We have determined the full magnetic dispersion relations of multiferroic BiFeO3. In particular, two excitation gaps originating from magnetic anisotropies have been clearly observed. The direct observation of the gaps enables us to accurately determine the Dzyaloshinskii-Moriya (DM) interaction and the single ion anisotropy. The DM interaction supports a sizable magnetoelectric coupling in this compound.

The spin-wave excitations of the geometrically frustrated triangular lattice antiferromagnet CuFeO2 have been measured using high resolution inelastic neutron scattering. Antiferromagnetic interactions up to third nearest neighbors in the ab plane (J1, J2, J3, with J{2}/J{1} approximately 0.44 and J{3}/J{1} approximately 0.57), as well as out-of-plane coupling (J{z}, with J{z}/J{1} approximately 0.29) are required to describe the spin-wave dispersion relations, indicating a three-dimensional character of the magnetic interactions. Two energy dips in the spin-wave dispersion occur at the incommensurate wave vectors associated with multiferroic phase and can be interpreted as dynamic precursors to the magnetoelectric behavior in this system.

Spectroscopic modes provide the most sensitive probe of the very weak interactions responsible for the properties of the long-wavelength cycloid in the multiferroic phase of BiFeO3 below TN ≈ 640 K. Three of the four modes measured by THz and Raman spectroscopies were recently identified using a simple microscopic model. While a Dzyaloshinskii-Moriya (DM) interaction D along [−1, 2, −1] induces the cycloid with wavevector (2π/a)(0.5 + δ, 0.5, 0.5 − δ) (δ ≈ 0.0045), easy-axis anisotropy K along the [1, 1, 1] direction of the electric polarization P induces higher harmonics of the cycloid, which split the Ψ1 modes at 2.49 and 2.67 meV and activate the Φ2 mode at 3.38 meV. However, that model could not explain the observed low-frequency mode at about 2.17 meV. We now demonstrate that an additional DM interaction D ′ along [1, 1, 1] not only produces the observed weak ferromagnetic moment of the high-field phase above 18 T but also activates the spectroscopic matrix elements of the nearly-degenerate, low-frequency Ψ0 and Φ1 modes, although their scattering intensities remain extremely weak. Even in the absence of easy-axis anisotropy, D ′ produces cycloidal harmonics that split Ψ1 and activate Φ2. However, the observed mode frequencies and selection rules require that both D ′ and K are nonzero. This work also resolves an earlier disagreement between spectroscopic and inelastic neutron-scattering measurements.

We have studied the magnetic field dependence of far-infrared active magnetic modes in a single ferroelectric domain BiFeO3 crystal at low temperature. The modes soften close to the critical field of 18.8 T along the [001] (pseudocubic) axis, where the cycloidal structure changes to the homogeneous canted antiferromagnetic state and a new strong mode with linear field dependence appears that persists at least up to 31 T. A microscopic model that includes two Dzyaloshinskii-Moriya interactions and easy-axis anisotropy describes closely both the zero-field spectroscopic modes as well as their splitting and evolution in a magnetic field. The good agreement of theory with experiment suggests that the proposed model provides the foundation for future technological applications of this multiferroic material. Due to the coupling between electric and magnetic properties, multiferroic materials are among the most important yet discovered. With a multiferroic material used as a storage medium, information can be written electrically and then read magnetically without Joule heating [1]. Hence, applications of a room-temperature multiferroic would radically transform the magnetic storage industry. Because it is the only known roomtemperature multiferroic, BiFeO 3 continues to attract intense interest.Although its ferroelectric transition temperature[2] T c ≈ 1100 K is much higher than its Néel transition temperature [3][4][5] T N ≈ 640 K, the appearance of a longwavelength cycloid [3,[6][7][8] with a period of 62 nm enhances the ferroelectric polarization below T N . The induced polarization has been used to switch between magnetic domains with an applied electric field [4,5,9].Progress in understanding the microscopic interactions in BiFeO 3 has been greatly accelerated by the recent availability of single crystals for both elastic and inelastic neutron-scattering measurements. By fitting the spin wave frequencies above a few meV, recent arXiv:1302.2491v2 [cond-mat.str-el]

Multiferroics permit the magnetic control of the electric polarization and the electric control of the magnetization. These static magnetoelectric (ME) effects are of enormous interest: The ability to read and write a magnetic state current-free by an electric voltage would provide a huge technological advantage. Dynamic or optical ME effects are equally interesting, because they give rise to unidirectional light propagation as recently observed in low-temperature multiferroics. This phenomenon, if realized at room temperature, would allow the development of optical diodes which transmit unpolarized light in one, but not in the opposite, direction. Here, we report strong unidirectional transmission in the room-temperature multiferroic BiFeO 3 over the gigahertz-terahertz frequency range. The supporting theory attributes the observed unidirectional transmission to the spin-current-driven dynamic ME effect. These findings are an important step toward the realization of optical diodes, supplemented by the ability to switch the transmission direction with a magnetic or electric field. DOI: 10.1103/PhysRevLett.115.127203 PACS numbers: 75.85.+t, 75.50.-y, 76.50.+g BiFeO 3 is by far the most studied compound in the populous family of multiferroic and magnetoelectric (ME) materials [1][2][3][4][5][6][7][8][9]. While experimental studies have already reported about the first realizations of the ME memory function using BiFeO 3 -based devices [6][7][8][9], the origin of the ME effect is still under debate due to the complexity of the material. Because of the low symmetry of iron sites and iron-iron bonds, the magnetic ordering can induce local polarization via each of the three canonical terms [10]-the spin-current, exchange-striction, and single-ion mechanisms. While the spin-current term has been identified as the leading contribution to the magnetically induced ferroelectric polarization in various studies [5,11,12], the spin-driven atomic displacements [13] and the electrically induced shift of the spin-wave (magnon) resonances [14] were interpreted based on the exchange-striction and single-ion mechanisms, respectively.In the magnetically ordered phase below T N ¼ 640 K, BiFeO 3 possesses an exceptionally large spin-driven polarization [13], if not the largest among all known multiferroic materials. Nevertheless, its systematic study has long been hindered by the huge lattice ferroelectric polarization (P 0 ) developing along one of the cubic h111i directions at T C ¼ 1100 K and by the lack of single-domain ferroelectric crystals. Owing to the coupling between P 0 and the spindriven polarization, in zero magnetic field they both point along the same [111] axis. A recent systematic study of the static ME effect revealed additional spin-driven polarization orthogonal to the [111] axis [12].The optical ME effect of the magnon modes in multiferroics, which gives rise to the unidirectional transmission in the gigahertz-terahertz frequency range, has recently become a hot topic in materials science [15][16][17][18][19]...

Spin waves in the the rare earth orthorferrite YFeO3 have been studied by inelastic neutron scattering and analyzed with a full four-sublattice model including contributions from both the weak ferromagnetic and hidden antiferromagnetic orders. Antiferromagnetic (AFM) exchange interactions of J1= -4.23±0.08 (nearest-neighbors only) or J1 = -4.77±0.08 meV and J2 = -0.21±0.04 meV lead to excellent fits for most branches at both low and high energies. An additional branch associated with the hidden antiferromagnetic order was observed. This work paves the way for studies of other materials in this class containing spin reorientation transitions and magnetic rare earth ions.

This work develops a new generalized technique for determining the static and dynamic properties of any non-collinear magnetic system. By rotating the spin operators into the local spin reference frame, we evaluate the zeroth, first, and second order terms in a Holstein-Primakoff expansion, and through a Green's functions approach, we determine the structure factor intensities for the spin-wave frequencies. To demonstrate this technique, we examine the spin-wave dynamics of the generalized Villain model with a varying interchain interaction. The new interchain coupling expands the overall phase diagram with the realization of two non-equivalent canted spin configurations. The rotational Holstein-Primakoff expansion provides both analytical and numerical results for the spin dynamics and intensities of these phases.

We have identified three of the four magnetoelectric modes of multiferroic BiFeO3 measured using THz spectroscopy. Excellent agreement with the observed peaks is obtained by including the effects of easy-axis anisotropy along the direction of the electric polarization. By distorting the cycloidal spin state, anisotropy splits the Ψ±1 mode into peaks at 20 and 21.5 cm −1 and activates the lower Φ±2 mode at 27 cm −1 (T = 200 K). An electromagnon is identified with the upper Ψ±1 mode at 21.5 cm −1 . Our results also explain recent Raman and inelastic neutron-scattering measurements. Multiferroic materials hold tremendous technological promise due to the coupling between the electric polarization and cycloidal magnetic order. Two classes of multiferroic materials have been identified. In "proper" multiferroics, the cycloid develops at a lower temperature than the ferroelectric polarization; in "improper" multiferroics, the electric polarization is directly coupled to the cycloid [1, 2] so they develop at the same temperature. Although the multiferroic coupling is typically stronger in "improper" multiferroics, those materials also have rather low transition temperatures. Due to the high magnetic transition temperatures of "proper" multiferroics like BiFeO 3 with T N ≈ 640 K [3-5], those materials continue to attract a great deal of interest. With the availability of single crystals, the physical understanding of BiFeO 3 has advanced rapidly over the past few years but the description of the distorted spin cycloid and microscopic interactions in BiFeO 3 remains incomplete.Recent inelastic neutron-scattering measurements on single-crystal samples of BiFeO 3 [6,7] were used to estimate the easy-axis anisotropy K along the polarization direction as well as the Dzyaloshinskii-Moriya (DM) coupling D that induces the long-period cycloidal order with wavevector Q = (2π/a)(0.5 + δ, 0.5, 0.5 − δ) and δ ≈ 0.0045 [8][9][10]. However, more precise estimates for those coupling constants may be obtained based on the magnetoelectric peaks recently measured using THz spectroscopy [11]. In this work, we evaluate the magnetoelectric peaks from a model that includes easy-axis anisotropy and DM interactions. In addition to providing excellent agreement for three of the four experimental peaks, we also provide several new predictions for the selection rules governing those three peaks and one higherenergy peak.