Magnetic Raman continuum in single crystalline H$_3$LiIr$_2$O$_6$

TL;DR

This study uses Raman spectroscopy on single crystals of H$_3$LiIr$_2$O$_6$ to identify a magnetic continuum indicative of Kitaev quantum spin liquid behavior, linking experimental observations with theoretical predictions.

Contribution

First Raman spectroscopy investigation of single crystalline H$_3$LiIr$_2$O$_6$, revealing magnetic continuum consistent with Kitaev quantum spin liquid physics.

Findings

Observation of a broad magnetic continuum in Raman spectra

Evidence supporting the Kitaev quantum spin liquid nature of H$_3$LiIr$_2$O$_6$

Synthesis of high-quality single crystals via chemical replacement

Abstract

Recently H$_3$LiIr$_2$O$_6$ has been reported as a spin-orbital entangled quantum spin liquid (QSL) [K. Kitagawa et al., Nature {\bf 554}, 341 (2018)], albeit its connection to Kitaev QSL has not been yet identified. To unveil the related Kitaev physics, we perform the first Raman spectroscopy studies on single crystalline H$_3$LiIr$_2$O$_6$ samples. We implement a soft chemical replacement of Li$^+$ with H$^+$ from $\alpha$-Li$_2$IrO$_3$ single crystals to synthesize the single crystal samples of the iridate second generation H$_3$LiIr$_2$O$_6$. The Raman spectroscopy can be used to diagnose the QSL state since the magnetic Raman continuum arises from a process involving pairs of fractionalized Majorana fermionic excitation in a pure Kitaev model. We observe a broad dome-shaped magnetic continuum in H$_3$LiIr$_2$O$_6$, in line with theoretical expectations for the two-spin process in the Kitaev QSL. Our results establish the close connection to the Kitaev QSL physics in H$_3$LiIr$_2$O$_6$.

Full text

Introduction. – The search for quantum spin liquid (QSL) state has been a currently active and challenging topic in the condensed matter physics Anderson (1973, 1987); Balents (2010); Savary and Balents (2017); Zhou et al. (2017); Shimizu et al. (2003); Nytko et al. (2008); Feng et al. (2017); Wen (2017a); Wei et al. (2017); Feng et al. (2018); Kitagawa et al. (2018). The spin degree of freedom in QSL does not freeze to display any magnetic order even at zero temperature, but highly entangles with each other  Kitaev (2006); Wen (2004); Kitaev and Preskill (2006); Levin and Wen (2006); Wen (2017b, 2019). In the early theoretical studies, the exact solvable Kitaev honeycomb spin model  Kitaev (2006) built confidence about the existence of QSL in a simple spin interacting system; furthermore, it has been currently initialing the materialization of the Kitaev QSL in the experiments Jackeli and Khaliullin (2009); Chaloupka et al. (2010); Takagi et al. (2019). With the help of the intertwining between magnetism, spin-orbital coupling, and crystal field, Ir4+ oxides and a Ru3+ chloride with a $d^{5}$ electronic configuration are promising to materialize the Kitaev model, e.g., $\alpha$-A2IrO3 (A=Na, Li) Choi et al. (2012); Singh et al. (2012); Hwan Chun et al. (2015) and $\alpha$-RuCl3 Plumb et al. (2014).

Due to other non-Kitaev interactions, magnetic orders appears in $\alpha$-A2IrO3 (A=Na, Li) and $\alpha$-RuCl3 at low temperatures Choi et al. (2012); Johnson et al. (2015); Williams et al. (2016). The suppression of magnetic ordering in $\alpha$-A2IrO3 (A=Na, Li) and $\alpha$-RuCl3 has been attempted by applying magnetic field Kasahara et al. (2018); Yu et al. (2018) , high pressure Hermann et al. (2018); Li et al. (2019); Note (2), and chemical modification Bette et al. (2017); Kitagawa et al. (2018). For the chemical modification of $\alpha$-Li2IrO3, a QSL state ground was recently established in the second generation of two-dimensional honeycomb iridates H3LiIr2O6 Bette et al. (2017); Kitagawa et al. (2018). No sign of magnetic order, but signatures of local low-energy excitations are observed in H3LiIr2O6, down to low temperatures in the magnetic susceptibility, specific heat, and NMR measurements Kitagawa et al. (2018). H3LiIr2O6 has immediately caught lots of theoretical investigation to explore the connection to the Kitaev QSL physics Slagle et al. (2018); Yadav et al. (2018); Li et al. (2018); Wang et al. (2018); Knolle et al. (2019), and the ranomness of H positions was also discussed as playing an important role in stabilizing the QSL state Yadav et al. (2018); Li et al. (2018). Currently, however, no spectroscopic information exists regarding the spin excitations and the possibility of spin fractionalization in H3LiIr2O6.

In this Letter, we report our attempts to diagnose the spin liquid signature in the single crystalline H3LiIr2O6 using the Raman spectroscopy methods. Single crystals of $\alpha$-Li2IrO3 are soaked in 4 mol/L H2SO4 aqueous solution for the soft chemical replacement of Li+ with H+. As well as single crystals of the target second generation of iridate H3LiIr2O6, we obtain the third iridate generation with the hypothesized formula H5LiIr2O6. We carry out the X-ray photoelectron spectroscopy (XPS) measurements, and confirm that H3LiIr2O6 has the same Ir4+ oxidation state as $\alpha$-Li2IrO3, while H5LiIr2O6 has lower oxidation state Ir3+. Submillimetre-size crystals are available for the Raman spectroscopy, that is capable of detecting magnetic excitations  Moriya (1968); Fleury and Loudon (1968); Lemmens et al. (2003), even the spin fractionalizations signaled by the magnetic Raman continuum in the Kitaev-type compoundsSandilands et al. (2015); Glamazda et al. (2016, 2017); Li et al. (2019); Note (2). We observe a broad two-spin process continuum in the dynamical Raman susceptibility for H3LiIr2O6, in a good agreement with the theoretically expected scattering from a pure Kitaev model Knolle et al. (2014a). Our results demonstrate Raman spectroscopic signautres of the fractionlized excitation for the Kiteav QSL state in H3LiIr2O6.

Single crystal synthesis and experimental setup. – We implement the soft chemical replacement of of Li+ with H+ in the iridate first generation $\alpha$-Li2IrO3 single crystals. We obtain single crystals of different generations of honeycomb iridate orxides, depending the growth condition, especially reaction (soaking) time. For the growth of $\alpha$-Li2IrO3 single crystal, we adopted the similar setup as described in Ref. Freund et al. (2016) with iridium metal (powder, 99.99%) and lithium (granule, 99.99%) used as starting materials. The whole setup was placed in a preheated furnace of 200 \celsius  heated to 1020 \celsius  and dwelled for 10 days. For cation exchange, $\alpha$-Li2IrO3 single crystals were added into in a 25 ml Teflon-lined steel autoclave with 20 ml H2SO4 aqueous solution (4 mol/L).

The XPS investigations were carried out on Thermo Fisher ESCALAB 250Xi using monochromated Al K$\alpha$ radiation at room temperature, and the electron flood gun was turned on to eliminate electric charging effect in our insulating samples. The binding energy in XPS was calibrated by 1s spectra of carbon. XRD measurements were conducted on Rigaku Smartlab 9KW using Cu K$\alpha$ radiation at room temperature.

The Raman spectra were measured in the quasi-back-scattering geometry, with light polarized in the basal plane. The experiments were performed on our home-built system using a HORIBA iHR550 spectrometer and the 632.8 nm excitation line of a He-Ne laser. The power of the laser was kept low enough (about 100 $\mu$W) to prevent from heating and damaging samples. We use 1200 grooves/mm grating to get the high resolution. Since the light scattering intensity is weak, we set the integral time to 1800 s. The samples were placed in a He-flow cryostat which evacuated to $2.0\times 10^{-6}$ Torr. The sample temperatures were calibrated according to the intensity ratio of anti-Stokes and Stokes phonon peaks.

Sample characterizations. – Single crystals of $\alpha$-Li2IrO3 have different appearances, e.g., the flake and pyramid shapes, probably due to different stacking patterns of LiIr2O6 layers. We find that the pyramid-shaped $\alpha$-Li2IrO3 have more ordered stacking pattern, however, the flake-shaped crystals are easily accessible for the soft chemical replacement as the present study in this work. Fig. 1 (a) is the image for typical single crystals of three generations of the iridate oxides. The parent generation $\alpha$-Li2IrO3 (the flake cyrstal) displays the black appearance. The second generation (H3Li2O6) has the reddish black color, and the third generation (hypothesized formula H5LiIr2O6) has the lustrous red appearance. During the soft-chemical-ion-exchange reaction (about 70 min), the interlayer Li+ will be replaced by H+, and we can get the target iridate second generation H3LiIr2O6. With longer soaking time (about 3 hours), more Hydrogen atoms intercalate into the inter-layers of [LiIr2O6] layers, and we get the crystals of the third generation H5LiIr2O6. While $\alpha$-Li2IrO3 and H5LiIr2O6 is very stable, H3LiIr2O6 may react with the vapour in the air.

Figure. 1 (b) is the powder X-ray diffraction (PXRD) result for three generations of iridate oxides. Apparently, they have very similar overall PXRD patterns since the acid treatment have caused a mild change in the constitution of the LiIr2O6 layers, adn only the ions situated in-between the layers are changed. The intense basal reflection $2\theta$ shifts up from $\alpha$-Li2IrO3 (18.36°) to H3LiIr2O6 (19.52°), and then down to H5LiIr2O6 (18.85°), corresponding to the interlayer distance 4.828 Å, 4.544 Å  and 4.704 Å, respectively. Strong anisotropic broadening of the reflections in the XRD-pattern revealed heavy stacking faulting of the samples. Fig. 1 (c) is the typical Raman result for the three generations at a room temperature. The Raman intensity of of H5LiIr2O6 rescales by multiplying by 1/2. During the crystal synthesis, we use the Raman spectra to monitor the soaking process of our samples.

We implement XPS to verify the oxidation state of iridium ions in the three generations. As shown in Fig. 1 (d), three generations have very similar Ir 4$f$ XPS spectra, indicating the similar local electronic environment of IrO6. The shift of the binding energy of Ir 4$f$ implies the changes of oxidation state of Ir, and lower binding energy represents lower valance state. The mild change can be seen from $\alpha$-Li2IrO3 to H3LiIr2O6 by comparing the position of 4f5/2 and 4f7/2 energy level, indicating the same electronic configuration of Ir4+. H5LiIr2O6 has a significant lower binding energy (about 0.7 eV). According to Ir-based compounds in the database111https://srdata.nist.gov/xps/Default.aspx, Ir3+ and Ir4+ usually have a difference of the binding energy about 0.5 eV. Comparing Ir4+ in $\alpha$-Li2IrO3 and H3LiIr2O6, we have Ir3+ in IrO6 octahedron in H5LiIr2O6. Ir3+ has the 3$d^{6}$ electronic configurations without partially occupied orbitals, and hence no magnetism. This explains the negligible magnetic Raman continuum in H5LiIr2O6 as shown in Fig. 1 (c) and Fig. 3.

Evolution of Raman spectra – Figures. 2 is the evolution of Raman spectra of H3LiIr2O6 at different temperatures. Comparing with our $\alpha$-Li2IrO3 results 222Gaomin Li, et. al., to be submitted., we can assign the sharp phonon modes by assuming that H3LiIr2O6 has the same space group (#12, C2/m) as $\alpha$-Li2IrO3. Three modes at 364.0 and 630.8 cm*-1* are assigned as $A_{g}$ modes, the mode at 131.9 cm*-1* is assigned as $B_{g}$ mode, and four modes at 189.6, 259.9, 490.0 and 541.0 cm*-1* are assigned as $A_{g}+B_{g}$ modes which are nearly doubly degenerate. 131.9 and 189.6 cm*-1* modes are the Ir-Ir out-of-phase motions along the out-of-plane and in-plane directions, respectively. The 259.9 cm*-1* mode is the twist of Ir-O-Ir-O plane, the 364.0 cm-1 mode is the relative twist of between the upper and lower oxygen triangles. The 490 cm*-1* mode is related to the Ir-O-Ir-O plane shearing, and the 541.0 cm*-1* mode is the breathing mode of Ir-O-Ir-O ring. The Ag mode at 630.8 cm*-1* can be assigned as the symmetrical breathing mode between the upper and lower oxygen layers. Several weak phonon peaks at around 155, 220, 325 and 600 cm*-1* become visible at low temperatures in H3LiIr2O6, and these modes don’t appear in $\alpha$-Li2IrO3 Note (2). We notice that Raman phonon modes in H3LiIr2O6 in this work and $\alpha$-Li2IrO3 Note (2) are quite similar to those in other Kitaev materials, e.g. $\alpha$-RuCl3 Sandilands et al. (2015); Li et al. (2019) and $\beta$- and $\gamma$- Li2IrO3 Glamazda et al. (2016), suggestive of similar local crystal RuCl6 and IrO6 octahedral structures.

Besides the phonon modes, we observe a strong continuum background with increasing intensity as increasing temperatures particularly for low Raman frequencies (Fig. 2). We attribute such a continuum background as the magnetic Raman scattering as observed in $\alpha$-RuCl3 Sandilands et al. (2015) and $\beta$- and $\gamma$-Li2IrO3 Glamazda et al. (2016) due to spin fractionalized excitations. H3LiIr2O6 is a layered material and there are heavily stacking faults which may lead to broad phonon modes that could explain the continuum. However, the static structural disorder cannot produce the significant temperature dependence. Furthermore, the damped phonon scenario couldn’t account for the Raman continuum according to the polarization dependence of the Raman spectra in H3LiIr2O6 as shown in Fig. 3 (a). As a matter of fact, the weak polarization dependence of Raman spectra in H3LiIr2O6 agrees well with theoretical calculations for the isotropic Kitaev model Knolle et al. (2014b).

As a control experiments, Fig. 3 (b) is the evolution of Raman spectra in H5LiIr2O6 at different temperatures. Actually, H5LiIr2O6 would have similar stacking faults to H3LiIr2O6 since they main difference in their synthesis is the soaking time of the soft chemical reaction. With increasing temperature, all phonon peaks in H5LiIr2O6 change very mild, and there is not any continuum background at all at the whole temperature range, which is in contrast to the spectra of H3LiIr2O6 in Fig. 2. On one hand, as a control experiment, the Raman spectra of H5LiIr2O6 in Fig. 3 (b) implies that the continuum background of H3LiIr2O6 in Fig. 2 is not due to the stacking faults, but has the magnetic origin. On the other hand, even if some regions of H3LiIr2O6 (Ir4+) turn into H5LiIr2O6 (Ir3+) due to the over soaking in the acid, they behave as handful impurities and do not contribute to the magnetic Raman continuum.

According to the fluctuation-dissipation theorem, the Raman intensity $I(\omega)$ is proportional to the dynamical Raman susceptibility as $I(\omega)=[1+n(\omega)]\chi^{\prime\prime}(\omega)$. Here $n(\omega)$ is the boson factor, and $\chi^{\prime\prime}(\omega)$ is the imaginary part of the correlation functions of Raman tensor $\tau(\mathbf{r},t)$, $\chi(\omega)=\int_{0}^{\infty}dt\int d\mathbf{r}(-i)\langle[\tau(0,0),\tau(\mathbf{r},t)]\rangle e^{-i\omega t}$. To examine the the magnetic Raman susceptibility $\chi^{\prime\prime}(\omega)$ in H3LiIr2O6 more explicitly, we remove phonon modes using the Gaussian-type line-shape. As a consequence, the obtained magnetic Raman susceptibility in H3LiIr2O6 displays a dome-shaped broad continuum at all temperatures, as shown in Fig. 4. With the temperature decreasing, the magnetic Raman continuum increases with the frequency between 150 cm*-1* and 410 cm*-1*, and decreases with the frequency less than 150 cm*-1*. Thus the dome shape of the magnetic continuum is more remarkable at low temperatures. From the Raman intensity in Fig. 2, we can see that the magnetic continuum extends to higher frequencies at least up to 700 cm*-1*. The phonon modes with the frequency between 410 cm*-1* and 710 cm*-1* are messy, and it is not easy to separate the phonon modes and magnetic continuum in the frequency region (between 410 cm*-1* and 710 cm*-1*). Therefore, we didn’t show the subtracted magnetic Raman continuum with the frequency between 410 cm*-1* and 710 cm*-1* in Fig. 4. We can see that the magnetic continuum is weakly temperature dependent in this frequency region according to the Raman spectra in H3LiIr2O6 in Fig. 2.

We extract the integrated Raman susceptibility $\chi_{R}$ in accordance with the Kramers-Kronig relation $\chi_{R}=\frac{2}{\pi}\int\frac{\chi^{\prime\prime}(\omega)}{\omega}d\omega$. To do the integration, we extrapolate the Raman conductivity $\frac{\chi^{\prime\prime}(\omega)}{\omega}$ in H3LiIr2O6 to 0 cm*-1*. The temperature dependent $\chi_{R}$ in H3LiIr2O6 is plotted in Fig. 5, in which the integration is carried out from 0 cm*-1* to 410 cm*-1*, taking into account the fact that the magnetic Raman continuum with the frequency between 410 cm*-1* and 710 cm*-1* is weakly temperature dependent. The integrated Raman susceptibility $\chi_{R}$ in H3LiIr2O6 essentially decreases monotonically as lowering the temperatures at least above 50 K, very different from that in $\alpha$-Li2IrO3Note (2), where $\chi_{R}$ increases monotonically with temperature decreasing. It is worthy to mention that the temperature dependence of $\chi_{R}$ in H3LiIr2O6 is similar to $\beta$- and $\gamma$-Li2IrO3 Glamazda et al. (2016). The integrated Raman susceptibility $\chi_{R}$ of $\alpha$-Li2IrO3 has a very similar temperature dependence behavior to $\alpha$-RuCl3, i.e. increasing monotonically with temperature decreasing Note (2); Glamazda et al. (2017). More specifically, the inelastic light scattering in H3LiIr2O6 and $\beta$- and $\gamma$-Li2IrO3 has different form from that in $\alpha$-RuCl3 and $\alpha$-Li2IrO3, which deserves further detail investigations.

Discussions and conclusions – With the help of strong spin-orbit coupling, crystal field splitting and electronic correlation, the Kitaev materials have the effective spin-1/2 moment Jackeli and Khaliullin (2009); Takagi et al. (2019). The magnetic Raman tensor $\tau(\mathbf{r})$ in these systems can be expanded in powers of the effective spin-1/2 operators, $\tau^{\alpha\beta}(\mathbf{r})=\tau_{0}^{\alpha\beta}(\mathbf{r})+\sum_{\mu}K^{\alpha\beta}_{\mu}S^{\mu}(\mathbf{r})+\sum_{\delta}\sum_{\mu\nu}M^{\alpha\beta}_{\mu\nu}(\mathbf{r},\delta)S_{\mathbf{r}}^{\mu}S_{\mathbf{r}+\delta}^{\nu}+...$. The first term corresponds to Rayleigh scattering, the second and third terms correspond to the one-spin and two-spin process, respectively Moriya (1968); Fleury and Loudon (1968); Lemmens et al. (2003). The complex tensors $K^{\alpha\beta}_{\mu}$ and $M^{\alpha\beta}_{\mu\nu}$ are determined by the strength of the spin-orbit couplings and the subtle coupling form of light to the spin system. If the one-spin process dominates the inelastic light scattering, the integrated Raman susceptibility $\chi_{R}$ is associated with the thermodynamic magnetic susceptibility $\chi$, as demonstrated in $\alpha$-RuCl3 Glamazda et al. (2017) and $\alpha$-Li2IrO3 Note (2). In $\beta$- and $\gamma$-Li2IrO3, the integrated Raman susceptibility $\chi_{R}^{0}$ is associated with the magnetic-specific heat $C_{m}$ multiplied by the temperature $T$, i.e., $C_{m}T$ Glamazda et al. (2016), indicating that the two-spin process dominates the magnetic Raman scattering.

The temperature dependence behavior of H3LiIr2O6 is similar to that in $\beta$- and $\gamma$-Li2IrO3, therefore, two-spin process dominates in the magnetic Raman continuum in Fig. 4. In the putative Kitaev QSL, the magnetic Raman scattering of two-spin process directly probes the pairs of the Majorana fermions which are characterization of the elusive spin fractionalizations Knolle et al. (2014b); Nasu et al. (2016). Particularly, Knolle et. al. have calculated the magnetic Raman scattering for the two-spin process, and our dome-shaped magnetic Raman continuum agrees very well with the simulated Raman response Knolle et al. (2014b). Therefore, our results demonstrate the emergence of spin fractionalization, and establish a Kitaev QSL in H3LiIr2O6. The theoretical simulated Raman response has a maximum at 1.5 $J_{k}$ (where $J_{k}$ is the Kitaev interaction for the effective spin-1/2 operators) Knolle et al. (2014b). Equating 1.5 $J_{K}$ with the experimental maximum of continuum scattering of 40 meV yields $J_{K}=26$ meV, in a good consistent with DFT estimations Yadav et al. (2018); Li et al. (2018); Wang et al. (2018).

H3LiIr2O6 have heavily stacking faults Kitagawa et al. (2018); Bette et al. (2017), and theoretical investigations of have discussed the important role of the randomness to stabilize the Kitaev QSL Slagle et al. (2018); Yadav et al. (2018); Li et al. (2018); Wang et al. (2018); Knolle et al. (2019). However, Raman scattering is not sensitive to the local randomness, and our results didn’t address the issue about the physics of disorder in quantum spin liquids. Knolle et. al. predicted a $\delta$-function peak reflecting the local two-particle density of states of Majorana fermions in the presence of four vison fluxes Knolle et al. (2014b). Such a vison peak is not resolved in our Raman data due to the severely bad resolution at small wave numbers.

In conclusion, we perform the Raman spectroscopy studies of single-crystal H3LiIr2O6 samples and observe a dome-shaped magnetic Raman continuum. Our results demonstrate the spin fractinalization in H3LiIr2O6, which is a defining feature of the Kitaev quantum spin liquid state.