Pressure-induced reentrant oblique antiferromagnetic phase in the spin-dimer system ${\text{TlCuCl}}_3$

Magnetization measurements under a hydrostatic pressure of $P=1.4\text{GPa}$ were performed on the coupled spin dimer system ${\text{TlCuCl}}_3$, which exhibits a pressure-induced quantum phase transition from a gapped singlet state to an antiferromagnetic state at $P_c=0.042\text{GPa}$. Antiferromagnetic ordering with ordered moments parallel to the $ac$ plane was observed at $T_N=16.7\text{K}$ at 1.4 GPa. The spin reorientation phase transition was observed at $T_R\simeq 9.2\text{K}$ for zero magnetic field, at which the ordered moments start to incline toward the $b$ axis. With increasing external field parallel to the $b$ axis, a second-order phase transition from the oblique antiferromagnetic (OAF) phase to the spin-flop (SF) phase occurs below $T_R$. We argue that the OAF phase arises from the competition between the anisotropic energies of the conventional second order and the fourth order, which increases with increasing pressure. We discuss the OAF-SF transition within the framework of the mean-field approximation.

Figure 1

Spin structure of pressure-induced ordered state in ${\text{TlCuCl}}_3$. The inset shows the definitions of the angles $\alpha$ and $\theta$ representing the spin direction. The angle $\theta$ denotes the angle between the ordered spin moment and the $ac$ plane, and the angle $\alpha$ denotes the angle between the $a$ axis and the ordered spin moment projected onto the $ac$ plane.

Figure 2

(Color online) Temperature dependence of magnetic susceptibilities in ${\text{TlCuCl}}_3$ measured at $H=0.1$ and 0.2 T for $P=1.4\text{GPa}$. The inset shows $dM/dT$ vs $T$ measured at $H=0.2\text{T}$.

Figure 3

(Color online) Phase diagram for magnetic field vs temperature at $P=1.4\text{GPa}$. The magnetic field is applied parallel to the $b$ axis. OAF, SF, and PM mean the oblique antiferromagnetic, spin-flop, and paramagnetic phases, respectively. Triangles and squares denote Néel temperature $T_N$ and spin reorientation transition temperature $T_R$, respectively, which are determined from the temperature scan of magnetization. Circles mean the magnetic field $H_c$ giving a peak in $dM/dH$ as shown in the inset of Fig. 4.

Figure 4

(Color online) Magnetization curves of ${\text{TlCuCl}}_3$ for $H\parallel b$ measured at various temperatures under hydrostatic pressure $P=1.4\text{GPa}$. Each plot is shifted upward successively by 2 emu/mol for clarity. The solid lines represent magnetization curves calculated using Eqs. (7, 8). The inset shows $dM/dH$ vs $H$ measured at $T=2.2\text{K}$.

Figure 5

Configuration of sublattice magnetizations ${\mathit{M}}_1$ and ${\mathit{M}}_2$. Dashed line denotes the spin axis that is canted from the $x$ axis by angle $\theta$.

Figure 6

(Color online) Calculated magnetization curves and its field derivative $dM/dH$ with $H_c=0.28\text{T}$, ${\theta }_0=70°$, and ${\chi }_{\perp }=3.0\times {10}^{-3}\text{emu}/\text{mol}$.

Figure 7

(Color online) Temperature dependence of the oblique angle at zero magnetic field ${\theta }_0$ between the ordered spin moments and the $b$ axis obtained by the present analysis. The solid line is a guide for the eyes.