Low energy electrodynamics of CrI3 layered ferromagnet

We report on the optical properties from terahertz (THz) to Near-Infrared (NIR) of the layered magnetic compound CrI3 at various temperatures, both in the paramagnetic and ferromagnetic phase. In the NIR spectral range, we observe an insulating electronic gap around 1.1 eV which strongly hardens with decreasing temperature. The blue shift observed represents a record in insulating materials and it is a fingerprint of a strong electron-phonon interaction. Moreover, a further gap hardening is observed below the Curie temperature, indicating the establishment of an effective interaction between electrons and magnetic degrees of freedom in the ferromagnetic phase. Similar interactions are confirmed by the disappearance of some phonon modes in the same phase, as expected from a spin-lattice interaction theory. Therefore, the optical properties of CrI3 reveal a complex interaction among electronic, phononic and magnetic degrees of freedom, opening many possibilities for its use in 2-Dimensional heterostructures.

www.nature.com/scientificreports/ structural and magnetic phase transitions, down to the liquid helium temperature. The NIR response of CrI 3 shows the presence of an optical gap associated to the crystal-field splitting of the Cr d-bands ( d xy,x 2 −y 2 and d xz,yz ) 30,45 , which is subjected to a giant frequency blue shift (nearly 2000 cm −1 ), from 300 to 5 K. Although this giant hardening is mainly related to a strong electron-phonon interaction, a further blue shift is observed below the ferromagnetic temperature, also suggesting a strong coupling among electronic and magnetic degrees of freedom.
In the far infrared, we show the presence of single and multiple-phonon excitations superimposed to a broad absorption background. We study the temperature dependence of these excitations and their modification with the appearance of a magnetic order.

Results and discussion
CrI 3 single crystals were synthesized by a chemical vapor transport technique (see Methods). The crystal structure of CrI 3 is shown in Fig. 1a. The Chromium (Cr) and Iodine (I) atoms are bonded to form honeycomb ordered layers. The arrows indicate the a, b and c crystal axes. The bulk crystal structure of CrI 3 at room temperature is described by a monoclinic (space group C2/m) unit cell. Below the structural phase transition at T struc ∼ 220 K, this changes to a rhombohedral symmetry (space group R 3 ) 30 . Reflectance (R) and Transmittance (T) measurements were performed in a broad spectral range from THz (20 cm −1 ) to NIR (15000 cm −1 ) (~ 2.5 meV-1.86 eV) and temperatures from 5 to 300 K. The spectroscopy set-up is discussed in the Methods section. In Fig. 1b we report the room temperature R and T of a CrI 3 single crystal with a 300 μm thickness. Fig. 1c shows the real part of the refraction index, while Fig. 1d the corresponding absorption coefficient, both extracted through the RefFit Kramers-Kronig consistent fitting process 46 . The reflectance spectrum is dominated by a strong phonon absorption near 230 −1 , which can be associated to the in-plane E u collective oscillations of Cr atoms 31 (see Fig. 1e). In the far-infrared transmittance, we are instead able to resolve (b) Optical reflectance and transmittance of a 300 μm thick CrI 3 crystal at 300 K. The reflectance is dominated by a single phonon mode at 230 cm −1 . The measured transmittance highlights instead a plethora of far infrared vibrational modes and a band-gap around 9200 cm −1 . (c) Real part of the refractive index of CrI 3 at 300 K. (d) Absorption coefficient at 300 K of CrI 3 . (e) In-plane phonon mode of the Cr atoms, associated to the strong vibrational mode at 230 cm −1 in the bulk CrI 3 . www.nature.com/scientificreports/ additional low energy absorption peaks, extending to nearly 400 cm −1 which are related to multi-phonon excitations (see below). Above 400 cm −1 , a flat transmittance (absorbance) is observed, extending up to the crystal-field electronic gap that can be observed both in transmittance and reflectance at room-T around 9200 cm −1 (1.14 eV). The transmittance minima (broad weak maxima in the absorption coefficient, Fig. 1d), appearing on the IR plateau at about 1600 and 3600 cm −1 , are instead associated to the bending and stretching vibrations of few intercalated water molecules among the CrI 3 layers 47 . Indeed, layered systems are common hosting materials for various intercalant species, ranging from small ions to atoms and molecules 48 .

Scientific Reports
Temperature dependence of the electronic gap. The temperature dependent transmittance measurements in the NIR spectral region are highlighted in Fig. 2a. Here, a huge blue shift (nearly 2000 cm −1 ) of the electronic gap E g can be observed with decreasing temperature from 300 K to 5 K. E g (T) values are extracted by a linear fitting of the decreasing transmittance through its intercept with the frequency axis 49 . E g (T) as a function of temperature is reported in Fig. 2b. In this Figure, both the ferromagnetic Curie temperature T c and the structural transition temperature T struc have been indicated by vertical dotted lines. While across the structural transition the electronic gap presents a smooth behavior, at the paramagnetic/ferromagnetic transition a discontinuity appears with a robust increase in the gap value below T c . Both the lattice expansion and the electronphonon interaction may induce a temperature dependence of the electronic gap 50,51 . Both terms can be modeled through the Manoogian and Leclerc empirical equation 50,52 where U, s, V and ǫ are temperature independent coefficients. U and V are the coupling constants weighting the lattice expansion and electron-phonon interaction contributions, respectively, while ǫ is an energy averaging all the acoustic and optical phonons. E g data in Fig. 2b for the paramagnetic phase have been fitted through Eq.
(1). The result is shown in Fig. 2b through a dashed purple line. Fitting coefficients in Eq. (1) are presented in Table 1, compared to other semiconductors from literature. The lattice expansion, parametrized by U, has been found to give a negligible contribution to the temperature dependence of E g . The strongest effect is thus given by the electron-phonon interaction, whose intensity is measured by the coefficient V, higher than the one found in most of the known semiconductors (see Table 1). The further blue shift of the electronic band gap below the Curie temperature suggests a further dependence of the electronic gap from the magnetic degrees of freedom.
In order to quantify this discontinuity, we define an extra gap-value �E g (T) as the difference between the actual gap value E g (T) and that corresponding to the paramagnetic extrapolation below T c , �E g (T) = E g (T) − E fit (T) . E fit (T) is determined by using the Eq. (1) fitting process (see Fig. 2b). At 5 K (the minimum temperature we reach in our optical measurements), �E g (T) = 35 meV . This value cannot be related to a modification of the electron-phonon interaction, since the phonon spectrum is unaltered across the transition (see Fig. 3a). From the theoretical point of view, a recent work 31 calculates the electronic structure of CrI 3 monolayers both in the magnetic and non-magnetic phase. This suggests that the electronic band structure is strongly perturbed by the magnetic state and depends on the magnetization (M) easy axis direction. In particular, the electronic gap is larger when M is along the c-axis than in the ab plane of the CrI 3 structure. This result, calculated for CrI 3 monolayer, seems to be valid also for bulk CrI 3 31 . In this framework, magnetic measurements 54 show that magnetization in bulk single crystals develops along the c-axis. In order to establish a correlation between optical and magnetic data, in the inset of Fig. 2b we show �E g (T) normalized to �E g (T = 5 K) . In the same inset, we also plot the magnetic moment along the c-axis 54 normalized to its lowest temperature (5 K), M(T)/M(5 K). Both quantities follow a very similar trend, suggesting that the extra gap value is related to the development of the magnetic  Table 1). The inset shows the comparison of the extra-gap values �E g (T) (normalized to �E g (5 K) , see text) and the magnetization order parameter M(T) normalized at the lowest temperature 54 . www.nature.com/scientificreports/ state. These results highlight a complex degrees of freedom interplay in CrI 3 , suggesting that the electronic gap hardening might be related to a non-trivial coupling between the electrons and the magnetic order 26,29,35 .
Far infrared response. The far-IR absorption coefficients at different temperatures are shown in Fig. 3a in an expanded vertical scale. The spectra are composed by several peaks located between 70 and 360 cm −1 and we observe an overall decrease of the absorption by reducing T. Due to the van der Waals nature of the CrI 3 crystal and the in-plane polarization of the incident radiation in this experiment, a single layer model for the lattice vibrations is expected to describe the experimental phonon absorption peaks. Indeed, CrI 3 layers can be described by the D 3d point group symmetry 31,55 , which predicts five IR-allowed transitions, namely three E u modes and two A 2u modes, three inactive modes (one A 1u and two A 2g ), and six Raman-active modes (two A 1g and four E g ). Raman spectra have already been measured in previous works 15,[56][57][58][59][60][61] , revealing the presence of magnons and a plethora of magneto-optical effect. The corresponding Raman peaks at room-T are reported in Table 2, together with numerical calculations (at 0 K) 61-63 and the IR absorption peaks observed at room-T in our experiment, as measured by absorption peak maxima. In the theoretical calculations, the heavier iodine atoms are predicted to dominate the phonon spectrum below 150 cm −131,64 , therefore being related to the strong absorption peaks at 82 cm −1 , 114 cm −1 ( E u modes) and 133 cm −1 ( A 2u mode). At higher energies, above the strong absorption at 230 cm −1 ( E u symmetry, mainly due to Cr vibrations), a series of peaks can be seen in Fig. 3a, with a strong spectral weight from 300 to 360 cm −1 . These higher frequency excitations are not predicted by the ab-initio calculations for CrI 3 31,62,64 . However, their frequencies can be captured by a linear combination of Raman and IR fundamental modes as reported in Table 2, suggesting an important role of anharmonicity in the phonon spectrum of CrI 3 . A general absorptive background is highlighted across the low energy spectrum, showing an increasing transparency with the lowering temperature. Visible differences in the absorption background behavior can be highlighted while crossing the Curie temperature. The inset shows the contribution of the absorptive background (black curve) to the total absorption coefficient at 300 K (blue curve). The gray curve shows the contributions coming from the known phonon peaks. Table 1. Coefficients for the band gap frequency shift of semiconductors as a function of temperature, as obtained by the model of Eq. (1). The symbol "-" highlights missing values from literature. The resulting temperature dependence for CrI 3 is shown in Fig. 2. , showing their dependence from the magnetic ordering. Indeed, their temperature dependence (they nearly disappear below T c ) is not trivial. A similar result is obtained for the A 2u predicted in-plane phonon at 133 cm −1 (as measured at T = 300 K ), which seems to disappear at low temperatures. These results have been explained in terms of a strong spin-phonon coupling 64 , which predicts the appearance of a gap in the phonon density of states between the two E u modes at 113 and 230 cm −1 .
The low-energy (THz) side of the absorption coefficient suggests the presence of a broad background. Its general shape and temperature dependence can be obtained by a best fitting process of the absorption coefficient at various temperatures, taking into account the phonon peaks previously discussed (see the inset of Fig. 3b for an example of fitting at 300 K). An absorption background has been observed in the THz range in α-RuCl 3 65,66 . Although strongly debated, this background has been mainly associated to Kitaev spin liquid excitations. In CrI 3 , at variance with α-RuCl 3 , this broad absorption, centered around 70 cm −1 , is already present at room-T and decreases with reducing T, nearly saturating below T c (see Fig. 3a). The broad temperature-dependent THz background could have electronic, lattice, or magnetic origins. Bulk CrI 3 is a very good electric insulator with an electronic gap around 1.2 eV. This implies that we do not expect thermally-induced free electrons in the material (in particular at low-T), which can affect the absorption in the THz range. This excludes an electronic origin of the THz background. In RuCl 3 Kitaev-like material, where many theoretical calculations exist for the 3D magnetism, a similar background (of magnetic origin) increases with decreasing T. In CrI 3 , instead, it is a decreasing function of T, nearly reaching an intensity saturation at T c . Moreover, it is located around 10 meV, an energy larger than the exchange magnetic energy in CrI 3 ( J ∼ 3 meV) 67 . This difference, associated to the decreasing T-dependence, suggests a non-magnetic origin. The last mechanism, i.e., acoustic phonon assisted absorption, has been proposed some years ago to explain extra absorptions in the THz and sub-THz regions in alkali-halides 68,69 . The extra absorption corresponds to processes in which optical modes are excited by photons concomitantly with the absorption of acoustic modes at high wavevectors. Due to the quasi-continuum distribution of acoustic modes, one expects a broad absorption band, which depends on T due to the modes T-dependence. In conclusion, the characteristic background energy (nearly 10 meV) and its temperature dependence seem to rule out both a magnetic and electronic origins, suggesting instead an acoustic assisted mechanism at the main contributor.

Conclusions
In this work we have investigated the optical response of a CrI 3 single crystal from Terahertz to Near-Infrared at various temperatures, both in the paramagnetic and ferromagnetic phase. We have observed an insulating optical gap around 1.1 eV at 300 K which strongly depends on temperature, showing a robust hardening for decreasing T. This hardening is due to a huge electron-phonon interaction which is reinforced below the Curie critical temperature at nearly 60 K. This indicates a complex interaction scenario among lattice, electronic and magnetic degrees of freedom in CrI 3 system.
By studying the far-IR/THz absorption spectrum we have observed several phonon peaks that have been assigned in agreement to the D 3d point group symmetry and DFT calculations. Our finding of some magneticsensitive peaks could be the first experimental evidence that these lowest-frequency absorptive terms exhibit strong spin-phonon coupling. The phonons absorption is also superimposed to a broad background already visible at 300 K and having a decreasing magnitude with T. This is at variance with the isostructural α-RuCl 3 compound, where the absorption background increases at low-T and has been associated mainly to Kitaev spin liquid excitations. Although CrI 3 has been suggested to be a candidate to host similar fractionalizated excitations, as indicated by recent theoretical results 70 and by the discovery of gapped Dirac magnon dispersions 43 , this absorption background could have a different origin probably related to the strong lattice anharmonicities. Although we studied the optical properties of CrI 3 in its bulk form, their dependence on the magnetic transition suggests that also for few-layer CrI 3 the electronic excitations should be strongly correlated to the magnetic ones. This suggests a complex interplay among different degrees of freedom in CrI 3 that, when controlled, could induce a rich variety of quantum phenomena. In conclusion, the present experiment clarifies the low-energy Table 2. CrI 3 vibrational modes frequencies (in cm −1 ) at 300 K. The values in the quadratic brackets highlight the in-plane Raman-and IR-active modes at 0 K, as obtained by DFT results 31 . The first column shows the experimental Raman modes 61,63 . The IR-active experimental modes obtained in this work are shown in the second and third columns. www.nature.com/scientificreports/ electrodynamics of bulk CrI 3 , fixing a solid point for the investigation of its optical behavior in the dimensionality crossover from 3D to 2D.

Methods
Sample Growth. CrI 3 single crystals were synthesized by a chemical vapor transport technique. A 1 g mixture of the stoichiometric ratio of Cr metal and I 2 pieces (Alfa Aesar, 99.99%) was packed in a sealed evacuated quartz glass tube (22 cm long and 16 mm wide) and heated in a three zone furnace, set at zone temperatures 650, 550, and 600 °C, for one week. The "charge" was placed in the 650 °C zone. Many CrI 3 crystals were formed in the 550 °C zone. The crystals are stable in air for a few hours.
Optical characterization. Optical measurements at various temperatures have been performed through a Bruker Vertex 70v Infrared interferometer, coupled with different detectors and beamsplitters covering the spectral region from THz (20 cm −1 ) to NIR (15000 cm −1 ). A liquid He-cooled bolometer has been used for measurements from 20 up to 600 cm −1 , while a room-temperature pyroelectric detector has been used for the higher frequencies. The optical measurements have been taken at various temperatures through a He-cooled ARS cryostat. www.nature.com/scientificreports/