Magnetic field and pressure phase diagrams of the triangular-lattice antiferromagnet ${\mathrm{CsCuCl}}_3$ explored via magnetic susceptibility measurements with a proximity-detector oscillator

The effect of pressure ($P$) on magnetic susceptibility of ${\mathrm{CsCuCl}}_3$ was examined in magnetic fields (${\mu }_{0}H$) of up to 51 T using a proximity-detector oscillator (PDO), and the $H\text{−}P$ phase diagram of ${\mathrm{CsCuCl}}_3$ was constructed over the saturation field ($H_{\mathrm{sat}}$). We found that, with increasing $P, H_{\mathrm{sat}}$ increases and the up-up-down phase that appeared at $P=0.7\mathrm{GPa}$ widened. Based on comparison between the experimental and calculated $H\text{−}P$ phase diagrams, the Y phase was predicted to appear above 1.7 GPa. The interchain antiferromagnetic exchange interaction in the $ab$ plane was evaluated and found to increase with increasing $P$, which is consistent with a previous study under high pressure [D. Yamamoto et al., Nat. Commun. 12, 4263 (2021)]. Moreover, an anomaly was observed below $P=0.6\mathrm{GPa}$ just below $H_{\mathrm{sat}}$ and might be a new phase transition derived from nonlinear response caused by the PDO technique.

Figure 1

(a) Magnetization ($M$) and $dM/dH$ curves at 1.4 K observed in ${\mathrm{CsCuCl}}_3$ for $H$ parallel to the $c$ axis. The change in resonance frequencies ($\mathrm{\Delta }{f}_{\mathrm{sub}}$) against applied magnetic field for the $c$ axis of ${\mathrm{CsCuCl}}_3$ at (b) 1.4 K and (c) various temperatures. $\mathrm{\Delta }{f}_{\mathrm{sub}}$ is the frequency difference obtained by subtracting the frequency at $T$ = 20 K as background from that at the measurement temperature. [In panels (a)-(c), solid and dotted lines are field ascending and descending processes, respectively.]

Figure 2

(a) $M$ ($H$) and $dM/dH$ curves for $H\perp c$ at 1.4 K. (b) The change in resonance frequency ($\mathrm{\Delta }{f}_{\mathrm{sub}}$) for $H\perp c$ at 1.4 K. $\mathrm{\Delta }{f}_{\mathrm{sub}}$ is the same definition as in the caption of Fig. 1.

Figure 3

Changes in resonance frequencies $\mathrm{\Delta }{f}_{\mathrm{sub}}$ of ${\mathrm{CsCuCl}}_3$ for $H\parallel c$ at indicated pressures at 1.4 K. $\mathrm{\Delta }{f}_{\mathrm{sub}}$ is the same definition as in the caption of Fig. 1. Each datum was taken from the field ascending process and shifts arbitrarily making it easier to see except for the ambient data. The small red circle at 1.67 GPa near $H_{\mathrm{c}1}$ is an anomaly which may correspond to the transition to the Y phase. The data at ambient pressure were taken without pressure cell.

Figure 4

Magnetic field (${\mu }_{0}H$) vs pressure ($P$) phase diagram of ${\mathrm{CsCuCl}}_3$ for $H\parallel c$ at 1.4 K constructed by the PDO measurements.

Figure 5

Pressure ($P$) dependence of the interchain (in-plane) exchange constant $J_1$ and the anisotropy parameter $\mathrm{\Delta }$, when the intrachain exchange constant $J_0$ is assumed to be constant under high pressure.

Figure 6

(a) $H/H_{\mathrm{sat}}$ vs $P$ phase diagram of ${\mathrm{CsCuCl}}_3$ for $H\parallel c$ at 1.4 K. Solid, broken, and dot-dashed lines are the phase boundary between the umbrella and 2-1 coplanar phases, between the umbrella and uud phases, and between the uud and 2-1 coplanar phases, respectively. (b) Calculated $H/H_{\mathrm{sat}}$ vs $\mathrm{\Delta }$ phase diagram constructed by reversing the horizontal axis from the phase diagram in Ref. [32]. The smaller $\mathrm{\Delta }$ means the higher $P$, and $\mathrm{\Delta }=0.07$ corresponds to ambient pressure. By comparison, $\mathrm{\Delta }=0.055$ may correspond to $P\approx 1.7\mathrm{GPa}$.

Figure 7

Angular ($\theta$) dependence of $H^{\prime }{}_{\mathrm{sat}}$ and $H_{\mathrm{sat}}$ of ${\mathrm{CsCuCl}}_3$ at 1.4 K. The solid lines are the fitting curves of $H_{\mathrm{sat}}$ and $H^{\prime }{}_{\mathrm{sat}}$ with $H_{\mathrm{sat}}=A$cos2$\theta +B$cos4$\theta +C$ and $H^{\prime }{}_{\mathrm{sat}}=A^{\prime }$cos2$\theta +B^{\prime }$cos4$\theta +C^{\prime }$ ($A, B, C, A^{\prime }, B^{\prime }$, and $C^{\prime }$ are fitting parameters).