Magnetoelectric effect in ytterbium aluminum borate YbAl<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript>

The anisotropic magnetoelectric properties of an ytterbium aluminum borate YbAl (BO single crystal having noncentrosymmetric crystal structure (space group R32) are studied, including the orientational, field, and temperature dependences of the polarization in magnetic fields up to 5 T in the temperature range of 2–300 K. It has been shown experimentally for the first time that the symmetry of the observed magnetoelectric effects exactly corresponds to the trigonal structure of the crystal and is characterized by two quadratic magnetoelectric constants. The polarization in the basal plane P _{a, b} is a quadratic function of the field at low fields and reaches 250–300 μC/m² in a field of 5 T at a temperature of 2 K, almost an order of magnitude exceeding the previously reported values. A theoretical model based on the spin Hamiltonian of the ground Kramers doublet of Yb³⁺ ions in the crystal field is proposed including magnetoelectric interactions allowed by the symmetry. This model makes it possible to quantitatively describe all observed magnetic and magnetoelectric properties of YbAl₃(BO₃)₄.     

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.     

Effect of Gd-Mn exchange on phase transitions in GdMn<Subscript>2</Subscript>O<Subscript>5</Subscript> induced by a strong magnetic field

Complex studies of the magnetic, magnetoelectric, and magnetoelastic properties of GdMn₂O₅ single crystals in strong pulsed magnetic fields are carried out in order to obtain additional indirect information on the character of the rare-earth and manganese spin ordering. It is shown that magnetic ordering of Gd³⁺ spins affects the manganese sublattice spin orientation and initiates new magnetic phase transitions. The observed magnetoelectric properties of the GdMn₂O₅ system are interpreted in terms of the theory of phase transitions.     

The magnetoelectric effects in weak ferromagnetic YMn<Subscript>2</Subscript>O<Subscript>5</Subscript> modulated structure: a Landau theory approach

According to the group theory approach, linear magnetoelectric effect (ME) can not be obtained for the spatial group of YMn₂O₅, which was known to be mmm. Regard to the magnetic structure of these type of materials, we propose a magnetic group structure for the YMn₂O₅ by considering spin orientation of the Mn³⁺ and Mn⁴⁺ ions. According to the landau theory of phase transition it can be shown, how symmetrical rules result in relationship between quantities such as magnetic order, polarization, and etc. This relation shows a weak ferromagnetic state, associated with spontaneous polarization, arisen by Dzyaloshinskii-Moriya type interaction and a field induced change in magnetoelectrical susceptibility.     

<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.     

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.     

Magnetoelectric effects in gadolinium iron borate GdFe<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript>

Magnetoelectric interactions have been investigated in a single crystal of gadolinium iron borate GdFe₃(BO₃)₄, whose macroscopic symmetry is characterized by the crystal class 32. Using the results of this study, the interplay of magnetic and electric orderings occurring in the system has been experimentally revealed and theoretically substantiated. The electric polarization and magnetostriction of this material that arise in spin-reorientation transitions induced by a magnetic field have been investigated experimentally. For H ‖ c and H ⊥ c, H-T phase diagrams have been constructed, and a strict correlation between the changes in the magnetoelectric and magnetoelastic properties in the observed phase transitions has been ascertained. A mechanism of specific noncollinear antiferroelectric ordering at the structural phase transition point was proposed to interpret the magnetoelectric behavior of the system within the framework of the symmetry approach in the entire temperature range. This ordering provides the conservation of the crystal class of the system when the temperature decreases to the antiferroelectric ordering point. The expressions that have been obtained for the magnetoelectric and magnetoelastic energy describe reasonably well the behavior of gadolinium iron borate observed experimentally.     

High-frequency properties of KNiPO<Subscript>4</Subscript> in alternating magnetic and electric fields

The dependences of the antiferromagnetic resonance frequencies on the constant magnetic field H and constant electric field E are calculated for a KNiPO₄ crystal with spontaneous electric polarization and antiferromagnetic order. It is demonstrated that the KNiPO₄ crystal is characterized by an exchange-enhanced effect of the electric field E on the antiferromagnetic resonance frequencies. This effect is not revealed in the magnetoelectric materials studied earlier. It is established that oscillations of both magnetization and electric polarization exhibit resonance response at antiferromagnetic resonance frequencies. The expressions for these responses in alternating magnetic and electric fields are presented.     

Specificity of magnetoelectric effects in a new GdMnO<Subscript>3</Subscript> magnetic ferroelectric

A complex study of the magnetic, electric, magnetoelectric, and magnetoelastic properties of GdMnO₃ single crystals has been performed in the low-temperature region in strong pulsed magnetic fields up to 200 kOe. An anomaly of the dielectric constant along the a axis of a crystal has been found at 20 K, where a transition from an incommensurate modulated phase to a canted antiferromagnetic phase, as well as electric polarization along the a and b axes of the crystal induced by the magnetic field H‖ b (H_cr ～ 40 kOe), is observed. Upon cooling the crystal in an electric field, the magnetic-field-induced electric polarization changes its sign depending on the sign of the electric field. The occurrence of the electric polarization is accompanied by anisotropic magnetostriction, which points to a correlation between the magnetoelectric and magnetoelastic properties. Based on these results, it has been stated that GdMnO₃ belongs to a new family of magnetoelectric materials with the perovskite structure.     

Peculiarities in the magnetic,magnetoelectric, and magnetoelastic properties of SmFe<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript> multiferroic

Results of a complex investigation of the magnetic, magnetoelectric, and magnetoelastic properties of a SmFe₃(BO₃)₄ single crystal are presented. Samarium iron borate is similar to another easy-plane iron borate, NdFe₃(BO₃)₄, in that it possesses a large value of the magnetic-field-induced polarization (about 500 μC/m²), the sign of which changes when the field direction is changed between axes a and b of the crystal. However, the temperature dependence of the magnetic susceptibility and the field dependence of polarization and magnetostriction of the two compounds are significantly different, which is explained by the weak effect of external magnetic field on the ground-state multiplet of samarium ion, which is characterized by an extremely small value of its g-factor.     

Magnetic and ferroelectric ordering in BiMn<Subscript>2</Subscript>O<Subscript>5</Subscript> oxide

A group-theoretical analysis of the magnetic phase of BiMn₂O₅ oxide is performed using the space symmetry group of the compound. Using the projection operator method, we determine the basis functions of the irreducible representation of the space group, which are expressed in terms of the magnetic vector components. This representation can govern two phase transitions from the paramagnetic state to the antiferromagnetic phase with close temperatures and ordering of the spins of manganese ions in two crystallographic positions. It is found from renorm group analysis of these transitions that when these transitions occur as second- order transitions, the electric polarization does not appear in the system because spin fluctuations in this case elevate the symmetry of the system. Polarization appears when at least one of these transitions becomes a first-order transition as a result of spin fluctuations.     

Magnetic and structural phase transitions in YMn<Subscript>2</Subscript>O<Subscript>5</Subscript> ferromagnetoelectric crystals induced by a strong magnetic field

Magnetic, magnetoelectric, and magnetoelastic properties of YMn₂O₅ ferromagnetoelectric single-crystals are investigated in strong pulsed magnetic fields of up to 250 kOe and in static magnetic fields of up to 12 kOe. It is found that, in YMn₂O₅ at T < T_N=42 K, a transverse weakly ferromagnetic moment of σ ₀=0.8 G cm³/g exists that is oriented along axis a and is attributed to the magnetoelectric interaction. When a magnetic field is directed along axis b, which is likely to be the axis of antiferromagnetism, a spin-flop transition is observed that is accompanied by jumps in magnetostriction and electric polarization. When a magnetic field is directed along axis a, the temperature of ferroelectric transition shifts from 20 to 25 K at H≈200 kOe. A theoretical analysis of the experimental results is given within phenomenological theory with regard to the fact that a YMn₂O₅ compound belongs to noncollinear antiferromagnetic crystals even in the exchange approximation.     

Peculiarities of magnetic phase separation in anion-deficient La<Subscript>0.70</Subscript>Sr<Subscript>0.30</Subscript>MnO<Subscript>2.85</Subscript> manganite

The temperature and field dependences of the specific magnetic moment of the anion-deficient La_0.70Sr_0.30MnO_2.85 manganite have been measured. It is established, that the magnetic state of the sample studied is a cluster spin glass and it is the result of frustration of exchange Mn³⁺-O-Mn³⁺ interactions due to the redistribution of oxygen vacancies. The increase of the magnetic field leads to an increase in the degree of polarization of local spins of manganese. It is established using the magnetic criterion that a phase transition into the paramagnetic state for the anion-deficient La_0.70Sr_0.30MnO_2.85 manganite is a thermodynamic second order phase transition. The causes and mechanism of the magnetic phase separation are discussed.     

Electronic structure of paramagnetic In<Subscript>1-x</Subscript>Mn<Subscript>x</Subscript> As nanowires

The electronic structure, spin splitting energies, and g factors of paramagnetic In_1-xMn_xAs nanowires under magnetic and electric fields are investigated theoretically including the sp-d exchange interaction between the carriers and the magnetic ion. We find that the effective g factor changes dramatically with the magnetic field. The spin splitting due to the sp-d exchange interaction counteracts the Zeeman spin splitting. The effective g factor can be tuned to zero by the external magnetic field. There is also spin splitting under an electric field due to the Rashba spin-orbit coupling which is a relativistic effect. The spin-degenerated bands split at nonzero k_z (k_z is the wave vector in the wire direction), and the spin-splitting bands cross at k_z = 0, whose k_z-positive part and negative part are symmetrical. A proper magnetic field makes the k_z-positive part and negative part of the bands asymmetrical, and the bands cross at nonzero k_z. In the absence of magnetic field, the electron Rashba coefficient increases almost linearly with the electric field, while the hole Rashba coefficient increases at first and then decreases as the electric field increases. The hole Rashba coefficient can be tuned to zero by the electric field.     

Quadratic magnetoelectric effect and the role of the magnetocaloric effect in the magnetoelectric properties of multiferroic BaMnF<Subscript>4</Subscript>

The magnetoelectric effects in BaMnF₄ in magnetic fields up to 250 kOe are experimentally studied and theoretically analyzed using the magnetic symmetry of the crystal. The presence of quadratic magnetoelectric effect tensor components that correspond to the electric polarization components along the b and c axes indicates triclinic distortions in the monoclinic symmetry of the crystal. The anomalous dependence of the magnetic field-induced polarization (P _a (H _b )) can be related to the pyroelectric effect caused by magnetocaloric heating of the crystal. The measured torque curves point to a 9° deviation of the spin orientation from the b axis.     

Magnetic state of the structural separated anion-deficient La<Subscript>0.70</Subscript>Sr<Subscript>0.30</Subscript>MnO<Subscript>2.85</Subscript> manganite

The results of neutron diffraction studies of the La_0.70Sr_0.30MnO_2.85 compound and its behavior in an external magnetic field are stated. It is established that in the 4–300 K temperature range, two structural perovskite phases coexist in the sample, which differ in symmetry (groups R[`3]cR\bar 3c and I4/mcm). The reason for the phase separation is the clustering of oxygen vacancies. The temperature (4–300 K) and field (0–140 kOe) dependences of the specific magnetic moment are measured. It is found that in zero external field, the magnetic state of La_0.70Sr_0.30MnO_2.85 is a cluster spin glass, which is the result of frustration of Mn³⁺-O-Mn³⁺ exchange interactions. An increase in external magnetic field up to 10 kOe leads to fragmentation of ferromagnetic clusters and then to an increase in the degree of polarization of local spins of manganese and the emergence of long-range ferromagnetic order. With increasing magnetic field up to 140 kOe, the magnetic ordering temperature reaches 160 K. The causes of the structural and magnetic phase separation of this composition and formation mechanism of its spin-glass magnetic state are analyzed.     

Electronic structure,lattice dynamics,and magnetoelectric properties of double perovskite La<Subscript>2</Subscript>CuTiO<Subscript>6</Subscript>

The results of ab initio calculations of the electronic structure, vibrational properties, and the magnetoelectric effect in the La₂CuTiO₆ crystal with double perovskite structure are presented. The lattice dynamics calculation shows the presence of unstable modes in the phonon spectrum of the high-symmetry cubic phase with space group \(Fm\overline 3 m\). Condensation of two most unstable modes belonging to the center and the boundary point X of the Brillouin zone leads to the formation of a nonpolar stable phase with space group P2₁/n. The calculation taking into account spin polarization shows that the magnetic ground state is E*-type antiferromagnetic with doubled magnetic cell and with the two spin-up and two spin-down configuration of magnetic moments of copper ions along the [010] crystallographic direction. Such ordering of magnetic moments leads to polar space group and polarization formation. The polarization magnitude is estimated as 71 μC/m².     

Magnetic and magnetoelectric properties of the Tb<Subscript>0.75</Subscript>Ho<Subscript>0.25</Subscript>Fe<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript> ferroborate

Single crystals of the Tb_0.75Ho_0.25Fe₃(BO₃)₄ ferroborate have been grown by the group method from a solution–melt based on bismuth trimolybdate. The magnetic and magnetoelectric properties of the ferroborate single crystals have been investigated in the temperature range from 4.2 to 300 K and in magnetic fields up to 9 T. Magnetically, this material is an antiferromagnet with the Néel temperature T _N = 38.8 K and easy-axis anisotropy. The magnitude of the magnetoelectric polarization has been found to be more than 1.5–2.0 times greater than the sum of the polarizations induced by the magnetic field for the ferroborates TbFe₃(BO₃)₄ and HoFe₃(BO₃)₄ taken in the corresponding shares.     

Excitons at the center of the Brillouin zone in CuB<Subscript>2</Subscript>O<Subscript>4</Subscript> magnetoelectric

The possibility of exciton excitation in CuB₂O₄ magnetoelectric at point Γ(0, 0, 0) of the Brillouin zone has been analyzed using group theory. All possible orientations of the electric and magnetic fields that permit the excitation of these excitons have been determined.     

Elastic,magnetic, and magnetoelectric properties of the CaBaCo<Subscript>4</Subscript>O<Subscript>7</Subscript> multiferroic

The structural, elastic, magnetic, and magnetoelectric properties of the CaBaCo₄O₇ multiferroic are experimentally studied and compared with the properties of the related YBaCo₄O₇ cobaltite, where Y³⁺ ions substitute for Ca²⁺ ions. Unlike the frustrated YBaCo₄O₇ magnet, the softening of Young’s modulus and the hysteresis in the ΔE(T)/E ₀ curve of ferrimagnetic CaBaCo₄O₇ in the paramagnetic region are weak, and the anomaly during the magnetic transition increases by almost an order of magnitude. This difference can point to different characters of the development of a long-range magnetic order in these two cobaltites. The distortion of the crystal structure that removes the frustrations of exchange interactions is found to correlate with the magnetic behavior of the cobaltites under study. The magnetization curves of the Ca cobaltite have two steps below 15 K, which can point to the presence of a metastable state in a high magnetic field. The study of the longitudinal and transverse magnetoelectric effects in a pulsed magnetic field demonstrates that their magnitudes are maximal near T _C and change their character from linear to quadratic during passage through this temperature.