$.     

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.     

The Bethe lattice treatment of sound attenuation for a spin- 3/2 Ising model

The sound attenuation phenomena is investigated for a spin- 3/2 Ising model on the Bethe lattice in terms of the recursion relations by using the Onsager theory of irreversible thermodynamics. The dependencies of sound attenuation on the temperature (T$T$), frequency (w$w$), Onsager coefficient (γ$\gamma$) and external magnetic field (H$H$) near the second-order (_Tc)$\left(T_c\right)$ and first-order (_Tt)$\left(T_t\right)$ phase transition temperatures are examined for given coordination numbers q$q$ on the Bethe lattice. It is assumed that the sound wave couples to the order-parameter fluctuations which decay mainly via the order-parameter relaxation process, thus two relaxation times are obtained and which are used to obtain an expression for the sound attenuation coefficient (α)$\left(\alpha \right)$. Our investigations revealed that only one peak is obtained near _Tt$T_t$ and three peaks are found near _Tc$T_c$ when the Onsager coefficient is varied at a given constant frequency for q=3$q=3$. Fixing the Onsager coefficient and varying the frequency always leads to two peaks for q=3,4$q=3,4$ and 6 near _Tc$T_c$. The sound attenuation peaks are observed near _Tt$T_t$ at lower values of external magnetic field, but as it increases the sound attenuation peaks decrease and eventually disappear.     

Lifshitz-point correlation length exponents from the large-n expansion

The large-n expansion is applied to the calculation of thermal critical exponents describing the critical behavior of spatially anisotropic d-dimensional systems at m  -axial Lifshitz points. We derive the leading non-trivial 1/n$1/n$ correction for the perpendicular correlation-length exponent _νL2${\nu }_{L2}$ and hence several related thermal exponents to order O(1/n)$O(1/n)$. The results are consistent with known large-n expansions for d  -dimensional critical points and isotropic Lifshitz points, as well as with the second-order epsilon expansion about the upper critical dimension d^?=4+m/2$d^{?}=4+m/2$ for generic m∈[0,d]$m\in [0,d]$. Analytical results are given for the special case d=4$d=4$, m=1$m=1$. For uniaxial Lifshitz points in three dimensions, 1/n$1/n$ coefficients are calculated numerically. The estimates of critical exponents at d=3$d=3$, m=1$m=1$ and n=3$n=3$ are discussed.     

Structural characterization and magnetization of Mg0.7Zn0.3SmxFe2−xO4 ferrites

Mg_0.7Zn_0.3Sm_xFe_2−xO₄ ferrites were prepared by the solid-state reaction method and were characterized by X-ray diffraction and magnetization measurements. A single spinel phase was obtained in the range 0.00?x?0.03$0.00?x?0.03$. The lattice parameter was found to increase at x=0.01$x=0.01$ and then decreases up to x=0.03$x=0.03$, which may indicate a distortion in the spinel lattice. The saturation magnetization was found to decrease with the increase in x up to 0.04, due to the replacement of the Fe³⁺ ions by the Sm³⁺ ions.     

Domain wall propagation in Permalloy nanowires with a thickness gradient

The magnetization reversal behavior of Permalloy nanowires has been investigated using a magneto-optic Kerr effect setup. Nanowires with various widths, w=250$w=250$ nm to 3 μm and a thickness of t=10$t=10$ nm were fabricated by electron-beam lithography and subsequent lift-off. Furthermore, similar nanowires but with a thickness gradient along the nanowire axis have been prepared to investigate the influence of the gradient on the magnetic domain wall propagation. Magnetization hysteresis loops recorded on individual nanowires without a gradient are compared to corresponding wires with a thickness gradient. The dependence of the coercive field, _Hc$H_c$ vs. t/w$t/w$ shows a linear behavior for wires without a gradient. However, wires with a gradient display a more complex crossover behavior. We find a plateau in the _Hc$H_c$ vs. t/w$t/w$ curve at values of w$w$, where a transformation from transverse to vortex domain wall type is expected.     

Comparative study between a two-dimensional anisotropic Heisenberg antiferromagnet with easy-axis single-ion anisotropy and one with easy-axis exchange anisotropy

Generally, in literature, easy-axis single ion anisotropy and easy-axis exchange anisotropy was treated in indistinct way. In this work we propose to perform a comparative study of the effects of these two easy-axis anisotropies on the behavior of the magnetization and the critical temperature (_Tc)$(T_{\mathrm{c}})$ in the 2D classical Heisenberg antiferromagnetic model. In order to study the low-temperature thermodynamics of this model, we should consider the contribution of anisotropic spin waves, using a self-consistent harmonic approximation (SCHA) theory. We compare the predictions of SCHA with numerical simulations on L×L$L\times L$ square lattices using Monte Carlo (MC) simulations, which include effects due to all thermodynamically allowed excitations. Our SCHA results are in good agreement with our MC simulations results and have shown that the strong K$K$ limit gives two different Ising-like behavior. In the exchange anisotropic case, the dependence of _Tc$T_{\mathrm{c}}$ on anisotropic parameter K$K$ becomes linear and in the single-ion anisotropic case, _Tc$T_{\mathrm{c}}$ becomes independent of K$K$. Also, using MC simulations and finite size scaling, we show that the critical exponents in the two anisotropic case are compatible with the 2D Ising values α=0.125$\alpha =0.125$ and γ=1.75$\gamma =1.75$.     

Force free projective motions of the sphere

Suppose that the sphere Sⁿ$S^n$ has initially a homogeneous distribution of mass and let G$G$ be the Lie group of orientation preserving projective diffeomorphisms of Sⁿ$S^n$. A projective motion of the sphere, that is, a smooth curve in G$G$, is called force free if it is a critical point of the kinetic energy functional. We find explicit examples of force free projective motions of Sⁿ$S^n$ and, more generally, examples of subgroups H$H$ of G$G$ such that a force free motion initially tangent to H$H$ remains in H$H$ for all time (in contrast with the previously studied case for conformal motions, this property does not hold for H=S_On+1$H=S{O}_{n+1}$). The main tool is a Riemannian metric on G$G$, which turns out to be not complete (in particular not invariant, as happens with non-rigid motions), given by the kinetic energy.     

Weak mirror symmetry of complex symplectic Lie algebras

A complex symplectic structure on a Lie algebra h$\mathfrak{h}$ is an integrable complex structure J$J$ with a closed non-degenerate (2,0)$(2,0)$-form. It is determined by J$J$ and the real part Ω$\Omega$ of the (2,0)$(2,0)$-form. Suppose that h$\mathfrak{h}$ is a semi-direct product g?V$\mathfrak{g}?V$, and both g$\mathfrak{g}$ and V$V$ are Lagrangian with respect to Ω$\Omega$ and totally real with respect to J$J$. This note shows that g?V$\mathfrak{g}?V$ is its own weak mirror image in the sense that the associated differential Gerstenhaber algebras controlling the extended deformations of Ω$\Omega$ and J$J$ are isomorphic.     

Half-monopole in the Weinberg–Salam model

We present new axially symmetric half-monopole configuration of the SU(2)×U(1) Weinberg–Salam model of electromagnetic and weak interactions. The half-monopole configuration possesses net magnetic charge 2π/e$2\pi /e$ which is half the magnetic charge of a Cho–Maison monopole. The electromagnetic gauge potential is singular along the negative z$z$-axis. However the total energy is finite and increases only logarithmically with increasing Higgs field self-coupling constant λ^1/2${\lambda }^{1/2}$ at sin²θ_W=0.2312${sin}^2{\theta }_W=0.2312$. In the U(1) magnetic field, the half-monopole is just a one dimensional finite length line magnetic charge extending from the origin r=0$r=0$ and lying along the negative z$z$-axis. In the SU(2) ’t Hooft magnetic field, it is a point magnetic charge located at r=0$r=0$. The half-monopole possesses magnetic dipole moment that decreases exponentially fast with increasing Higgs field self-coupling constant λ^1/2${\lambda }^{1/2}$ at sin²θ_W=0.2312${sin}^2{\theta }_W=0.2312$.     

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.