Spin-flop-like transition as quantum critical point in Cs$_2$RuO$_4$

Abstract

We report thermodynamic, neutron diffraction, and inelastic neutron scattering measurements on Cs$_2$RuO$_4$, a member of the celebrated family of frustrated magnets Cs$_2$MX$_4$ (M = Cu, Co, X = Br, Cl). Unlike the previously studied members, it is based on $4d$ transition metal ions with $S=1$. Mapping out the $H-T$ magnetic phase diagram reveals an unusual continuous spin-flop-like phase transition associated with a quantum critical point within the antiferromagnetically ordered phase. A quantitative analysis of the complex magnetic excitation spectrum measured in zero field allows us to derive a model magnetic Hamiltonian for this compound. Its main feature is a frustration of magnetic anisotropy on a level that is much higher than in any of the previously studied species. This frustration naturally explains the peculiar phase transition observed.

Figures (12)

• Figure 1: Crystal structure and magnetic exchange paths in Cs$_2$RuO$_4$. (a) Schematic overview of the unit cell, indicated by a black line. The four magnetic ions per unit cell are labeled by Ru-1 to Ru-4. (b) Schematic overview of the relevant symmetry allowed magnetic exchange paths. The exchange pathways are labeled $J_1$-$J_5$ and $J_8$.
• Figure 2: Main panel: magnetic susceptibility of Cs$_2$RuO$_4$ single crystal in applied fields $\mu_0 H$ = 0.1 T along the three crystallographic directions (symbols). The response along the $a$ and $c$ directions is almost indistinguishable in the plot. The solid lines indicate fits to the data as described in the text. Lower inset: a schematic view of the local ionic easy-planes as seen along the $b$ axis. Right inset: orientation of the two types of easy-planes relative the the crystallographic axes.
• Figure 3: (a) High field magnetization per Ru$^{6+}$ measured at 1.3 K in Cs$_2$RuO$_4$ for magnetic fields along the crystallographic $a$, $b$, and $c$ directions. Horizontal lines indicate the saturation magnetization for each curve. (b) Magnetization per Ru$^{6+}$ measured at 250 mK for a magnetic field along the crystallographic $b$ direction. Magnetic torque ($\Delta C$) (c) and its field derivative (d) measured at constant temperatures against magnetic field along the crystallographic $b$ direction. For all the datasets a capacitance reference value at zero field has been chosen and subtracted.
• Figure 4: False-color plot of the temperature-scales specific heat measured in Cs$_2$RuO$_4$ in a magnetic field applied along two crystallographic directions. Symbols indicate the positions of sharp lambda anomalies at the phase boundary and the additional low-temperature feature.
• Figure 5: (a) Same as Fig. \ref{['fig:hc_ht']} (b), zoomed in below 1.75 K and with enhanced color scale. (b) Specific heat measured at a constant temperature against applied magnetic field along the $b$ direction. Each curve is displaced with a constant offset of 0.05 J/K$^2$ mol$_\mathrm{Ru^{6+}}$ for visibility. (c) Activation gap $\Delta$ as a function of applied magnetic field along the $b$ direction. The dashed line indicates the critical field $\mu_0 H_c\approx 4.3$ T. Inset: specific heat as function of temperature measured at $\mu_0 H_c$. Note the logarithmic scale.