TY - JOUR
T1 - Spin state and spectroscopic modes of multiferroic BiFeO3
AU - Fishman, Randy S.
AU - Haraldsen, Jason T.
AU - Furukawa, Nobuo
AU - Miyahara, Shin
PY - 2013/4/19
Y1 - 2013/4/19
N2 - 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 terahertz (THz) and Raman spectroscopies were recently identified using a simple microscopic model. While a Dzyaloshinskii-Moriya (DM) interaction D along [-1,2,-1] induces a cycloid with wave vector (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.
AB - 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 terahertz (THz) and Raman spectroscopies were recently identified using a simple microscopic model. While a Dzyaloshinskii-Moriya (DM) interaction D along [-1,2,-1] induces a cycloid with wave vector (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.
UR - http://www.scopus.com/inward/record.url?scp=84876955116&partnerID=8YFLogxK
U2 - 10.1103/PhysRevB.87.134416
DO - 10.1103/PhysRevB.87.134416
M3 - Article
AN - SCOPUS:84876955116
SN - 1098-0121
VL - 87
JO - Physical Review B - Condensed Matter and Materials Physics
JF - Physical Review B - Condensed Matter and Materials Physics
IS - 13
M1 - 134416
ER -