Thermodynamic evidence of fermionic behavior in the vicinity of one-ninth plateau in a kagome antiferromagnet

Abstract

The spin-1/2 kagome Heisenberg antiferromagnets are believed to host exotic quantum entangled states. Recently, the report of 1/9 magnetization plateau and magnetic oscillations in a kagome antiferromagnet YCu$_3$(OH)$_6$Br$_2$[Br$_x$(OH)$_{1-x}$] (YCOB) have made this material a promising candidate for experimentally realizing quantum spin liquid states. Here we present measurements of the specific heat $C_p$ in YCOB in high magnetic fields (up to 41.5 Tesla) down to 0.46 Kelvin, and the 1/9 plateau feature has been confirmed. Moreover, the temperature dependence of $C_p/T$ in the vicinity of 1/9 plateau region can be fitted by a linear in $T$ term which indicates the presence of a Dirac spectrum, together with a constant term, which indicates a finite density of states (DOS) contributed by other Fermi surfaces. Surprisingly the constant term is highly anisotropic in the direction of the magnetic field. Additionally, we observe a double-peak feature near $30$~T above the 1/9 plateau which is another hallmark of fermionic excitations in the specific heat.

Figures (11)

• Figure 1: Magnetic field dependence of magnetization, the corresponding derivative, and specific heat around 1/9 plateau phase. (a) The thinner double lines represent the $M$ vs. $H$ data measured at 0.6 K with applied field along the $c$ (blue) and $ab$ (orange) directions. The magnetic susceptibilities $\chi_M \equiv {\rm d}M/{\rm d}H$ are plotted as the thicker dots corresponding to the vertical scale on the left side. The 1/9 magnetization plateau is observed along the $c$ axis between 15 T and 28 T and in the $ab$ plane between 20 T and 27 T. (b) The field dependence of specific heat measured at 0.46 K. The valleys centered around $\mu_0 H_0=22$ T confirmed the 1/9 plateau in magnetization.
• Figure 2:
• Figure 3: Field evolution of fermionic behavior in the vicinity of 1/9 plateau region. (a) $T$ dependence of $C_p/T$ for different fields with $H \parallel c$. The star-shaped data are cut from Fig.\ref{['fig4']}(a) at fixed fields. (b) The field dependence of experimental values of $\gamma$ (red dots) and $\beta$ (blue dots), and the simulated $\gamma$ (thick red curve) and $\beta$ (thick blue curve) obtained from linear fits of $C_p/T$ vs $T$ via Eq. \ref{['eq_linear']} in the temperature range $0.5\leq T\leq 1.2$ K. The complete experimental and simulated $C_p/T$ vs $T$ data used for fits are shown in Fig. \ref{['FigS_fieldcut']} and Fig. \ref{['FigS_Diracsimu']}, respectively. The simulation is based on a 2D Dirac spinon (gray bands) centered at the spin-down chemical potential $\mu_{\downarrow}(H_0)=E_0$ combined with a set of particle and hole like bands (orange bands) that cross the spin-up chemical potential $\mu_{\uparrow}(H_0)$, as sketched in (c). The spinon model is described in Section \ref{['sec_Dirac']}.
• Figure 4: Double-peak structure in the specific heat. (a) the field dependence of $C_p$ at different $T$ with $H$ along the $c$ direction. The black dashed line traces the location of a peak located at $\mu_0 H_p\sim 16$ T at low $T$ and its evolution with increasing $T$, the blue dashed line marks the middle of 1/9 plateau region, and the orange and red dashed lines are guides for tracking the shift of two split peaks at $\mu_0 H^*\sim 30$ T. (b) Field dependence of the derivative of the specific heat ${\rm d}C_p/{\rm d}H$ at different $T$ with a constant offset for clarity. $H^{\prime *}$ indicates the peak-splitting field in ${\rm d}C_p/{\rm d}H$ at 0 K. (c) The dots are the peak or valley locations taken from (a) with the corresponding color codes, and the lines are the fits as described in the main text. (d) The orange and red circles are field locations of two peaks shown by the orange and red dashed lines in (b). The orange and red lines in (d) are two linear fits for the corresponding data points, while the hollow-red circles are excluded from the fits.
• Figure 5: Specific heat contributions from Schottky and phonon terms. (a) The red dots represent the $C_p$ data taken from Fig. 1(b) in the main text for $H\parallel c$ after subtracting a linear background. The gray curve is the Schottky contribution fitted using Eq. \ref{['eq_C_sc']} in the range of $0-2.5$ T. (b) The red dots are the raw $C_p$ data taken from 1.8 K to 110 K at 0 T in the PPMS. The blue curve is the phonon specific heat fitted using Eq. \ref{['eq_phonon']}. The best-fit parameters are listed in the figure. (c) The red dots are the $\mu_0 H=14$ T $C_p$ data presented in Fig. \ref{['fig3']}(a) in the main text. The blue dots are the result of $C_p-C_{ph}$, i.e. a phonon contribution is subtracted from the red dots obtained from the fits in (b).