Mössbauer study of magnetism in FeII − III (oxy-)hydroxycarbonate green rusts; ferrimagnetism of FeII − III hydroxycarbonate

Fe^II???III hydroxycarbonate Fe $^{\rm II}_{4}$ Fe $^{\rm III}_{2}$ (OH)₁₂CO₃, green rust GR(CO $_{3}^{2-})$ , reveals a ferrimagnetic behaviour. Moments that lie within two-dimensional cation layers are parallel for same species and antiparallel between Fe^II and Fe^III. Respective ordering temperatures are 5.2 and 7 K. A sextet with distribution from 350 to 580 kOe for Fe^III and an octet reflecting a mixture of states with field of 130 kOe and quadrupole splitting of ?3.0 mm s^???1 for Fe^II are observed at 1.4 K. Ferric oxyhydroxycarbonate Fe $^{\rm III}_{6}$ O₁₂H₈CO₃ is ferromagnetic and displays at 4 K a sextet with field between 400 and 500 kOe (maximum at 480 kOe) and transition at 80 K. GR(CO $_{3}^{2-})$ deprotonation gives magnetic domains with compositions at x?=?1/3, 2/3 and 1 due to long range order.     

Magnetic phase transitions and iron valence in the double perovskite Sr 2 FeOsO 6

The insulating and antiferromagnetic double perovskite Sr₂FeOsO₆ has been studied by ⁵⁷Fe Mössbauer spectroscopy between 5 and 295 K. The iron atoms are essentially in the Fe^3?+? high spin $( {t_{2\mathrm{g}}{^3} e_\mathrm{g}{^2} } )$ and thus the osmium atoms in the Os $^{5+} ( {t_{2\mathrm{g}}{^3} } )$ state. Two magnetic phase transitions, which according to neutron diffraction studies occur below T _N?= 140 K and T ₂?= 67 K, give rise to magnetic hyperfine patterns, which differ considerably in the hyperfine fields and thus, in the corresponding ordered magnetic moments. The evolution of hyperfine field distributions, average values of the hyperfine fields, and magnetic moments with temperature suggests that the magnetic state formed below T _N is strongly frustrated. The frustration is released by a magneto-structural transition which below T ₂ leads to a different spin sequence along the c-direction of the tetragonal crystal structure.     

Form factors of η c in light-front quark model

We study the form factors of the η _c meson in the light-front quark model. We explicitly show that the transition form factor of η _c →γ ^? γ as a function of the momentum transfer is consistent with the experimental data by the BaBar collaboration, while the decay constant of η _c is found to be $f_{\eta_{c}}=230.5^{+52.2}_{-61.0}$ and $303.6^{+115.2}_{-116.4}~\mathrm{MeV}$ for $\eta_{c}\sim c\bar{c}$ by using two η _c →γγ decay widths of 5.3±0.5 and 7.2±2.1 keV, given by Particle Data Group and Lattice QCD calculation, respectively.     

The crystal magnetic field in a proton-polarized lanthanum magnesium nitrate single crystal

Knowledge of the crystal magnetic fieldH _c is necessary for proton polarization measurements in polarized targets by the internal field method [1, 2]. Because of the importance of lanthanum magnesium nitrate (LMN) single crystals for low-energy polarized proton targets [3],H _c has been calculated for LMN on the basis of new x-ray diffraction data. We find thatH _c=ApP₂(cosθ), wherep is the proton polarization andP ₂ the second Legendre polynomial depending onθ, the angle between crystalc-axis and external magnetic field, andA is a constant characteristic for LMN. Our result \(A = - \left( {0.242 \pm \begin{array}{*{20}c} {0.028} \\ {0.090} \\ \end{array} } \right) Oe\) leads to a field only about half as large as expected according to previous assumptions. The difference is due to the markedly different proton positions, revealed by the x-ray structure analysis.     

Z 0 boson decays to B^{(*)}_{c} meson and its uncertainties

The planned new e ⁺ e ^? collider with high luminosity shall provide another useful platform to study the properties of the doubly heavy B _c meson in addition to the hadronic colliders as LHC and TEVATRON. In the ‘New Trace Amplitude Approach’, we calculate the production of the spin-singlet B _c and the spin-triplet $B^{*}_{c}$ mesons through the Z ⁰ boson decays, where uncertainties for the production are also discussed. Our results show $\varGamma_{(^{1}S_{0})}=81.4^{+102.1}_{-40.5}$  KeV and $\varGamma_{(^{3}S_{1})}=116.4^{+163.9}_{-62.8}$  KeV, where the errors are caused by varying m _b and m _c within their reasonable regions.     

A Weighted Dispersive Estimate for Schrödinger Operators in Dimension Two

Let H = ?Δ + V, where V is a real valued potential on ${\mathbb {R}^2}$ satisfying ${\|V(x)|\lesssim \langle x \rangle^{-3-}}$ . We prove that if zero is a regular point of the spectrum of H = ?Δ + V, then $${\| w^{-1} e^{itH}P_{ac}f\|_{L^\infty(\mathbb{R}^2)} \lesssim \frac{1}{|t|\log^2(|t|)} \| w f\|_{L^1(\mathbb{R}^2)},\,\,\,\,\,\,\,\, |t| \geq 2}$$ , with w(x) = (log(2 + |x|))². This decay rate was obtained by Murata in the setting of weighted L ² spaces with polynomially growing weights.     

On the Second Mixed Moment of the Characteristic Polynomials of 1D Band Matrices

We consider the asymptotic behavior of the second mixed moment of the characteristic polynomials of 1D Gaussian band matrices, i.e., of the Hermitian N × N matrices H _N with independent Gaussian entries such that 〈H _ij H _lk 〉 = δ _ik δ _jl J _ij , where ${J=(-W^2\triangle+1)^{-1}}$ . Assuming that ${W^2=N^{1+\theta}}$ , ${0 < \theta \leq 1}$ , we show that the moment’s asymptotic behavior (as ${N\to\infty}$ ) in the bulk of the spectrum coincides with that for the Gaussian Unitary Ensemble.     

Structural characterization,magnetic properties and magnetocaloric effects of La0.75Sr0.25Mn1–x Cr x O3 (x = 0.15, 0.20, and 0.25)

The effect of Cr doping on the structural, magnetic and magnetocaloric properties of perovskite manganites La_0.75Sr_0.25Mn_1–x Cr _x O₃ (x = 0.15, 0.20, and 0.25) has been investigated. Crystalline structure and magnetic properties are investigated by using X-ray powder diffraction and magnetization measurements, respectively. All samples show a single phase and are found to crystallize in the distorted rhombohedral system with \( R\overline{3} \,c \) space group. A monotonous change of Curie temperature (T _C), from 314 to 253 K, is observed when content doping increases. Substantial magnetic entropy change reaching 4.20 J/kg K is revealed. Relative cooling power was estimated as well. It was found to reach 289, 323, and 386 J/kg for x = 0.15, 0.20, and 0.25, respectively. Field dependence of the magnetic entropy change showing the power law dependence \( \Delta S_{\rm M} \propto \,\,\left( {\mu_{ 0} \rm H} \right)^{n} \) is also analyzed and discussed.     

Temperature dependence of the hyperfine fields in NiFe2O4 and CuFe2O4 oxides

We report the temperature dependence of the magnetic properties of (Ni, Cu)Fe₂O₄ spinel oxides. Mössbauer spectra for NiFe₂O₄ at various temperatures (79 ≤?T?≤ 900 K) are well fitted by two sextets associated with ⁵⁷Fe nuclei at tetrahedral (A) and octahedral (B) sites. The Curie point T _C was deduced by zero velocity Mössbauer technique to be 873 ± 3 K. The hyperfine fields are observed to vary with temperature according to the equation $B_{\rm hf} (T)=B_{\rm hf} (0)[{1-(T/T_{\rm C})^n}]^{\beta_n}$ where n?=?1 (based on the Landau–Ginzburg theory) and n?=?2 (based on the Stoner theory). A systematic decrease of the Mössbauer spectrum shift with increasing temperature is observed.     

On the free energy of the hopfield model

The general theory of inhomogeneous mean-field systems of Raggio and Werner provides a variational expression for the (almost sure) limiting free energy density of the Hopfield model $$H_{N,p}^{\{ \xi \} } (S) = - \frac{1}{{2N}}\sum\limits_{i,j = 1}^N {\sum\limits_{\mu = 1}^N {\xi _i^\mu \xi _j^\mu S_i S_j } } $$ for Ising spinsS _i andp random patterns ξ^μ=(ξ ₁ ^μ ,ξ ₂ ^μ ,...,ξ _N ^μ ) under the assumption that $$\mathop {\lim }\limits_{N \to \gamma } N^{ - 1} \sum\limits_{i = 1}^N {\delta _{\xi _i } = \lambda ,} \xi _i = (\xi _i^1 ,\xi _i^2 ,...,\xi _i^p )$$ exists (almost surely) in the space of probability measures overp copies of {?1, 1}. Including an “external field” term ?ξ _μ ^p h^μμξ _i=1 ^N ξ _i ^μ S_i, we give a number of general properties of the free-energy density and compute it for (a)p=2 in general and (b)p arbitrary when λ is uniform and at most the two componentsh ^μ1 andh ^μ2 are nonzero, obtaining the (almost sure) formula $$f(\beta ,h) = \tfrac{1}{2}f^{ew} (\beta ,h^{\mu _1 } + h^{\mu _2 } ) + \tfrac{1}{2}f^{ew} (\beta ,h^{\mu _1 } - h^{\mu _2 } )$$ for the free energy, wheref ^cw denotes the limiting free energy density of the Curie-Weiss model with unit interaction constant. In both cases, we obtain explicit formulas for the limiting (almost sure) values of the so-called overlap parameters $$m_N^\mu (\beta ,h) = N^{ - 1} \sum\limits_{i = 1}^N {\xi _i^\mu \left\langle {S_i } \right\rangle } $$ in terms of the Curie-Weiss magnetizations. For the general i.i.d. case with Prob {ξ _i ^μ =±1}=(1/2)±?, we obtain the lower bound 1+4?²(p?1) for the temperatureT _c separating the trivial free regime where the overlap vector is zero from the nontrivial regime where it is nonzero. This lower bound is exact forp=2, or ε=0, or ε=±1/2. Forp=2 we identify an intermediate temperature region between T_*=1?4?² and T_c=1+4?² where the overlap vector is homogeneous (i.e., all its components are equal) and nonzero.T _* marks the transition to the nonhomogeneous regime where the components of the overlap vector are distinct. We conjecture that the homogeneous nonzero regime exists forp≥3 and that T_*=max{1?4?²(p?1),0}.     

Magnetic and Mössbauer spectra observed for mixed-metal magnets NBu4 {\bf Fe}^{\bf II}_{\bf n}MA II 1 − n [FeIII(OX)3] (MA=Mn, Fe)

Mixed-metal molecular-based magnets NBu₄ ${\rm Fe}^{\rm II}_{\rm n}$ M_A ^II _1???n[Fe^III(OX)₃] (M_A=Mn, Fe) were investigated by magnetic and Mössbauer measurements. The magnetic susceptibility of NBu₄ ${\rm Fe}^{\rm II}_{0.07}{\rm Mn}^{\rm II}_{0.93}$ [Fe^III(OX)₃] can be fitted to a Curie-Weiss law with a Weiss paramagnetic Curie temperature of θ?=??114.76 K. The negative Weiss constant indicates an intramolecular antiferromagnetic coupling interaction between the adjacent Fe(II) and Fe(III) ions through the oxalate bridge. In the complex NBu₄Fe^II[Fe^III(OX)₃], the Mössbauer results indicate that the Fe^II and Fe^III sublattices experience spontaneous magnetizations. The compound contains two different spin carriers; i.e. Fe^II(S = 2), Fe^III(S = 5/2). Two magnetic sublattices are defined. The appearance of nuclear Zeeman splittings suggests that long range magnetic ordering takes place below 50 K.     

Tracking iron oxide nanoparticles in plant organs using magnetic measurements

Common bean plants were grown in soil and irrigated with water solutions containing different concentrations of \(\hbox{Fe}_3\hbox{O}_4\) nanoparticles (NPs) with a mean diameter close to 10 nm. No toxicity on plant growth has been detected as a consequence of Fe deficiency or excess in leaves. In order to track the \(\hbox{Fe}_3\hbox{O}_4\) NPs, magnetization measurements were performed in soils and in three different dried organs of the plants: roots, stems, and leaves. Some magnetic features of both temperature and magnetic field dependence of magnetization M(T, H) arising from \(\hbox{Fe}_3\hbox{O}_4\) NPs were identified in all the three organs of the plants. Based on the results of saturation magnetization \(M_\mathrm{s}\) at 300 K, the estimated number of \(\hbox{Fe}_3\hbox{O}_4\) NPs was found to increase from 2 to 3 times in leaves of common bean plants irrigated with solutions containing magnetic material. The combined results indicated that M(T, H) measurements, conducted in a wide range of temperature and applied magnetic fields up to 70 kOe, constitute a useful tool through which the uptake, translocation, and accumulation of magnetic nanoparticles by plant organs may be monitored and tracked.     

Diffusion Effects on the Breakdown of a Linear Amplifier Model Driven by the Square of a Gaussian Field

We investigate solutions to the equation ? _t ?? $\mathcal{D}$ Δ?=λS ²?, where S(x, t) is a Gaussian stochastic field with covariance C(x?x′, t, t′), and x∈ $\mathbb{R}$ ^d . It is shown that the coupling λ _cN (t) at which the N-th moment <? ^N (x, t)> diverges at time t, is always less or equal for $\mathcal{D}$ >0 than for $\mathcal{D}$ =0. Equality holds under some reasonable assumptions on C and, in this case, λ _cN (t)=Nλ _c (t) where λ _c (t) is the value of λ at which <exp[λ ∫ ^t ₀ S ²(0, s) ds]> diverges. The $\mathcal{D}$ =0 case is solved for a class of S. The dependence of λ _cN (t) on d is analyzed. Similar behavior is conjectured when diffusion is replaced by diffraction, $\mathcal{D}$ →i $\mathcal{D}$ , the case of interest for backscattering instabilities in laser-plasma interaction.     

Asymptotic Number of Scattering Resonances for Generic Schrödinger Operators

Let ?Δ + V be the Schrödinger operator acting on ${L^2(\mathbb{R}^d,\mathbb{C})}$ with ${d\geq 3}$ odd. Here V is a bounded real or complex function vanishing outside the closed ball of center 0 and of radius a. Let n _V (r) denote the number of resonances of ?Δ + V with modulus ≤  r. We show that if the potential V is generic in a sense of pluripotential theory then $$n_V(r)=c_d a^dr^d+ O(r^{d-{3\over 16}+\epsilon}) \quad \mbox{as } r \to \infty$$ for any ε > 0, where c _d is a dimensional constant.     

The Spectrum of the Cubic Oscillator

We prove the simplicity and analyticity of the eigenvalues of the cubic oscillator Hamiltonian, $$\begin{array}{ll}H(\beta)=-\frac{d^2}{dx^2}+x^2+i\sqrt{\beta}x^3\end{array}$$ , for β in the cut plane ${\mathcal{C}_c:=\mathcal{C}\backslash \mathcal{R}_-}$ . Moreover, we prove that the spectrum consists of the perturbative eigenvalues {E _n (β)} _{n ≥ 0} labeled by the constant number n of nodes of the corresponding eigenfunctions. In addition, for all ${\beta \in \mathcal{C}_c, E_n(\beta)}$ can be computed as the Stieltjes-Padé sum of its perturbation series at β = 0. This also gives an alternative proof of the fact that the spectrum of H(β) is real when β is a positive number. This way, the main results on the repulsive PT-symmetric and on the attractive quartic oscillators are extended to the cubic case.     

On Endomorphisms of Quantum Tensor Space

We give a presentation of the endomorphism algebra ${\rm End}_{\mathcal {U}_{q}(\mathfrak {sl}_{2})}(V^{\otimes r})$ , where V is the three-dimensional irreducible module for quantum ${\mathfrak {sl}_2}$ over the function field ${\mathbb {C}(q^{\frac{1}{2}})}$ . This will be as a quotient of the Birman–Wenzl–Murakami algebra BMW _r (q) : =  BMW _r (q ^?4, q ² ? q ^?2) by an ideal generated by a single idempotent Φ _q . Our presentation is in analogy with the case where V is replaced by the two-dimensional irreducible ${\mathcal {U}_q(\mathfrak {sl}_{2})}$ -module, the BMW algebra is replaced by the Hecke algebra H _r (q) of type A _r-1, Φ _q is replaced by the quantum alternator in H ₃(q), and the endomorphism algebra is the classical realisation of the Temperley–Lieb algebra on tensor space. In particular, we show that all relations among the endomorphisms defined by the R-matrices on ${V^{\otimes r}}$ are consequences of relations among the three R-matrices acting on ${V^{\otimes 4}}$ . The proof makes extensive use of the theory of cellular algebras. Potential applications include the decomposition of tensor powers when q is a root of unity.     

Neutral strange particle exclusive production in charged current high-energy antineutrino interactions

The cross section of the quasi-elastic reactions \(\bar v_\mu p \to \mu ^ + \Lambda (\Sigma ^0 )\) in the energy range 5–100 GeV is determined from Fermilab 15′ bubble chamber antineutrino data. TheQ ² analysis of quasi-elastic Λ events yieldsM _A=1.0±0.3 GeV/c² for the axial mass value. With zero µΛ K ⁰ events observed, the 90% confidence level upper limit \(\sigma (\bar v_\mu p \to \mu ^ + \Lambda {\rm K}^0 )< 2.0 \cdot 10^{ - 40} cm^2 \) is obtained. At the same time, we found that the cross section of reaction \(\bar v_\mu p \to \mu ^ + \Lambda {\rm K}^0 + m\pi ^0 \) is equal to \(\left( {3.9\begin{array}{*{20}c} { + 1.6} \\ { - 1.3} \\ \end{array} } \right) \cdot 10^{ - 40} cm^2 \) .     

Annealing embrittlement of Fe78Si9B13 (METGLAS-2605S2)

The ductile to brittle transition that occurs in amorphous Fe₇₈Si₉B₁₃ (METGLAS-2605S2) has been investigated using mechanical measurements over the temperature range 250–370 °C. The fracture toughness values, K _Ic , have been determined for a range of annealing times (5–30 min) and cooling rates of 15–45 °C/min. A pronounced ductile to brittle transition is observed around 310(10) °C although no obvious structural changes are evident as indicated by x-ray diffraction. Comparison of transmission and back-scattered conversion electron ⁵⁷Fe Mössbauer spectra for the bulk as-received ribbon in the ductile state ( $K_{Ic}=52~{\rm MPa} \cdot \sqrt{m}$ ) and the ribbon annealed to the brittle state ( $K_{Ic}\sim10~{\rm MPa} \cdot \sqrt{m}$ ) indicates magnetic texture effects in both the bulk and on the surface of these amorphous ribbons, related to the magnetostriction resulting from the quenched-in stress during the ribbon production process, and the ensuing stress-relief upon annealing.