Magnetic Signature of Chiral Phonons Revealed by Neutron Spectroscopy in Ferrimagnetic Fe$_{1.75}$Zn$_{0.25}$Mo$_3$O$_8$

Abstract

Lattice vibrations can carry angular momentum and magnetic moments under broken inversion or time-reversal symmetry, forming so-called chiral phonons. While such excitations have been explored in nonmagnetic systems via optical probes, their direct detection in magnetic materials and coupling to spin excitations remain largely unexplored. Here, using neutron spectroscopy, sensitive to both nuclear and magnetic scattering, we reveal the magnetic signature of chiral phonons in ferrimagnetic Fe$_{1.75}$Zn$_{0.25}$Mo$_3$O$_8$ with Curie temperature $T_{\rm C}\sim49$ K. Below $T_{\rm C}$, we observe enhanced magnetic scattering of phonons at small momenta, arising from strong magnon-phonon coupling. In addition, out-of-plane intensity modulation, phonon mode splitting, and field-induced Zeeman shifts are observed, all closely associated with the ferrimagnetic order. These features vanish above $T_{\rm C}$, where phonon spectra are dominated by nuclear scattering. These observations demonstrate the existence of chiral phonons carrying substantial magnetic moments that directly contribute to magnetic scattering, and establish neutron spectroscopy as a powerful, momentum-resolved probe of their magnetic character.

Figures (4)

• Figure 1: (a) Schematic of neutron probing of lattice vibrations: conventional linear phonons give only nuclear (N) scattering, whereas chiral phonons with phonon magnetic moments ($\mu_{\rm ph}$) yield both N and magnetic (M) signals. (b) Room-temperature powder XRD pattern and Rietveld refinement. Inset: ferrimagnetic structure and Zn-induced lattice distortions in FZMO, with Fe--O bond lengths labeled (values for FMO in parentheses). (c) Magnetic susceptibility of an FZMO single crystal under zero-field-cooled (ZFC) and field-cooled (FC) conditions in a 0.1-T field. Inset: $M$-$H$ curves at 10 K. (d) Temperature dependence of the integrated intensity of the (1, 0, 1) magnetic Bragg peak measured on EIGER. Error bars denote one standard deviation throughout the paper. The red curve is a power-law fit and the dashed line is a guide to the eye. Inset: elastic scans along (1, 0, $L$) at 1.5 and 53.5 K.
• Figure 2: (a)-(c) INS spectra of FZMO at 6 K along the [100], [110], and [001] (left), compared with calculated spin-wave spectra (right). Data were measured on 4SEASONS with $E_{\rm i}$ = 18 and 30 meV, scaled to incoherent elastic scattering. Integration ranges are listed in Table S3sm. (d), (e) Brillouin zone in 3D and its 2D projection with high-symmetry paths. (f) Energy scans at (1.2, 0, 0) under varying magnetic fields, measured on EIGER. Diamonds and circles denote data collected in normal- and high-resolution configurations, respectively, with vertical offsets applied for clarity. Curves are Gaussian fits and dashed lines are guides to the eye. (g) Extracted peak positions as a function of field, compared with model predictions (solid lines). Up and down arrows denote spin quantum numbers $\Delta S_z=+1$ and $-1$.
• Figure 3: (a)-(c) Phonon spectra at 6 K along ($H$, 0, 0), (1, 0, $L$), and (2, 0, $L$). (d)-(f) Corresponding spectra at 100 K. Data with $E_{\rm i} = 12$ meV are corrected by Bose factor. (g) Schematic illustrating the coupling between phonon magnetic moments ($M_{\rm p}$) arising from in-plane rotation of Fe1 ions (right-handed example shown) and net spin moments ($M_{\rm s}$) in adjacent layers for ferrimagnetic (FIM) and antiferromagnetic (AFM) states. (h) Constant-$E$ cuts along (1, 0, $L$) for FZMO (red circles) and FMO (blue squares). (i) Corresponding cuts along (2, 0, $L$). The energy interval is $5.4\pm0.4$ meV. Curves are Lorentzian fits. Solid (dashed) arrows mark intense zone-center chiral optical phonons in FZMO (FMO), while triangles indicate dominant nuclear scattering contributions in (h), (i); the same symbols appear in (b), (c) for guidance.
• Figure 4: (a) Phonon spectra of FZMO at 6 K along [001], integrated over equivalent Brillouin zones. Black circles mark peak positions from Lorentzian fits to various constant-$q$ cuts. (b), (c) Constant-$q$ cuts at zone center for 6 K and 100 K. (d)-(f) Corresponding data for FMO. Dashed and solid lines denote transverse acoustic (TA) and chiral optical phonon (CH) modes, respectively.