EPR and longitudinal response signals in spin systems consisting of localized (<Emphasis Type="Italic">s</Emphasis>=1/2) and delocalized spins

The spin system of many new promising materials, such as high-temperature superconductors, fullerenes, fullerides, or manganites with colossal magnetoresistance, consists of localized spins (s-spins of impurity paramagnetic centers) and delocalized spins (e-spins of charge carriers). The two sorts of spins are coupled by exchange interaction, which leads to coupled precession of the corresponding magnetizations. When the materials mentioned above are investigated by EPR methods, the measured longitudinal (T₁) and transverse (T₂) relaxation times provide the most valuable information. However, the presence of inhomogeneous broadening of the EPR of s-spins often makes it difficult to measure T₂, while small values of T₁ do not allow one to measure it by conventional methods. Atsarkin and colleagues [4, 7, 8] proposed a new version of the method for measuring T₁ by longitudinal response signals induced in a longitudinal spin coil (oriented along the constant magnetic field) under low-frequency modulation of the microwave power, which saturates the EPR, even though very weakly. Earlier, the results obtained in experiments on measuring the longitudinal response for samples containing interacting s-and e-spins were interpreted using formulas for an individual sort of spins. In this paper, the magnetization of s-and e-spins that precess under the condition of relaxational coupling is considered, which is characteristic, for example, of fullerides. The complete EPR susceptibility is represented in a form that makes it possible to determine the origin (from s-or e-spins) of two Lorentzians, each of which is characterized by one of the normal decay rates of two coupled oscillators (i.e., of precessing transverse magnetization components). The common EPR line analytically decomposed into those Lorentzians, and special factors take into account the influence of the other sort of spins on the amplitude of the signal generated by the sort under consideration. Similarly to the EPR absorption signals, the expressions for the longitudinal response are decomposed into parts originating from s-and e-spins, and each part is proportional to the form factor of one of the modes (s-or e-like). The qualitative comparison shows good agreement with experimental data in terms of EPR and longitudinal response in a fulleride.     

On the <Emphasis Type="Italic">g</Emphasis>-factor value of canted antiferromagnet CoCO<Subscript>3</Subscript>

Experimental data on the magnetization of canted antiferromagnet CoCO₃ (T_N = 18.1 K) in the paramagnetic region are described by the isotropic g factor g_‖ = g_⊥ = 6.5 that differs from the anisotropic values g_‖ = 3.05 and g_⊥ = 4.95 obtained in electron paramagnetic resonance (EPR) measurements at T = 4.2 K on Co²⁺ ions in magnetically diluted crystals. The g-factor values calculated in the Abragam-Pryce and Weiss molecular field approximations using the magnetization data in the magnetic ordered region correspond to data obtained in EPR measurements. It is shown that the absence of the anisotropy of the g factor at high temperatures cannot be explained in the approximations used. Causes of the observed discrepancies are discussed.     

Crossover from polaron to band conduction upon doping CaMnO<Subscript>3</Subscript> with La ions

In studying the specular reflection IR spectra of manganite polycrystals with electron doping Ca_1?x La _x MnO₃ (0 ≤ x ≤ 0.050) at room temperature, a crossover from polaron to band conduction is observed at x = 0.030. It has been shown that the observed changes in the electronic subsystem is associated with the crossover in the behavior of the magnetization and magnetoresistance in the magnetically ordered and paramagnetic phases that occurs at the same concentration and is described in [C. Chiorescu et al., Phys. Rev. B 73, 014406 (2006)].     

Anomalously strong relaxation of the polarization of muons in the magnetically ordered and paramagnetic states of the TbMnO<Subscript>3</Subscript> multiferroic

An anomalously strong relaxation of the muon polarization in a magnetically ordered state in the TbMnO₃ multiferroic has been revealed by the method below the μSR Néel temperature (42 K). Such a relaxation is due to the muon channel of relaxation of the polarization and the interaction of the magnetic moment of the muon with inhomogeneities of the internal magnetic field of an ordered state in the form of a cycloid. Above the Néel temperature, beginning with temperatures depending on the applied magnetic field, a two-phase state has been revealed where one phase has an anomalously strong relaxation of the muon polarization for a paramagnetic state. These features of the paramagnetic state are due to short-range magnetic order domains that appear in strongly frustrated TbMnO₃. A true paramagnetic state has been observed only at T ≥ 150 K.     

Some specific features of the NMR study of fluid flows

Some specific features of studying fluid flows with a NMR spectrometer are considered. The consideration of these features in the NMR spectrometer design makes it possible to determine the relative concentrations of paramagnetic ions and measure the longitudinal and transverse relaxation times (T₁ and T₂, respectively) in fluid flows with an error no larger than 0.5%. This approach allows one to completely avoid errors in determining the state of a fluid from measured relaxation constants T₁ and T₂, which is especially urgent when working with medical suspensions and biological solutions. The results of an experimental study of fluid flows are presented.     

Relativistic theory of the electric quadrupole moment of a hydrogen-like atom in the <Emphasis Type="Italic">s</Emphasis>1/2 and <Emphasis Type="Italic">p</Emphasis>1/2 states

Relativistic analytical expressions are derived for the electric quadrupole moment induced by the hyperfine interaction of the electron with the nucleus of a hydrogen-like atom in the ns_1/2 and np_1/2 states. The magnetic dipole and electric quadrupole hyperfine interactions are taken into account. The calculations are performed using the generalized virial relationships for the Dirac equation in a central field. The dependences of the electric quadrupole moment on the nuclear charge Z and the principal quantum number n are analyzed. The induced quadrupole moments are compared with the nuclear quadrupole moments.     

Effect of a structural disorder on the magnetic properties of the sodium–cobalt tellurate Na<Subscript>3.70</Subscript>Co<Subscript>1.15</Subscript>TeO<Subscript>6</Subscript>

A new layered oxide, sodium–cobalt tellurate Na_3.70Co_1.15TeO₆, is synthesized and structurally characterized, and its static and dynamic magnetic properties are studied. This compound has a new monoclinic structure type with quasi-one-dimensional cation ordering in magnetically active layers. This compound is antiferromagnetically ordered at a Néel temperature T _N ~ 3.3 K, and the temperature and field dependences of magnetization suggest competing antiferromagnetic and ferromagnetic interactions. EPR spectroscopy reveals complex spin dynamics when temperature changes and the presence of two different paramagnetic centers, which is attributed to the existence of two structurally nonequivalent (regular and antisite) positions for magnetic Co²⁺ ions.     

Nuclear magnetic relaxation induced by the relaxation of electron spins

A physical mechanism responsible for the relaxation of nuclear spins coupled by the hyperfine interaction to relaxed electron spins in materials with spin ordering is proposed. The rate of such induced nuclear spin relaxation is proportional to the dynamic shift of the nuclear magnetic resonance (NMR) frequency. Therefore, its maximum effect on the NMR signal should be expected in the case of nuclear spin waves existing in the system. Our estimates demonstrate that the induced relaxation can be much more efficient than that occurring due to the Bloch mechanism. Moreover, there is a qualitative difference between the induced and Bloch relaxations. The dynamics of nuclear spin sublattices under conditions of the induced relaxation is reduced to the rotation of m₁ and m₂ vectors without any changes in their lengths (m ₁ ² (t) = m ₂ ² (t) = m ₀ ² (t)= const). This means that the excitation of NMR signals by the resonant magnetic field does not change the temperature T _n of the nuclear spin system. This is a manifestation of the qualitative difference between the induced and Bloch relaxations. Indeed, for the latter, the increase in T _n accompanying the saturation of NMR signals is the dominant effect.     

Magnetic behaviour of nano-particles of Fe<Subscript>2.9</Subscript>Zn<Subscript>0.1</Subscript>O<Subscript>4</Subscript>

DC magnetization measurements are reported in the temperature range 20–100 K on a poly-disperse nano-particle sample of the spinel ferrite Fe_2.9Zn_0.1O₄ with a log-normal size distribution of median diameter 43.6 Å and standard deviation 0.58. Outside a core of ordered spins, moments in surface layer are disordered. Results also show some similarities with conventional spin glasses. Blocking temperature exhibits a near linear variation with two-third power of the applied magnetic field and magnetizationM evolves nearly linearly with logarithm of timet. Magnetic anisotropy has been estimated by analysing theM-logt curve. Anisotropy values show a large increase over that of bulk particle samples. Major contribution to this enhancement comes from the disordered surface spins.     

Spin excitations in granular structures with ferromagnetic nanoparticles

Spin excitations and relaxation in a granular structure which contains metallic ferromagnetic nanoparticles in an insulating amorphous matrix are studied in the framework of the s-d exchange model. As the d system, we consider the granule spins, and the s system is represented by localized electrons in the amorphous matrix. In the one-loop approximation with respect to the s-d exchange interaction for a diagram expansion of the spin Green’s function, the spin excitation spectrum is found, which consists of spin-wave excitations in the granules and of polarized spin excitations. In polarized spin excitations, a change in the granule spin direction is accompanied by an electron transition with a spin flip between two sublevels of a split localized state in the matrix. We considered polarized spin relaxation (relaxation of the granule spins occurring by means of polarized spin excitations) determined by localized deep energy states in the matrix and the thermally activated electronic cloud of the granule. It is found that polarized spin relaxation is efficient over a wide frequency range. Estimates made for structures with cobalt granules showed that this relaxation could be observed in centimetric, millimetric, and submillimetric wavelength ranges.     

Γ<Subscript>8</Subscript>-band electron momentum relaxation involving a mixed-valence iron ion system,and electronic transport in HgSe: Fe at low temperatures

Specific features of Γ₈-band electron scattering on a spatially correlated mixed-valence iron ion system in HgSe: Fe crystals are investigated. The s-p hybridization and Bloch wave function amplitudes are taken into account in calculating the probability of electron scattering by mixed-valence iron ions. The relaxation time and mobility of Γ₈-band electrons in HgSe and HgSe: Fe at low temperatures are calculated, and the energy dependence of the electron relaxation time is analyzed. This dependence for Γ₈-band electrons is shown to change radically when mixed-valence iron ions are ordered in space.     

Nature of luminescence of PbS quantum dots synthesized in a Langmuir–Blodgett matrix

We calculate current (shot) noise in a metallic diffusive conductor generated by spin imbalance in the absence of a net electric current. This situation is modeled in an idealized three-terminal setup with two biased ferromagnetic leads (F-leads) and one normal lead (N-lead). Parallel magnetization of the F-leads gives rise to spin-imbalance and finite shot noise at the N-lead. Finite spin relaxation results in an increase in the shot noise, which depends on the ratio of the length of the conductor (L) and the spin relaxation length (l _s). For L >> l _s the shot noise increases by a factor of two and coincides with the case of the antiparallel magnetization of the F-leads.     

Magnetic Properties of Composite Materials Based on a Solid Solution of Type (CuInSe<Subscript>2</Subscript>)<Subscript>1 – <Emphasis Type="Italic">x</Emphasis></Subscript>(MeSe)<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> (Me = Mn,Fe) and Polyethylene

Basic magnetic characteristics (coercive force H_c, residual magnetization M_r, magnetization M, and saturation magnetization M_s) of solid solutions of type (CuInSe₂)_1–x(MeSe)_x (Me = Mn, Fe) have been investigated in a wide temperature interval (100–300 K). The existence of a magnetic phase transition has been established for all studied solid solutions at low temperatures, and the Néel temperatures have been determined from the temperature dependences of the magnetization. It is shown that the temperature dependences of coercive force H_c and of magnetization M can be described using the thermal relaxation (fluctuation) theory.     

A tilted rotatory frame method for the measurement of nuclear spin diffusion coefficients in solids doped with paramagnetic centers: Mn-Doped CaF<Subscript>2</Subscript>

Nuclear magnetic resonance (NMR) experiments recording the recovery of the magnetization of the nuclei in one phase, following the excitation of the nuclei in the other phase, is a classical way of studying blends inhomogeneous at the nanometer scale. Interpretation of the time recovery in terms of the spatial dimension requires knowledge of the two-phase spin diffusion coefficientsD ₀. A new method of measurement of_{D 0} is proposed on the basis of variable angle-tilted rotatory frame relaxation in homogeneous samples doped with paramagnetic centers. The choice of the tilt angle allows one to finely balance the direct relaxation by the paramagnetic center and the spin diffusion. The shape of the relaxation is analyzed with the solution for the diffusion-limited regimeM(t)/M(0)=exp[?(r ₂ t)^1/2?r ₁ t] andD ₀ then calculated fromr ₁,r ₂ and the concentration of paramagnetic centers. Conditions where reliable results can be obtained both theoretically and numerically are explored. The method has been implemented and applied to polycrystalline Mn-doped CaF₂ leading toD ₀=540±60 nm²/s, in agreement with existing values on this model compound.     

Angular dependence of the relaxation times of <Superscript>139</Superscript>La nuclei in La<Subscript>1 − <Emphasis Type="Italic">x</Emphasis></Subscript>Sr<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>MnO<Subscript>3</Subscript>

Relaxation of the magnetization of ¹³⁹La nuclei is considered in lanthanum manganites, which are materials with anisotropic interactions of localized electronic spins, namely, the Dzyaloshinski?-Moriya interactionand the interaction with a crystal field. Expressions are derived for the relaxation times of the longitudinal and transverse components of the nuclear magnetization, and the angular dependences of these relaxation times are found for the La_0.95Sr_0.05MnO₃ compound. In contrast to electronic relaxation, the anisotropy of nuclear relaxation contains a contribution from the shift in the electron Zeeman frequency. The theoretically calculated numerical values of the nuclear relaxation times and their ratios correspond to the range of experimental values in the compounds studied. The results can be of importance for designing devices based on these materials and for further investigation.     

<Superscript>55</Superscript>Mn spin relaxation with the participation of mobile carriers in doped perovskites

Analytical expressions are derived for the rates of longitudinal and transverse nuclear spin relaxation under conditions of fast modulation of the magnitude and direction of a hyperfine field induced by unpaired electrons of an ion. The results obtained are used to explain the data available in the literature on the ⁵⁵Mn spin relaxation in the ferromagnetic metallic phase of doped perovskites, in which the modulation of the hyperfine field is caused by the hopping of e _g electrons between Mn³⁺ and Mn⁴⁺ ions. It is demonstrated that, within this model, the rates of longitudinal and transverse relaxation are characterized by the same temperature dependence and their ratio is independent of temperature, which is in agreement with the experimental data.     

Longitudinal response of the spin system of a metal to modulated EPR saturation at arbitrary modulation frequency and detuning of the saturating field

The theory of the longitudinal (with respect to an external magnetic field) response of a combined spin system of localized paramagnetic centers (s subsystem) and free charge carriers (e subsystem) of a solid semiconductor to modulated saturation of EPR is developed. In contrast to relevant studies made earlier, the general case is considered of an arbitrary modulation frequency and arbitrary detuning of the saturating microwave field with respect to the central EPR frequency. A theoretical approach is used in which normal modes are considered in analyzing coupled oscillations of the spin magnetizations of the s and e subsystems. It is shown that, in the case of relaxation coupling between the subsystems, the longitudinal response recorded at the modulation frequency can be represented as the sum of the responses of the normal modes, each of which is described by a universal resonance lineshape that is different, in general, from the Lorentzian lineshape characteristic of EPR signals. In the extreme cases of weak and strong coupling, simple analytical formulas are derived. The results presented form a theoretical basis for applying the method of modulated longitudinal response for measuring very short longitudinal spin relaxation times in semiconductors with paramagnetic impurities. As an example, experimental data are presented for activated carbon containing stable free radicals.     

Duality-mediated critical amplitude ratios for the (2 + 1)-dimensional S = 1XY model

The phase transition for the (2 + 1)-dimensional spin-S = 1XY model was investigated numerically. Because of the boson-vortex duality, the spin stiffness ρ _s in the ordered phase and the vortex-condensate stiffness ρ _v in the disordered phase should have a close relationship. We employed the exact diagonalization method, which yields the excitation gap directly. As a result, we estimate the amplitude ratios ρ _s,v /Δ (Δ: Mott insulator gap) by means of the scaling analyses for the finite-size cluster with N ≤ 22 spins. The ratio ρ _s /ρ _v admits a quantitative measure of deviation from selfduality.     

Quantum Oscillations of Magnetization in Antiferromagnetic Semimetals on a Triangular Lattice

The specific features of magnetization in antiferromagnetic semimetals with a low charge carrier density on a triangular lattice in a high magnetic field are studied. It is demonstrated that the well-known plateau in the magnetic field dependence of the magnetization manifesting itself in the subsystem of localized S = 1/2 spins is actually not strictly horizontal but has a slight positive slope. It is found that an abrupt change in the frequency of quantum oscillations of the magnetization in the itinerant subsystem should be observed at the magnetic field values corresponding to the edges of this plateau owing to the strong s–d(f) exchange coupling.