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The work summarizes the literature data on the use of pesticides in agriculture, as well as the damage they cause to the environment and human health. The possibilities and prospects for the development of complex biocompatible plant protection products based on some natural nitrogen compounds to solve agricultural problems and reduce damage from the use of pesticides are analyzed.

The magnetic, magnetoelectric, and magnetoelastic properties of RFe3(BO3)4 ferroborates are studied. The measurement of the field dependences of the magnetoelectric polarization along the a axis in holmium ferroborate and in the mixed composition Ho0.5Sm0.5Fe3(BO3)4 revealed the following dependences for easy-plane ferroborates: (a) the longitudinal and transverse magnetoelectric effects have the opposite signs and (b) magnetically induced polarization changes its sign in a field close to the field of exchange between rare-earth and iron ions. These dependences agree well with theoretical predictions based on the symmetry of the compounds. The relatively low f-d exchange field in holmium ferroborate (about 20 kOe), which magnetizes the rare-earth subsystem, causes smaller polarization jumps (about 30 μC/m2) in fields lower than 10 kOe as compared to the jumps in other easy-plane ferroborates (R = Sm, Nd). The increase in the electric polarization induced in HoFe3(BO3)4 in magnetic fields higher than 100 kOe (200–300 μC/m2) is found to be significantly smaller than in neodymium ferroborate, which indicates a substantial dependence of the magnetoelectric effects on the electronic structure of a rare-earth ion.

Resonance modes that are due to magnetic excitations in the exchange-coupled subsystems of rare-earth ions (R = Nd3+, Sm3+, and Gd3+) and Fe3+ ions have been detected in submillimeter transmission spectra (0.1–0.6 THz) of RFe3(BO3)4 iron borate-multiferroic single crystals. The strong interaction between spin oscillations of the Fe and R subsystems has been revealed, which determines the behavior of the modes depending on the anisotropy of the exchange splitting of the ground doublet of the R ion. It has been shown that the intensities of coupled modes (contributions to the magnetic permeability) depend strongly on the difference between the g factors of Fe and R ions. This dependence makes it possible to determine the sign of the latter g factor. In particular, a noticeable intensity of exchange Nd modes in NdFe3(BO3)4 is due to an increase in their contribution at g ⊥, ‖ Nd < 0, while in GdFe3(BO3)4 with g Gd ≈ g Fe ≈ 2, the Fe and Gd contributions compensate each other and the exchange (Gd) mode is not observed. In spite of the weak interaction of Sm ions with the magnetic field, SmFe3(BO3)4 exhibits resonance modes, which are attributed to the excitation of Sm ions through the Fe subsystem.

The magnetoresonance and dielectric properties of a number of crystals of a new family of multiferroics, namely, rare-earth ferroborates RFe3(BO3)4 (R = Y, Eu, Pr, Tb, Tb0.25Er0.75), are studied in the sub-millimeter frequency range (ν = 3–20 cm−1). Ferroborates with R = Y, Tb, and Eu exhibit permittivity jumps at temperatures of 375, 198, and 58 K, respectively, which are caused by the R32 → P3121 phase transition. Antiferromagnetic resonance (AFMR) modes in the subsystem of Fe3+ ions are detected in the range of anti-ferromagnetic ordering (T < TN = 30–40 K) in all ferroborates that have either an easy-plane (Y, Eu) or easy-axis (Pr, Tb, Tb0.25Er0.75) magnetic structure. The AFMR frequencies are found to depend strongly on the magnetic anisotropy of a rare-earth ion and its exchange interaction with the Fe subsystem, which determine the type of magnetic structure and the sign and magnitude of an effective anisotropy constant. The basic parameters of the magnetic interactions in these ferroborates are found, and the magnetoelectric contribution to AFMR is analyzed.

The colossal (more than threefold) decrease in the dielectric constant ɛ in the easy-plane SmFe3(BO3)4 ferroborate in a magnetic field of ∼5 kOe applied in the basal ab plane of the crystal has been found. A close relation of this effect to anomalies in the field dependence of the electric polarization has been established. It has been shown that this magnetodielectric effect is due to the contribution to ɛ from the electric susceptibility, which is related to the rotation of spins in the ab plane, arises in the region of the antiferromagnetic ordering T < TN = 33 K, and is suppressed by the magnetic field. A theoretical model describing the main features of the behavior of ɛ and electric polarization in the magnetic field has been proposed, taking into account the additional anisotropy in the basal plane induced by the magnetoelastic stresses.

The magnetic and magnetoelectric properties of terbium aluminum borate are studied. It is established that temperature dependences of the magnetoelectric effects of terbium aluminum borate are analogous to those of terbium ferroborate, despite the difference in effective magnetic fields acting on rare-earth ions in these compounds. This confirms the general assumption on the decisive role of the rare-earth element in the magnetoelectric properties of borates.

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.

The magnetic, electric, magnetoelectric, and magnetoelastic properties of rare-earth ferroborates RFe3(BO3)4 (R=Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er) as well as yttrium ferroborate YFe3(BO3)4 have been studied comprehensively. A strong dependence not only of the magnetic but also magnetoelectric properties on the type of rare-earth ion, specifically, on its anisotropy, which determines the magnetic structure and the large contribution to the electric polarization, has been found. This is manifested in the strong temperature dependence of the polarization below the Neel point TN and its specific field dependence, which is determined by the competition between the external and exchange f-d fields. A close correlation has been found between the magnetoelastic properties of ferroborates and the magnetoelastic and magnetic anomalies at magnetic-field induced phase transitions. It is found that in easy-plane ferroborates, together with magnetic-field induced electric polarization spontaneous polarization also ari...

Magnetic and magnetoelectric properties of ferroborate single crystals with complex composition (Tb1 − xErxFe3(BO3)4, x = 0, 0.75) and with competing exchange Tb-Fe and Er-Fe interactions are investigated. Jumps in electric polarization, magnetostriction, and magnetization are observed as a result of spin-flop transitions, as well as a considerable decrease in the critical field upon an increase in the Er concentration, in a field Hc parallel to the c axis. The observed behavior of phase-transition fields is analyzed and explained using a simple model taking into account anisotropy in g factors and exchange splitting of funda-mental doublets of the easy-axis Tb3+ ion and easy-plane Er3+ ion. It is established that magnetoelectric and magnetostriction anomalies under spin-flop transitions are mainly controlled by the Tb subsystem. The Tb subsystem makes a nonmonotonic contribution ΔPa(Ha, T) to polarization along the a axis: the value of ΔPa reverses its sign and increases with temperature due to the contribution from the excited states of the Tb3+ ion.

The magnetic, magnetoelectric, and magnetoelastic properties of DyFe3(BO3)4 single crystals and the Nd0.75Dy0.25Fe3(BO3)4 substituted compound with the competitive Nd-Fe and Dy-Fe exchange interactions have been investigated in magnetic fields up to 210 kOe. It has been shown that the antiferromagnetic state in Nd0.75Dy0.25Fe3(BO3)4 below the Neel temperature is easy-plane and a spontaneous spin-reorientation transition to a uniaxial state occurs near 25 K. Anomalies are observed in various physical characteristics in a spin-flop transition induced by the magnetic field along the trigonal axis. The H-T phase diagrams are constructed; they are in good agreement with a simple model taking into account the anisotropy of the exchange splitting and g factors of the ground doublets of the Dy3+ and Nd3+ ions. The features of the magnetoelectric effect in various magnetic phases have been studied. Spontaneous electric polarization has been revealed in the region of the existence of an easy-plane antiferromagnetic state in the substituted compound. A qualitative theoretical justification of the possibility of the appearance of the spontaneous spin-reorientation transition in the Nd0.75Dy0.25Fe3(BO3)4 substituted compound is given.

A change in electric polarization (up to 300 {mu}C/m{sup 2}) upon magnetic-field suppression of a charge-ordered antiferromagnetic state upon a transition to the ferromagnetic conducting phase (H{sub cr} {approx} 65-80 kOe at 4.2 K) is discovered in Pr{sub 0.6}Ca{sub 0.4}MnO{sub 3} and Nd{sub 0.6}Ca{sub 0.4}MnO{sub 3} single crystals. The transition is also accompanied by a jump in magnetization and magnetostriction. The dependence of the induced polarization sign on the polarity of the electric field in which the sample was preliminarily cooled indicates the existence of spontaneous electric polarization. The effect is the strongest in Nd{sub 0.6}Ca{sub 0.4}MnO{sub 3} and is weaker by a factor of 5-10 in Pr{sub 0.6}Ca{sub 0.4}MnO{sub 3}, for which the tolerance factor is higher. The observed effect may be associated with recently predicted noncentrosymmetric structures in doped manganites with x {approx} 0.5 (see D.V. Efremov, J. van den Brink, and D.I. Khomskii, Nature Materials 3, 853 (2004)), in which e{sub g} electrons are not localized upon charge and orbital ordering at one manganese ion, but are distributed among neighboring ions, thus forming an ordered polar dimer structure.

The magnetic, magnetoelectric, and magnetoelastic properties of a PrFe 3 (BO 3 ) 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 Fe 3+ spin reorientation to the basal plane takes place. The reorientation is accompanied by anomalies in magnetization, magnetostric- tion, 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 Pr 3+ 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.

Magnetic-field-induced phase transitions in single crystals of the rare-earth ferroborates GdFe3(BO3)4 and NdFe3(BO3)4 have been studied by measuring magnetoelectric dependences and torque curves. These phase transitions can serve as one of the possible mechanisms for magnetic control of electric polarization. Magnetic phase transitions in GdFe3(BO3)4 are analyzed theoretically.

For the DyMnO3 multiferroic with a modulated magnetic structure, switching of its spontaneous electric polarization (P ‖ c axis) near the ferroelectric transition (T < TFE ∼ 20 K) is revealed by measuring the dielectric hysteresis loops. It is found that the coercive field strongly increases as the temperature decreases (up to 2.6 kV/mm at 17.6 K). The values obtained for the spontaneous polarization are found to agree well with the data obtained from pyroelectric measurements. In addition, anomalies are observed in the temperature dependences of the spontaneous polarization Pc, dielectric constant ɛc, and magnetic susceptibility xb at T ∼ 6 K; these anomalies are attributed to the antiferromagnetic ordering of the Dy3+ ions.

Anomalous magnetic susceptibility χ has been observed in mono-and polycrystalline (ceramic) samples of lanthanum strontium manganites. The oscillations of χ observed for single crystal samples in the vicinity of the Curie temperature (and in the paramagnetic region) are explained by the existence of magnetic clusters. The appearance of susceptibility oscillations in ceramic samples is attributed to the formation of magnetic clusters, which may occur both in grains (at the interface between ferro-and antiferromagnetic phases) and at the grain boundaries.

Magnetic phase transitions in multiferroic bismuth ferrite (BiFeO3) induced by magnetic field, epitaxial strain, and composition modification are considered. These transitions from a spatially modulated spin spiral state to a homogenous antiferromagnetic one are accompanied by the release of latent magnetization and a linear magnetoelectric effect that makes BiFeO3-based materials efficient room-temperature single phase multiferroics., Comment: In this version Figure 7 is replaced to more informative one. The footnotes are added to reflect the up-to-date situation in the area

The family of multiferroics comprised of the orthorhombic manganates RMn2O5 (R=Eu,Gd,Er,Y), in which the coexistence of antiferromagnetism and ferroelectricity has been reported previously, is investigated at high magnetic fields. These compounds, unlike the members of the family RMnO3 (where R=Eu,Ge,Tb,Dy) have two subsystems of magnetic mixed-valence d ions Mn3+ and Mn4+, the direct and indirect interactions between which, being of the ferro- or antiferromagnetic type, depending on the particulars of the environment and properties of the rare-earth ions, enhance substantially the role of the frustrations observed in RMnO3 compounds. These systems, as a consequence of the specific combination of the additional magnetic degeneracy realized in them (due to competition between nearest- and next-nearest-neighbor interactions of nearly equal magnitude) and their strong magnetoelastic coupling, display a cascade of magnetic phase transitions, with the appearance/disappearance of incommensurate (modulated) magn...

Complex experimental and theoretical investigations of the magnetic, magnetoelectric, and magnetoelastic properties of neodymium iron borate NdFe3(BO3)4 along various crystallographic directions have been carried out in strong pulsed magnetic fields up to 230 kOe in a temperature range of 4.2–50 K. It has been found that neodymium iron borate, as well as gadolinium iron borate, is a multiferroic. It has a much larger (above 300 μC/m2) electric polarization controlled by the magnetic field and giant quadratic magnetoelectric effect. The exchange field between the rare-earth and iron subsystems (∼50 kOe) has been determined for the first time from experimental data. The theoretical analysis based on the magnetic symmetry and quantum properties of the Nd ion in the crystal provides an explanation of the unusual behavior of the magnetoelectric and magnetoelastic properties of neodymium iron borate in strong magnetic fields and correlation observed between them.

Various aspects of magnetic field control of magnetoelectric (ME) and electric properties of multiferroics are considered: linear ME effect appearance at magnetic field-induced incommensurate–commensurate phase transition, polarization switching and reversal by magnetic field and magnetic field-induced polarization flop transition. The correlation between magnetic, electric, and magnetoelastic properties is shown.

Multiferroic ground states with a spatially modulated antiferromagnetic structure and electric polarization have been revealed in Eu1−xYxMnO3 ( 0.2 ⩽ x ⩽ 0.5 ) single crystals. While the slightly substituted ( x ⩽ 0.1 ) compounds exhibited a transition from the incommensurate (IC) to the canted antiferromagnetic (CAF) state at T CA T N , the transitions from IC to commensurate ferroelectric (C/FE) phase were observed at T lock T N for x > 0.2 . Various phase transitions were observed in the magnetic fields up to 250 kOe along a, b, c axes by magnetization, magnetostriction and electric polarization measurements which show an existence of a spontaneous electric polarization below Tlock.

Our experimental and theoretical investigation was aimed at the study of different gadolinium ferroborate single-crystal properties both at spontaneous and high magnetic field-induced phase transitions.

A tendency to form multiferroic states with a spatially modulated antiferromagnetic structure and electric polarization in pure orthorhombic manganites RMnO 3 upon decreasing of the rare-earth ionic radii has been realized in single crystals of substituted compounds Eu 1x- Y x MnO 3 (0.2 ≤ x ≤ 0.5) and Gd 1-y Y y MnO 3 (0 < y ≤ 0.2). While the parent pure and slightly substituted (x ≤ 0,1) compounds exhibited a spontaneous transition from the incommensurate (IC) to the canted antiferromagnetic (CAF) state at T CA < T N = 45-50 K, the transitions from IC to commensurate ferroelectric (C/FE) phase were observed at T lock < T N for x ≥ 0.3 and y ≥ 0.05 accompanied by dielectric anomalies. Various phase transitions were observed in magnetic fields up to 250 kOe along the a-, b-, c-axes by magnetization, magnetostriction and electric polarization measurements. The latter indicate the existence of a spontaneous electric polarization below T lock .

In Gd1−x SrxMnO3 (x = 0.5, 0.6, 0.7) single crystals, a change in electric polarization (ΔP ∼ 100 μK/m2) is found to accompany the suppression of the charge-ordered spin-glass state and the transition to the ferromagnetic conducting phase (H cr ∼ 100 kOe at 4.5 K). The transition is also characterized by jumps in magnetization and magnetostriction. The sign of the induced polarization depends on the polarity of the electric field in which the sample was preliminarily cooled. This dependence testifies to the presence of spontaneous electric polarization in the system. The effect is maximal at x = 0.5 and decreases by more than an order of magnitude as x increases to 0.7. The phenomenon observed in the experiment may be associated with the new noncentrosymmetric structures with an electric dipole moment that were recently predicted for manganites (x ∼ 0.5) [Nature Materials 3, 853 (2004)]. These structures exhibit charge-orbital ordering such that e g electrons are not localized by one of the manganese ions but distributed between neighboring ions, thus forming an ordered dimer structure.

The transformation of various properties of gadolinium ferroborate single crystals at phase transitions, both spontaneous and induced by magnetic fields up to 200 kOe, is investigated theoretically and experimentally. Particular attention is paid to elucidating the role of magnetoelectric interactions and the change in them at spin-reorientation transitions accompanied by a change of magnetic symmetry. With that goal the magnetoelastic and magnetoelectric properties of the system are investigated over a wide range of temperatures for two orientations of the magnetic field, H∥c and H⊥c, and a fundamental difference of the character of the field dependences of the magnetostriction and electric polarization is found. In the framework of a symmetry approach a description of the magnetic structures and their transformations in the system GdFe3(BO3)4 is proposed, and an interpretation of the experimentally observed properties is given.

It is found that the spin-flop transition in EuMnO3 manganite induced by a magnetic field H parallel to the b axis is accompanied not only by a magnetization jump and magnetostriction anomalies but also by the appearance of electric polarization in the vicinity of the transition field Hcr ∼ 200 kOe. This phenomenon can be associated with the occurrence of magnetically inhomogeneous (modulated) states in the vicinity of Hcr. In these states, the system loses the center of symmetry, which allows for the appearance of the polarization. The formation of such states in a magnetic field is caused by the general tendency of the occurrence of magnetically inhomogeneous (incommensurate) structures in the RMnO3 series due to the frustration of exchange interactions with decreasing ionic radius of the rare-earth ion R starting with R = Eu.

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.

The magnetic, magnetoelectric, and magnetoelastic properties of ErMn2O5 single crystals have been studied at low temperatures and strong magnetic fields (up to 250 kOe) and compared to the analogous results obtained previously for YMn2O5. Based on these data, the possible mechanisms of various spontaneous and magnetic-field-induced phase transitions in these compounds are considered within the framework of the theory of representations of the Pbam-D 2 9 space group. It is shown that a biquadratic exchange plays an important role in the formation (and mutual transformation) of magnetic structures revealed by neutron diffraction in the RMn2O5 oxide family.

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 (Hcr ∼ 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.

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.

This paper reports on the results of investigations into the magnetic and magnetoelastic properties of Nd0.5Sr0.5MnO3 single crystals in pulsed magnetic fields up to 250 kOe, the magnetic and kinetic properties of these crystals in weak static magnetic fields, and their thermal expansion. It is demonstrated that the studied properties exhibit a number of anomalies due to a transition from the antiferromagnetic semiconducting state to the ferromagnetic metallic state upon suppression of charge ordering.

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 < TN=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.

We have shown that in the chromium oxide the components of the tensor of magnetoelectric susceptibility f 33 ( T ) in the original phase and f 31 ( T ) in the spin-flop phase exhibit similar temperature dependencies. It's proved in the present paper that noted above behavior of these components can be explained in the framework of the phenomenological theory if one takes into account invariants of the third and fifth order of magnitude in the components of the antiferromagnetic vector in the phenomenological thermodynamic potential with explicitly separated exchange and relativistic terms. Also, the form of thermodynamic potentials elaborated in this paper suggests that the transition to the spin-flop phase in the chromium oxide is incomplete and f 33 cannot be equal to zero in the spin-flop phase.

The electric polarization of single crystal YMn 2 O 5 was investigated in strong pulsed magnetic fields up to H = 250 kOe at low temperatures. It was shown that at T ∼ 40 K magnetic and structural phase transitions occur, with the structural changes taking place improperly (magnetically induced). We have also shown the existence of the structural phase transition at T ∼ 20 K with the onset of spontaneous polarization P b . The quadratic magnetoelectric effect at temperatures T < 40 K was observed (with b-component domination), the magnetoelectric susceptibility below T = 20 K greatly increased for all field orientations. When H A a the magnetoelectric effect changed its sign which in analogue with EuMn 2 O 5 was attributed to non-commensurate to commensurate structural change. The polarization anomalies in strong magnetic fields were observed with the former being due to complex magnetic structure changes and the process of spontaneous polarization induction by magnetic field.

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Recently discovered magnetoelectricity in the rare-earth aluminum borates RAl${}_{3}$(BO${}_{3}$)${}_{4}$ has attracted attention due to the large values of magnetoinduced electric polarization. We have observed for the first time the magnetoelectric polarization in TbAl${}_{3}$(BO${}_{3}$)${}_{4}$ exhibiting anomalous temperature dependence: an electric polarization induced by in-plane magnetic field ($P||a,H\ensuremath{\perp}c$ axis) which is small at low temperatures ($4\phantom{\rule{0.16em}{0ex}}\mathrm{K}$), remarkably increases by almost an order of magnitude at high temperatures ($150--300\phantom{\rule{0.28em}{0ex}}\mathrm{K}$). The observed nonmonotonic temperature behavior of the field-induced polarization, including a change of sign at $\ensuremath{\sim}65--70\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, is attributed to the competition of the ground and excited crystal-field states of Tb${}^{3+}$ ions. Quantum theory analysis, involving the combination of analytical and numerical methods, has enabled us to quantitatively describe the observed magnetic and magnetoelectric properties of TbAl${}_{3}$(BO${}_{3}$)${}_{4}$.

The magnetostriction of Pr0.6Ca0.4MnO3 and Pr0.65Ca0.28Sr0.07MnO3 manganite crystals is investigated in pulsed magnetic fields up to 250 kOe. The field-induced phase transitions from the charge-ordered antiferromagnetic (paramagnetic) state to the metallic ferromagnetic state are studied. It is found that these transitions are accompanied by abrupt negative jumps in the longitudinal and transverse magnetostrictions and a strong hysteresis at low temperatures. The threshold fields of transitions are determined, and the H-T phase diagrams are constructed.

A study is reported on phase transitions in the La1−x SrxMnO3 system, both spontaneous and induced by a pulsed magnetic field of up to 250 kOe, accompanied by anomalies in magnetoelastic properties. The temperatures of the polaron (charge) and magnetic ordering, as well as those of structural transitions, are observed to be in good agreement with the results obtained by other methods. Jumps in the field dependence of longitudinal and transverse magnetostriction associated with field-induced orbital ordering have been found. A strong temperature dependence of the corresponding threshold fields is observed.

Complex magnetic, magnetoelectric and magnetoelastic studies of spontaneous and field-induced phase transitions in TmMn 2 O 5 were carried out. In the vicinity of spontaneous phase transition temperatures (35 and 25 K) the magnetoelectric and magnetoelastic dependences demonstrated the jumps of polarization and magnetostriction induced by the field ∼150 kOe. These anomalies can be attributed to the influence of magnetic field on the conditions of incommensurate–commensurate phase transition at 35 K and the reverse one at 25 K. In b -axis dependences the magnetic field-induced spin-reorientation phase transition was also observed below 20 K. Finally the magnetoelectric anomaly associated with metamagnetic transition is observed below the temperature of rare-earth subsystem ordering at relatively small critical fields of 5 kOe. This variety of spontaneous and induced phase transitions in RMn 2 O 5 stems from the interplay of three magnetic subsystems: Mn 3+ , Mn 4+ , R 3+ . The comparison with YMn 2 O 5 highlights the role of rare earth in low-temperature region (metamagnetic and spin-reorientation phase transitions), while the phase transition at higher temperatures between incommensurate and commensurate phases should be ascribed to the different temperature dependences of Mn 3+ and Mn 4+ ions. The strong correlation of magnetoelastic and magnetoelectric properties observed in the whole class of RMn 2 O 5 highlights their multiferroic nature.

The appearance of a toroidal moment is observed in the magnetoelectric Cr2O3 in a strong magnetic field above the spin-flop transition field. This conclusion is based on the experimentally established fact that the off-diagonal components of the magnetoelectric susceptibility tensor of Cr2O3 contains an antisymmetric part that is dual to the toroidal moment. Therefore it has been shown that the magnetoelectric Cr2O3 in the spin-flop phase can be classified as a toroic.

Chaotic oscillations of the low-frequency magnetic susceptibility χ in a Nd0.5Sr0.5MnO3 (NSMO) manganite single crystal have been observed in the temperature interval of the coexistence of the ferro- and antiferromagnetic phases of the given composition. It is established that the amplitude of χ oscillations depends on the constant bias magnetic field. The appearance of susceptibility oscillations in NSMO single crystals is attributed to the formation of magnetic transition regions, which can exist at the boundaries between ferro- and antiferromagnetic phases.

Coexistence of an antiferromagnetic (modulated) structure and electric polarization has been revealed in single crystals of Eu1 − x YxMnO3 (0.2 ≤ x ≤ 0.5) and Gd1 − x YxMnO3 (0 ≤ x ≤ 0.2) manganites. Hence, these compounds can be considered as a new family of multiferroics. Various phase transitions, both spontaneous and induced by magnetic fields up to 250 kOe, accompanied by anomalies in magnetization, magnetostriction, permittivity, and electric polarization, have been found, and phase T-x diagrams have been constructed. In the submillimeter range (8–40 cm−1), new spin excitations—electromagnons—have been revealed; they are excited by an electric field. It is established that suppression of the modulated structure by a magnetic field leads to the disappearance of electromagnons; this process is accompanied by significant changes in the permittivity in a wide frequency range.

The magnetoelectric effect and phase transitions induced by a strong magnetic field (up to 200 kOe) in single crystals EuMn 2 O 5 have been investigated. It is known that these compounds have an incommensurate magnetic structure. The electric polarization of the single crystals were measured along the a -, b -, and c -axes of the crystals, and the magnetic field was oriented along the c -axis. At low magnetic fields ( H H cf of these jumps are of 100 kOe order and depend more on the temperature. There is in general, a large linear contribution of the electric polarization into the magnetic field dependence at H > H cf . This favors that the field induced `incommensurate-homogeneous' phase transition probably takes place at the critical field.

The field dependence of the magnetoelectric effect and longitudinal magnetostriction of Ga2−x FexO3 single crystals is studied in magnetic fields up to 200 kOe in the temperature range from 4.2 to 300 K. It is shown that the magnetoelectric effect in these materials is determined mainly by the toroidal moment T and is not related to magnetostriction, as was previously theorized. A new method for determining the toroidal moment by measuring the electric polarization in a strong magnetic field is proposed. The value of the toroidal moment of the unit cell in Ga1.15Fe0.85O3 is calculated: T=(T a ,0,0), where T a =24.155µ B A per unit cell. Experimental data are analyzed using a theory of toroidal spin ordering, which gives good agreement with experiment.

The magnetic and magnetoelastic properties of single crystals of electron-doped rare-earth manganites La1−x Sr x MnO3 are studied. Phase transitions from the A-type antiferromagnetic phase to the C-type anti-ferromagnetic phase in a strong magnetic field are revealed in La1−x Sr x MnO3 manganites with a strontium content x = 0.65. A similar phase transition is observed in manganites with a strontium content x = 0.8, at which the La0.2Sr0.8MnO3 manganite is assumed to transform from the C-type antiferromagnetic phase to the G-type antiferromagnetic phase.

The magnetoelectric effect in (Fe x Cr1-x )2O3 (x=0, 0.02, 0.05, 0.1) single crystals has been studied under a magnetic field of up to 200 kOe. We have found that various magnetic phase transitions due to the restructuring of the spatial spin structure and leading to radical changes in the magnetoelectric effect take place in substitutional alloys. We have also detected a spontaneous phase transition from a conical helix to a cycloidal spin structure taking place at x = 0.1 and a temperature of 45 K. The experimental data are in agreement with the theoretical concept based on the thermodynamic model and can be accounted for in terms of competition among exchange energies of different modes.

The field-dependencies of the ME-effect and longitudinal magnetostriction of single crystals GaxFe2-xO3 in magnetic fields up to 200 kOe have been studied. For analysis of the experimental data the representation about toroidal spin ordering has been used, which is in qualitative conformity with the experimental data.

Measurements of the magnetic and magnetoelastic properties of Nd0.5Ca0.5MnO3, Nd0.55Ca0.45MnO3, and Nd0.6Ca0.4MnO3 single crystals have revealed correlations between the observed anomalies in magnetization and magnetostriction associated with suppression of the antiferromagnetic phase and charge ordering by a strong magnetic field followed by transition to the ferromagnetic state. H-T phase diagrams are constructed.

By studying the magnetic and magnetoelastic properties, it is established that, as the temperature is lowered, Sm1−xSrxMnO3 single crystals (x=0.5, 0.55) undergo spontaneous phase transitions from the paramagnetic to a local charge-ordered state at Tco=220 K and to an A-type antiferromagnetic state at TN=175 K. It is shown that strong magnetic fields (Hcr ∼ 200 kOe) break up the antiferromagnetic order and charge ordering and drive a phase transition to a conducting ferromagnetic state. H-T phase diagrams are constructed for single crystals with x=0.5 and 0.55.