NMR and Mössbauer study of multiferroic BiFeO<Subscript>3</Subscript>

Pulse nuclear magnetic resonance (NMR) was applied in studying the effect of ⁵⁷Fe isotope content in multiferroic BiFeO₃ on the shape of NMR spectra at 4.2 K. Strong dependences of the NMR line shape on the isotope content and transverse relaxation time were found. Consideration of these effects on NMR line shape shows that there is an undisturbed (with no anharmonicity effect) space spin-modulated structure of the cycloid type in BiFeO₃. The Mössbauer effect was also used to investigate the perovskite BiFeO₃ at 650, 295, and 87 K. Experimental spectra allowed us to obtain the distribution of hyperfine fields, which was found to be consistent with studies of the NMR line shape. The local electronic and magnetic states of the iron ion were measured.     

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.     

Temperature investigations of the spatial spin-modulated structure of multiferroic BiFeO<Subscript>3</Subscript> by means of Mössbauer spectroscopy

The results from ⁵⁷Fe Mössbauer spectroscopic studies of multiferroic BiFeO₃ in a range of tem-peratures including that of the magnetic phase transition are presented. The Mössbauer spectra are processed and analyzed by reconstructing the hyperfine magnetic field distributions and interpreting the spectra with a cycloid-type spatial spin-modulated structure model. The temperature dependences of the hyperfine spectrum parameters (the Mössbauer line shift, the quadrupole shift, and the isotropic and anisotropic contributions to the hyperfine magnetic field) are obtained, along with the anharmonicity parameter of an incommensurate spin wave.     

Mössbauer studies of spatial spin-modulated structure and hyperfine interactions in multiferroic Bi<Superscript>57</Superscript>Fe<Subscript>0.10</Subscript>Fe<Subscript>0.85</Subscript>Cr<Subscript>0.05</Subscript>O<Subscript>3</Subscript>

Results of Mössbauer investigations on ⁵⁷Fe nuclei in multiferroic material Bi⁵⁷Fe_0.10Fe_0.85Cr_0.05O₃ in the temperature range from 5.2 to 300 K are presented. Bulk rhombohedral samples were obtained by solidstate synthesis at high pressure. Mössbauer spectra were analyzed using the model of spatial incommensurate spin-modulated structure of the cycloidal type. Information on the influence of substituting Cr cations for Fe cations on hyperfine spectral parameters was obtained: the shift and quadrupolar shift of a Mössbauer line, and isotropic and anisotropic contributions into the hyperfine magnetic field. The anharmonicity parameter m of the spatial spin-modulated structure increases almost 1.7 times at 5.2 K when BiFeO₃ is doped with chromium. The data on m were used for calculation of the uniaxial magnetic anisotropy constants and their temperature dependences for pure and chromium-doped BiFeO₃.     

Effect of spatial spin modulation on the relaxation and NMR frequencies of 57Fe nuclei in a ferroelectric antiferromagnet BiFeO3

The ⁵⁷Fe NMR spectra of the ⁵⁷Fe-enriched (95.43%) ceramics of a ferroelectric antiferromagnet BiFeO₃ with a spatially modulated magnetic structure have been studied. It is established that a cycloidal spin modulation in BiFeO₃ causes a spatial modulation of the spin-spin relaxation rate along the magnetic cycloid period and results in inhomogeneous broadening of the local NMR lineshape. It is also found that the local magnetic moments of Fe ions in various parts of the cycloid depend differently on the temperature, which is indicative of a difference in the spin wave excitation. The observed phenomena can be explained in terms of the Shul-Nakamura indirect nuclear interaction which becomes effective at high concentrations of the magnetoactive nuclei and low temperatures. Similarity of the obtained experimental results to the regularities of NMR in the Bloch walls is discussed.     

Magnetic order in the structurally disordered helicoidal magnet Cr<Subscript>1/3</Subscript>NbS<Subscript>2</Subscript>: NMR at <Superscript>53</Superscript>Cr nuclei

The Cr_1/3NbS₂ magnet is studied by nuclear magnetic resonance (NMR) at ⁵³Cr nuclei in a zero applied magnetic field. The following two frequency ranges are distinguished in the ⁵³Cr NMR spectrum at T = 4.2 K: ν ₁ = 64–68 MHz and ν ₂ = 49–51 MHz. They can be related to two valence states of chromium ions, namely, Cr⁴⁺ and Cr³⁺. The components of the electric field gradient, the hyperfine fields, and the magnetic moment at chromium atoms are determined. The NMR data demonstrate that the magnetic moments of chromium lie in plane ab and form a magnetic structure consisting of regions with a helicoidal magnetic order and regions where this order is broken.     

Composition-induced transition of spin-modulated structure into a uniform antiferromagnetic state in a Bi<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>La<Subscript>x</Subscript>FeO<Subscript>3</Subscript> system studied using <Superscript>57</Superscript>Fe NMR

By analyzing the NMR line shape, the transformation of a spatially spin-modulated magnetic structure in BiFeO₃ into an ordinary spatially uniform structure of the LaFeO₃ orthoferrite in Bi_1?xLa_xFeO₃ solid solutions is studied. The measurements are made using a spin-echo technique at temperatures of 77 and 4.2 K on ceramics with compositions x=0, 0.1, 0.2, 0.61, 0.9, and 1.0 enriched by the ⁵⁷Fe isotope. It is shown that the spin-modulated structure disappears near the concentration x=0.2, which corresponds, according to the published data, to the phase transition with a change in the unit-cell symmetry R3c → C222. A formula is obtained describing the NMR absorption line shape for the spin-modulated structure with account of local line-width. Theoretical spectra adequately describe the evolution of the experimental spectrum in the concentration range 0≤x≤0.2. Highly nonuniform local magnetic fields in the intermediate compositions make it impossible to detect NMR signals in a sample with x=0.61. A uniform magnetic structure characterized by a single narrow line arises in the range of existence of a phase with the symmetry Pnma typical of the pure orthoferrite LaFeO₃.     

<Superscript>209</Superscript>Bi NMR spectrum of BiFeO<Subscript>3</Subscript> in the presence of spatial modulation of hyperfine fields

A complicated spin-echo spectrum was observed for ²⁰⁹Bi nuclei in a ferroelectric antiferromagnet BiFeO₃ in zero external field. This spectrum is the first example of nuclear quadrupole resonance of a system of diamagnetic atoms in a hyperfine magnetic field produced by the spatially modulated Fe³⁺ spin system and varying in orientation and magnitude. An attempt is undertaken to theoretically simulate the spectrum.     

Spatial spin-modulated structure and hyperfine interactions of 57Fe nuclei in multiferroics BiFe1–x T x O3 (T = Sc,Mn; x = 0, 0.05)

The results of the Mössbauer studies on ⁵⁷Fe nuclei in multiferroics BiFe_1–x T _x O₃ (T = Sc, Mn; x = 0, 0.05) in the temperature range of 5.2–300 K have been presented. The Mössbauer spectra have been analyzed in terms of the model of an incommensurate spatial spin-modulated structure of cycloid type. Information has been obtained about the effect of the substitution of Sc and Mn atoms for Fe atoms on the hyperfine parameters of the spectrum: the shift and the quadrupole shift of the Mössbauer line, the isotropic and anisotropic contributions to the hyperfine magnetic field, and also the parameter of anharmonicity of the spatial spin-modulated structure.     

<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.     

Structural investigation of non-stoichiometric CuInS<Subscript>2</Subscript> by <Superscript>63</Superscript>Cu and <Superscript>115</Superscript>In nuclear magnetic resonance

Results of studies of non-stoichiometric CuInS₂ semiconductor by ⁶³Cu and ¹¹⁵In nuclear magnetic resonance are presented. It was established that deviation of the composition from stoichiometry causes a quadrupolebroadened region of the NMR spectrum to change most. In this case a central peak whose shape is governed by the chemical shift anisotropy remains unaffected. NMR spectra reveal two types of structural distortions in the nearest surroundings of the In atoms.     

Magnetic and valence states of iron ions in the Perovskite Bi<Subscript>0.9</Subscript>Sr<Subscript>0.1</Subscript>FeO<Subscript>3</Subscript>

Single-phase rhombohedral perovskites (Bi_0.9Sr_0.1)FeO₃ were studied by Mössbauer spectroscopy at temperatures of 293, 87, and 680 K. The Neel temperature T _N = 652 ± 2 K of the magnetic transition was measured. Three states of trivalent iron ions in the octahedral states were discovered. Substitution of Sr²⁺ for 0.1 mol % Bi³⁺ breaks the spatially spin-modulated structure.     

Specific features of the thermal,magnetic, and dielectric properties of multiferroics BiFeO<Subscript>3</Subscript> and Bi<Subscript>0.95</Subscript>La<Subscript>0.05</Subscript>FeO<Subscript>3</Subscript>

Thermophysical, magnetic, and dielectric properties of multiferroic BiFeO₃ and Bi_0.95La_0.05FeO₃ ceramic compounds were comprehensively studied. Anomalies of the permittivity near an antiferromagnetic phase transition related to the structural variations were detected. The temperature T _N was determined from the temperature dependences of the thermal expansion coefficient, heat capacity, and differential susceptibility. It is shown that the transition point is shifted to higher temperatures as the rare-earth La ion substitutes for Bi. It is established that an insignificant substitution of lanthanum for bismuth enhances the magnetic properties of bismuth ferrite and the magnetodielectric effect.     

Atomic and magnetic structures of Fe<Subscript>70</Subscript>Al<Subscript>5</Subscript>B<Subscript>25</Subscript> amorphous alloys

The short-range order around boron, aluminum, and iron atoms in Fe₇₅B₂₅ and Fe₇₀Al₅B₂₅ amorphous alloys has been studied by ¹¹B and ²⁷Al nuclear magnetic resonance at 4.2 K and ⁵⁷Fe Mössbauer spectroscopy at 87 and 295 K. The average magnetic moment of iron atoms μ(Fe) in these alloys has been measured by a vibrating sample magnetometer. It has been revealed that the substitution of aluminum atoms for iron atoms does not disturb μ(Fe) in the Fe₇₀Al₅B₂₅ alloy, gives rise to an additional contribution to the ¹¹B NMR spectrum in the low-frequency range, and shifts maxima of the distribution of hyperfine fields at the ⁵⁷Fe nuclei. In the Fe₇₀Al₅B₂₅ amorphous alloy, the aluminum atoms substitute for iron atoms in the nearest coordination shells of boron and iron atoms. This alloy consists of nanoclusters in which boron and iron atoms have a short-range order of the tetragonal Fe₃B phase type.     

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.     

Spin Kinetics of Liquid <Superscript>3</Superscript>He in Contact with a DyF<Subscript>3</Subscript> Micropowder at Ferromagnetic Ordering of Dy<Superscript>3+</Superscript> Ions

The spin kinetics of liquid ³He in contact with a mixture of LaF₃ (99.67%) and DyF₃ (0.33%) micropowders at temperatures of 1.5–3 K has been studied by pulsed nuclear magnetic resonance (NMR). The DyF3 is a dipolar dielectric ferromagnet with the phase transition temperature T_c= 2.55 K, whereas the diamagnetic fluoride LaF₃ is a diluting substance for the optimal observation conditions of ³Не NMR in powder pores. The magnetic phase transition in DyF₃ is accompanied by a considerable change in the character of fluctuations of the magnetic moments of dysprosium ions, which affect the spin kinetics of ³Не in contact with the substrate. Significant changes in the relaxations rates of the longitudinal and transverse magnetizations of 3Не have been discovered in the region of magnetic ordering of the solid matrix. The technique of studying the static and fluctuating magnetic fields of a solid matrix at low temperatures using liquid ³He as a probe has been proposed.     

Magnetic and dielectric response of cobalt-chromium spinel CoCr<Subscript>2</Subscript>O<Subscript>4</Subscript> in the terahertz frequency range

The nature of the phonon and magnon modes in the CoCr₂O₄ multiferroic with a cubic spinel structure has been studied using submillimeter spectroscopy and infrared Fourier spectroscopy. This paper reports on the first measurement of the evolution with temperature of the exchange optical magnon in the ferrimagnetic (T _C = 94 K) and two low-symmetry (T _S ≈ 26 K, T _lock-in = 14.5 K) phases of CoCr₂O₄ down to T = 5 K in zero magnetic field. It has been shown that the detected magnon is not a ferrimagnetic order parameter and originates, most probably, from spin precession in the cobalt sublattices. At the points of the magnetic phase transitions, the oscillator parameters of the two lowest-frequency phonon modes reveal an anomalous temperature behavior, thus evidencing the presence of significant interaction between the magnetic and phonon subsystems. The increase by 25% of the damping parameter of the phonon mode originating from vibrations of the CoO₄ tetrahedra during the transition of CoCr₂O₄ to the multiferroic state (T < T _S ) suggests structural changes in the lattice involving loss of spatial central symmetry of the medium.     

Spin dynamics in LiCu<Subscript>2</Subscript>O<Subscript>2</Subscript> and NaCu<Subscript>2</Subscript>O<Subscript>2</Subscript> low-dimensional helical magnets

Comprehensive NMR investigation of low-frequency spin dynamics of LiCu₂O₂ (LCO) and NaCu₂O₂ (NCO) low-dimensional helical magnets in the paramagnetic state has been carried out for the first time. Temperature dependences of the spin–lattice relaxation rate and anisotropy on various LCO/NCO nuclei have been determined at various orientations of single crystals in an external magnetic field. The spatial asymmetry of spin fluctuations in LCO multiferroic has been discovered. The quantitative analysis of the anisotropy of spin–lattice relaxation in LCO/NCO has allowed estimating the contributions of individual neighboring Cu²⁺ ions to the transferred hyperfine field on Li⁺(Na⁺) ions.     

<Superscript>77</Superscript>Se Low-Temperature NMR in the Bi<Subscript>2</Subscript>Se<Subscript>3</Subscript> Single Crystalline Topological Insulator

⁷⁷Se nuclear magnetic resonance (NMR) measurements in the Bi₂Se₃ topological insulator single crystal were carried out at temperatures 15.8, 88, and 293 K. Bismuth selenide single crystalline plate was studied in the orientation when the crystallographic c-axis was parallel to the external magnetic field B₀. We observed two component NMR spectra at the three temperatures. It was shown that the NMR spectrum almost did not move with decreasing temperature and the density of charge carriers did not follow the thermal activation law.