Singlet—triplet oscillations of spin-correlated radical pairs due to the Larmor precession in low magnetic fields

Singlet—triplet oscillations in spin-correlated radical pairs have been studied at magnetic field strengths low for one radical and high for the other. Oscillations with frequencies close to the Larmor frequency ω₀ of electron spin precession have been predicted under these conditions. Both numerical and exact analytical solutions in arbitrary magnetic fields are presented for three cases of hyperfine couplings in wide-spectrum radical. For the case of unresolved spectrum, singlet—triplet evolution was found to contain a single oscillating term with frequency ω₀. In the case of one spin-I magnetic nucleus, there are two low frequency oscillating terms with frequencies ω_? = ω₀ ? ω₀/(2I + 1) and ω₊ = ω₀ + ω₀/(2I + 1), the amplitude of the first term being larger than that of the second. The case of a number of equivalent protons also has been analysed as a superposition of one-nucleus oscillations. The predicted oscillations were observed in a time resolved magnetic field effect for several radical ion pairs produced by X-ray irradiation of alkane solutions with charge acceptors. For pairs (p-terphenyl-d ₁₄)^?./(isooctane)^+. and (p-terphenyl-d ₁₄)^?./(2,4-dimethylpentane)^+. the oscillation frequency in a field B ₀ of 0.5–4mT is about 20% lower than ω₀. Oscillations were observed also in pairs with equivalent nuclei: (p-terphenyl-d ₁₄)^+./(C₆F₆)^?. and (p-terphenyl-d ₁₄)^?./(hexamethylethane)^+.     

Investigation of the character of the exchange interaction in the system Hg1−xMnxSe

A new method is proposed for determining the magnetic characteristics (magnitude and sign of the exchange interaction energy and the average size of clusters of magnetic ions) of dilute solid solutions of semimagnetic semiconductors at low temperatures based on oscillation measurements. The method makes it possible to find the magnetic characteristics of the indicated systems at temperatures between the point of the transition into the spin glass state and the temperature corresponding to the characteristic binding energy of magnetic atoms in clusters, for which standard methods based on the measurement of the magnetic susceptibility are not effective. The method is used to study the character of the exchange interaction in the system of solid solutions Hg_1–xMn_xSe as a function of their composition as well as under conditions of hydrostatic compression. To this end the oscillations of the magnetoresistance (Shubnikov-de Haas (SH) effect) in single-crystalline samples of Hg_1–xMn_xSe in the region of compositions 0.001 x 0.23 in magnetic fields H up to 65 kOe at temperatures T = (0.4–20) K and pressures up to 16 kbar were studied.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 29–39, November, 1989.     

Spin dynamics in the spin glass phase of Y(Mn1−xAlx)2

Zero field SR has been used to probe spin dynamics in the concentrated spin glass Y(Mn_0.9Al_0.1)₂. The spectra follow a stretched exponential form, G_z(t)=exp(–(t)), with reaching 1/3 as the freezing temperature, T_g=60K, is approached. The evolution of G_z(t) with temperature is suggestive of the behaviour of the spin correlation function found by Ogielski in Monte Carlo simulations of the dynamics of the Ising spin glass model. The SR results are correlated with results previously obtained by inelastic neutron scattering.     

Spin precession of Po in Ni detected by In-beam conversion electrons and the magnetic moment of the 15− isomer in204Po

The magnetic moment of the 11 ns, 15^? isomer in²⁰⁴Po and the internal magnetic field of Po in Ni were determined in an in-beam recoil implantation experiment. Time-differential perturbed angular distributions of conversion electrons were measured in an iron-free orange spectrometer. The magnetic hyperfine field of ¦H(PoNi)¦=555(22) kOe is in agreement with the systematic trend for the 6p elements. Theg-factorg(15^?) =0.41(2) is discussed, together with theB (E2, 15^?→13^?). within the shell model.     

Separation of the contributions to the magnetization of Tm1 − x Yb x B12 solid solutions in steady and pulsed magnetic fields

The magnetization of substitutional Tm_{1 ? x} Yb _x B₁₂ solid solutions is studied in the composition range 0 < x ≤ 0.81. The measurements are performed at low temperatures (1.9–300 K) in steady (up to 11 T) and pulsed (up to 50 T, pulse duration of 20–100 ms) magnetic fields. An analysis of the experimental data allowed the contributions to the magnetization of the paramagnetic phase of the Tm_{1 ? x} Yb _x B₁₂ compounds to be separated. These contributions include a Pauli component, which corresponds to the response of the heavy-fermion manybody states that appears in the energy gap in the vicinity of the Fermi level (density of states (3?4) × 10²¹ cm^?3 meV^?1), and a contribution with saturation in high magnetic fields attributed to the localized magnetic moments ((0.8–3.7)μ_B per unit cell) of the nanoclusters formed by rare-earth ions with an antiferromagnetic interaction.     

Karhunen–Loeve analysis and order reduction of the transient dynamics of linear coupled oscillators with strongly nonlinear end attachments

The Karhunen–Loeve (K–L) decomposition method has become a popular technique to create low-dimensional, reduced-order models of dynamical systems. In this paper this technique is applied to a multi-degree-of-freedom chain of linear coupled oscillators with a strongly nonlinear (nonlinearizable), lightweight end attachment. By performing K–L decomposition we show that the lightweight nonlinear attachment (possessing 0.5% of the total mass of the chain) can affect the global dynamics of the linear chain, exhibiting nonlinear energy-pumping phenomena; that is, irreversible passive targeted energy transfers from the linear chain to the nonlinear end attachment, where this energy is locally confined and dissipated without ‘spreading back’ to the primary system. It is shown that the occurrence of energy pumping can be identified by studying the dominant K–L modes of the dynamics, as well as, the energy distribution among them. Moreover, by comparing the action of the strongly nonlinear attachment to the classical linear vibration absorber, we show robustness of passive nonlinear energy absorption over wide parameter ranges. On the other hand, the case-sensitive nature of K–L-based reduced-order models has always been a constraint for K–L decomposition, since one cannot quantify a priori the error bound of such low-dimensional reduced-order models when different initial conditions are applied to the system. To alleviate this constraint, the paper proposes a multiple correlation coefficient (MCC) as a quantitative measure to effectively assess the applicability of a K–L-based reduced-order model derived for a specific set of initial conditions to a small neighborhood of initial conditions containing that initial state. The derived reduced-order models are validated through reconstruction of the system responses and comparisons to direct numerical integrations.     

Biquadratic exchange and critical behaviour in the diluted antiferromagnet EuxSr1−xTe

Magnetization, specific heat, magnetocaloric effect, and neutron diffraction measurements have been performed in order to better understand the magnetic interactions and phase transitions in the diluted antiferromagnetic system Eu_xSr_1–xTe. Due to the low Néel temperature ofT _N =9.8 K and the associated small critical field ofB _C (T=0)=7.5 T, EuTe provides the opportunity to change the angle between the antiferromagnetic moments continuously between 180° and 0° by applying a magnetic field and allows thus to probe the type of the magnetic interaction. It is found that in addition to the common bilinear Heisenberg exchange mechanism there is evidence for a small biquadratic exchange term, which has important consequences on the critical behaviour of Eu_xSr_1–xTe. In the case of EuTe the biquadratic exchange supports the antiferromagnetic order, such that virtually no anisotropy exists and this restricts the anti-Herromagnetic (AF) to spin-flop (SF) transition toB ₀=0. On dilution with strontium, the biquadratic interaction decreases strongly and changes its sign at x0.83 thus favouring the perpendicular moment orientation. This acts like an anisotropy on the dominating antiferromagnetic bilinear interaction and shifts the AF-SF phase line to finite fields which reach values of 0.3 T forT0. No bicritical behaviour is observed, but instead, the SF phase is the state of lowest energy in a small temperature interval belowT _N . The critical exponent (x) of the specific heat decreases in a non-linear way with dilution starting from a large positive value for EuTe. (x) is close to the Heisenberg value –0.12 nearx0.83 where the biquadratic interaction is zero. The same applies for the exponent of the sublattice magnetization.     

Matter-wave solutions of Bose—Einstein condensates with three-body interaction in linear magnetic and time-dependent laser fields

We construct, through a further extension of the tanh-function method, the matter-wave solutions of Bose-Einstein condensates (BECs) with a three-body interaction. The BECs are trapped in a potential comprising the linear magnetic and the time-dependent laser fields. The exact solutions obtained include soliton solutions, such as kink and antikink as well as bright, dark, multisolitonic modulated waves. We realize that the motion and the shape of the solitary wave can be manipulated by controlling the strengths of the fields.     

The closed-orbit and the photoabsorption spectra of lithium atom in varying＇magnetic fields

Using a simple analytic formula from closed orbit theory, we have calculated the photoabsorption spectra of Li atom in different magnetic fields. Closed orbits in the corresponding classical system have also been obtained for B=5.96T.We demonstrate schematically that the closed orbits disappear gradually with the decrease of the magnitude of the magnetic field. This gives us a good method to control the closed orbits in the corresponding system by changing the magnetic field, and thus changing the peaks in the photoabaorption spectra. By comparing the photoabsorption spectra of Li atom with those of hydrogen case, we find the core-scattered effects play an important role in multi-electron Rydberg atoms.     

Heat capacity of La1−x SrxMnO3 single crystals in different magnetic states

The heat capacity of three single-crystal samples of La_1?x Sr_xMnO₃ (x=0, 0.2, and 0.3) is measured in the temperature range 4–400 K. It is found that the heat capacity undergoes abrupt changes due to the transitions from the antiferromagnetic phase to the paramagnetic phase (x=0) and from the ferromagnetic phase to the paramagnetic phase (x=0.2 and 0.3). The phonon contribution to the heat capacity and the Debye characteristic temperatures for the La_0.7Sr_0.3MnO₃ sample are determined over a wide range of temperatures. The electronic density of states at the Fermi level is evaluated. It is demonstrated that an increase in the strontium concentration x brings about an increase in the electronic density of states at the Fermi level. The contributions of spin waves to the heat capacity and the entropy are estimated under the assumption that the phonon spectrum remains unchanged upon doping with Sr.     

Exact solution of the Dirac–Weyl equation in graphene under electric and magnetic fields

In this paper, we have obtained exact analytical solutions for the bound states of a graphene Dirac electron in magnetic fields with various q-parameters under an electrostatic potential. In order to solve the time-independent Dirac–Weyl equation, the Nikoforov–Uvarov (NU) and Frobenius methods have been used. We have also investigated the thermodynamic properties by using the Hurwitz zeta function method for one of the states. Finally, some of the numerical results are also shown.     

Spin states of cobalt and the thermodynamics of Sm1 − x Ca x CoO3 − δ solid solutions

In the rare-earth SmCoO₃ perovskite, Co³⁺ ions at low temperatures appear to be in the low-spin state with S = 0, t _2g ² e _g ⁰ . If Ca²⁺ ions partially substitute Sm³⁺ ions, oxygen deficient Sm_{1 ? x} Ca _x CoO_{3 ? δ} solid solutions with δ = x/2 appear. The oxygen deficiency leads to the formation of pyramidally coordinated cobalt ions Co _pyr ³⁺ in addition to the existing cobalt ions Co _oct ³⁺ within the oxygen octahedra. Even at low temperatures, these ions have a magnetic state, either S = 1, t _2g ⁵ e _g ¹ or S = 2, t _2g ⁴ e _g ² . At low temperatures, the magnetization of Sm_{1 ? x} Ca _x CoO_{3 ? δ} is mainly determined by the response of Co _pyr ³⁺ ions. Owing to the characteristic features of the crystal structure of the oxygen deficient perovskite, these ions form a set of nearly isolated dimers. At high temperatures, the magnetization of Sm_{1 ? x} Ca _x CoO_{3 ? δ} is mainly determined by the response of Co _oct ³⁺ ions, which exhibit a tendency to undergo the transition from the S = 0, t _2g ⁶ e _g ⁰ state to the S = 1, t _2g ⁵ e _g ¹ or S = 2, tt _2g ⁴ e _g ² state. In addition, the magnetization and specific heat of the solid solutions under study include the contribution from the rare-earth subsystem, which undergoes a magnetic ordering at low temperatures.     

Short-ranged potential effects on the recurrence spectra of lithium M = 1 atoms in parallel electric and magnetic fields

This paper presents recurrence spectra of highly excited lithium atoms with M = 1 state in parallel electric and magnetic fields at a fixed scaled energy ε = -0.03. Short-ranged potentials including ionic core potential and centrifugal barrier are taken into account. Their effects on the states and photo-absorption spectrum are analysed in detail. This demonstrates that the geometric features of classical orbits are of special importance for modulations of the spectral pattern. Thus the weak polarization as well as the reduction of correlation of electrons induced by short-ranged potentials give rise to the recurrence spectra of lithium M = 1 atoms more compact than that of the M = 0 one, which is in good agreement with the experimental prediction.     

Comparison between the magnetic susceptibilities of Pd1−xAgx and single phase PdHn

The rapid decrease of the isothermal magnetic susceptibility χ of single phase PdH_n with n ( = atomic ratio H/Pd) above the critical temperature T_c = 564 differs from that of the magnetically similar single phase system Pd_1−xAg_x (x: silver mole fraction) at the same temperature and at equal valence electron concentrations (n = x), i.e. χ (PdH_n)−χ(Pd_1−xAg_x) <0. By use of a semiphenomenological susceptibility ansatz related to the nonideal solution behaviour of H (Ag) in Pd the susceptibility difference is interpreted as an electronic excess effect.The analysis of the steep descent of the magnetic susceptibility also applies to the Pd-rich side of PdH_n in the subcritical temperature region (so-called α-phase) and can be supported by ¹⁰⁵Pd Knight shift data at 348 K.     

Crystal structure and magnetic state of the LaMn1−x VxO3 perovskites

The crystal structure and the magnetic state of polycrystalline LaMn_1?x V_xO₃ (0.1<x<0.9) compounds have been studied by x-ray and neutron diffraction methods, as well as by magnetization and ac susceptibility measurements. It is shown that substitution of vanadium for manganese ions leaves the orthorhombic crystal structure of the compounds (space group Pnma) unchanged. The magnetic structure is observed to change from a canted antiferromagnetic ordering (wavevector k=[0, 0, 0], with the antiferromagnetic moments aligned with the a axis and the ferromagnetic component of the magnetic moment parallel to the b axis) at vanadium concentrations x<0.4 to a collinear antiferromagnetic ordering (with the magnetic moments parallel to the b axis) at x>0.8; at this transition occurs through an intermediate state exhibiting spin-glass properties.     

Electron spin relaxation of exchange coupled pairs of transition metal ions in solids. Ti2+–Ti2+ pairs and single Ti2+ ions in SrF2 crystals

EPR (X- and Q-band) and electron spin relaxation measured by electron spin echo method (X-band) were studied for ${\text{Ti}}^{2+}(S=1)$ and ${\text{Ti}}^{2+}''–''{\text{Ti}}^{2+}$ pairs in ${\text{SrF}}_2$ crystal at room temperature and in the temperature range 4.2–115 K. EPR spectrum consists of a strong line from ${\text{Ti}}^{2+}$ and quartets 2:3:3:2 from titanium pairs $(S=2)$. Spin-Hamiltonian parameters of the pairs are $g_{\parallel }=1.883$, $g_{\perp }=1.975$ and $D=0.036{\text{cm}}^{-1}$. Temperature behavior of the dimer spectrum indicates ferromagnetic coupling between ${\text{Ti}}^{2+}$. Spin–lattice relaxation of individuals ${\text{Ti}}^{2+}$ is dominated by the ordinary two-phonon Raman process involving the whole phonon spectrum up to the Debye temperature ${\Theta }_{\text{D}}=380\text{K}$ with spin–phonon coupling parameter equal to $215{\text{cm}}^{-1}$. Important contribution to the relaxation arises from local mode vibrations of energy $133{\text{cm}}^{-1}$. The pair relaxation is faster due to the exchange coupling modulation mechanism with the relaxation rate characteristic for ferromagnetic ground state of the pairs $1/T_1\propto [\exp (2J/\mathit{kT})-1{]}^{-1}$ which allowed to estimate the exchange coupling $J=36{\text{cm}}^{-1}$. The theories of electron–lattice relaxation governed by exchange interaction are outlined for extended spin systems, for clusters and for individual dimers. Electron spin echo decay is strongly modulated by coupling with surrounding ¹⁹F nuclei. FT-spectrum of the modulations shows a dipolar splitting of the fluorine lines, which allows the evaluation of the off-center shift of ${\text{Ti}}^{2+}$ in pair as 0.132 nm. The electron spin echo dephasing is dominated by an instantaneous diffusion at low temperatures and by the spin–lattice relaxation processes above 18 K.     

Spin and pseudospin symmetric Dirac particles in the field of Tietz-Hua potential including Coulomb tensor interaction＊

Approximate analytical solutions of the Dirac equation for Tietz-Hua (TH) potential including Coulomb-like tensor (CLT) potential with arbitrary spin-orbit quantum number κ are obtained within the Pekeris approximation scheme to deal with the spin-orbit coupling terms κ(κ± 1)r-2 . Under the exact spin and pseudospin symmetric limitation, bound state energy eigenvalues and associated unnormalized two-component wave functions of the Dirac particle in the field of both attractive and repulsive TH potential with tensor potential are found using the parametric Nikiforov-Uvarov (NU) method. The cases of the Morse oscillator with tensor potential, the generalized Morse oscillator with tensor potential, and the non-relativistic limits have been investigated.     

Comparative study of the magnetic and electrical properties of Pr1−xBaxMnO3−δ manganites depending on the preparation conditions

Magnetization, electrical resistivity and magnetoresistance of Pr_0.50Ba_0.50MnO_3−δ manganites with perovskite structure have been investigated as a function of preparation conditions. It was found that the as-prepared samples (prepared in air) show T_C=110 K (first order phase transition), whereas for those annealed in flowing argon the T_C value increases up to 340 K without change of cubic symmetry (second order phase transition). Ferromagnet–paramagnet transition is accompanied by both a metal–insulator transition and a magnetoresistance peak. The X-ray study has revealed that the samples annealed in argon have broad peaks apparently due to microstrains and crystal structure defects. The argon-treated samples improve the magnetization after subsequent annealing in air at T⩽1000°C. T_C of argon-treated samples is stable with respect to annealing in air up to 1300°C where it becomes again 110 K. In contrast, a treatment in vacuum destroys the ferromagnetic order. Auger-spectroscopy has not revealed any additional ions except Pr, Ba, Mn and O for all the samples. External pressure enhances the Curie point of the sample prepared in air at a rate of 43 K/GPa. We have observed that the samples Pr_1−xBa_xMnO_3−δ, x⩾0.30, exhibited the above-mentioned effect of increasing T_C after treatment in flowing argon without changes of the phase state, whereas the samples x<0.30 decomposed into different phases. The dramatic increase of T_C after argon treatment is supposed to result from microstrains and crystal structure defects in the sample.