我们提出了宏观和中子衍射数据的多铁性轻掺杂Ni $_3$ V $_2$ O $_8$。掺杂Co到母体化合物中抑制了四个磁性相变的顺序，并且可以观察到仅两个磁性有序相，顺电高温无公度（HTI）和铁电低温无公度（LTI）。有趣的是，具有螺旋（摆线）磁性结构的LTI多铁性相被稳定到至少1.8 K，这可以通过测量电极化的强度来揭示，并通过单晶样品上的中子衍射来证实。所提取的LTI相位的磁矩除了包含主交换之外，还包含对称性所允许的摆线的精细分量，这导致由于混合表示的位置相关对称性而导致沿着摆线传播的磁矩的小幅度变化。在HTI阶段，可以推导出脊柱磁矩的有限虚部，从而产生自旋摆线，而不是对于不同的脊柱自旋链具有相反的自旋手征的纯正弦结构。在这两个阶段中的交叉结网站的磁性排序是不同的，在纯Ni化合物中的相应的。与Ni $_3$ V $_2$ O $_8$相比，已经观察到HTI相的更宽的温度稳定性范围，这可以通过由于Co掺杂而导致的额外的单离子易轴各向异性来解释。Co掺杂的化合物的较大的不相容性在竞争的次近邻和最近邻相互作用之间产生较大的比率，与母体化合物中的0.39相比，对于7%（10%）Co的掺杂水平，该比率为$J_2/J_1$ =0.43（0.47）。
英文摘要：
We present macroscopic and neutron diffraction data on multiferroic lightly Co-doped Ni$_3$V$_2$O$_8$. Doping Co into the parent compound suppresses the sequence of four magnetic phase transitions and only two magnetically ordered phases, the paraelectric high temperature incommensurate (HTI) and ferroelectric low temperature incommensurate (LTI), can be observed. Interestingly, the LTI multiferroic phase with a spiral (cycloidal) magnetic structure is stabilized down to at least 1.8 K, which could be revealed by measurements of the electric polarization and confirmed by neutron diffraction on single crystal samples. The extracted magnetic moments of the LTI phase contain besides the main exchange also fine components of the cycloid allowed by symmetry which result in a small amplitude variation of the magnetic moments along the cycloid propagation due to the site-dependent symmetry properties of the mixed representations. In the HTI phase a finite imaginary part of the spine magnetic moment could be deduced yielding a spin cycloid instead of a purely sinusoidal structure with an opposite spin chirality for different spine spin chains. The magnetic ordering of the cross-tie sites in both phases is different in comparison to the respective ones in the pure Ni compound. A wider temperature stability range of the HTI phase has been observed in comparison to Ni$_3$V$_2$O$_8$ which can be explained by an additional single-ion easy-axis anisotropy due to Co-doping. The larger incommensurability of the Co-doped compounds yields a larger ratio between the competing next-nearest neighbour and nearest neighbour interaction, which is $J_2/J_1$=0.43 (0.47) for a doping level of 7% (10%) Co compared to 0.39 in the parent compound.
The magnetic field induced rearrangement of the cycloidal spin structure in ferroelectric mono-domain single crystals of the room-temperature multiferroic BiFeO$_3$ is studied using small-angle neutron scattering (SANS). The cycloid propagation vectors are observed to rotate when magnetic fields applied perpendicular to the rhombohedral (polar) axis exceed a pinning threshold value of $\sim$5\,T. In light of these experimental results, a phenomenological model is proposed that captures the rearrangement of the cycloidal domains, and we revisit the microscopic origin of the magnetoelectric effe…
In multiferroic BiFeO$_3$ a cycloidal antiferromagnetic structure is coupled to a large electric polarization at room temperature, giving rise to magnetoelectric functionality that may be exploited in novel multiferroic-based devices. In this paper, we demonstrate that by substituting samarium for 10% of the bismuth ions the periodicity of the room temperature cycloid is increased, and by cooling below $\sim15$ K the magnetic structure tends towards a simple G-type antiferromagnet, which is fully established at 1.5 K. We show that this transition results from $f-d$ exchange coupling, which ind…
Coupled magnetic and ferroelectric domains in multiferroic Ni3V2O8
通过极化磁中子衍射证实了多铁性畴的电控制。在电场（E）中冷却到Ni 3V 2 O 8的摆线多铁性相，导致无公度布拉格反射变为中子自旋极化，中子极化的方向与E相反。定量分析表明，E处理的样品具有手性，可以被E逆转。我们进一步通过E驱动的自旋和电极化的强度滞后显示了摆线畴和铁电畴之间的密切联系。我们认为，明确的摆线手性是通过磁弹性诱导的Dzyaloshinskiii-Moriya相互作用。
Goldstone modes and electromagnon fluctuations in the conical cycloid state of a multiferroic
本文用唯象的Ginzburg-Landau理论讨论了立方尖晶石CoCr $_{2}$ O $_{4}$中多铁性磁性锥旋轮线态的低能涨落谱。我们确定的Goldstone模式的圆锥摆线顺序，并推导出他们的色散关系，其签名各向异性的动量空间反映了对称性打破了有序状态。我们讨论了软极化波动，“电磁子”，与这些磁模式，并作出了一些实验预测，可以在中子散射和光学实验进行测试。
Dynamics of Multiferroic Domain Wall in Spin-Cycloidal Ferroelectric DyMnO$_{3}$
本文报道了多铁性DyMnO $_{3}$在宽频率范围内的巨磁电容（GMC）的介电色散。GMC被发现是归因于不软化的电磁振子，但电场驱动的运动的多铁性畴壁（DW）。与传统的铁电DW相比，本发明的多铁性DW运动即使在低温下也保持$\sim$ $10^{7}$ s $^{-1}$的极高弛豫速率。这种移动的性质以及模型模拟表明，多铁性DW不是原子薄的铁电体，但厚，反映其磁性起源。
We report a neutron diffraction study of the multiferroic mechanism in (ND4)2FeCl5D2O, a molecular compound that exhibits magnetically induced ferroelectricity. This material exhibits two successive magnetic transitions on cooling: a long-range order transition to an incommensurate (IC) collinear sinusoidal spin state at TN=7.3 K, followed by a second transition to an IC cycloidal spin state at TFE=6.8 K, the later of which is accompanied by spontaneous ferroelectric polarization. The cycloid structure is strongly distorted by spin-lattice coupling as evidenced by the observations of both odd …
Broadband microwave spectroscopy has been performed on single-crystalline GaV$_4$S$_8$, which exhibits a complex magnetic phase diagram including cycloidal, Néel-type skyrmion lattice, as well as field-polarized ferromagnetic phases below 13 K. At zero and small magnetic fields two collective modes are found at 5 and 15 GHz, which are characteristic of the cycloidal state in this easy-axis magnet. In finite fields, entering the skyrmion lattice phase, the spectrum transforms into a multi-mode pattern with absorption peaks near 4, 8, and 15 GHz. The spin excitation spectra in GaV$_4$S$_8$ and t…
Tungstates $A$WO$_4$ with the wolframite structure characterized by the $A$O$_6$ octahedral zigzag chains along the $c$-axis, can be magnetic if $A$=Mn, Fe, Co, Cu, Ni. Among them, MnWO$_4$ is a unique member with a cycloid Mn$^{2+}$ spin order developed at low temperature, leading to an interesting type-II multiferroic behavior. However, so far no other multiferroic material in the tungstate family has been found. In this work, we present the synthesis and the systematic study of the double tungstate LiFe(WO$_4$)$_2$. Experimental characterizations including structural, thermodynamic, magneti…
We have performed dielectric measurements and neutron diffraction experiments on the double perovskite In2NiMnO6. A ferroelectric polarization, P ~ 30 μC/m2, is observed in a polycrystalline sample below TN = 26 K where a magnetic phase ransition occurs. The neutron diffraction experiment demonstrates that a complex noncollinear magnetic structure with "cycloidal" and "proper screw" components appears below TN, which has the incommensurate propagation vector k = (ka,0,ks; ka ~ 0.274, ks ~ -0.0893). The established magnetic point group 21' implies that the macroscopic ferroelectric polarization…
The magnetoelectric coupling, i.e., cross-correlation between electric and magnetic orders, is a very desirable property to combine functionalities of materials for next-generation switchable devices. Multiferroics with spin-driven ferroelectricity presents such a mutual interaction concomitant with magneto- and electro-active excitations called electromagnons. TbMnO3 is a paradigmatic material in which two electromagnons have been observed in the cycloidal magnetic phase. However, their observation in TbMnO3 is restricted to the cycloidal spin phase and magnetic ground states that can support…
We report the magnetic field dependence of the THz absorption and non-reciprocal directional dichroism spectra of BiFeO$_3$ measured on the three principal crystal cuts for fields applied along the three principal directions of each cut. From the systematic study of the light polarization dependence we deduced the optical selection rules of the spin-wave excitations. Our THz data, combined with small-angle neutron scattering results showed that i) an in-plane magnetic field rotates the $\mathbf{q}$ vectors of the cycloids perpendicular to the magnetic field, and ii) the selection rules are mos…
We report a soft x-ray resonant magnetic scattering study of the spin configuration in multiferroic thin films of Co$_{0.975}$Ge$_{0.025}$Cr$_2$O$_4$ (Ge-CCO) and CoCr$_2$O$_4$ (CCO), under low- and high-magnetic fields, from 0.2 T up to 6.5 T. A characterization of Ge-CCO at a low magnetic field is performed and the results are compared to those of pure CCO. The ferrimagnetic phase transition temperature $T_C \approx 95$ K and the multiferroic transition temperature $T_S \approx 27$ K in Ge-CCO are comparable to those observed in CCO. In Ge-CCO, the ordering wave vector $\textit{(qq0)}$ obser…
Our results describe an unprecedented example of change in the mechanism of magnetically-induced electric polarization from spin current to spin-dependent p-d hybridization model. We have followed the evolution of the magnetic structures of (ND4)2[FeCl5 D2O] compound using single crystal neutron diffraction under external magnetic field. The spin arrangements change from incommensurate cycloidal to commensurate distorted-cycloidal and finally to quasi-collinear. The determination of the magnetic structures allows us to explain the observed electric polarization in the different ferroelectric p…
We report new results of a 57Fe Mössbauer study of multiferroic 3R-AgFeO2 powder samples performed in a wide temperature range, including two points, TN1 ~ 14 K and TN2 ~ 9 K, of magnetic phase transitions. At the intermediate temperature range, TN2 < T < TN1, the 57Fe Mössbauer spectra can be described in terms of collinear spin-density-waves (SDW) with the inclusion of many high-order harmonics, indicating that the real magnetic structure of this ferrite appears to be more complicated than a pure sinusoidally modulated SDW. The spectra at low temperatures, T < TN2, consist of a Zeeman patter…
The magnetic-field-induced 90-degree flop of ferroelectric polarization P in a spin-spiral multiferroic material TbMnO3 is theoretically studied based on a microscopic spin model. We find that the direction of the P-flop or the choice of +Pa or -Pa after the flop is governed by magnetic torques produced by the applied magnetic field H acting on the Mn spins and thus is selected in a deterministic way, in contradistinction to the naively anticipated probabilistic flop. This mechanism resolves a puzzle of the previously reported memory effect in the P direction depending on the history of the ma…
We investigate the demagnetization dynamics of the cycloidal and sinusoidal phases of multiferroic TbMnO$_3$ by means of time-resolved resonant soft x-ray diffraction following excitation by an optical pump. Using orthogonal linear x-ray polarizations, we suceeded in disentangling the response of the multiferroic cycloidal spin order from the sinusoidal antiferromagnetic order in the time domain. This enables us to identify the transient magnetic phase created by intense photoexcitation of the electrons and subsequent heating of the spin system on a picosecond timescale. The transient phase is…
Magnetic excitations and optical transitions in the multiferroic spin-1/2 system LiCu$_2$O$_2$
利用太赫兹吸收光谱研究了摆线磁体LiCu $_2$ O $_2$在12 T以下磁场中的磁激发.在自旋有序温度以下，我们观察到8个旋光跃迁的LiCu $_2$ O $_2$的自旋系统中的能量范围从4到30厘米$^{-1}$。在磁场中，模式的数量增加，并且电极化的强度翻转被看作模式能量的磁场依赖性的变化。零磁场下两个模式的偏振依赖性符合从bc平面倾斜$θ=41\pm1^{\circ}$的摆线的选择规则。对于其余六种模式的电和磁偶极子近似不能解释所观察到的偏振依赖性。我们没有看到在探索的能量范围内的电磁子，虽然有证据表明，它可以存在于4厘米以下的$^{-1}$。
We have carried out neutron diffraction and small angle neutron scattering measurements on a high quality single crystal of the cubic lacunar spinel multiferroic, GaV$_4$S$_8$, as a function of magnetic field and temperature to determine the magnetic properties for the single electron that is located on the tetrahedrally coordinated V$_4$ molecular unit. Our results are in good agreement with the structural transition at 44 K from cubic to rhombohedral symmetry where the system becomes a robust ferroelectric, while long range magnetic order develops below 13 K in the form of an incommensurate …
Electric field control of multiferroic domains in Ni$_3$V$_2$O$_8$ imaged by X-ray polarization enhanced topography
用非共振X射线磁散射研究了多铁性NiPDMATHABMM V $_2$ O $_8$的磁结构。入射的圆偏振X射线结合全偏振分析的散射光束示出产生高灵敏度的摆线磁顺序的组件，包括它们的相对相位。在铁电相的磁结构上的新信息，它被发现，在“交叉领带”网站上的磁矩淬火相对于那些“脊柱”网站。这意味着铁电性的发生主要与脊柱网站磁序。我们还表明，我们的技术，使成像的多铁性域通过极化增强地形。这种方法是用来成像的域作为样品是由一个电场循环通过其磁滞回线，揭示了域的逐渐切换没有成核。
Orthorhombic HoMnO3 is a multiferroic in which Mn antiferromagnetic order induces ferroelectricity. A second transition occurs within the multiferroic phase, in which a strong enhancement of the ferroelectric polarization occurs concomitantly to antiferromagnetic ordering of Ho 4f magnetic moments. Using the element selectivity of resonant X-ray diffraction, we study the magnetic order of the Mn 3d and Ho 4f moments. We explicitly show that the Mn magnetic order is affected by the Ho 4f magnetic ordering transition. Based on the azimuthal dependence of the (0 q 0) and (0 1-q 0) magnetic reflec…
We report on the slow magnetization dynamics observed upon the magnetic phase transitions of GaV4S8, a multiferroic compound featuring a long-ranged cycloidal magnetic order and a Néel-type skyrmion lattice in a relatively broad temperature range below its Curie temperature. The fundamental difference between GaV4S8 and the chiral helimagnets, wherein the skyrmion phase was first discovered, lies within the polar symmetry of GaV4S8, promoting a cycloidal instead of a helical magnetic order and rendering the magnetic phase diagram essentially different from that in the cubic helimagnets. Our ac…
We report a comprehensive inelastic neutron scattering study of the hybrid molecule-based multiferroic compound (ND4)2FeCl5D2O in the zero-field incommensurate cycloidal phase and the high-field quasi-collinear phase. The spontaneous electric polarization changes its direction concurrently with the field-induced magnetic transition, from mostly aligned with the crystallographic a-axis to the c-axis. To account for such change of polarization direction, the underlying multiferroic mechanism was proposed to switch from the spin-current model induced via the inverse Dzyalloshinskii-Moriya interac…
From magnetic susceptibility, dielectric permittivity, electric polarization and specific heat measurements, we discover spin-induced ferroelectricity and magnetoelectric coupling in Mn3TeO6 and observe two successive magnetic transitions at low temperatures. A non-ferroelectric intermediate magnetic state occurs below 23 K and a multiferroic ground state emerges below 21 K. Moreover, Mn3TeO6 is a candidate for a multiferroic material where two types of incommensurate spin structures, cycloidal and helical, coexist. Theoretically, both spin substructures may contribute to the macro electric po…
We investigate the spin excitation spectra in chiral and polar magnets by the linear spin-wave theory for an effective spin model with symmetric and antisymmetric long-range interactions. In one dimension, we obtain the analytic form of the dynamical spin structure factor for proper-screw and cycloidal helical spin states with uniform twists, which shows a gapless mode with strong intensity at the helical wave number. When introducing spin anisotropy in the symmetric interactions, we numerically show that the stable spin spirals become elliptically anisotropic with nonuniform twists and the sp…
We have directly imaged reversible electrical switching of the cycloidal rotation direction (magnetic polarity) in a (111)-BiFeO3 epitaxial-film device at room temperature by non-resonant x-ray magnetic scattering. Consistent with previous reports, fully relaxed (111)-BiFeO3 epitaxial films consisting of a single ferroelectric domain were found to comprise a sub-micron-scale mosaic of magneto-elastic domains, all sharing a common direction of the magnetic polarity, which was found to switch reversibly upon reversal of the ferroelectric polarization without any measurable change of the magneto-…
Hexagonal LuFeO$_3$ has drawn a lot of research attention due to its contentious room-temperature multiferroicity. Due to the unstability of hexagonal phase in the bulk form, most experimental studies focused on LuFeO$_3$ thin films which can be stabilized by strain using proper substrates. Here we report on the hexagonal phase stabilization, magnetism, and magnetoelectric coupling of bulk LuFeO$_3$ by partial Sc-substitution of Lu. First, our first-principles calculations show that the hexagonal structure can be stabilized by partial Sc substitution, while the multiferroic properties includin…
Low-energy magnon excitations in multiferroic BiFeO$_3$ were measured in detail as a function of temperature around several Brillouin zone centers by inelastic neutron scattering experiments on single crystals. Unique features around 1 meV are directly associated with the interplay of the Dzyaloshinskii-Moriya interaction and a small single-ion anisotropy. The temperature dependence of these and the exchange interactions were determined by fitting the measured magnon dispersion with spin-wave calculations. The spectra best fits an easy-axis type magnetic anisotropy and the deduced exchange and…
Magnetic order and the underlying magnetic model of the multiferroic pyroxene NaFeGe2O6 are systematically investigated by neutron powder diffraction, thermodynamic measurements, density-functional bandstructure calculations, and Monte-Carlo simulations. Upon cooling, NaFeGe2O6 first reveals one-dimensional spin-spin correlations in the paramagnetic state below about 50 K, revealed by magnetic diffuse scattering. The sinusoidal spin-density wave with spins along the a-direction sets in at 13 K, followed by the cycloidal configuration with spins lying in the (ac) plane below 11.6 K. Microscopic…
Skyrmions are whirl like topological spin objects with high potential for future magnetic data storage. It is a fundamental question, relevant for both basic research and application, if a ferroelectric (FE) polarization can be associated with their magnetic texture and if these objects can be manipulated by electric fields. Here, we study the interplay between magnetism and electric polarization in the lacunar spinel GaV4S8, which undergoes a structural transition associated with orbital ordering at 44 K and reveals a complex magnetic phase diagram below 13 K, including a ferromagnetic (FM), …
Anisotropic multiferroic properties of SrMnGe2O6 pyroxene single crystals were systematically investigated by means of magnetization, heat capacity, pyroelectric current measurement and elastic and inelastic neutron scattering experiments. Single crystal neutron diffraction allows us to unambiguously reveal the presence of two incommensurate magnetic orderings: a non-polar amplitude-modulated collinear sinusoidal magnetic structure emerges at TN1=4.36(2)K followed by a polar elliptical cycloidal spin structure below TN2=4.05(2)K. Pyroelectric current measurements on single crystal confirm the …
Neutron spherical polarimetry, which is directly sensitive to the absolute magnetic configuration and domain population, has been used in this work to unambiguously prove the multiferroicity of (ND4)2[FeCl5(D2O)]. We demonstrate that the application of an electric field upon cooling results in the stabilization of a single-cycloidal magnetic domain below 6.9 K, while poling in the opposite electric field direction produces the full population of the domain with opposite magnetic chirality. We prove the complete switchability of the magnetic domains at low temperature by the applied electric fi…
