Angle-resolved photoemission study of the electronic structure of the quantum spin liquid ${\text{EtMe}}_3\text{Sb}[{\text{Pd}\left(\text{dmit}\right)}_2{]}_2$

The electronic structure of a quantum spin liquid compound, ${\text{EtMe}}_3\text{Sb}[{\text{Pd}\left(\text{dmit}\right)}_2{]}_2$, has been studied with angle-resolved photoemission spectroscopy, together with two other ${\text{Pd}\left(\text{dmit}\right)}_2$ salts in the valence bond solid or antiferromagnetic state. ${\text{EtMe}}_3\text{Sb}[{\text{Pd}\left(\text{dmit}\right)}_2{]}_2$, being a Mott insulator, has its lower Hubbard band identified, with a soft energy gap at the chemical potential. In addition, the spectral features exhibit anomalously broad linewidth and negligible dispersion, which fit well to the calculated energy levels of an isolated $[{\text{Pd}\left(\text{dmit}\right)}_2{]}_2$ dimer. We suggest that these electronic characteristics might be the manifestation of the spin-charge separation in a two-dimensional quantum spin liquid.

Figure 1

The structure aspects of EtMe${}_3$Sb[Pd(dmit)${}_2$]${}_2$. (a) A view from the $\mathbf{b}$ axis. The crystal structure consists of two-dimensional Pd(dmit)${}_2$ layers separated by layers of cation EtMe${}_3$Sb. (b) An in-plane sketch of the spin arrangement on the Pd(dmit)${}_2$ layer. Each lattice (encircled by solid lines) stands for a strongly dimerized [Pd(dmit)${}_2$]${}_2^{-}$ unit with spin-1/2. Three nearest-neighbor exchange interactions, J${}_B$, J${}_S$, and J${}_r$, are similar and estimated to be 220–250 K. (c) The Laue picture of the EtMe${}_3$Sb[Pd(dmit)${}_2$]${}_2$ single crystal. Because the dimer units in (a) stack along the $\mathbf{a}+\mathbf{b}$ direction in one layer and along the $\mathbf{a}-\mathbf{b}$ direction in the next layer [14], the crystal shows twofold symmetry. The inset shows the photo of a single crystal. (d) The low-energy electron diffraction pattern. The dashed lines are a guide for the eye, and we note that the pattern is slightly distorted at the edge.

Figure 2

(a) The x-ray diffraction data of an EtMe${}_3$Sb[Pd(dmit)${}_2$]${}_2$ single crystal. (b) The rocking curve of the (008) Bragg peak, which is fitted by a Gaussian. The intensity is in counts per second (counts/s).

Figure 3

(a) The two-dimensional Brillouin zone of EtMe${}_3$Sb[Pd(dmit)${}_2$]${}_2$. (b) The normal-emission photoemission spectra of EtMe${}_3$Sb[Pd(dmit)${}_2$]${}_2$ excited by p, s, left-handed circular (C+), and right-handed circular (C$-$) polarized 8-eV photons. The inset shows the normal-emission spectra collected with p-polarized 8-, 15-, and 21-eV photons. (c) The photoemission intensity along the $(0,-\pi /a)$-$(0,\pi /a)$ line as indicated in (a). (d) ARPES spectra of EtMe${}_3$Sb[Pd(dmit)${}_2$]${}_2$ acquired at momenta 1–15 as coded in (a). The photoemission data in (c) and (d) were taken with p-polarized 8-eV photons. (e) Temperature dependence of the normal-emission valence band spectra of EtMe${}_3$Sb[Pd(dmit)${}_2$]${}_2$. The data in (e) were acquired with 21.2-eV photons from a helium lamp, and others were collected at UVSOR.

Figure 4

(a) The normal-emission valence-band spectrum of EtMe${}_3$Sb[Pd(dmit)${}_2$]${}_2$ is fitted with three Gaussians plus a Shirley-type background. Data were taken with p-polarized 8-eV photons at UVSOR. (b) Left: The centroid of the peaks obtained from the fitting. The black arrows represent the electron spins. Right: The calculated energy levels of the isolated Pd(dmit)${}_2$ monomer and [Pd(dmit)${}_2$]${}_2$ dimer in EtMe${}_3$Sb[Pd(dmit)${}_2$]${}_2$. (c) A schematic spectral function of a single electron coupled to a bath of bosons of frequency ${\omega }_0$ in the weak- and strong-coupling conditions. (d) Drawing of the spin-charge separation in a QSL, where a photohole splits into spinon and holon excitations.

Figure 5

(a) The normal-emission spectra of Et${}_2$Me${}_2$P[Pd(dmit)${}_2$]${}_2$ (AFM compound) and EtMe${}_3$P[Pd(dmit)${}_2$]${}_2$ (VBS compound) are fitted with three Gaussian peaks plus a Shirley-type background, respectively. Data were taken with p-polarized 8-eV photons at UVSOR. (b) The schematic diagram for the experimental (expt.) and calculated (calc.) energy levels of these materials. The calculated Ha bands are individually aligned to the experimental positions of their peak 1's. The unit is electron volts. (c) The $\Gamma$-point spectra of the three Pd(dmit)${}_2$ salts in the vicinity of the chemical potential, which are fitted to a power-law relation ${A\times |E-\mu |}^{\alpha }$ (solid lines). The fitted $\alpha$ is 2.8, 1.78, and 1.65 for the QSL, VBS, and AFM compounds, respectively.

Figure 6

Photoemission charging effects in EtMe${}_3$Sb[Pd(dmit)${}_2$]${}_2$. (a) Temperature dependence of the photoemission energy-distribution curve (EDC) at the $\Gamma$ point of EtMe${}_3$Sb[Pd(dmit)${}_2$]${}_2$. The sample temperature was first lowered, and then raised as indicated. (b) EDC at the $\Gamma$ point of EtMe${}_3$Sb[Pd(dmit)${}_2$]${}_2$ as a function of the photon intensity. Data were taken at 30 K. All the data were collected at UVSOR with $p$-polarized 8-eV photons. Arrows with dashed lines indicate the shift of the features due to the photoemission charging effects.

Figure 7

Radiation damage and aging effects in EtMe${}_3$Sb[Pd(dmit)${}_2$]${}_2$. (a) EDC at $\Gamma$ as a function of time with high-flux 21-eV photons. (b) EDC at $\Gamma$ as a function of photon flux with 8-eV photons. (c) EDC at $\Gamma$ as a function of time with low-flux 8-eV photons. The photon intensity is measured by a calibrated photodiode, and $I$ is its readout photocurrent. All the data were collected at UVSOR with $p$-polarized light. The spectra are overlaid for a better comparison in the insets.