Quadratic Magnetoelectric Effect Research Articles

Microscopic origin of the spin-induced linear and quadratic magnetoelectric effects

Understanding of the intimate cross-coupling between electric and magnetic degrees of freedom in solids usually requires sophisticated models and time-consuming calculation methods. Instead of macroscopic symmetry analysis, we present a simple but general approach to explore the microscopic mechanism of magnetoelectric (ME) effects in magnetic ordered materials based on local spin and lattice symmetry analysis. Our methods are successfully applied to Cr$_2$O$_3$ and orthorhombic RMnO$_3$ with linear and quadratic ME effects, respectively. We revealed all the possible microscopic origins of every non-zero ME coefficients that cannot be easily fulfilled by other theoretical methods. Moreover, the contribution from each mechanism can be located down to specific spins or spin pairs. Our theoretical approach is capable of providing a detailed guide to explore rich spin-induced magnetoelectrics with strong ME effects.

Crystal structure of bismuth-containing NdFe3(BO3)4 in the temperature range 20-500 K.

Neodymium iron borate NdFe3(BO3)4 is an intensively studied multiferroic with high electric polarization values controlled by a magnetic field. It is characterized by a large quadratic magnetoelectric effect, rigidity in the base plane and a rather strong piezoelectric effect. In this work, the atomic structure of (Nd0.91Bi0.09)Fe3(BO3)4 was studied by single-crystal X-ray diffraction in the temperature range 20-500 K (space group R32, Z= 3). The Bi atoms found in the composition partially substitute the Nd atoms in the 3a position; they entered the structure due to the growth conditions in the presence of Bi2Mo3O12. It was shown that in the temperature range 20-500 K there is no structural phase transition R32→P3121, which occurs in rare-earth iron borates (RE= Eu-Er, Y) with an effective rare-earth cation radius smaller than that of Nd. The temperature dependence of the unit-cell c parameter reveals a slight increase on cooling below 90 K, which is similar to the results obtained previously for iron borates of Gd, Y and Ho. The atomic distances (Nd,Bi)-O, (Nd,Bi)-B, (Nd,Bi)-Fe, Fe-O, Fe-B and Fe-Fe in the iron chains and between chains decrease steadily with decreasing temperature from 500 to 90 K, whereas the B1(3b)-O distance does not change and the average B2(9e)-O distance increases slightly. There is a uniform decrease in the atomic displacement parameters with decreasing temperature, with a more pronounced decrease for the Nd(3a) and O2(9e) atoms. The O2(9e) atoms are characterized by the maximum atomic displacement parameters and the most elongated atomic displacement ellipsoids. The characteristic Debye and Einstein temperatures, and the static component in the atomic displacements were determined for cations using multi-temperature diffraction data. It was shown that the Nd cations have the weakest bonds with the surrounding atoms and the B cations have the strongest.

Quadratic magnetoelectric effect during field cooling in sputter grown Cr2O3 films

${\mathrm{Cr}}_{2}{\mathrm{O}}_{3}$ is the archetypal magnetoelectric (ME) material, which has a linear coupling between electric and magnetic polarizations. Quadratic ME effects are forbidden for the magnetic point group of ${\mathrm{Cr}}_{2}{\mathrm{O}}_{3}$, due to space-time inversion symmetry. In ${\mathrm{Cr}}_{2}{\mathrm{O}}_{3}$ films grown by sputtering, we find a signature of a quadratic ME effect that is not found in bulk single crystals. We use Raman spectroscopy and magnetization measurements to deduce the removal of space-time symmetry and corroborate the emergence of the quadratic ME effect. We propose that metastable site-selective trace dopants remove the space, time, and space-time inversion symmetries from the original magnetic point group of bulk ${\mathrm{Cr}}_{2}{\mathrm{O}}_{3}$. We include the quadratic ME effect in a model describing the switching process during ME field cooling and estimate the effective quadratic susceptibility value. The quadratic magnetoelectric effect in a uniaxial antiferromagnet is promising for multifunctional antiferromagnetic and magnetoelectric devices that can incorporate optical, strain-induced, and multiferroic effects.

Magnetoelectric Effect in Ce3Fe5O12 Films

Hysteresis in the dependence of the electric polarization on the electric field has been found in polycrystalline cerium iron garnet films. The linear and quadratic magnetoelectric effects have been detected and it has been found that the magnetoelectric tensor components change sign with the variation of the temperature. The magnetoelectric effect has been explained within the magnetostriction model of the flexoelectric interaction with a magnetic subsystem.

Magnetic structures and quadratic magnetoelectric effect in LiNiPO4 beyond 30 T

Neutron diffraction with static and pulsed magnetic fields is used to directly probe the magnetic structures in LiNiPO$_4$ up to 25T and 42T, respectively. By combining these results with magnetometry and electric polarization measurements under pulsed fields, the magnetic and magnetoelectric phases are investigated up to 56T applied along the easy $c$-axis. In addition to the already known transitions at lower fields, three new ones are reported at 37.6, 39.4 and 54T. Ordering vectors are identified with ${\bf Q}_{\mathrm{VI}}$ = (0, 1/3, 0) in the interval 37.6--39.4T and ${\bf Q}_{\mathrm{VII}}$ = (0, 0, 0) in the interval 39.4-54T. A quadratic magnetoelectric effect is discovered in the ${\bf Q}_{\mathrm{VII}}$ = (0, 0, 0) phase and the field-dependence of the induced electric polarization is described using a simple mean-field model. The observed magnetic structure and magnetoelectric tensor elements point to a change in the lattice symmetry in this phase. We speculate on the possible physical mechanism responsible for the magnetoelectric effect in LiNiPO4.

Effect of a Substrate on the Magnetoelectric Effect in Rare-Earth-Doped Bismuth Iron Garnet

The mechanism of relaxation of the electric polarization in thin films of rare-earth-doped bismuth iron garnet on glass and gallium gadolinium garnet substrates is determined in magnetic fields of 0 and 12 kOe in the temperature range of 80–380 K. The change in the sign of the residual electric polarization after switching off the electric field and the magnetic-field-induced shift of the hysteresis loop in the applied magnetic field are found. Linear and quadratic magnetoelectric effects with the tensor components depending on the substrate type are observed. The linear magnetoelectric effect is related to the spin–orbit coupling of electrons at the film–substrate interface, whereas the quadratic one is determined by the exchange–striction mechanism.

Helical magnetic state in the distorted triangular lattice ofα-CaCr2O4

The magnetic properties of the high temperature alpha form of the CaCr2O4 compound have been investigated for the first time by magnetic susceptibility, specific heat and powder neutron diffraction. The system undergoes a unique magnetic phase transition at 43K to a long range order incommensurate helical phase with magnetic propagation vector k=(0,0.3317(2),0). The magnetic model proposed from neutron diffraction data shows that the plane of rotation of the spins is perpendicular to the wave-vector, and that the magnetic modulation is consistent with two modes belonging to distinct irreducible representations of the group. The magnetic point group 2221' is not compatible with ferroelectricity unlike the CuCrO2 delafossite [Kimura et al., Phys. Rev. B, 78 140401 (2008)] but predicts the existence of quadratic magnetoelectric effects, discussed based on a Landau analysis.

Symmetry and magnetoelectric interactions in BaMnF4

Symmetry analysis is used to study magnetic anisotropy and magnetoelectric interactions in the ferroelectric antiferromagnet BaMnF4 theoretically. It is shown that symmetry admits the existence in this material of a nonuniform magnetoelectric interaction (flexomagnetoelectric type) with a specific dependence on the magnitude and orientation of the external magnetic field. With increasing magnetic field this interaction can cause a phase transition into a magnetic incommensurate phase with a characteristic jump of the electric polarization. The linear and quadratic magnetoelectric effects and the question of the relativistic canting of the sublattices, which is due to the magnetoelectric interaction, are examined. The proposed approach is a natural generalization of the method of constructing invariants from the magnetic modes of the crystal to the case of phase transitions with a doubled unit cell of the crystal and can be used for symmetry analysis of other ferroelectric magnetic compounds.

Quadratic magnetoelectric effect and the role of the magnetocaloric effect in the magnetoelectric properties of multiferroic BaMnF4

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 (Pa(Hb)) 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.

Two-phase magnetoelectric nanopowder/polyurethane composites

This study deals with the observation of magnetoelectric (ME) effect in nanocomposite films constituted of semicrystalline polyurethane matrix filled with magnetic Fe3O4 (hard) or Ni (soft) nanoparticles. The measurement of the magnetic field-induced ground current of the so-called particulate composites enabled the precise determination of true ME current after extraction of the part corresponding to the inductively coupled (loop) current. Experimental ME current could be successfully simulated considering coexistence of both true linear and quadratic ME effects and by taking into account the nonlinear variation of applied dc bias and ac field magnitude due to the magnetization saturation of the magnetic field generator. Although linear ME coefficients of particulate composites are lower than those of laminate composites, they are of the same order of magnitude than that of reference ME material Cr2O3 (up to 18 mV/cm Oe). Besides, nanocomposites are simple to prepare, flexible, easily integrable, and sensitive to magnetic field anomaly at room temperature. At last, they present a linear ME coupling apparently not triggered by magnetostrictive phenomenon.

Magnetoelectric and magnetoelastic interactions in NdFe3(BO3)4 multiferroics

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.

Structural and magnetoelectric properties ofGa2−xFexO3single crystals grown by a floating-zone method

Lattice-structural, magnetic, and magnetoelectric (ME) properties have been investigated for single crystals of prototypical polar ferrimagnet ${\mathrm{Ga}}_{2\ensuremath{-}x}{\mathrm{Fe}}_{x}{\mathrm{O}}_{3}$ $(0.8\ensuremath{\leqslant}x\ensuremath{\leqslant}1.4)$ as melt-grown by a floating-zone (FZ) method. Magnetization measurements show that the saturated magnetization as well as the ferrimagnetic phase transition temperature $({T}_{C})$ increases with as increase of $\mathrm{Fe}$ content $x$, while the coercive force decreases. A neutron powder diffraction study indicates fairly low ordering of $\mathrm{Ga}$ and $\mathrm{Fe}$ arrangement at cation sites, which is likely related to the lower ${T}_{C}$ in the FZ crystals than in the corresponding flux-grown crystals. Coefficients of linear and quadratic ME effects have been obtained with measurements of change in electric polarization induced by sweeping a magnetic field. Electric polarization was largely modulated in a magnetic field applied parallel to the direction of spontaneous magnetization, but not in a field parallel to that of the spontaneous polarization. A simple model to explain the sharp contrast is presented.

Magnetoelectric Effect in YMn 2 O 5 in Strong Pulsed Magnetic Fields

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 Á 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.

Magnetoelectric measurements of magnetite (Fe3O4) at low temperatures

Abstract Magnetoelectric (ME) effect of magnetite (Fe3O4) below 35 K is discussed, mainly on the basis of the results of two experiments. One experiment shows that the magnetic field induced ME polarization along either the a axis or the b axis is reversed after reversing the electric field to the respective axes. Another experiment indicates the existence of the anomaly in the temperature dependence of ME polarizations at about 10 K. The ME polarization in both of these experiments is interpreted to be caused by the quadratic ME effect in domain structures. Through this, the following is concluded: 1) The point group of magnetite is most probably triclinic 1 below 35 K. 2) Magnetite is probably pyroelectric and ferroelectric. 3) A possible magnetic phase transition exists at about 10 K.

Magnetoelectric (Bi, Ln)Feo3compounds: Crystal growth, structure and properties

Abstract Growth conditions for Bi1−xLnxFeO3 (Ln˭La, Nd, Sm, Gd, Dy) crystals have been determined. Polymorphism, polar and magnetic properties of several structures have been studied. The quadratic magnetoelectric effect is found in rhombohedra1 and triclinic crystals with x < 0.25. The linear magnetoelectric effect is observed in the mm 2 orthorhombic structure, the magnitude of which depends on the nature of the rare-earth element. It is very large for (Bi, Dy)FeO3 crystals.

Synthesis and magnetoelectric properties of single crystals of metastable KCOPO4

Abstract Single crystals of the metastable phase of KCOPO4 (α-KCP) have been synthesized in a gel of tetra-methoxysilane. The crystals have a hexagonal symmetry which belongs to space group P63 (cell parameters a = 18.206(1), c = 8.5135(8) [A] and Z = 24). The crystals have been characterized by x-ray diffraction and by polarized light microscopy. The magnetoelectric properties of this compound have been studied at 4.4 K. No linear magnetoelectric effect has been detected and all coefficients of the tensor corresponding to the quadratic magnetoelectric effect (ME)H, have been determined at 4.4 K: β123 = -β213 = 2.3 10−18, β113 = β223 = 7.1 10−18, β311 = β322 = 12.2 10−18 and β333 = 7.2 10−18 in [s A−1] (estimated error less than 5%). The absence of a linear magnetoelectric effect and the form of the tensor of the quadratic effect indicate that the magnetic symmetry of the crystal at this temperature must belong either to the antiferromagnetic magnetic point group 6′ or to the paramagnetic one 61′. The pyr...

Low temperature magnetoelectric effects on Co3B7O13I

Abstract A linear and a quadratic magnetoelectric effect have been detected in cobalt-iodine boracite (Co3B7O13I). Second order αB32 (linear effect) and third order β311 and β322 (quadratic effect) magnetoelectric coefficients have been measured versus temperature from 4 K to 70 K. The values of the coefficients obtained at 4 K are: α32 = 4.17 × 10−11 s.m−1, β311 = -3.0 × 10−48 s.A−1, β322 = -1.9 × 10−18 s.A−1 and β333 = -1.7 × 10−19 s.A−1.

Linear and quadratic magnetoelectric effect in boracite Co3B7013Br

Abstract Linear and quadratic magnetoelectric (ME) effects have been simultaneously detected in Co-Br boracite(Co3B7O13 Br) ME coefficients a23, a32 and B311. have been measured versus temperature. The results are consistent with the symmetry m′m2′ down to 4 K.

Measurement of the Quadratic Magnetoelectric Effect on Single Crystalline BiFeO3

By means of the quadratic magnetoelectric effect the components of the non-linear magnetoelectric susceptibility tensor βijk of the antiferromagnetic ferroelectric ferroelastic phase of BiFeO3 have been determined at 4 K: β_111 =5.0·10^-19[sA^-1],β_113=8.1·10^-19[sA^-1], β_311 =0.3·10^-19[sA^-1],β_333=2.1·10^-19[sA^-1]