Observation of electromagnons in a monolayer multiferroic

Abstract

Van der Waals multiferroics have emerged as a promising platform to explore novel magnetoelectric phenomena. Recently, it has been shown that monolayer NiI$_2$ hosts robust type-II multiferroicity down to the two-dimensional limit, a giant dynamical magnetoelectric coupling at terahertz frequencies, and an electrically switchable spin polarization. These developments present the possibility of engineering ultrafast, low-energy-consumption, and electrically-tunable spintronic devices based on the collective excitations of the multiferroic order, electromagnons. However, the direct visualization of these bosonic modes in real space and within the monolayer limit remains elusive. Here, we report the atomic-scale observation of electromagnons in monolayer NiI$_2$ using low-temperature scanning tunneling microscopy. By tracking the thermal evolution of the multiferroic phase, we establish the energy scale and resolve coherent in-gap excitations of the symmetry-broken multiferroic state. Comparison with first-principles and spin-model calculations reveals that the low-energy modes originate from electromagnon excitations. Spatially resolved inelastic tunneling spectroscopy maps show a stripe-like modulation of the local spectral function at electromagnon energies, matching theoretical predictions. These results provide direct evidence of the internal structure of electromagnons and establish a methodology to probe these modes at the atomic scale, opening avenues for electrically tunable spintronics.

Figures (3)

• Figure 1: Multiferroic order and collective modes in monolayer multiferroic NiI$_2$. a: Schematic of monolayer multiferroic NiI$_2$. The spin-spiral magnetic order and the electric polarization, with half the periodicity of the magnetic order, are depicted as red and blue arrows, respectively. b: Theoretical density of states (DOS) of the low-energy excitations associated with the symmetry-breaking orders of monolayer NiI$_2$. The DOS of electromagnons and phonons is depicted in green and pink, respectively. c: Schematic of the electromagnon excitations. The local magnetization ($\textbf{S}_i$) is directly coupled to the emergent electric polarization ($\textbf{P}_i$) through the inverse Dzyaloshinskii-Moriya interaction. Electromagnons entail the simultaneous excitation of $\textbf{S}_i$ and $\textbf{P}_i$. d: Schematic of the electromagnon local spectral function of a spin-spiral multiferroic. The coupling between $\textbf{S}_i$ and $\textbf{P}_i$ induces a spatial modulation in the electromagnon spectrum. e: Spatially-resolved IETS of the in-gap excitations enables the observation of the modulated electromagnon modes in the monolayer multiferroic.
• Figure 2: Temperature-dependence of the multiferroic order. a: Large area STM scan of monolayer NiI$_2$ on HOPG (image size $495\times 495 \mathrm{~nm}^{2}, V= 1.2 \mathrm{~V}, I= 3.6 \mathrm{~pA}$). b: STM scan of multiferroic stripes in monolayer NiI$_2$ (image size $30\times 30 \mathrm{~nm}^{2}, V= 1 \mathrm{~V}, I= 25 \mathrm{~pA}$). Inset is a zoomed-in atomic resolution scan of the same island ($7\times 7 \mathrm{~nm}^{2}, V=-1 \mathrm{~V}, I=300 \mathrm{~pA}$). c: The corresponding FFT of the data in panel b. The green circles indicate the peaks associated with the stripe modulation. d: STM scan of multiferroic domains as a function of temperature. At high temperatures, the multiferroic stripes disappear (image size $30\times 30 \mathrm{~nm}^{2}, V= 0.7 \mathrm{~V}, I= 10 \mathrm{~pA}$). e: Corresponding FFT of each scan at different temperatures. The green circles highlight the peaks associated with the multiferroic stripe modulation. f: Spin structure factor ($S(q)$) computed from MC simulations at different temperatures. g: Evolution of the FFT peak gaussian-width inverse (1/$\sigma$) as a function of temperature. h: Evolution of the spin structure peak gaussian-width inverse (1/$\sigma$) as a function of the temperature. The multiferroic transition temperature and spin model parameters can be determined from the fittings.
• Figure 3: Low-energy excitations and electromagnon internal structure in monolayer multiferroic NiI$_2$. a: Temperature evolution of the low-energy in-gap inelastic excitations of monolayer NiI$_2$. b: d$I$/d$V$ point spectrum showing the low-energy excitations of monolayer NiI$_2$. c: Integrated total DOS ($I_{TDOS}$), computed from the contribution from electromagnon and phonon total DOS. The inflection points associated with the electromagnon and phonon excitations are depicted as green and pink dots, respectively. d: Statistical analysis of the symmetrized features of $d^2I/dV^2$ low-temperature IETS. The number of counts as a function of the bias provides a statistical estimation of the inelastic spectrum of monolayer NiI$_2$.The excitation peaks can be attributed to electromagnons or phonons, green and pink peaks respectively, by comparison with the inflection points of the theoretical $I_{TDOS}$. e: Constant current d$I$/d$V$ maps at 0, -3, -4, -5, -8 and -12 mV. f: Corresponding theoretical d$I$/d$V$ maps computed from the integrated total local spectral function from electromagnon and phonons at the same bias as the experimental ones. At low bias, where the electromagnon excitations are dominant, a stripe modulation (direction is indicated with a red arrow in panel e) with the periodicity of the spin spiral can be identified.