Magnetic excitons in a suspended 2D antiferromagnetic membrane

Abstract

Layered magnetic and strongly correlated materials present a rich platform for condensed matter physics with intrinsic properties intertwined by magnetism and low-dimensionality. A suspended light-emitting 2D antiferromagnetic membrane forms a highly controllable hybrid system in which the interplay between spin ordering, optical and mechanical degrees of freedom can be uniquely explored. NiPS$_3$ hosts excitons responsible for a puzzling luminescence down to a few atomic layers, linked to its zigzag antiferromagnetic order. The nature of these excitons remains unclear. Here we report on the magnetic excitons of a suspended few-layer NiPS$_3$ membrane. We reveal nematic zigzag states and study the optical transitions induced by the magnon-mediated motion of the excitation in the magnetic lattice, resulting in magnon-dressed excitons. We observe a strain tuning of these emission lines, dependent on their microscopic origin, with rates that sign a strong localization of the magnetic excitons, fading with the number of magnon-mediated hops.

Figures (4)

• Figure 1: A light-emitting drum-like antiferromagnetic membrane.a, The magnetic structure of NiPS$_3$ (top and side views) displays a zigzag antiferromagnetic order supported by the Ni$^{2+}$ ions in a preferential direction determined by the monoclinic stacking along cOuvrard1985. b, Optical picture of a 10-layer NiPS$_3$ suspended membrane on a Si/SiO$_2$ pre-patterned substrate (see Methods). The membrane is addressed by a focused laser beam in vacuum at 5.5 K and contacted by a gold electrode to apply a gate voltage $V_\mathrm{G} = V_\mathrm{DC} + V_\mathrm{AC} \cos \Omega t$. c, Spatially-resolved static reflectance of the membrane, with its boundaries marked by white dashes, measured as a function of the applied static gate voltage (i-v: $V_\mathrm{DC} =$ 0, 54, 64, 70 and 74 V). The system reflectance is modeled as a function of the membrane deflection, plotted as a solid line in vi, with the relative reflectance measured at the center of the membrane appearing as color dots as a function of the static gate voltage from 0 V (yellow) to 75 V (blue). The integrated static in-plane strain $\epsilon$ can be then estimated (see SI). d, Mechanical response of the membrane fundamental mode to an electrostatic drive upon increasing static voltage ($V_\mathrm{AC} = 10\,$mV). The inset is a zoom on the low-voltage region. e, Photoluminescence spectrum from the center of the 10-layer NiPS$_3$ membrane at $V_\mathrm{DC}=0$ V. The dashed rectangle corresponds to the region of interest with emission peaks exhibiting sub-meV linewidths, originating from a triplet-to-singlet magnetic excitation with $J$ Hund's exchange energy ($2J \sim 1.47$ eV). The two arrows within hexagonal tiles picture the particles spin in the two relevant effective orbitals centered on a Ni site, forming the triplet ground state or the singlet superposition, in blue and yellow respectively.
• Figure 2: Polarization of the light emitted by a few-layer NiPS$_3$ membrane revealing nematic families.a, Photoluminescence spectra from the center of the membrane for analyzing angles between 0 and 360$^\circ$ revealing transitions from two distinct nematic families (labeled with subscripts A and B). b, Polarized Raman spectroscopy at the center of a few-layer NiPS$_3$ membrane involving the phonon modes A$_g^2$ and B$_g^2$ used as the angle reference. c, Zoom on the PL spectra from 0$^\circ$ to 90$^\circ$. The color dashed lines indicate the location of the spectra shown in e. d, Extracted energy and Voigt full width at half maximum of the main peaks from the membrane and its immediate surroundings for three different analyzing polarization marked in red, green and blue dotted lines in a. The top sketches represent the magnetic ground state of nematic families A and B. The transparency scales on the peak relative intensity, the color scales with the DC reflectance to highlight the suspended region (see SI). For each analyzing polarization, the S and S' peaks properties are reported as a function of the relative energy and linewidth of the main peak. e, Photoluminescence spectra for analyzer angles of 4$^\circ$ (gold), 54$^\circ$ (silver) and 79$^\circ$ (bronze). Solid lines are fit to Voigt profiles (see SI). Inset: normalized integrated intensity in the range $1.4758\pm 1\times10^{-4}$ eV for X$_\mathrm{A}$ (light blue dots), $1.4761\pm 1\times10^{-4}$ eV for X$_\mathrm{B}$ (red dots), and $1.4776\pm 3\times10^{-4}$ eV for S$_\mathrm{A}$ (purple dots) as a function of the analyzing angle $\theta_A$. The solid lines are fit to $\cos^2(\theta_A - \theta_{\mathrm{X_i}})$, leading to the relative polarization angles $\theta_{\mathrm{X_A}} = 0^\circ = \theta_{\mathrm{S_A}}$ and $\theta_{\mathrm{X_B}} = 72^\circ$.
• Figure 3: Strain-tuned photoluminescence of the main magnetic exicton in a few-layer NiPS$_3$ membrane.a, Photoluminescence spectra zoomed on the main emission peak as a function of the static gate voltages $V_\mathrm{DC}$ from 0 to 80 V, with an analyzing polarization favoring X$_\mathrm{A}$, at the center of the membrane. b, Photoluminescence spectra acquired on a nearby supported area in the same conditions. c, Comparison of the extracted photoluminescence peak energy shifts $\mathrm{E_{XA}}-\mathrm{E_{XA}}(0\,\mathrm{V})$ as a function of increasing and decreasing static gate voltages at the center of the membrane (red) and at nearby supported location (blue) (i). The solid lines are fits in $a_V V^4_\mathrm{DC}$, where $a_V =-4.3$ peV/V$^4$ ($-4.0$ peV/V$^4$) for increasing (decreasing) voltages, corresponding to an energy shift of meV/% of radial strain. The insets (ii) and (iii) show respectively the variation of linewidth and normalized peak intensity extracted from the suspended membrane photoluminescence. The intensity follows $V_\mathrm{DC}^2$ as the vertical deflection of the membrane. d, Spatially-resolved comparison of the photoluminescence spectra in the vicinity of the drum, for a static gate voltage of 75 and 0 V: (i) the energy, (ii) the linewidth and (iii) the integrated photoluminescence. The dashed lines represent the membrane contour determined from the DC optical reflectance at 633 nm measured simultaneously on a photodiode.
• Figure 4: Strain tuning and nature of the different magnetic excitons.a, Spatial correlation between the energy shifts observed on X$_\mathrm{B}$ and the energy shifts on X$_\mathrm{A}$ at 75 V (0 V being the reference) over the membrane and its surroundings. The transparency scales on the peak relative intensity, the color scales with the DC reflectance (see d and SI). Lines with slopes of 1, 2 and 4 are indicated as a guide for the eyes. b, (i) Energy shift for S$_\mathrm{A}$ (purple), and corresponding X$_\mathrm{A}$ (light blue), with 0 V as the reference. The solid lines are fits in $a_V V^4_\mathrm{DC}$, where $a_V^\mathrm{SA} =-10.3$ peV/V$^4$ and $a_V^\mathrm{XA} = -4.5$ peV/V$^4$. (ii) Correlations between the shift in X$_\mathrm{A}$ and S$_\mathrm{A}$. c, Spatial correlation between the energy shifts at 75 V (0 V being the reference) of S' and X. The transparency scales on S' peak relative intensity, the color scales with the DC reflectance. d,(i) DC reflectance used to map the spatial correlation in a and c, highlighting in red and in yellow the suspended and supported parts, respectively. (ii-iv) Spatially-resolved energy shifts on S' analyzed with the three analyzing polarizations shown in Fig. \ref{['fig:fig3']} (red, green, blue, favoring $X_\mathrm{B}$ for the former and $X_\mathrm{A}$ for the latter). e, Sketches of the magnetic configuration before the recombination of the X exciton (bare exciton), of the S exciton after one hop of the excitation (exciton dressed by one magnon) and of the S' exciton after two hops of the excitation (exciton dressed by two magnons), respectively.