Neutron inelastic scattering measurements of low energy phonons in the multiferroic BiFeO3

Abstract: We present neutron inelastic scattering measurements of the low-energy phonons in single crystal BiFeO3. The dispersions of the three acoustic phonon modes (LA along [100], TA1 along [010] and TA2 along [110]) and two low energy optic phonon modes (LO and TO1) have been mapped out between 300 K and 700 K. Elastic constants are extracted from the phonon measurements. The energy linewidths of both TA phonons at the zone boundary clearly broaden when the system is warmed toward the magnetic ordering temperature TN = 640 K. This suggests that the magnetic and low-energy lattice dynamics in this multiferroic material are coupled.

• The paper demonstrates that TA phonon modes experience significant broadening near the antiferromagnetic transition (TN ≈ 640 K) due to dynamic spin-phonon coupling.
• The study employs high-precision neutron inelastic scattering on high-quality single crystals to map acoustic and optic phonon dispersions and extract elastic constants such as C11 = 58 GPa and C44 = 42 GPa.
• The results offer critical insights into magnetoelastic interactions in BiFeO3, highlighting their potential impact on the design of magnetoelectric devices.

Neutron Inelastic Scattering of Low-Energy Phonons in Multiferroic BiFeO$_3$

Introduction

This work presents high-precision measurements of low-energy phonon excitations in the archetypal multiferroic BiFeO$_3$ via neutron inelastic scattering over a broad temperature range (300–700 K) (1410.2316). The study explicitly focuses on mapping the detailed dispersion for long-wavelength acoustic (LA, TA$_1$, TA$_2$) and low-energy optic (LO, TO$_1$) phonon modes and extracting bulk elastic properties. The central finding is the observation of significant broadening in the energy linewidths of transverse acoustic (TA) phonons as the system approaches the antiferromagnetic transition temperature $T_N \approx 640$ K, providing evidence for dynamic coupling between magnetic and lattice degrees of freedom.

Experimental Approach

Single crystals of BiFeO$_3$ of high crystalline quality (mosaicity <1$^\circ$) were grown using the traveling-solvent floating-zone method. Neutron time-of-flight spectroscopy (HYSPEC at SNS, $E_i$ = 20 meV) allowed comprehensive sampling of the reciprocal space by rotating the crystal, enabling full mapping of phonon dispersions along principal symmetry directions within the pseudocubic cell. Measurements were conducted across three Brillouin zones and at three temperatures: 300 K, 500 K, and 700 K, straddling the antiferromagnetic ordering temperature $T_N$.

Phonon Dispersion and Elastic Properties

The dispersions of the longitudinal (LA, [100]) and transverse acoustic phonons (TA$_1$, [010]/[100]; TA$_2$, $[1\bar{1}0]$/[110]) were extracted by fitting the dynamic structure factor to Lorentzian lineshapes convoluted with instrumental resolution. Optic phonon branches (LO, TO$_1$) were also measured near the zone center, though their intensities were notably weaker.

The extracted limiting slopes provided direct access to sound velocities, from which the following elastic constants were deduced at room temperature:

• $C_{11} = 58(6)$ GPa
• $C_{44} = 42(4)$ GPa
• $C_{12} = 17(2)$ GPa
• Bulk modulus $B = 31(3)$ GPa

These values are consistent with some neutron-scattering and theoretical studies but notably contradict higher $C_{11}$ values (up to 207 GPa) reported from x-ray experiments and ultrasonic measurements, which can be traced to differences in coordinate system, averaging over polycrystalline samples, and LA mode definitions.

The measured optic mode energies around 8 meV also align with zone-center features observed by Raman (57 cm$^{-1}$) and infrared spectroscopy (66 cm$^{-1}$), as well as previous powder neutron studies. The lowest TO branch appears below 9 meV, somewhat at variance with alternative claims ($\sim$9.2 meV) from previous works.

Temperature Dependence and Spin-Phonon Coupling

A detailed comparison of phonon line shapes as a function of temperature reveals a pronounced, selective broadening of the TA phonon energy widths (i.e., inverse lifetimes) at the Brillouin zone boundaries as $T_N$ is approached from below, without appreciable broadening for LA phonons or TA phonons near the zone center. No significant phonon softening was observed except for the zone-boundary TA modes, where the magnitude is comparable to experimental uncertainty ($\lesssim$0.3 meV).

This selective broadening is highly correlated with the onset of the magnetic transition, indicating that the lifetimes of long-wavelength TA phonons are strongly influenced by magnetic fluctuations. The coupling, most evident at large $q$, is attributed to a combination of spin–polar phonon and TA-TO phonon interactions, where the energy gap between TA and TO modes decreases at the zone boundary, amplifying mode hybridization effects. No analogous coupling or broadening was observed for the LA-LO modes, consistent with the larger separation of their energies.

The results build direct evidence for magnetoelastic coupling impacting low-energy acoustic phonons, expanding upon Raman-based observations that had been limited to optic modes. The data support the scenario in which melting of long-range antiferromagnetic order at $T_N$ triggers dynamical instabilities in specific lattice modes, potentially enabling or enhancing multiferroic functionalities mediated by spin-lattice entanglement.

Implications and Outlook

These findings have direct implications for the understanding and engineering of multiferroic phenomena in perovskite oxides. The coupling between magnetic and vibrational DOF in BiFeO$_3$ may play a critical role in the stability and dynamics of the cycloidal spin structure and in determining the effectiveness of phonon- or magnon-mediated device operations, particularly those relying on dynamic or non-equilibrium properties.

The observed broadening of TA phonons at the approach to $T_N$ suggests that the design of room-temperature magnetoelectric devices based on BiFeO$_3$ or related materials should account for the impact of dynamic magnetic-lattice interactions on phonon transport, mechanical Q-factors, and possibly heat dissipation. Such couplings could also be exploited for the non-linear control of material responses by external fields.

Further investigations—potentially combining polarized neutron scattering, ultrafast optical probes, or inelastic x-ray scattering in reduced dimensions—could elucidate the microscopic details of the coupling mechanism and map its response to epitaxial strain, doping, or engineered interfaces, providing a pathway for functional optimization.

Conclusion

Comprehensive neutron inelastic scattering experiments on single-crystal BiFeO$_3$ have revealed the full dispersion of low-energy acoustic and optic phonons and established precise values for bulk elastic constants. The data demonstrate a selective, temperature-dependent broadening of TA phonon modes at the zone boundary linked to the melting of antiferromagnetic order, unambiguously evidencing strong spin-phonon dynamic coupling. These results contribute critical spectroscopic insight into the interplay between lattice and magnetic subsystems in multiferroic BiFeO$_3$, with substantial consequences for both the fundamental physics and application potential of these correlated systems.