Anisotropic spin-wave excitations in multiferroic ${\mathrm{BiFeO}}_{3}$

Anisotropic spin-wave excitations in multiferroic ${BiFeO}_{3}$

Depei Zhang, Sachith Dissanayake, Barry Winn, Masaaki Matsuda, Toshimitsu Ito, and Randy Fishman

Phys. Rev. B 105, 144426 – Published 21 April 2022

Abstract

Polarized inelastic neutron-scattering experiments have been performed to elucidate the anisotropic behavior of the low-energy spin-wave excitations in a multiferroic ${BiFeO}_{3}$ , which shows a cycloidal spin structure below 640 K. Using neutron polarization analysis for single magnetic domain crystals, magnetic excitation modes in and out of the cycloidal plane below 6 meV were separated successfully. The magnetic excitation spectra were analyzed using linear spin-wave theory. The low-energy magnon density of states consist of several magnon modes, including the two anisotropic modes, $Φ$ and $Ψ$ modes, distributed in and out of the cycloidal plane, respectively, which were previously observed using optical spectroscopies. Furthermore, there are other magnon modes that are not active in optical measurements. A model spin Hamiltonian, which reproduces the spin-wave frequencies observed using optical spectroscopies, explains the overall spectra reasonably well.

Received 8 January 2022
Revised 24 March 2022
Accepted 4 April 2022

DOI:https://doi.org/10.1103/PhysRevB.105.144426

Physics Subject Headings (PhySH)

Magnetoelectric effect Spin dynamics

Multiferroics

Neutron scattering

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Depei Zhang, Sachith Dissanayake^*, Barry Winn , and Masaaki Matsuda ^†

Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA

Toshimitsu Ito

National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Ibaraki 305-8565, Japan

Randy Fishman

Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA

^*Present address: Department of Mechanical Engineering, University of Rochester, Rochester, New York 14627, USA.
^†Corresponding author: matsudam@ornl.gov

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Vol. 105, Iss. 14 — 1 April 2022

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Figure 1
Crystal and magnetic structures of ${BiFeO}_{3}$ . (a) The nuclear structure of ${BiFeO}_{3}$ where the black and red arrows represent the hexagonal and pseudocubic unit cells, respectively, and the violet, gold, and red spheres represent the $Bi, Fe$ , and $O$ atoms, respectively. The coordinate transformation equations between the hexagonal and pseudocubic cells are listed. (b) The cycloidal magnetic structure of ${BiFeO}_{3}$ in the pseudocubic cell where the magnetic wave vector is $q_{m} = {[δ, δ, 3]}_{hex}$ with $δ \approx \frac{1}{222}$ , and the cycloidal plane is tilted by $τ = 0 . 46^{\circ}$ from the ${[H, H, L]}_{hex}$ plane. Both $δ$ and $τ$ are exaggerated by 20 times for clarification.
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Figure 2
Contour plots of the polarized inelastic neutron-scattering spectra of ${BiFeO}_{3}$ measured at 300 K. Panels (a)–(c) and (d)–(f) show the neutron intensity $S (Q, ℏ ω)$ as a function of the momentum transfer $Q$ and the energy transfer $ℏ ω$ for the NSF and SF components, respectively, along three orthogonal directions, ${[h, h, 3]}_{hex}$ [(a) and (d)], ${[h, - h, 3]}_{hex}$ [(b) and (e)], and ${[0, 0, l]}_{hex}$ [(c) and (f)]. In panels (a) and (d), $S (Q, ℏ ω)$ is integrated over ${[h, - h, 0]}_{hex}$ for $- 0.05 \leq h \leq + 0.05$ and ${[0, 0, l]}_{hex}$ for $2.9 \leq l \leq 3.1$ ; in panels (b) and (e), the integration is applied over ${[h, h, 0]}_{hex}$ for $- 0.01 \leq h \leq + 0.01$ and ${[0, 0, l]}_{hex}$ for $2.9 \leq l \leq 3.1$ ; whereas in panels (c) and (f), the integration is applied over ${[h, h, 0]}_{hex}$ for $- 0.01 \leq h \leq + 0.01$ and ${[h, - h, 0]}_{hex}$ for $- 0.05 \leq h \leq + 0.05$ . The counting time for each SF and NSF channel is approximately 40 h. The wider excitations in panels (b) and (e) originate from the broader instrumental $Q$ resolution due to the vertical focusing. The intrinsic width is considered to be similar to that along the two other directions. The observed intensities were corrected with the transmission and the flipping ratio factors.
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Figure 3
Energy dependence of the magnetic excitations of ${BiFeO}_{3}$ measured with polarized neutrons. The NSF and SF components correspond to the magnetic excitations out of and in the cycloidal plane, respectively. Panels (a) and (b) compare the experimental and calculated spin-wave intensities for the NSF and SF components, respectively. The filled squares show the $Q$ -integrated neutron intensity $S_{\exp} (ℏ ω) = \int d^{3} Q S_{\exp} (Q, ℏ ω)$ , obtained from the experimental results displayed in Fig. 2 where the integration is applied over ${[h, h, 0]}_{hex}$ for $- 0.01 \leq h \leq + 0.01, {[h, - h, 0]}_{hex}$ for $- 0.05 \leq h \leq + 0.05$ and ${[0, 0, l]}_{hex}$ for $2.9 \leq l \leq 3.1$ . The red solid line represents the calculated $ℏ ω$ dependence of spin-wave intensity $S_{calc} (ℏ ω)$ . The $S_{calc} (ℏ ω)$ is integrated over the the $Q$ points in the vicinity of ${(0, 0, 3)}_{hex}$ considering the experimental $Q$ resolution, which integrates most of the spin-wave excitations in the energy range. The blue and magenta dashed lines show the spin-wave mode contribution of $S_{calc} (ℏ ω)$ from the $Φ$ and $Ψ$ modes, respectively [18]. The excitation signal below 0.5 meV containing the elastic component is not shown.
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Figure 4
Magnetic dispersion relations in the vicinity of ${(0, 0, 3)}_{hex}$ calculated using the linear spin wave theory for ${BiFeO}_{3}$ . The spin wave energies and intensities were calculated using the equations-of-motion technique for noncollinear spins [31] on a pseudocommensurate magnetic supercell containing $M = 2 \times 222$ pseudocubic cells [18]. Panels (a)–(c) and (d)–(f) show the calculated spin-wave intensity, $S (Q, ℏ ω)$ , as a function of the momentum transfer $Q$ and the energy transfer $ℏ ω$ for the NSF and SF components, respectively, along three orthogonal directions, ${[h, h, 3]}_{hex}, {[\sqrt{3} h, - \sqrt{3} h, 3]}_{hex}$ , and ${[0, 0, 3 + 2 \sqrt{6} l]}_{hex}$ , which are consistent with the geometry used in Fig. 2. The wave-vector components $h$ and $l$ are rescaled so that they display the equivalent unit in the horizontal axis.
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Figure 5
Magnetic dispersion relations in the vicinity of ${(δ, δ, 3)}_{hex}$ calculated using the linear spin-wave theory for ${BiFeO}_{3}$ . Panels (a)–(c) and (d)–(f) show the calculated spin-wave intensity $S (Q, ℏ ω)$ for the NSF and SF components, respectively, along three orthogonal directions, ${[δ + h, δ + h, 3]}_{hex}, {[δ + \sqrt{3} h, δ - \sqrt{3} h, 3]}_{hex}$ , and ${[δ, δ, 3 + 2 \sqrt{6} l]}_{hex}$ .
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Physical Review B

covering condensed matter and materials physics

Anisotropic spin-wave excitations in multiferroic ${BiFeO}_{3}$

Depei Zhang, Sachith Dissanayake, Barry Winn, Masaaki Matsuda, Toshimitsu Ito, and Randy Fishman

Phys. Rev. B 105, 144426 – Published 21 April 2022

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Physical Review B

covering condensed matter and materials physics

Anisotropic spin-wave excitations in multiferroic BiFeO3

Depei Zhang, Sachith Dissanayake, Barry Winn, Masaaki Matsuda, Toshimitsu Ito, and Randy Fishman

Phys. Rev. B 105, 144426 – Published 21 April 2022

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Anisotropic spin-wave excitations in multiferroic ${BiFeO}_{3}$