Spectroscopic study of magnetic phase transitions in Nd<Subscript>x</Subscript>Gd<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Fe<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript>

Magnetic ordering and spin reorientation in iron borates Nd_xGd_1?xFe₃(BO₃)₄ (x = 0.01, 0.04, 0.25, 1.0) are studied using a rare-earth spectroscopic probe.     

Magnetic and thermal properties of single-crystal NdFe<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript>

The neodymium ferroborate NdFe₃(BO₃)₄ undergoes an antiferromagnetic transition at T _N = 30 K, which manifests itself as a λ-type anomaly in the temperature dependence of the specific heat C and as inflection points in the temperature dependences of the magnetic susceptibility χ measured at various directions of an applied magnetic field with respect to the crystallographic axes of the sample. Magnetic ordering occurs only in the subsystem of Fe³⁺ ions, whereas the subsystem of Nd³⁺ ions remains polarized by the magnetic field of the iron subsystem. A change in the population of the levels of the ground Kramers doublet of neodymium ions manifests itself as Schottky-type anomalies in the C(T) and χ(T) dependences at low temperatures. At low temperatures, the magnetic properties of single-crystal NdFe₃(BO₃)₄ are substantially anisotropic, which is determined by the anisotropic contribution of the rare-earth subsystem to the magnetization. The experimental data obtained are used to propose a model for the magnetic structure of NdFe₃(BO₃)₄.     

Spin reorientation effects in GdFe<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript> induced by applied field and temperature

Magnetic properties of GdFe₃(BO₃)₄ single crystals were investigated by ⁵⁷Fe-Mössbauer spectroscopy and static magnetic measurements. In the ground state, the GdFe₃(BO₃)₄ crystal is an easy-axis compensated antiferromagnet, but the easy axis of iron moments does not coincide with the crystal C₃ axis, deviating from it by about 20°. The spontaneous and field-induced spin reorientation effects were observed and studied in detail. The specific directions of iron magnetic moments were determined for different temperatures and applied fields. Large values of the angle between the Fe³⁺ magnetic moments and the C₃ axis in the easy-axis phase and between Fe³⁺ moments and the a₂ axis in the easy-plane phase reveal the tilted antiferromagnetic structure.     

Optical properties and electronic structure of rare-earth ferroborates

The optical absorption spectra of single-crystal ferroborate GdFe₃(BO₃)₄ and GdFe_2.1Ga_0.9(BO₃)₄ are measured and interpreted. It is found that the absorption edge and the absorption bands A, B, and C observed below the edge are close to those for FeBO₃. A many-electron model of the band structure of GdFe₃(BO₃)₄ is suggested including strong electron correlations between the iron d states. It is shown that GdFe₃(BO₃)₄ has a charge-transfer dielectric gap. A rise in pressure is predicted to result in a crossover between the high-spin and low-spin states of the Fe³⁺ ion, collapse of the magnetic moment, a weakening of Coulomb correlations, an abrupt reduction in the energy gap, and an insulator-semiconductor transition.     

Structure and lattice dynamics of rare-earth ferroborate crystals: Ab initio calculation

The ab initio calculation of the crystal structure and the phonon spectrum of crystals RFe₃(BO₃)₄ (R = Pr, Nd, Sm) has been performed in the framework of the density functional theory. The ion coordinates in the unit cell, the lattice parameters, the frequencies and the types of fundamental vibrations, and also the intensities of lines in the Raman spectrum and infrared reflection spectra have been found. The elastic constants of the crystals have been calculated. For low-frequency A₂ mode in PrFe₃(BO₃)₄, a “seed” vibration frequency that strongly interacts with the electronic excitation on a praseodymium ion was found. The calculation results satisfactory agree with the experimental data.     

Positive magnetoresistance effect in rare earth cobaltites

The structure, magnetic, and magnetotransport properties of the Pr_0.5Sr_0.5Co_{1 ? x} Fe _x O₃ system have been studied. The ferromagnet-spin glass (x = 0.5)-G-type antiferromagnet (x = 0.7) transitions and the metal—insulator transitions (x = 0.25) have been revealed. It has been established that the magnetoresistance of the metallic ferromagnetic cobaltites changes sign from positive to negative as the external magnetic field increases. The positive component increases and the negative component decreases with decreasing temperature. The negative magnetoresistance increases sharply in the insulating spinglass phase. Possible causes of the low-magnetic-field positive magnetoresistance in the rare earth metallic cobaltites are discussed.     

IR spectroscopy of rare-earth aluminum borates RAl3(BO3)4 (R = Y,Pr-Yb)

Rare-earth aluminum borates RAl₃(BO₃)₄ (R = Y, Nd-Yb) obtained by spontaneous high-temperature flux crystallization form two polytype modifications described by the space groups R32 (D ₃ ⁷ ) and C2/c (C _2h ⁶ ). They differ in the symmetry versions in mutual arrangement of layers. These borates have been investigated by mid- and far-IR spectroscopy in combination with factor-group analysis of the vibrations of BO ₃ ^3? ions; translational motions of Al³⁺, R³⁺ (Y, Nd-Yb), and BO ₃ ^3? ions; and BO ₃ ^3? rotations. Rare-earth aluminum borates are assigned to different space groups according to their IR spectra. Borates with large rare-earth Nd and Pr cations are crystallized into the space group C2/c (C _2h ⁶ ), while borates with smaller (Y, Sm-Yb) ions are crystallized into the space group R32 (D ₃ ⁷ ). The rhombohedral structure of the latter compounds includes monoclinically ordered domains, as is evidenced by the presence of monoclinic-phase bands in the IR spectrum. NdAl₃(BO₃)₄ and SmAl₃(BO₃)₄ can form both monoclinic and rhombohedral polytypes. The IR spectrum of the monoclinic SmAl₃(BO₃)₄ phase contains bands due to the rhombohedral phase, while the IR spectrum of NdAl₃(BO₃)₄ (which is described by the space group R32) contains bands due to the monoclinic polytype. The presence of domains with another arrangement of layers in the polytype structure is a characteristic sign that corresponds to the order-disorder theory; this theory explains the structure of polytypes.     

Magnetoresistance hysteresis in granular HTSCs as a manifestation of the magnetic flux trapped by superconducting grains in YBCO + CuO composites

Hysterestic behavior of the magnetoresistance of granular HTSCs and its interaction with the magnetic hysteresis are studied by measuring magnetoresistance R(H) and critical current I _c(H) of composites formed by HTSC Y_0.75Lu_0.25Ba₂Cu₃O₇ and CuO. A network of Josephson junctions is formed in such composites, in which the nonsuperconducting component plays the role of barriers between HTSC grains. Hysteretic dependences R(H) of magnetoresistance are studied in a wide range of transport current density j and are analyzed in the framework of the two-level model of a granular superconductor, in which dissipation takes place in the Josephson medium and the magnetic flux can be pinned both in grains and in the Josephson medium. The interrelation between the hysteresis of critical current I _c(H) and the evolution of the hysterestic dependence R(H) of the magnetoresistance upon transport current variation is demonstrated experimentally. The effect of the magnetic past history on the hysteretic behavior of R(H) and the emergence of a segment with a negative magnetoresistance are analyzed. It is shown for the first time that the R(H) dependences are characterized by a parameter that is independent of the transport current, viz., the width of the R(H) hysteresis loop.     

Nitrogen-containing compounds <Emphasis Type="Italic">R</Emphasis>Fe<Subscript>11</Subscript>TiN<Subscript>x</Subscript> (<Emphasis Type="Italic">R</Emphasis> = Gd or Lu)

The structure and magnetic properties of RFe₁₁TiN compounds (R=Gd or Lu) containing nitrogen are investigated. Magnetic measurements are performed on a magnetometer in magnetic fields up to 100 kOe in the temperature range from 4.2 to 750 K with the use of RFe₁₁TiN single crystals, RFe₁₁TiN powders placed in a ceramic cell, and samples oriented in an external magnetic field. It is found that the nitridation leads to an increase in the Curie temperature and the saturation magnetization. The samples studied are uniaxial over the entire temperature range of magnetic ordering. The magnetic anisotropy decreases upon nitridation. It is demonstrated that, within the local anisotropy model, the decrease in the magnetic anisotropy constant K₁ can be explained by the redistribution of the electron density in the vicinity of the crystallographic positions occupied by iron atoms.     

On correlators for high multiplicity events

We present the results of the study of the energy correlators K₂(n) and K₃(n) and their ratio R₃(n) as a function of the hadron multiplicity at the LHC. The PYTHIA generator has been used. PYTHIA predicts that R₃(n) is not dependent on multiplicity. K₂(n), K₃(n), and the R₃(n) ratio can be studied at ATLAS.     

Surface and volume phase states of Fe<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Ga<Subscript>x</Subscript>BO<Subscript>3</Subscript> crystals in the vicinity of the Néel point

The behavior of the magnetic system of a surface layer of macroscopic Fe_1?xGa_xBO₃ crystal (x=0, 0.3) in the vicinity of the Néel temperature T_N was studied. The studies were made by a method involving simultaneous gamma, x-ray, and electron Mössbauer spectroscopy that made it possible to obtain information simultaneously from surface layers and from the bulk of a macroscopic crystal. It was found that the temperature T_N(L) at which a thin layer at a depth L from the surface switches to a disordered state is lower than T_N for the bulk and is lower the closer this layer is to the surface. In the vicinity of T_N, a nonuniform state is observed in which the bulk of the crystal is magnetically ordered and the surface layer is disordered. The transition temperature T_N(L) decreases from T_N to its surface value within a surface layer of a “critical” thickness.     

Hyperfine interactions in Sc<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Y<Subscript>x</Subscript>Fe<Subscript>2</Subscript> cubic Laves alloys

Effects of hybridization of 3d bands of iron with 3d bands of scandium and 4d bands of yttrium in Sc_1?xY_xFe₂ cubic Laves alloys (0≤_x≤1) are studied by the nuclear magnetic resonance method. The concentration dependences of the lattice parameters a, saturation magnetization σ, and hyperfine fields at the ⁵⁷Fe, ⁴⁵Sc, and ⁸⁹Y nuclei—as well as the ²⁷Al impurity nuclei, whose atoms substitute iron atoms in the lattices of these alloys—are measured. The “local” and “induced” contributions to hyperfine fields at the ⁵⁷Fe nuclei are separated and the magnetic moments at iron atoms are estimated. It is found that the hybridization effect leads to the formation of magnetic moments at Sc and Y atoms (whose direction is opposite to the direction of the magnetic moment at iron atoms) and is responsible for the ferrimagnetic structure in Sc_1?xY_xFe₂ alloys.     

Distribution of cations in magnetite prepared by mechanochemical synthesis

The distribution of iron cations in the crystal lattice of the Fe_3?vO₄ (v=0.153) cation-deficient spinel produced by mechanical dispersion of α-Fe₂O₃ hematite in water is investigated using x-ray diffraction and Mössbauer spectroscopy. Analysis of the Mössbauer data shows that the Fe_2.847O₄ magnetite prepared by mechanochemical synthesis is a chemically heterogeneous compound. The crystal structure of Fe_2.847O₄ is characterized by local environments of the (Fe^2.5+)₀ cations at v₀≤0.1, v₁?0.12, v₂?0.18, and v₃?0.26, which are responsible for a broad distribution of magnetic hyperfine fields with the P(H) probability maxima near 37.0, 36.0, 34.0, and 30.0 MA m^?1.     

Influence of oxidized interlayers on magnetic properties of multilayer films based on amorphous ferromagnet–dielectric nanocomposites

Films of composites (Co₄₅Fe₄₅Zr₁₀)_x(Al₂O₃)_100–x, (Co₈₄Nb₁₄Ta₂)_x(SiO₂)_100–x, (Co₄₁Fe₃₉B₂₀)_x(SiO₂)_100–x and multilayer heterogeneous composite–composite structures {[(Co₄₅Fe₄₅Zr₁₀)_x(Al₂O₃)_100–x]/[(Co₄₅Fe₄₅Zr₁₀)_x(Al₂O₃)_100–x + N₂]}_n, {[(Co₄₅Fe₄₅Zr₁₀)_x(Al₂O₃)_100–x]/[(Co₄₅Fe₄₅Zr₁₀)_x(Al₂O₃)_100–x + O₂]}_n, {[(Co₄₁Fe₃₉B₂₀)_x(SiO₂)_100–x]/[(Co₄₁Fe₃₉B₂₀)_x(SiO₂)_100–x + O₂]}_n, and {[(Co₈₄Nb₁₄Ta₂)_x(SiO₂)_100–x]/[(Co₈₄Nb₁₄Ta₂)_x(SiO₂)_100–x + O₂]}_n have been deposited using the ionbeam sputtering method with a cyclic supply of reaction gases during deposition. The structure and magnetic properties of the films have been studied. It has been shown that the introduction of an oxidized interlayer makes it possible to suppress the perpendicular magnetic anisotropy in the (Co₄₅Fe₄₅Zr₁₀)_x(Al₂O₃)_100–x composite with the metallic phase concentration higher than the percolation threshold.     

Crystal-structure and magnetic phase transformations in solid solutions of BiFeO<Subscript>3</Subscript>-AFe<Subscript>0.5</Subscript>Nb<Subscript>0.5</Subscript>O<Subscript>3</Subscript> (A = Ca,Sr, Ba,Pb)

Solid solutions of Bi_{1 ? x} A _x (Fe_{1 ? x/2}Nb _x/2)O₃, where A = Ca, Ba, and Pb, are obtained and their crystal structure and magnetic properties are investigated. It is shown that for A = Ca and x ≈ 0.15, the symmetry of the unit cell changes from rhombohedral (space group R3c) to orthorhombic (Pbnm). The transformation leads to the emergence of spontaneous magnetization due to the Dzyaloshinskii-Moriya interaction. Solid solutions with A = Pb remain rhombohedral up to a concentration of x = 0.3. Spontaneous magnetization sharply increases in the compound with x ≈ 1 at low temperatures and is due to the formation of the spin-glass component.     

Relaxation of the remanent resistance of granular HTSC Y-Ba-Cu-O + CuO composites after magnetic field treatment

The hysteresis of magnetoresistance R(H) and relaxation of the remanent resistance R _rem with time after magnetic field treatment of HTSC (Y-Ba-Cu-O) + CuO composites are studied. Such a composite constitutes a network of Josephson junctions wherein the nonsuperconducting component (CuO) forms Josephson barriers between HTSC grains. By comparing the experimental R _rem(t) and R(H) dependences, it is shown that the relaxation of the remanent resistance is caused by the decreased magnetic field in the intergrain medium due to relaxation of magnetization. The reason is uncovered for the differences between the published values of pinning potentials determined by measuring the relaxation of magnetization or resistance and fitting them by the Anderson law.     

Influence of the ground state of the Pr<Superscript>3+</Superscript> ion on magnetic and magnetoelectric properties of the PrFe<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript> multiferroic

The magnetic, magnetoelectric, and magnetoelastic properties of a PrFe₃(BO₃)₄ single crystal and the phase transitions induced in this crystal by the magnetic field are studied both experimentally and theoretically. Unlike the previously investigated ferroborates, this material is characterized by a singlet ground state of the rare-earth ion. It is found that, below T _N = 32 K, the magnetic structure of the crystal in the absence of the magnetic field is uniaxial (l ∥ c), while, in a strong magnetic field H ∥ c (H _cr ～ 43 kOe at T = 4.2 K), a Fe³⁺ spin reorientation to the basal plane takes place. The reorientation is accompanied by anomalies in magnetization, magnetostriction, and electric polarization. The threshold field values determined in the temperature interval 2–32 K are used to plot an H-T phase diagram. The contribution of the Pr³⁺ ion ground state to the parameters under study is revealed, and the influence of the praseodymium ion on the magnetic and magnetoelectric properties of praseodymium ferroborate is analyzed.     

Quantum entanglement in nitrosyl iron complexes

Recent magnetic susceptibility measurements for polycrystalline samples of binuclear nitrosyl iron complexes, [Fe₂(C₃H₃N₂S)₂(NO)₄] (I) and [Fe₂(SC₃H₅N₂)₂(NO)₄] (II), suggest that quantum-mechanical entanglement of the spin degrees of freedom exists in these compounds. Entanglement E exists below the temperature T _E that we have estimated for complexes I and II to be 80–90 and 110–120 K, respectively. Using an expression of entanglement in terms of magnetic susceptibility for a Heisenberg dimer, we find the temperature dependence of the entanglement for complex II. Having arisen at the temperature T _E , the entanglement increases monotonically with decreasing temperature and reaches 90–95% in this complex at T = 25 K, when the side effects are still small.     

High-resolution spectroscopy of HoFe<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript> crystal: a study of phase transitions

The transmission spectra of HoFe₃(BO₃) multiferroic single crystals are studied by optical Fourier-transform spectroscopy at temperatures of 1.7–423 K in polarized light in the spectral range 500–10 000 cm^–1 with a resolution up to 0.1 cm^–1. A new first-order structural phase transition close to the second-order transition is recorded at T_c = 360 K by the appearance of a new phonon mode at 976 cm^–1. The reasons for considerable differences in T_c for different samples of holmium ferroborate are discussed. By temperature variations in the spectra of the f–f transitions in the Ho³⁺ ion, we studied two magnetic phase transitions, namely, magnetic ordering into an easy-plane structure as a second-order phase transition at T_N = 39 K and spin reorientation from the ab plane to the c axis as a first-order phase transition at T_SR = 4.7 ± 0.2 K. It is shown that erbium impurity in a concentration of 1 at % decreases the spin-reorientation transition temperature to T_SR = 4.0 K.     

Magnetic and electrical properties of Fe<Subscript>1.91</Subscript>V<Subscript>0.09</Subscript>BO<Subscript>4</Subscript> warwickite

We have performed a complex investigation of the structure and the magnetic and electrical properties of a warwickite single crystal with the composition Fe_1.91V_0.09BO₄. The results of Mössbauer measurements at T=300 K indicate that there exist “localized” (Fe²⁺, Fe³⁺) and “delocalized” (Fe_2.5+) states distributed over two crystallographically nonequivalent positions. The results of magnetic measurements show that warwickite is a P-type ferrimagnet below T=130 K. The material exhibits hopping conductivity involving strongly interacting electrons. The experimental data are analyzed in comparison to the properties of the initial (unsubstituted) Fe₂BO₄ warwickite. The entire body of data on the electric conductivity and magnetization are interpreted on a qualitative basis.