NMR study of the paramagnetic state of low-dimensional magnets LiCu<Subscript>2</Subscript>O<Subscript>2</Subscript> and NaCu<Subscript>2</Subscript>O<Subscript>2</Subscript>

A comprehensive NMR study of the magnetic properties of single crystal LiCu₂O₂ (LCO) and NaCu₂O₂ (NCO) is carried out in the paramagnetic region of the compounds for various orientations of single crystals in an external magnetic field. The values of the electric-field gradient (EFG) tensor, as well as the dipole and transferred hyperfine magnetic fields for ^63,65Cu, ⁷Li, and ²³Na nuclei are determined. The results are compared with the data obtained in previous NMR studies of the magnetically ordered state of LCO/NCO cuprates.     

EPR Study of Sc<Subscript>2</Subscript>SiO<Subscript>5</Subscript>:Nd<Superscript>143</Superscript> Isotopically Pure Impurity Crystals

The Sc₂SiO₅ single crystals doped with 0.001 at.% of the ¹⁴³Nd³⁺ ion were studied by continuous-wave and pulse electron paramagnetic resonance methods. The g-tensors and hyperfine structure tensors for two magnetically non-equivalent Nd ions were obtained. The spin–spin and spin–lattice relaxation times were measured at 9.82 GHz in the temperature range from 4 to 10 K. It was established that three relaxation processes contribute to the spin–lattice relaxation processes. There are one-phonon spin–phonon interaction, two-phonon Raman interaction and two-phonon Orbach–Aminov relaxation processes. It was established that spin–spin relaxation time is of the same magnitude for neodymium ion doped in Sc₂SiO₅ and in Y₂SiO₅.     

Magnetic Resonance Study of Fe-Implanted TiO<Subscript>2</Subscript> Rutile

Single-crystal (100) and (001) TiO₂ rutile substrates have been implanted with 40 keV Fe⁺ at room temperature with high doses in the range of (0.5–1.5) × 10¹⁷ ions/cm². A ferromagnetic resonance (FMR) signal has been observed for all samples with the intensity and the out-of-plane anisotropy increasing with the implantation dose. The FMR signal has been related to the formation of a percolated metal layer consisting of close-packed iron nanoparticles in the implanted region of TiO₂ substrate. Electron spin resonance (ESR) signal of paramagnetic Fe³⁺ ions substituting Ti⁴⁺ positions in the TiO₂ rutile structure has been also observed. The dependences of FMR resonance fields on the DC magnetic field orientation reveal a strong in-plane anisotropy for both (100) and (001) substrate planes. An origin of the in-plane anisotropy of FMR signal is attributed to the textured growth of the iron nanoparticles. As result of the nanoparticle growth aligned with respect to the structure of the rutile host, the in-plane magnetic anisotropy of the samples reflects the symmetry of the crystal structure of the TiO₂ substrates. Crystallographic directions of the preferential growth of iron nanoparticles have been determined by computer modeling of anisotropic ESR signal of substitutional Fe³⁺ ions.     

Resonance Frequency and NMR Relaxation Times in Two Inequivalent <Superscript>133</Superscript>Cs in Cs<Subscript>2</Subscript>CuBr<Subscript>4</Subscript> and Cs<Subscript>2</Subscript>ZnBr<Subscript>4</Subscript> Single Crystals

The resonance frequencies and relaxation mechanisms of Cs₂CuBr₄ and Cs₂ZnBr₄ were examined by static nuclear magnetic resonance (NMR) method. Here, the two inequivalent Cs(1) and Cs(2) sites surrounded by Br ions were distinguished. The saturation recovery traces for ¹³³Cs nuclei in Cs₂CuBr₄ with the paramagnetic ions, and those in Cs₂ZnBr₄ without the paramagnetic ions were each fitted by four exponential functions. From these results, the spin–lattice relaxation times T₁ in the laboratory frame of ¹³³Cs nuclei in the two crystals were obtained, and Cs(1) surrounded by 11 bromide ions has a longer relaxation time than Cs(2) surrounded by 9 bromide ions.     

Quenching of the Haldane gap in LiVSi<Subscript>2</Subscript>O<Subscript>6</Subscript> and related compounds

We report results of susceptibility χ and ⁷Li NMR measurements on LiVSi₂O₆. The temperature dependence of the magnetic susceptibility χ(T) exhibits a broad maximum, typical for low-dimensional magnetic systems. Quantitatively it is in agreement with the expectation for an S=1 spin chain, represented by the structural arrangement of V ions. The NMR results indicate antiferromagnetic ordering below T_N=24 K. The intra- and interchain coupling J and J_p for LiVSi₂O₆, and also for its sister compounds LiVGe₂O₆, NaVSi₂O₆ and NaVGe₂O₆, are obtained via a modified random phase approximation which takes into account results of quantum Monte Carlo calculations. While J_p is almost constant across the series, J varies by a factor of 5, decreasing with increasing lattice constant along the chain direction. The comparison between experimental and theoretical susceptibility data suggests the presence of an easy-axis magnetic anisotropy, which explains the formation of an energy gap in the magnetic excitation spectrum below T_N, indicated by the variation of the NMR spin-lattice relaxation rate at T≪T_N.     

<Superscript>53</Superscript>Cr NMR study of CuCrO<Subscript>2</Subscript> multiferroic

The magnetically ordered phase of the CuCrO₂ single crystal has been studied by the nuclear magnetic resonance (NMR) method on ⁵³Cr nuclei in the absence of an external magnetic field. The ⁵³Cr NMR spectrum is observed in the frequency range ν_res = 61–66 MHz. The shape of the spectrum depends on the delay tdel between pulses in the pulse sequence τ_π/2–t _del–τ_π–t _del–echo. The spin–spin and spin–lattice relaxation times have been measured. Components of the electric field gradient, hyperfine fields, and the magnetic moment on chromium atoms have been estimated.     

Investigation of ion transport in Li<Subscript>8</Subscript>ZrO<Subscript>6</Subscript> and Li<Subscript>6</Subscript>Zr<Subscript>2</Subscript>O<Subscript>7</Subscript> solid electrolytes

Lithium ionic conductivity and spin-lattice relaxation rates were measured in Li₈ZrO₆ and Li₆Zr₂O₇ solid electrolytes. It was found that the Li₈ZrO₆ solid electrolyte undergoes a transition to the superionic state in the temperature range 673–703 K. It was shown that Li⁺ ions are mobile in particular lattice positions of the Li₆Zr₂O₇ phase, and that ionic conductivity is monotonic at an activation energy of 79.4 kJ/mol.     

Specific features of magnetic states of impurity iron ions in the perovskite La<Subscript>0.75</Subscript>Sr<Subscript>0.25</Subscript>Co<Subscript>0.98</Subscript> <Superscript>57</Superscript>Fe<Subscript>0.02</Subscript>O<Subscript>3</Subscript>

Single-phase polycrystalline La_0.75Sr_0.25Co_0.98⁵⁷Fe_0.02O₃ samples have been prepared by solidstate ceramic technology. The samples have the rhombohedral structure (space group \(R\bar 3c\)). The studies of perovskite La_0.75Sr_0.25Co_0.98⁵⁷Fe_0.02O₃ by Mössbauer spectroscopy on impurity ⁵⁷Fe nuclei in the temperature range of 5–293 K have revealed the existence of a superparamagnetic relaxation in the temperature range of 100–210 K. The parameters of hyperfine interactions (hyperfine magnetic fields, line shifts, and quadrupole shifts) and the anisotropy energy have been measured, and the frequencies of magnetic moment relaxation of iron ions have been estimated.     

Magnetic properties of LiNi<Subscript>0.5</Subscript>Mn<Subscript>0.47</Subscript>Al<Subscript>0.03</Subscript>O<Subscript>2</Subscript> as positive electrode for Li-ion batteries

The layered LiNi_0.5Mn_0.47Al_0.03O₂ was synthesized by wet chemical method and characterized by X-ray diffraction and analysis of magnetic measurements. The powders adopted the α-NaFeO₂ structure. This substitution of Al for Mn promotes the formation of Li(Ni_0.47²⁺Ni_0.03³⁺Mn_0.47⁴⁺Al_0.03³⁺)O₂ structures and induces an increase in the average oxidation state of Ni, thereby leading to the shrinkage of the lattice unit cell. The concentration of antisite defects in which Ni²⁺ occupies the (3a) Li lattice sites in the Wyckoff notation has been estimated from the ferromagnetic Ni²⁺(3a)–Mn⁴⁺(3b) pairing observed below 140 K. The substitution of 3% Al for Mn reduces the amount of antisite defects from 7% to 6.4–6.5%. The analysis of the magnetic properties in the paramagnetic phase in the framework of the Curie–Weiss law agrees well with the combination of Ni²⁺ (S = 1), Ni³⁺ (S = 1/2) and Mn⁴⁺ (S = 3/2) spin-only values. Delithiation has been made by the use of K₂S₂O₈. According to this process, known to be softer than the electrochemical one, the nickel ions in the (3b) sites are converted into Ni⁴⁺ in the high spin configuration, while Ni²⁺(3a)–Mn⁴⁺(3b) ferromagnetic pairs remain, as the Li⁺(3b) ions linked to the Ni²⁺(3a) ions in the antisite defects are not removed. The results show that the antisite defect is surrounded by Mn⁴⁺ ions, implying the nonuniform distribution of the cations in agreement with previous NMR and neutron experiments.     

Grain size effects on dynamics of Li-ions in Li<Subscript>3</Subscript>V<Subscript>2</Subscript>(PO<Subscript>4</Subscript>)<Subscript>3</Subscript> glass-ceramic nanocomposites

Li₃V₂(PO₄)₃ glass-ceramic nanocomposites, based on 37.5Li₂O-25V₂O₅-37.5P₂O₅ mol% glass, were successfully prepared via heat treatment (HT) process. The structure and morphology were investigated by X-ray diffraction (XRD) and scanning electron microscope (SEM). XRD patterns exhibit the formation of Li₃V₂(PO₄)₃ NASICON type with monoclinic structure. The grain sizes were found to be in the range 32–56 nm. The effect of grain size on the dynamics of Li⁺ ions in these glass-ceramic nanocomposites has been studied in the frequency range of 20 Hz–1 MHz and in the temperature range of 333–373 K and analyzed by using both the conductivity and modulus formalisms. The frequency exponent obtained from the power law decreases with the increase of temperature, suggesting a weaker correlation among the Li⁺ ions. Scaling of the conductivity spectra has also been performed in order to obtain insight into the relaxation mechanisms. The imaginary modulus spectra are broader than the Debye peak-width, but are asymmetric and distorted toward the high frequency region of the maxima. The electric modulus data have been fitted to the non-exponential Kohlrausch–Williams–Watts (KWW) function and the value of the stretched exponent β is fairly low, suggesting a higher ionic conductivity in the glass and its glass-ceramic nanocomposites. The advantages of these glass-ceramic nanocomposites as cathode materials in Li-ion batteries are shortened diffusion paths for Li⁺ ions/electrons and higher surface area of contact between cathode and electrolyte.     

Electron paramagnetic resonance in YbNiAl<Subscript>2</Subscript> single crystals with strong magnetic anisotropy

Anisotropy in the magnetic properties of YbNiAl₂ intermetallide has been studied. Electron paramagnetic resonance (EPR) signals assigned to the localized magnetic moments of trivalent ytterbium have been detected at temperatures below 20 K. Spin–lattice relaxation processes like the Orbach–Aminov process with participation of the first excited Stark sublevel of the Yb³⁺ ion with an energy of 96 K govern electron–spin dynamics and the disappearance of spectrum lines with a further increase in temperature. Strong magnetic anisotropy effects are discussed as a main reason for the appearance of electron paramagnetic resonance.     

Three types of photomagnetic effects in Sp<Subscript>3</Subscript>Cr(C<Subscript>2</Subscript>O<Subscript>4</Subscript>)<Subscript>3</Subscript> crystals

Three different photomagnetic effects caused by ultraviolet light in paramagnetic crystals based on molecules of spiropyrans (Sp) Sp₃Cr(C₂O₄)₃ and SpI have been revealed and separated: (1) in the high-temperature range (30–300 K), the photomagnetic effect in Sp₃Cr(C₂O₄)₃ is determined by the charge transfer between chromium ions and spiropyran molecules; (2) in the low-temperature range (2 K), the photomagnetic effect in Sp₃Cr(C₂O₄)₃ is due to the photoisomerization of spiropyran molecules, the change in the crystal field, and the splitting of the levels of Cr³⁺ ions in zero field; and (3) in the temperature range 2–20 K, the generation of radiation-induced paramagnetic defects contributes to the magnetic moment of the organic sublattice Sp⁺.     

EPR and optical absorption studies of Cu<Superscript>2+</Superscript> ions in [ZnPd(CN)<Subscript>4</Subscript>(C<Subscript>4</Subscript>H<Subscript>12</Subscript>N<Subscript>2</Subscript>O<Subscript>2</Subscript>)] single crystals

A Cu²⁺-doped single crystal of catena-trans-bis(N-(2-hydroxyethyl)-ethylenediamine) zinc(II)-tetra-m-cyanopaladate(II) [ZnPd(CN)₄(C₄H₁₂N₂O₂)] complex has been investigated by electron paramagnetic resonance (EPR) technique at room temperature. EPR spectra indicate that Cu²⁺ ions substitute for magnetically equivalent Zn²⁺ ions and form octahedral complexes in [ZnPd(CN)₄(C₄H₁₂N₂O₂)] hosts. The crystal field affecting the Cu²⁺ ion is nearly axial. The optical absorption studies show two bands at 322 nm (30864 cm⁻¹) and 634 nm (15337 cm⁻¹) which confirm the axial symmetry. The spin Hamiltonian parameters and the relevant wave function are determined.     

Spin transition and thermal expansion in the layered cobaltite GdBaCo<Subscript>2</Subscript>O<Subscript>5.5</Subscript>

The electrical conductivity and thermal expansion coefficient of GdBaCo₂O_5.5 samples have been measured in order to reveal the mechanism of the metal-insulator transition in cation-ordered cobaltites RBaCo₂O_5.5 (where R is a rare-earth element) and its relation to the change in the spin state of cobalt ions. It has been established that the unit cell volume considerably increases upon the transition to the metallic state at T _MI ≈ 360–365 K and that the thermal expansion exhibits anomalies (which are two orders of magnitude weaker) due to the ferromagnetic and antiferromagnetic orderings. The data obtained confirm that the spin transition in Co³⁺ ions actually proceeds simultaneously with the metal-insulator transition and excludes the possibility of stepwise spin transitions occurring at lower temperatures.     

<Superscript>27</Superscript>Al NMR Study of the Structure and Dynamics of Natrolite

The temperature dependences of nuclear magnetic resonance and magic angle spinning nuclear magnetic resonance spectra of ²⁷Al nuclei in natrolite (Na₂Al₂Si₃O₁₀· 2H₂O) have been studied. The influence of water molecules and sodium ions mobility on the shape of the ²⁷Al NMR spectrum and framework dynamics have been discussed The temperature dependences of the spin–lattice relaxation times T₁ of ²⁷Al nuclei in natrolite have also been studied. It has been shown that the spin–lattice relaxation of the ²⁷Al is governed by the electric quadrupole interaction with the crystal electric field gradients modulated by translational motion of H₂O molecules in the natrolite pores. The dipolar interactions with paramagnetic impurities become significant as a relaxation mechanism of the ²⁷Al nuclei only at low temperatures (<270 K).     

Incommensurate helical magnetic order in LiCu<Subscript>2</Subscript>O<Subscript>2</Subscript> and NaCu<Subscript>2</Subscript>O<Subscript>2</Subscript> quasi-one-dimensional compounds

The results of the measurements of the ^{6, 7}Li and ²³Na nuclear magnetic resonance (NMR) and ^{63, 65}Cu nuclear quadrupole resonance in LiCu₂O₂ and NaCu₂O₂ quasi-one-dimensional compounds with a spin chains in the paramagnetic and magnetically ordered states are presented. The shape of the NMR line below T _c = 24 and 13 K for LiCu₂O₂ and NaCu₂O₂, respectively, is characteristic of the incommensurate static modulation of the local magnetic field matching with the incommensurate spiral modulation of the magnetic moments. The differences in the shape of the NMR spectra of ²³Na and ⁷Li are discussed in terms of the features of the crystal structure of LiCu₂O₂ and NaCu₂O₂.     

Helical magnetic structure in a quasi-one-dimensional LiCu<Subscript>2</Subscript>O<Subscript>2</Subscript> multiferroic crystal according to <Superscript>63,65</Superscript>Cu NMR studies

The NMR spectra of ⁶³Cu and ⁶⁵Cu natural copper isotopes in a LiCu₂O₂ multiferroic single crystal compound have been measured above and below the temperature of magnetic phase transition (T _c = 23 K) in zero magnetic field and in applied magnetic field H ₀ = 94 kOe parallel to the c axis of the crystal. In LiCu₂O₂ below T _c, a complicated helical magnetic structure with the magnetic moment of copper ions Cu²⁺ varying along the chain according to the harmonic law with the wave vector being incommensurate to the crystal lattice constants has been revealed. The experimental results have been successfully interpreted using the model based on the planar helical magnetic structure. It has been found that the plane of rotation for Cu²⁺ magnetic moments in LiCu₂O₂ does not coincide at H ₀ = 0 with the ab plane. The high magnetic field (H ₀ = 94 kOe) applied along the c axis of the single crystal does not affect the spatial orientation of the plane of rotation.     

Anisotropy of g-factor of Cu<Subscript>2+</Subscript> ion and Anisotropic exchange interaction between Spins in antiferromagnetic Bi<Subscript>2</Subscript>CuO<Subscript>4</Subscript>

To study the anisotropy of g-factor of Cu²⁺ ion in the antiferromagnetic Bi₂CuO₄ having an interesting crystal structure, we calculate the energy splitting of the orbital state of Cu²⁺ ion due to the electric crystalline field arising from the surrounding O²⁺, Bi³⁺ and Cu²⁺ ions. On the basis of Pryce's spin Hamiltonian we evaluate g-tensor of each Cu²⁺ ion in the unit cell. We also discuss the anisotropic exchange interaction which is important as the origin of the anisotropy energy for Cu²⁺ ion with S=1/2. The results are discussed in connection with observations.     

Magnetic properties of Pb<Subscript>2</Subscript>Fe<Subscript>2</Subscript>Ge<Subscript>2</Subscript>O<Subscript>9</Subscript> single crystals

Single crystals of Pb₂Fe₂Ge₂O₉ have been grown. They were subjected to X-ray diffraction, magnetic, neutron diffraction, Mössbauer and spin resonance studies. It has been established that Pb₂Fe₂Ge₂O₉ is a weak ferromagnet with a Néel temperature T _N = 46 K, and the exchange and spin-flop transition fields have been estimated. It has been demonstrated that the weak ferromagnetic moment is actually the result of the single-ion anisotropy axes for the magnetic moments of different magnetic sublattices being not collinear.