Crossover from impurity-induced ordered phase to uniform antiferromagnetic phase under hydrostatic pressure in the doped spin-gap system ${\mathrm{TlCu}}_{1-x}{\mathrm{Mg}}_x{\mathrm{Cl}}_3$

The magnetic phase transition under hydrostatic pressure in ${\mathrm{TlCu}}_{0.988}{\mathrm{Mg}}_{0.012}{\mathrm{Cl}}_3$ was investigated by magnetization measurements. The parent compound ${\mathrm{TlCuCl}}_3$ is a coupled-spin-dimer system, which undergoes a pressure-induced quantum phase transition from a gapped ground state to an antiferromagnetic state at $P_{\mathrm{c}}=0.42\mathrm{kbar}$ due to the shrinkage of the gap. At ambient pressure, the present doped system exhibits impurity-induced magnetic ordering at $T_{\mathrm{N}}=2.5\mathrm{K}$. With increasing pressure, $T_{\mathrm{N}}$ increases. This is because the effective exchange interaction $J_{\mathrm{eff}}$ between unpaired spins is enhanced by the shrinkage of the gap. With a further increase in pressure, the present system undergoes a phase transition to a uniform antiferromagnetic phase due to the closing of the triplet gap in the intact dimers. The crossover from the impurity-induced ordered phase to the uniform antiferromagnetic phase occurs at $P\simeq 1.3\mathrm{kbar}$.

Figure 1

Temperature dependences of magnetic susceptibilities in ${\mathrm{TlCuCl}}_3$ and ${\mathrm{TlCu}}_{0.988}{\mathrm{Mg}}_{0.012}{\mathrm{Cl}}_3$ measured at ambient pressure for $H\Vert [2,0,1]$. The arrow denotes Néel temperature $T_{\mathrm{N}}$.

Figure 2

Low-temperature magnetic susceptibilities in ${\mathrm{TlCu}}_{0.988}{\mathrm{Mg}}_{0.012}{\mathrm{Cl}}_3$ measured at various pressures for $H\Vert [2,0,1]$. For clarity, the values of the susceptibilities are shifted upward consecutively by $1\times {10}^{-3}\mathrm{emu}∕\mathrm{mol}$ with increasing pressure. Arrows denote Néel temperatures $T_{\mathrm{N}}$.

Figure 3

Transition temperature $T_{\mathrm{N}}$ as function of pressure in ${\mathrm{TlCu}}_{0.988}{\mathrm{Mg}}_{0.012}{\mathrm{Cl}}_3$. The solid line is a visual guide. The dashed line denotes the transition temperature of pressure-induced magnetic ordering in pure ${\mathrm{TlCuCl}}_3$ (Ref. 23).

Figure 4

Magnetization curves in ${\mathrm{TlCu}}_{0.988}{\mathrm{Mg}}_{0.012}{\mathrm{Cl}}_3$ measured at $T=1.8\mathrm{K}$ under various pressures. The values of magnetizations are shifted upward consecutively by $5\times {10}^{-3}{\mu }_{\mathrm{B}}$ per ${\mathrm{Cu}}^{2+}$ with increasing pressure.

Figure 5

Magnetization curves around the spin-flop field region measured at $T=1.8\mathrm{K}$ under various pressures. The values of magnetizations are shifted upward consecutively by $2\times {10}^{-3}{\mu }_{\mathrm{B}}$ per ${\mathrm{Cu}}^{2+}$ with increasing pressure.

Figure 6

Spin-flop field $H_{\mathrm{sf}}$ at $T=1.8\mathrm{K}$ as function of pressure in ${\mathrm{TlCu}}_{0.988}{\mathrm{Mg}}_{0.012}{\mathrm{Cl}}_3$.

Figure 7

Magnetizations in ${\mathrm{TlCu}}_{0.988}{\mathrm{Mg}}_{0.012}{\mathrm{Cl}}_3$ under $P=5.21\mathrm{kbar}$ as functions of temperature measured at various magnetic fields parallel to $[2,0,1]$ direction. Arrows denote transition temperatures $T_{\mathrm{N}}$ and $T_{\mathrm{sf}}$.

Figure 8

Low-field magnetization curves in ${\mathrm{TlCu}}_{0.988}{\mathrm{Mg}}_{0.012}{\mathrm{Cl}}_3$ measured at various temperatures for $H\Vert [2,0,1]$ at $P=5.21\mathrm{kbar}$. Arrows denote spin-flop fields $H_{\mathrm{sf}}$.

Figure 9

Magnetic phase diagrams for $H\Vert [2,0,1]$ in ${\mathrm{TlCu}}_{0.988}{\mathrm{Mg}}_{0.012}{\mathrm{Cl}}_3$ obtained at $P=5.21$ (closed marks) and $1.05\mathrm{kbar}$ (open marks).

Figure 10

Phase diagram of ground state proposed by Mikeska et al. (Ref. 12) Solid and dashed lines are boundaries for the pure and doped systems, respectively. The thin arrow denotes the $(Z{J}^{\prime }∕J)$ corresponding to ${\mathrm{TlCuCl}}_3$. The thick solid and dashed arrows denote the changes of the ground state induced by applications of pressure and magnetic field, respectively.