Session X23: Focus Session: Multiferroics III: Other

Pyroxenes: A novel class of multiferroics

Pyroxenes with the general formula AMSi$_{2}$O$_{6 }$(A - mono- or divalent metal, M = di- or trivalent metal) are shown to be a new class of multiferroic materials. In particular, we have found so far that NaFeSi$_{2}$O$_{6}$ becomes ferroelectric in a magnetically ordered state below 6 K. Similarly, magnetically driven ferroelectricity is also detected in the Li homologues, LiFeSi$_{2}$O$_{6}$ (T$_{C}$ =18 K) and LiCrSi$_{2}$O$_{6}$ (T$_{C}$ =11 K). In all these monoclinic systems the electric polarization can be strongly modified by magnetic fields. Measurements of magnetic susceptibility, pyroelectric current and dielectric constants (and their dependence on magnetic field) are performed using a natural crystal of aegirine (NaFeSi$_{2}$O$_{6}$) and synthetic crystals of LiFeSi$_{2}$O$_{6}$ and LiCrSi$_{2}$O$_{6}$ grown from melt solution. For NaFeSi$_{2}$O$_{6}$ a temperature versus magnetic field phase diagram is proposed. Exchange constants are computed on the basis of ab initio band structure calculations. The possibility of a spiral magnetic structure caused by frustration as origin of the multiferroic behaviour is discussed. We propose that other pyroxenes may also be multiferroic, and that the versatility of this family offers an exceptional opportunity to study general conditions for and mechanisms of magnetically driven ferroelectricity.   

Magnetic field induced ferroelectricity in Mn$_{0.9}$Fe$_{0.1}$WO$_{4}$

We discovered the external magnetic field induce ferroelectric phase in Mn$_{0.9}$Fe$_{0.1}$WO$_{4}$, which is paraelectric at zero magnetic field. The ferroelectricity appears in fields above 4 Tesla applied along the easy axis of magnetization and the spontaneous polarization along the b-axis was measured by the pyroelectric current method as a function of temperature and magnetic field. The temperature and magnetic field dependence of spontaneous polarization shows strong coupling between magnetic and ferroelectric orders. We interpret that the improper ferroelectricity in this compound is driven by non collinear spin structure which breaks the inversion symmetry. We propose high-field neutron scattering experiments to characterize the magnetic structure in the ferroelectric phase.   

Quantum theory of multiferroics in quasi-one-dimensional spin-1/2 frustrated magnets

A theory is developed to understand recent experimental findings on quasi-one-dimensional spin-$1/2$ multiferroics LiCuVO$_4$ and LiCu$_2$O$_2$. For this purpose, weakly coupled frustrated quantum spin chains with and without the zigzag structure are studied by means of an effective field theory based on the bosonization in one dimension. A chiral ground state with gapless incommensurate spin excitations can be stabilized in the presence of an easy-plane anisotropy. This state is driven by a three-dimensional coupling to the incommensurate helimagnetic state, in accordance with the experimental observations. We also reveal the quantum dynamics of the spin, the chirality and the electromagnon as well as the finite-temperature phase diagram, which reflect the one-dimensional nature of the quantum fluctuations.   

Correlation between spin helicity and electric polarization vector in quantum chain magnet LiCu$_2$O$_2$

Measurements of polarized neutron scattering were performed on the multiferroic quantum chain magnet LiCu$_2$O$_2$. In the ferroelectric ground phase, the existence of transverse spiral spin component in the $bc$-plane was confirmed. When the direction of electric polarization is reversed, the vector spin chirality as defined as ${\bf C}_{ij} = {\bf S}_i \times {\bf S} _j$ is also reversed. This directly proves that the spin- current model ${\bf P}_{ij} \propto {\bf e}_{ij} \times {\bf C}_ {ij}$ is applicable even to this $e_{\mathrm{g}}$-electron quantum $S$=1/2 system. Differential scattering intensity of polarized neutrons shows a large discrepancy from that expected for the classical $bc$-cycloidal spin structure, implying either the complexity of magnetic structure or the effect of quantum fluctuation.   

Multiferroics versus Quantum Fluctuations in Spin-1/2 Frustrated Chains

We study interplay of the chiral spin ordering and quantum fluctuations in a spin-1/2 frustrated chain, which is the simplest model for one-dimensional multiferroic cuprates like LiCuVO$_4$ and LiCu$_2$O$_2$. In a Heisenberg chain, it is known that the classical helical magnetic order is suppressed by strong quantum fluctuations and valence-bond solid phases emerge. In fact, weak easy-plane spin anisotropies exist in the above materials, because of the XXZ-type anisotropy and a phonon-induced biquadratic Dzyaloshinskii-Moriya interaction. In particular, when the nearest-neighbor exchange coupling is much weaker than the antiferromagnetic second-neighbor one, our exact-diagonalization calculations combined with the bosonization analyses show that such anisotropies bring about the vector-chiral spin ordering and the associated multiferroic behavior. This chiral state is accompanied by slightly incommensurate algebraic spin correlations, which, with a three-dimensional coupling, explains the magnetic order experimentally observed in LiCuVO$_4$.   

Optical spectroscopic study on magnetoelectric MnWO$_{4}$

We report optical spectroscopic investigation on a multiferroic oxide compound, MnWO$_{4}$. This compound is known to exhibit ferroelectricity induced by the incommensurate spiral magnetic ordering in a temperature range of 7.6 K and 12.7 K [1]. We grew single crystals of MnWO$_{4}$ by using the floating zone method. To examine the optical anisotropy originating from the monoclinic crystal structure, we measured reflectivity spectra of MnWO$_{4}$ with light polarizations along three crystallographic axes, and calculated the optical conductivity spectra through the Kramers-Kronig transformation for each axis. We discuss the anisotropic phonon structures and electronic structures with temperature and magnetic field dependence in relation to its multiferroic properties. \newline [1] K. Taniguchi \textit{et al}., Phys. Rev. Lett. \textbf{97}, 097203 (2006).   

Ferroelectric domain topology of the multiferroic spin spiral system MnWO$_4$

The strong interest in magnetoelectric multiferroics is due to their potential concerning the design of novel multifunctional devices, as well as to their unusual physical properties. Among these, TbMnO$_3$, Ni$_3$V$_2$O$_8$, and MnWO$_4$ form a particularly challenging group: The key factor for ferroelectricity lies in the long-wavelength magnetic order. Many aspects of the precise nature of the ferroelectric state in such a \textit{spiral magnet}, and in particular their coupling to the magnetic order, are still largely unclear. Here we report about the three-dimensional spatial distribution of ferroelectric domains in MnWO$_4$, revealed by optical second harmonic generation (SHG). Although ferroelectricity is induced by cycloidal spiral magnetic order, 180$^{\circ}$ domains as in a conventional ferroelectric are observed. Their coupling to the coexisting magnetic order and modifications of this coupling by external parameters such as temperature variation are discussed using spatially resolved SHG for probing both the magnetic and the ferroelectric order in one experimental run.   

Magnetic field control of the ferroelectric polarization in multiferroic MnWO$_{4}$

The relationship between magnetic order and ferroelectric properties has been investigated for MnWO$_{4}$. Spontaneous electric polarization is observed in a cycloidal spiral spin phase. The magnetic-field dependence of electric polarization indicates that the noncollinear spin configuration plays a key role for the appearance of ferroelectric phase. Destabilization of the ferroelectric phase and an electric polarization flop from the $b$ direction to the $a$ direction have been observed when a magnetic field is applied along the $b$ axis. On the other hand, the ferroelectric phase is stabilized when a magnetic field is applied along the $a$-, $c$- and the spin easy axes. We have also found that the magnetic field induced ferroelectric polarization disappears in a high magnetic field above 12T along the spin easy axis. Theses phenomena provide us useful information for gigantic magnetoelectric effects because MnWO$_{4}$ is a simple system without rare-earth f-moments.   

Ferroelectricity in Mn$_{0.9}$Fe$_{0.1}$WO$_{4}$ induced by magnetic fields: A simple model calculation

Replacing Mn$^{2+}$ by Fe$^{2+}$ in multiferroic MnWO$_{4}$ results in the complete loss of ferroelectricity at zero magnetic field. However, it was shown that in Mn$_{0.9}$Fe$_{0.1}$WO$_{4}$ an external magnetic field restores the ferroelectric state. We present a simple mean field calculation of the Heisenberg model with ferromagnetic nearest and antiferromagnetic next nearest neighbor interactions and uniaxial anisotropy in an external magnetic field. The various commensurate and incommensurate magnetic phases in Mn$_{1-x}$Fe$_{x}$WO$_{4}$ are well described by the model. The loss of the non collinear helical spin structure (which is associated with the ferroelectric order) with increasing Fe substitution is explained by the enhancement of the anisotropy. We show that the external field does indeed restore the helical spin structure in Mn$_{0.9}$Fe$_{0.1}$WO$_{4}$ and that the observed field-induced ferroelectricity can be explained.   

Correlation between magnetic, dielectric properties and strain in a Mn$_{3}$O$_{4}$ single crystal

Mn$_{3}$O$_{4}$ has a tetragonally distorted spinel structure below 1443 K and exhibits a ferrimagnetic ordering at $T_{N}$ = 43 K. This compound exhibits further magnetic phase transitions at 39 K and 33 K, where Mn$^{2+}$ and Mn$^{3+}$ spins are canted from the collinear spin structure. We measured the dielectric constant and strain of a Mn$_{3}$O$_{4}$ single crystal. We found that both dielectric constant and strain have clear anomalies at the magnetic transition temperatures. We also found that dielectric constant is suppressed (enhanced) by 2 \% when magnetic field is applied parallel (perpendicular) to the direction of electric field within the $ab$ plane below $T_ {N}$. In addition, strain along the $ab$ plane also has anisotropic magnetic field dependence. These results can be explained as follows: (1) There is an orthorhombic distortion below $T_{N}$, presumably induced by the orbital ordering of Mn$^{3+} $, (2) anisotropy of dielectric constant and strain within the $ab$ plane appears due to the orthorhombic distortion, and (3) the alignment of crystalline domains with applied magnetic field occurs, resulting in the large magnetic field dependence of dielectric constant and strain.   

Polar Behavior in a Magnetic Oxide Via A-Site Size Disorder

Density functional calculations are used to test a new mechanism for ferroelectricity in magnetic perovskites based on A-site size disorder. Calculations of the structure and magnetic ordering of (La,Lu)MnNiO$_6$ show that this mechanism is effective for this material, which is predicted to be both polar (ferroelectric or relaxor) and ferromagnetic, depending on the Lu concentration.   

Electric field control of magnetic phase transitions in Ni$_{3}$V$_{2}$\O$_{8}$

In certain multiferroics, including Ni$_{3}$V$_{2}$O$_{8}$, the ferroelectric order is induced by the magnetic structure, leading to the simultaneous onset of spin and charge ordering. We have prepared thin films of Ni$_{3}$V$_{2}$O$_{8}$ by sputter deposition. Films annealed at 1000$^{0}$C crystallize with closely packed rod-like grains. XRD confirms that the films are single phase Ni$_{3}$V$_{2}$O$_{8}$ and highly oriented along the $b$-axis. We observe a hysteretic magnetic anomaly at 3.6 K, which is consistent with a first order phase transition from a canted magnetic state to incommensurate magnetic order. This transition temperature is suppressed by $\Delta $T=0.2 K in an electric field of 30MV/m. An anomaly in the dielectric constant is observed at 6.3K, corresponding to a transition between two incommensurate magnetic states. Because the electric field acts as a field conjugate to the order parameter, it causes a rounding of the phase transition and an apparent increase in the transition temperature by $\Delta $T=0.2 K when the sample is biased at 25 MV/m. The E-T phase boundary for the 3.6 K transition is linear, while the 6.3 K phase boundary shifts roughly like E vs.T$^{2}$, consistent with estimates from critical scaling. We will discuss the electric field control of magnetic order parameter in these films and some important implications of this result for the multiferoic material thin film research.   

Direct Evidence of Magnetoelastic Coupling in Ni$_{3}$V$_{2}$O$_{8}$.

We investigate the infrared active phonons of the Kagome staircase compound Ni$_{3}$V$_{2}$O$_{8}$ as a function of temperature to elucidate changes in magnetoelastic coupling through the cascade of low-temperature magnetic transitions. A detailed analysis of the $a$- and $c$- polarized vibrational mode trends demonstrates that: i) the approach to the cascade of magnetic transitions is driven by the high frequency stretching modes and the highest frequency bending mode along $a$; ii) the paramagnetic to high-temperature incommensurate phase transition is driven by low frequency $c$-polarized modes; and iii) the high-temperature to low-temperature incommensurate phase transition is driven by all $a$-polarized modes plus the NiO$_{6}$ stretching mode along $c$. Work is in progress to elucidate the trends along $b$. Overall, we find that the phonons are sensitive to the magnetic state, indicating that the lattice is flexible, coupling strongly to the spin system in this multiferroic material.   

Magnetic field effect on the magnetic structure of Ba$_{2}$CoGe$_{2}$O$_{7}$

Multiferroic materials have recently attracted much interest fueled by the discovery of the coexistence and mutual interference of long range magnetic and ferroelectric order in them. Further attention to these compounds is gained due to their potential for device applications made possible by the controllability of the spontaneous polarization by a magnetic field or the bulk magnetization by an electric field via the sizable magneto-dielectric coupling in them. The fundamental microscopic mechanism for the phenomena is yet to be fully understood but an essential component has been suggested to be the non-linear coupling of the ferroelectric and magnetic order parameters with a spatially varying magnetization. It is thus the focus of this work to study the static magnetic structure of the compound Ba$_{2}$CoGe$_{2}$O$_{7}$ below its magnetic and ferroelectric ordering temperature of 7K. Neutron diffraction measurements were done on the compound under applied magnetic fields up to 7 T along the crystal's $c$-axis.