Magnetic and calorimetric studies on rare-earth iron borates LnFe3(BO3)4 (Ln=Y, La–Nd, Sm–Ho)

Temperature- and Field-Induced Transformation of the Magnetic State in Co2.5Ge0.5BO5

A tetravalent-substituted cobalt ludwigite Co_2.5Ge_0.5BO₅ has been synthesized using the flux method. The compound undergoes two magnetic transitions: a long-range antiferromagnetic transition at T_N1 = 84 K and a metamagnetic one at T_N2 = 36 K. The sample-oriented magnetization measurements revealed a fully compensated magnetic moment along the a- and c-axes and an uncompensated one along the b-axis leading to high uniaxial anisotropy. A field-induced enhancement of the ferromagnetic correlations at T_N2 is observed in specific heat measurements. The DFT+GGA calculation predicts the spin configuration of (↑↓↓↑) as a ground state with a magnetic moment of 1.37 μ_B/f.u. The strong hybridization of Ge(4s, 4p) with O (2p) orbitals resulting from the high electronegativity of Ge⁴⁺ is assumed to cause an increase in the interlayer interaction, contributing to the long-range magnetic order. The effect of two super-superexchange pathways Co²⁺-O-B-O-Co²⁺ and Co²⁺-O-M4-O-Co²⁺ on the magnetic state is discussed.

Pressure–Temperature Phase Diagram of Multiferroic TbFe2.46Ga0.54(BO3)4

The pressure–temperature phase diagram of the multiferroic TbFe2.46Ga0.54(BO3)4 was studied for hydrostatic pressures up to 7 GPa and simultaneously with temperatures up to 400 K by the Raman spectroscopy technique. The structural phase transition from the R32 phase to the P3121 phase was determined by observing the condensation of soft modes and the appearance of new lines. An increase in pressure leads to an increase in the temperature of the structural phase transition. These phases are stable over the entire investigated temperature and pressure range. No other phases have been found.

Crystal structure, absolute configuration and characteristic temperatures of SmFe3(BO3)4 in the temperature range 11-400 K

The crystal structure of samarium iron borate was analyzed with regard to growth conditions and temperature. The inclusion of about 7% Bi atoms in the crystals grown using the Bi₂Mo₃O₁₂-based flux was discovered and there were no impurities in the crystals grown using the Li₂WO₄-based flux. No pronounced structural features associated with Bi inclusion were observed. The different absolute configurations of the samples grown using both fluxes were demonstrated. Below 80 K, a negative thermal expansion of the c unit-cell parameter was found. The structure of (Sm_0.93Bi_0.07)Fe₃(BO₃)₄ belongs to the trigonal space group R32 in the temperature range 90-400 K. A decrease in the (Sm,Bi)-O, Sm-B, Sm-Fe, Fe-O, Fe-B and Fe-Fe distances is observed with a lowering of the temperature, B1-O does not change, B2-O increases slightly and the B2O₃ triangles deviate from the ab plane. The strongest decrease in the equivalent isotropic atomic displacement parameters (U_eq) with decreasing temperature is observed for atoms Sm and O2, and the weakest is observed for B1. The O2 atoms have the highest U_eq values, the most elongated atomic displacement ellipsoids of all the atoms and the smallest number of allowed vibrational modes of all the O atoms. The largest number of allowed vibrational modes and the strongest interactions with neighbouring atoms is seen for the B atoms, and the opposite is seen for the Sm atoms. The quadrupole splitting Δ(T) of the paramagnetic Mössbauer spectra increases linearly with cooling. The Néel temperature [T_N = 31.93 (5) K] was determined from the temperature dependence of the hyperfine magnetic field B_hf(T), which has a non-Brillouin character. The easy-plane long-range magnetic ordering below T_N was confirmed.

X-ray Natural Circular Dichroism Imaging of Multiferroic Crystals

The polarizing spectroscopy techniques in visible range optics have been used since the beginning of the 20th century to study the anisotropy of crystals based on birefringence and optical activity phenomena. On the other hand, the phenomenon of X-ray optical activity has been demonstrated only relatively recently. It is a selective probe for the element-specific properties of individual atoms in non-centrosymmetric materials. We report the X-ray Natural Circular Dichroism (XNCD) imaging technique which enables spatially resolved mapping of X-ray optical activity in non-centrosymmetric materials. As an example, we present the results of combining micro-focusing X-ray optics with circularly polarized hard X-rays to make a map of enantiomorphous twinning in a multiferroic SmFe3(BO3)4 crystal. Our results demonstrate the utility and potential of polarization-contrast imaging with XNCD as a sensitive technique for multiferroic crystals where the local enantiomorphous properties are especially important. In perspective, this brings a novel high-performance method for the characterization of structural changes associated with phase transitions and identification of the size and spatial distribution of twin domains.

Structural features associated with multiferroic behavior in the RX3(BO3)4 system

The magnetoelectric effect in the RX₃(BO₃)₄ system (R  =  Ho, Eu, Sm, Nd, Gd; X  =  Fe, Al) varies significantly with the cation R despite very similar structural arrangements. Our structural studies reveal a symmetry reducing tilting of the BO₃ planes and of the FeO₆ polyhedra in the systems exhibiting low magnetic field induced electric polarization. Neutron scattering measurements reveal a lack of magnetic ordering indicating the primary importance of the atomic structure in the multiferroic behavior of this system.

Crystal structure and structural phase transition in bismuth-containing HoFe3(BO3)4 in the temperature range 11-500 K

An accurate single-crystal X-ray diffraction study of bismuth-containing HoFe₃(BO₃)₄ between 11 and 500 K has revealed structural phase transition at T_str = 365 K. The Bi atoms enter the composition from Bi₂Mo₃O₁₂-based flux during crystal growth and significantly affect T_str. The content of Bi was estimated by two independent methods, establishing the composition as (Ho_0.96Bi_0.04)Fe₃(BO₃)₄. In the low-temperature (LT) phase below T_str the (Ho_0.96Bi_0.04)Fe₃(BO₃)₄ crystal symmetry is trigonal, of space group P3₁21, whereas at high temperature (HT) above 365 K the symmetry increases to space group R32. There is a sharp jump of oxygen O1 (LT) and O2 (LT) atomic displacement parameters (ADP) at T_str. O1 and O2 ADP ellipsoids are the most elongated over 90-500 K. In space group R32 specific distances decrease steadily or do not change with decreasing temperature. In space group P3₁21 the distortion of the polyhedra Ho(Bi)O₆, Fe1O₆ and Fe2O₆, B2O₃ and B3O₃ increases with decreasing temperature, whereas the triangles B1O₃ remain almost equilateral. All BO₃ triangles deviate from the ab plane with decreasing temperature. Fe-Fe distances in Fe1 chains decrease, while distances in Fe2 chains increase with decreasing temperature. The Mössbauer study confirms that the FeO₆ octahedra undergo complex dynamic distortions. However, all observed distortions are rather small, and the general change in symmetry during the structural phase transition has very little influence on the local environment of iron in oxygen octahedra. The Mössbauer spectra do not distinguish two structurally different Fe1 and Fe2 positions in the LT phase. The characteristic temperatures of cation thermal vibrations were calculated using X-ray diffraction and Mössbauer data.

Crystallochemical Design of Huntite-Family Compounds

Huntite-family nominally-pure and activated/co-activated LnM3(BO3)4 (Ln = La–Lu, Y; M = Al, Fe, Cr, Ga, Sc) compounds and their-based solid solutions are promising materials for lasers, nonlinear optics, spintronics, and photonics, which are characterized by multifunctional properties depending on a composition and crystal structure. The purpose of the work is to establish stability regions for the rare-earth orthoborates in crystallochemical coordinates (sizes of Ln and M ions) based on their real compositions and space symmetry depending on thermodynamic, kinetic, and crystallochemical factors. The use of diffraction structural techniques to study single crystals with a detailed analysis of diffraction patterns, refinement of crystallographic site occupancies (real composition), and determination of structure–composition correlations is the most efficient and effective option to achieve the purpose. This approach is applied and shown primarily for the rare-earth scandium borates having interesting structural features compared with the other orthoborates. Visualization of structures allowed to establish features of formation of phases with different compositions, to classify and systematize huntite-family compounds using crystallochemical concepts (structure and superstructure, ordering and disordering, isostructural and isotype compounds) and phenomena (isomorphism, morphotropism, polymorphism, polytypism). Particular attention is paid to methods and conditions for crystal growth, affecting a crystal real composition and symmetry. A critical analysis of literature data made it possible to formulate unsolved problems in materials science of rare-earth orthoborates, mainly scandium borates, which are distinguished by an ability to form internal and substitutional (Ln and Sc atoms), unlimited and limited solid solutions depending on the geometric factor.

Crystal structure, phase transition and structural deformations in iron borate (Y0.95Bi0.05)Fe3(BO3)4 in the temperature range 90-500 K

An accurate X-ray diffraction study of (Y_0.95Bi_0.05)Fe₃(BO₃)₄ single crystals in the temperature range 90-500 K was performed on a laboratory diffractometer and used synchrotron radiation. It was established that the crystal undergoes a diffuse structural phase transition in the temperature range 350-380 K. The complexity of localization of such a transition over temperature was overcome by means of special analysis of systematic extinction reflections by symmetry. The transition temperature can be considered to be T_str ≃ 370 K. The crystal has a trigonal structure in the space group P3₁21 at temperatures of 90-370 K, and it has a trigonal structure in the space group R32 at 375-500 K. There is one type of chain formed by the FeO₆ octahedra along the c axis in the R32 phase. When going into the P3₁21 phase, two types of nonequivalent chains arise, in which Fe atoms are separated from the Y atoms by a different distance. Upon lowering the temperature from 500 to 90 K, a distortion of the Y(Bi)O₆, FeO₆, B(2,3)O₃ coordination polyhedra is observed. The distances between atoms in helical Fe chains and Fe-O-Fe angles change non-uniformly. A sharp jump in the equivalent isotropic displacement parameters of O1 and O2 atoms within the Fe-Fe chains and fluctuations of the equivalent isotropic displacement parameters of B2 and B3 atoms were observed in the region of structural transition as well as noticeable elongation of O1, O2, B2, B3, Fe1, Fe2 atomic displacement ellipsoids. It was established that the helices of electron density formed by Fe, O1 and O2 atoms may be structural elements determining chirality, optical activity and multiferroicity of rare-earth iron borates. Compression and stretching of these helices account for the symmetry change and for the manifestation of a number of properties, whose geometry is controlled by an indirect exchange interaction between iron cations that compete with the thermal motion of atoms in the structure. Structural analysis detected these changes as variations of a number of structural characteristics in the c unit-cell direction, that is, the direction of the helices. Structural results for the local surrounding of the atoms in (Y_0.95Bi_0.05)Fe₃(BO₃)₄ were confirmed by EXAFS and Mössbauer spectroscopies.

Switching of Magnons by Electric and Magnetic Fields in Multiferroic Borates

Electric manipulation of magnetic properties is a key problem of materials research. To fulfill the requirements of modern electronics, these processes must be shifted to high frequencies. In multiferroic materials, this may be achieved by electric and magnetic control of their fundamental excitations. Here we identify magnetic vibrations in multiferroic iron borates that are simultaneously sensitive to external electric and magnetic fields. Nearly 100% modulation of the terahertz radiation in an external field is demonstrated for SmFe_{3}(BO_{3})_{4}. High sensitivity can be explained by a modification of the spin orientation that controls the excitation conditions in multiferroic borates. These experiments demonstrate the possibility to alter terahertz magnetic properties of materials independently by external electric and magnetic fields.

Optical spectroscopy of ErFe3(BO3)4: detection of phase transitions and crystal-field levels of the Er3+ ground multiplet

High-resolution spectra of oriented ErFe3(BO3)4 single crystals are registered in the spectral range 500 – 8000 cm-1 at various temperatures (4 – 470 K). The temperature behaviour of the phonon mode at 976 cm-1 allowed us to register a structural phase transition at TS=431 K. The energies of crystal-field levels of the ground 4I15/2 and the first excited 4I13/2 multiplets of the Er3+ ion are determined in the paramagnetic state of ErFe3(BO3)4. The exchange splitting of the ground Kramers doublet in the magnetically ordered state was found to be Δ0=6.3±1 cm-1. The interference occurring due to birefringence in the single crystals was also registered. The temperature dependence of the position of the maximum of the interference band demonstrates two anomalies, at TN and TS, associated with the phase transitions in ErFe3(BO3)4.

Transformation from an easy-plane to an easy-axis antiferromagnetic structure in the mixed rare-earth ferroborates Pr x Y1-x Fe3(BO3)4: magnetic properties and crystal field calculations

The magnetic structure of the mixed rare-earth system Pr x Y1-x Fe3(BO3)4 (x  =  0.75, 0.67, 0.55, 0.45, 0.25) was studied via magnetic and resonance measurements. These data evidence the successive spin reorientation from the easy-axis antiferromagnetic structure formed in PrFe3(BO3)4 to the easy-plane one of YFe3(BO3)4 associated with the weakening of the magnetic anisotropy of the Pr subsystem due to its diamagnetic dilution by nonmagnetic Y. This reorientation occurs through the formation of an inclined magnetic structure, as was confirmed by our previous neutron research in the range of x  =  0.67 ÷ 0.45. In the compounds with x  =  0.75 and 0.67 whose magnetic structure is close to the easy-axis one, a two-step spin reorientation takes place in the magnetic field H||c. Such a peculiarity is explained by the formation of an interjacent inclined magnetic structure with magnetic moments of Fe ions located closer to the basal plane than in the initial state, with these intermediate states remaining stable in some ranges of the magnetic field. An approach based on a crystal field model for the Pr(3+) ion and the molecular-field approximation is used to describe the magnetic characteristics of the system Pr x Y1-x Fe3(BO3)4. With the parameters of the d-d and f-d exchange interactions, of the magnetic anisotropy of the iron subsystem and of the crystal field parameters of praseodymium thus determined, it is possible to achieve a good agreement between the experimental and calculated temperature and field dependences of the magnetization curves (up to 90 kOe) and magnetic susceptibilities (2-300 K).

Observation of quadrupole helix chirality and its domain structure in DyFe3(BO3)4

Resonant X-ray diffraction (RXD) uses X-rays in the vicinity of a specific atomic absorption edge and is a powerful technique for studying symmetry breaking by motifs of various multipole moments, such as electric monopoles (charge), magnetic dipoles (spin) and electric quadrupoles (orbital). Using circularly polarized X-rays, this technique has been developed to verify symmetry breaking effects arising from chirality, the asymmetry of an object upon its mirroring. Chirality plays a crucial role in the emergence of functionalities such as optical rotatory power and multiferroicity. Here we apply spatially resolved RXD to reveal the helix chirality of Dy 4f electric quadrupole orientations and its domain structure in DyFe3(BO3)4, which shows a reversible phase transition into an enantiomorphic space-group pair. The present study provides evidence for a helix chiral motif of quadrupole moments developed in crystallographic helix chirality.

Effect of chemical bond parmeters on hardness, isomer shift, and dielectric constant of rare earth ferroborates

The ionicity, average band gaps, and bond polarization of the rare earth iron ferroborates were calculated using the chemical bond dielectric theory of complex structural crystals. The environment factor defined by electron polarizabilities and covalency was employed to calculate Mössbauer isomer shift of the rare earth iron ferroborates. The calculated isomer shifts of EuFe3(BO3)4 and GdFe3(BO3)4 are in agreement with their experimental values. The hardnesses of rare earth iron ferroborates were predicted using Gao's model, which are also in agreement with the experimental values.

Determination of the magnetic structure of SmFe3(BO3)4 by neutron diffraction: comparison with other RFe3(BO3)4 iron borates

Temperature dependent neutron diffraction studies were performed on SmFe(3)(BO(3))(4). The crystallographic structure was determined to stay as R32 over the whole studied temperature range of 2 K < T < 300 K. A magnetic phase transition characterized by the magnetic propagation vector κ = [0 0 3/2] takes place at T(N) = 34 K. The magnetic structure sees an easy-plane arrangement within the trigonal basal a-b-plane of ferromagnetic layers of iron and samarium having a canting angle of about 70° relative to each other. Neighbouring layers in the c-direction are antiferromagnetically coupled; at 2 K the magnetic moment values amount to μ(Fe ) = 4.2(1) μ(B ) and μ(Sm) = 0.8(2) μ(B). The non-Brillouin type increase of the iron magnetic moment below T(N) points to a strong Fe-Sm exchange and to the simultaneous appearance of long range magnetic order on both sublattices.

Phase transitions and crystal-field and exchange interactions in TbFe3(BO3)4 as seen via optical spectroscopy

High-resolution polarized broadband (1800-23 000 cm(-1)) optical absorption spectra of Tb(3+) in TbFe(3)(BO(3))(4) single crystals are studied between room temperature and 4.2 K. The spectral signatures of the structural (R32-P3(1)21, T(S ) = 192 K) and magnetic (T(N ) = 41 K) phase transitions are found and analyzed. Energies and symmetries of the Tb(3+) crystal-field (CF) levels were determined for both the high-temperature R32 and the low-temperature P3(1)21 structures of TbFe(3)(BO(3))(4) and compared with the calculated ones. It follows unambiguously from the spectral data that the ground state is the Γ(1) + Γ(2) quasi-doublet of the local D(3) point symmetry group for Tb(3+) in the R32 high-temperature structure. The CF calculations revealed the CF parameters and wavefunctions for Tb(3+) in TbFe(3)(BO(3))(4). The value of the Tb-Fe exchange integral and of the effective magnetic field created by the ordered Fe subsystem were estimated as J(fd) = 0.26 K and B(eff) = 3.92 T, using the observed splitting Δ = 32 cm(-1) of the Tb(3+) ground quasi-doublet at the temperature 5 K. The reliability of the obtained parameters was proven by modeling the literature data on the magnetic susceptibility of TbFe(3)(BO(3))(4). Lattice distortions below T(S) were evidenced by the observed changes of probabilities of the forced electric dipole transitions of Tb(3+).

Magnetic structure in iron borates RFe(3)(BO(3))(4) (R = Er, Pr): a neutron diffraction and magnetization study

Neutron diffraction, susceptibility and magnetization measurements (for R = Er only) were performed on iron borates RFe(3)(BO(3))(4) (R = Pr, Er) to investigate details of the crystallographic structure, the low temperature magnetic structures and transitions and to study the role of the rare earth anisotropy. PrFe(3)(BO(3))(4), which crystallizes in the spacegroup R32, becomes antiferromagnetic at T(N) = 32 K, with τ = [0 0 3/2], while ErFe(3)(BO(3))(4), which keeps the P3(1)21 symmetry over the whole studied temperature range 1.5 K < T < 520 K, becomes antiferromagnetic below T(N) = 40 K, with τ = [0 0 1/2]. Both magnetic propagation vectors lead to a doubling of the crystallographic unit cell in the c-direction. Due to the strong polarization of the Fe-sublattice, the magnetic ordering of the rare earth sublattices appears simultaneously at T(N). The moment directions are determined by the rare earth anisotropy: easy-axis along c for PrFe(3)(BO(3))(4) and easy-plane a-b for ErFe(3)(BO(3))(4). There are no spin reorientations present in either of the two compounds but there is the appearance below 10 K of a minority phase in the Er-compound adopting a 120° arrangement of the Er-moments.

Magnetic and specific heat properties of YFe3(BO3)4 and ErFe3(BO3)4

The present paper reports on the specific heat and magnetization of the YFe(3)(BO(3))(4) and ErFe(3)(BO(3))(4) single crystals. In both compounds, antiferromagnetic order of the iron spins evolves at T(N) = 38 K. The experimental data suggest that the magnetic moments are in the basal plane of the trigonal crystal for both compounds. In the magnetically ordered state the crystal is subdivided into three types of domains, the magnetic moments of the Fe(3+) ions being aligned along the a axis within each domain. For ErFe(3)(BO(3))(4), two non-equivalent magnetic positions of the Er(3+) ions in each domain are observed.

Low-temperature magnetic phase diagram of HoFe(3)(BO(3))(4) holmium ferroborate: a magnetic and heat capacity study

We present the results of the magnetic and heat capacity study of a magnetic phase diagram of a HoFe(3)(BO(3))(4) single crystal. Two magnetic phase transitions are found in the low-temperature region. The transition from the paramagnetic to easy-plane antiferromagnetic state occurs at T(N) = 37.4 K and is independent of an applied magnetic field. The sharp heat capacity peaks and magnetization jumps corresponding to the spontaneous and field-induced spin-reorientation transitions between the easy-axis and easy-plane states are observed below 4.7 K. Also, the additional heat capacity peaks, which can be attributed to the Schottky anomalies with the field-dependent characteristic temperatures, are found. According to the magnetic and thermal measurement data, the magnetic phase diagrams of HoFe(3)(BO(3))(4) for the magnetic field parallel and perpendicular to the crystal axis are constructed.

Breaking of the selection rules for optical transitions in the dielectric PrFe3(BO3)4 crystal by a praseodymium-iron exchange interaction

We report on the emergence of new lines in the optical spectrum of the PrFe3(BO3)4 single crystal at the magnetic ordering temperature. The transitions between singlet crystal-field sublevels of Pr3+ ion with the same transformational properties, strictly forbidden for the trigonal D3 point symmetry of this ion in PrFe3(BO3)4, appear below the Néel temperature and grow in intensity as a square of the order parameter. We show that the phenomenon originates from the mixing of wave functions of different Pr3+ sublevels by the Pr-Fe exchange interaction.