Hall coefficient in heavy fermion metals

Experimental studies of the antiferromagnetic (AF) heavy fermion metal YbRh₂Si₂ in a magnetic field B indicate the presence of a jump in the Hall coefficient at a magnetic-field tuned quantum state in the zero temperature limit. This quantum state occurs at B ≥ B_c0 and induces the jump even though the change of the magnetic field at B = B_c0 is infinitesimal. We investigated this by using the model of heavy electron liquid with the fermion condensate. Within this model, the jump takes place when the magnetic field reaches the critical value B_c0 at which the ordering temperature T_N(B = B_c0) of the AF transition vanishes. We show that at B → B_c0, this second order AF phase transition becomes the first order one, making the corresponding quantum and thermal critical fluctuations vanish at the jump. At T → 0 and B = B_c0 the Grüneisen ratio as a function of the temperature T diverges. We demonstrate that both the divergence and the jump are determined by the specific low temperature behavior of the entropy \(S(T) \propto S_0 + a\sqrt T + bT\) with S₀; a and b are temperature independent constants.     

A Fast Algorithm for the First-Passage Times of Gauss-Markov Processes with Hölder Continuous Boundaries

Even for simple diffusion processes, treating first-passage problems analytically proves intractable for generic barriers and existing numerical methods are inaccurate and computationally costly. Here, we present a novel numerical method that is faster and has more tightly controlled accuracy. Our algorithm is a probabilistic variant of dichotomic search for the computation of first passage times through non-negative homogeneously Hölder continuous boundaries by Gauss-Markov processes. These include the Ornstein-Uhlenbeck process underlying the ubiquitous “leaky integrate-and-fire” model of neuronal excitation. Our method evaluates discrete points in a sample path exactly, and refines this representation recursively only in regions where a passage is rigorously estimated to be probable (e.g. when close to the boundary).As a result, for a given temporal accuracy in the location of the first passage time, our method is orders of magnitude faster than direct forward integration such as Euler or stochastic Runge-Kutta schemata. Moreover, our algorithm rigorously bounds the probability that such crossings are not true first-passage times.     

Phasenumwandlung zweiter Art als kritische Erscheinung eines inneren Phasengleichgewichtes

It is demonstrated that the transition in a state with two internal phases is a second order phase transition. The term internal phases means phase-like regions inside the system which are not separated by boundaries in the sense of ordinary phase boundaries, and the dimensions and shape of which as well as their properties as such are object of an equilibrium. In a generalization (quasi phases) a long ranged correlation of alternating or periodical character is considered as a typical element of the low temperature state. Such states can be described thermodynamically with the help of a new pair of variablesQ-η. The transition intoQ-η-T is generally analogous to the critical point of ordinary phase transitions inP-V-T, andη ～(?t)^1/3 andC _p～(?t)^?2/3 with a small constant of proportionality are obtained (t=T-T _u). Using the Pippard-relations in the formV-V _γ=(dT _γ/dP) (S-S _γ) the low temperature behaviour of the entropy and density surface as a function ofP andT near the transition line can be completely described. E.g. the saturation magnetization of a ferromagnetic model is derived proportional to (?t)^1/3. Under the action of a magnetic field the transition will be of first order when the saturation magnetization is achieved, without the outer field being analogous toP orQ. Should only one internal phase differ from the high temperature state we obtain an edge point (x=0 analogous to theμ ₁?x-diagram of solutions) with finite jump inC _p andη～({t). A possible relationship to the BCS- model of the supraconductors is indicated.     

Superconductivity and metal-insulator transition in Cu(Ir<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Rh<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>)<Subscript>2</Subscript>S<Subscript>4</Subscript>

A new thiospinel CuIr₂S₄ exhibits a metal-insulator (M-I) transition at 226 K, while CuRh₂S₄ shows a superconducting transition at 4.70 K. We present a systematic study of electrical and magnetic properties of Cu(Ir_1?x Rh _x )₂S₄. TheM-I transition of CuIr₂S₄ is accompanied by a structural phase transition from tetragonal symmetry in insulating phase to cubic symmetry in high temperature metallic phase. With increasing Rh contentx, the sharpM-I transition shifts to lower temperature forx≦0.10. The samples show semiconductive behavior for 0.10≦0.30 between 4.2 and 300 K, and recover the metallic state forx≧0.50. The superconducting transition may occur for very close tox=1.00. Magnetic susceptibility shows the jump at theM-I transition temperature and the variation ofx leads to a systematic change of the magnetic susceptibilities, which is consistent with the electrical characteristic feature.     

Electronic and structural transitions in NdFeO<Subscript>3</Subscript> orthoferrite under high pressures

The effect of high pressure up to 65 GPa on the crystal structure and optical absorption spectra of NdFeO₃ orthoferrite single crystals is studied in diamond anvil cells. At P～37.5 GPa, an electronic transition at which the optical absorption edge jumps from ～2.2 to ～0.75 eV is observed. The equation of state V(P) is studied on the basis of the X-ray diffraction data obtained under pressure. This study reveals a first-order structural phase transition at P～37 GPa with a jump of ～4% in the unit cell volume. It is shown that the phase transition observed in rare-earth orthoferrites at 30–40 GPa is a transition of the insulator-to-semiconductor type.     

Superposition of M<Subscript>5</Subscript>X<Subscript>5</Subscript> superstructures and X-ray diffraction in TiO<Subscript>1.0</Subscript> titanium monoxide

The interpretation of diffraction spectra of ordered high-temperature phases of solid solutions and strongly nonstoichiometric compounds is discussed. It has been shown that variations of the intensities of superstructure reflections, which cannot be explained within simple ordering models, can be due to the superposition of superstructures with different symmetries in the matrix of the basis crystal structure. Using an example of atom–vacancy ordering in TiO_1.0 titanium monoxide, a model of the order–order transition state formed by the superposition of low-temperature monoclinic (space group A2/m (C2/m)) and high-temperature cubic (space group Pm3?m) M₅X₅ superstructures has been proposed. It has been shown that the transition state is thermodynamically equilibrium and should be implemented instead of the M₅X₅ cubic superstructure. The transition state model can be considered as an M_(5–i)X_(5–i) superstructure (i = 1, 14/18, 11/18) with the monoclinic symmetry (space group P1m1).     

Elementary-oscillator model for color centers with degenerate levels

Quantum transitions between nondegenerate and degenerate (with respect to angular momentum projection) levels of color centers in crystals are described in terms of classical electric-dipole oscillators. It is shown that, upon absorption of elliptically polarized exciting radiation, the system under study transfers to a definite state and the transition is described in general by an elliptical oscillator. An electric-dipole transition accompanied by the creation of a photon is described by a random vector, i.e., by an arbitrary elliptical oscillator lying in the corresponding plane. For an ensemble of n identically oriented centers undergoing a given transition, the luminescence intensity is described by a set of n/2 right-handed rotators and n/2 left-handed rotators. The results obtained are important for solving problems related to quantum information.     

The effect of the spatial variation of the order parameter on the tunneling density of states of superconducting alloys

In the first part of the paper we derive expressions of the Ginzburg-Landau (GL) type for the local tunneling density of states of superconducting alloys. These expressions are quite generally applicable at high excitation energies. One can see immediately that the density of states,N(r, ω), at any positionr and high energiesω is always larger than the local BCS density of states if the space dependence of the order parameter is governed by the GL-equation. This effect is largest for long mean free pathsl. In the second part of the paper we calculate the spatial average of the density of states,¯N, at all energiesω for a lattice of vortex lines in a magnetic field slightly below the upper critical field. The resulting curve of [¯N? N(0)]/N(0) versus co shows no gap and has a zero at about the gap value in zero field. Its value at ω=0 depends onl like ln(ξ₀/l) for l?ξ₀ [N(0) denotes the normal density of states, and ξ₀ is the BCS coherence length].     

Elastic and kinetic properties of single-crystal La<Subscript>0.75</Subscript>Ba<Subscript>0.25</Subscript>MnO<Subscript>3</Subscript>

An experimental study of the temperature behavior of longitudinal sound velocity, internal friction, electrical resistivity, and thermopower of single-crystal La_0.75Ba_0.25MnO₃ is reported. A structural transition accompanied by a large jump (18%) in the sound velocity was found to occur at T _S ≈170 K. Within the interval 156–350 K, the temperature dependences of the sound velocity and internal friction reveal a temperature hysteresis. An internal-friction peak due to relaxation processes was detected. The metallic and semiconducting regions are separated by a transition domain about 80 K wide lying below the Curie temperature T _C =300 K.     

Magnetic and structural phase transitions in systems with spin crossover under pressure

The effect of the exchange interaction between excited high-spin terms of transition metal ions in magnetic Mott–Hubbard insulators on the thermodynamics of the system with singlet terms of ions in the ground state near the crossover of singlet and high-spin terms with the increase in the pressure is studied with the effective Hamiltonian. It is shown that the crossover at the temperature below the critical T* < T _N is a first-order phase transition and is accompanied by a volume jump. The crossover at the temperature above T* is accompanied by a smooth change in the crystal volume.     

Gravitational phase transitions with an exclusion constraint in position space

We discuss the statistical mechanics of a system of self-gravitating particles with anexclusion constraint in position space in a space of dimension d. Theexclusion constraint puts an upper bound on the density of the system and can stabilize itagainst gravitational collapse. We plot the caloric curves giving the temperature as afunction of the energy and investigate the nature of phase transitions as a function ofthe size of the system and of the dimension of space in both microcanonical and canonicalensembles. We consider stable and metastable states and emphasize the importance of thelatter for systems with long-range interactions. For d ≤ 2, there is nophase transition. For d > 2, phase transitions can take place betweena “gaseous” phase unaffected by the exclusion constraint and a “condensed” phase dominatedby this constraint. The condensed configurations have a core-halo structure made of a“rocky core” surrounded by an “atmosphere”, similar to a giant gaseous planet. For largesystems there exist microcanonical and canonical first order phase transitions. Forintermediate systems, only canonical first order phase transitions are present. For smallsystems there is no phase transition at all. As a result, the phase diagram exhibits twocritical points, one in each ensemble. There also exist a region of negative specificheats and a situation of ensemble inequivalence for sufficiently large systems. We showthat a statistical equilibrium state exists for any values of energy and temperature inany dimension of space. This differs from the case of the self-gravitating Fermi gas forwhich there is no statistical equilibrium state at low energies and low temperatures whend ≥ 4. By a proper interpretation of the parameters, our results haveapplication for the chemotaxis of bacterial populations in biology described by ageneralized Keller-Segel model including an exclusion constraint in position space. Theyalso describe colloids at a fluid interface driven by attractive capillary interactionswhen there is an excluded volume around the particles. Connexions with two-dimensionalturbulence are also mentioned.     

Ferroelectric phase transition in orthorhombic CdTiO<Subscript>3</Subscript>: First-principles studies

Parameters of the crystal structure and phonon spectra for orthorhombic cadmium titanate with space group Pbnm and its two possible ferroelectrically distorted phases (with space groups Pbn2₁ and Pb2₁ m) were calculated from first principles within the density functional theory. The obtained structural parameters and frequencies of Raman- and infrared-active modes are in good agreement with available experimental data for the Pbnm phase. Expansion of the total energy in a Taylor series of two order parameters showed that the ground state of the system corresponds to the Pbn2₁ structure into which the Pbnm phase transforms through a second-order phase transition without intermediate phases. A substantial discrepancy between calculated and experimentally observed lattice distortions and spontaneous polarization in the polar phase was explained by quantum fluctuations, as well as by existence of twins and competing long-period structures.     

Thermodynamics of a Magnetic Transition in MnS<Subscript>2</Subscript> at High Pressures

The behavior of the specific heat of MnS₂ at high pressures has been studied. A significant increase in the transition temperature T_N to an antiferromagnetic state with the pressure from 48.2 K at atmospheric pressure to 76 K at a pressure of 5.3 GPa has been revealed. The initial pressure derivative is dT _N /dP = 4.83 K/GPa. It has been found that the parameter α = d(logT _N )/d(logV ) = ?6.6 ± 0.1 is significantly different from the value α = ?10/3 ≈ ?3.3 (Bloch relation), which is typical of numerous antiferromagnetic insulators—transition- metal oxides and fluorides. The volume jump at the magnetic transition point has been estimated. The necessity of direct dilatometric measurements of the volume has been justified.     

Bound States for a Klein–Gordon Particle in Vector Plus Scalar Generalized Hulthén Potentials in D Dimensions

The Green’s function associated with a Klein–Gordon particle moving in a D-dimensional space under the action of vector plus scalar q-deformed Hulthén potentials is constructed by path integration for \({q \geq 1}\) and \({\frac{1}{\alpha} \ln q < r < \infty}\). An appropriate approximation of the centrifugal potential term and the technique of space-time transformation are used to reduce the path integral for the generalized Hulthén potentials into a path integral for q-deformed Rosen–Morse potential. Explicit path integration leads to the radial Green’s function for any l state in closed form. The energy spectrum and the correctly normalized wave functions, for a state of orbital quantum number \({l \geq 0}\), are obtained. Eventually, the vector q-deformed Hulthén potential and the Coulomb potentials in D dimensions are considered as special cases.     

Nonlinear interference in a mean-field quantum model

Using similar nonlinear stationary mean-field models for both a 2D axisymmetricalBose-Einstein Condensate and an electron pair in a parabolic trap, we propose to describethe original many-particle ground state as a one-particle mixed state (in contrast to apure state), i.e. as a statistical ensemble of several one-particle quantum states. Thesequantum states are the eigenfunctions of the corresponding stationary nonlinearSchrödinger equation (hence called “nonlinear eigenstates”). Due to their nonlinearity,they are not orthogonal. Therefore, taking the simple example of a two-level system, weshow that each of these two nonlinear eigenstates |i? and|j? occurs with a probability (or statistical weight) that isdefined by their non-orthogonality ?i|j? 0. We givethe corresponding density matrix. We search for physical grounds in the interpretation ofour two main results, namely, a quantum-classical nonlinear transition and theinterference between two “nonlinear eigenstates”.     

Theoretical prediction of a surface-induced spin-reorientation phase transition in BaFe<Subscript>12</Subscript>O<Subscript>19</Subscript> nanocrystals

The equation of the magnetization of a hexagonal crystal is derived for the first time for an arbitrary orientation of the external magnetic field relative to the crystallographic c axis. In order to clarify the magnetization mechanism for a real ensemble of small particles in the framework of the given problem, surface anisotropy (which is significant for nanosize objects) was taken into account along with crystalline magnetic anisotropy and anisotropy in the particle shape. Model computer experiments prove that the magnetization curves for nanocrystals oriented in a polar angle range of 65–90° exhibit an anomaly in the form of a jump, indicating a first-order spin-reorientation phase transition. This explains a larger steepness of the experimental curve reconstructed taking into account the interaction between particles as compared to the theoretical dependence obtained by Stoner and Wohlfarth [IEEE Trans. Magn. MAG 27 (4), 3469 (1991)]. An analysis of variation of the characteristic anisotropy surface and its cross section with increasing ratio |K₂|/K₁ of the crystalline magnetic anisotropy constants upon a transition from a macroscopic to a nanoscopic crystal shows that surface anisotropy leads to a change in the magnetic structure. As a result, an additional easy magnetization direction emerges in the basal plane apart from the easiest magnetization direction (along the c axis). The direction of hard magnetization emerges from the basal plane, the angle of its orientation relative to the c axis being a function of the ratio | K₂|/K₁.     

Doppelkonversion

An excited nuclear state can decay by three different modes of double quantum emission, namely doubleγ-emission,γ-electron emission and double conversion electron emission. The emission of twoγ-quanta has been considered in an earlier paper¹. The purpose of the present work is to treat all three processes together in a systematic manner. It is shown that the connection between the transition rates forγ-electron emissionT _γc and doubleγ-quantum emissionT _γγ is more complicated than in the case of single quantum processes. However,T _γc can still be expressed in terms of the usual conversion coefficients. This is also true for the transition rate T_cc for the emission of twoK-shell electrons, although only approximately. For the emission of electrons from different atomic shells the formulas become rather complicated, because of interference effects. The electron andγ-quantum spectra in all of the three second order processes are discussed in detail for the decay of the isomeric level in Xe¹³¹.     

Investigation of semicoherent interactions of 1-GeV protons with silicon

An experiment on studying the ²⁸Si(p, p′ γ ₀ X)²⁴Mg semicoherent reaction is carried out at the MAG setup on the 1-GeV proton beam of the U-10 ITEP accelerator. Two particles, proton and γ-ray photon, which accompanies the transition of the ²⁴Mg* nucleus from the first excited state to the ground state, are detected. When the events with the proton emission angle from 3° to 6.5° are selected, the following four processes are observed: the direct knockout of a nuclear α cluster by a proton, the formation of a _ΔSi isobaric nucleus, the formation of a Δ₁₂₃₂ isobar, and the production of a π ⁰ meson at rest in the nuclear coordinate system. The cross sections for the indicated processes are obtained.     

Brownian motion on a manifold as a limit of Brownian motions with drift

Let ?ⁿ be n-dimensional Euclidean space and let M ? ?ⁿ be a smooth compact m-dimensional Riemannian manifold (without boundary) embedded in ?ⁿ. By a Brownian motion on M we mean a Markovian process whose transition semigroup is defined by the generator ?½Δ_M, where Δ_M stands for the Laplace-Beltrami operator on M (see, e.g., [2]). This note extends a series of papers in which a measure generated by a Brownian motion on M on the space of trajectories (with values in M) can be represented as the weak limit of measures on the space of trajectories in the ambient space ?ⁿ (see [7–10]). Namely, we claim that a sequence of diffusion processes on ?n which are Brownian motions with drift (in the direction of the manifold) with infinitely increasing modulus converges in distribution to a Brownian motion on the manifold.     

A study of the effect of gradual substitution NH<Subscript>4</Subscript> → Cs on phase transitions in NH<Subscript>4</Subscript>LiSO<Subscript>4</Subscript> crystals

Solid solutions in the Cs_x(NH₄)_1?xLiSO₄ (0≤x≤0.35) system are grown and investigated. The birefringence (n_a?n_b) and the heat capacity are measured in the temperature range 100–530 K. The (x-T) phase diagram is constructed. It is demonstrated that the substitution of cesium for ammonium in the NH₄LiSO₄ crystal affects the transition temperatures in such a way that the region of the ferroelectric phase increases and the ferroelastic phase disappears at x>0.22. The character of the high-temperature transition remains unchanged (2β=0.24±0.01 for all compositions), but the birefringence anomaly and enthalpy decrease. As the concentration x increases, the low-temperature transition becomes more similar to a first-order transition: the birefringence jump δn and the temperature hysteresis ΔT increase.