Spin state and spectroscopic modes of multiferroic BiFeO3

Abstract

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.

Spin-induced polarizations and nonreciprocal directional dichroism of the room-temperature multiferroicBiFeO3

“…Due to the very long cycloidal period p ≫ a of BiFeO 3 , the equilibrium and dynamical properties of these two Hamiltonians are the same up to errors of order δ 2 ≈ 2 × 10 −5 . Specifically, earlier predictions for the SW mode frequencies 27,28 and critical magnetic field 39 are unchanged. However, the earlier DM interaction D 1 is now multiplied by √ 2.…”

“…As mentioned above, the DM interactions D 1 and D 2 only couple nearest-neighbor sites. In a previous formulation 27,28 of this microscopic model, D 1 coupled next-neighbor sites within the same hexagonal layer. Due to the very long cycloidal period p ≫ a of BiFeO 3 , the equilibrium and dynamical properties of these two Hamiltonians are the same up to errors of order δ 2 ≈ 2 × 10 −5 .…”

“…The parameters K, D 1 , and D 2 were estimated by fitting the frequencies 27 of the four observed zero-field THz modes. With no remaining adjustable parameters, that same model predicted 28 the evolution and activation of the THz modes 19 in a magnetic field along [0, 0, 1].…”

Spin and lattice excitations of aBiFeO3thin film and ceramics

“…25 Time-domain THz spectroscopy, 26 inelastic neutron scattering measurements [27][28][29][30] and absorbance spectroscopy in the THz range 31 have revealed modes similar to the Raman-active onespredicted by theoretical calculations. [31][32][33][34][35] The best agreement between the experimental and theoretical spin-excitation frequencies (including their splitting in external magnetic field) was obtained for a microscopic model that takes into ac-count the nearest and next-nearest neighbor exchange interactions, two Dzyaloshinskii-Moriya interactions and an easy-axis anisotropy. 31,35 The same model successfully described the low-energy inelastic neutron scattering spectra.…”

Giant Spin-Driven Ferroelectric Polarization inBiFeO3at Room Temperature

“…Recall that [16] To calculate the electric-field-induced lattice distortion and the associated change in J 1 , we employ a method [17] that was successfully applied to other multiferroic oxides. The resulting ESP coefficients are given in Table I.…”