Interplay of frustration and magnetic field in the two-dimensional quantum antiferromagnet $\text{Cu}\left(\text{tn}\right){\text{Cl}}_2$

Specific heat and ac magnetic susceptibility measurements, spanning low temperatures $\left(T\ge 40\text{mK}\right)$ and high-magnetic fields $\left(B\le 14\text{T}\right)$, have been performed on a two-dimensional (2D) antiferromagnet $\text{Cu}\left(\text{tn}\right){\text{Cl}}_2$ $\left(\text{tn}=1,3\text{-diaminopropane}={\text{C}}_3{\text{H}}_{10}{\text{N}}_2\right)$. The compound represents a $S=1/2$ spatially anisotropic triangular antiferromagnet realized by a square lattice with nearest-neighbor $\left(J/k_B=3\text{K}\right)$, frustrating next-nearest-neighbor $\left(0<J^{\prime }/J<0.6\right)$, and interlayer $\left(\left|J^{″}/J\right|\approx {10}^{-3}\right)$ interactions. The absence of long-range magnetic order down to $T=60\text{mK}$ in $B=0$ and the $T^2$ behavior of the specific heat for $T\le 0.4\text{K}$ and $B\ge 0$ are considered evidence of a high degree of 2D magnetic order. In fields lower than the saturation field, $B_{\text{sat}}=6.6\text{T}$, a specific heat anomaly, appearing near 0.8 K, is ascribed to bound vortex-antivortex pairs stabilized by the applied magnetic field. The resulting magnetic phase diagram is remarkably consistent with the one predicted for a square lattice without a frustrating interaction, expect that $B_{\text{sat}}$ is shifted to values lower than expected. Potential explanations for this observation, as well as the possibility of a Berezinski-Kosterlitz-Thouless (BKT) phase transition in a spatially anisotropic triangular magnet with the collinear Néel ground state, are discussed.

Figure 1

Realization of Heisenberg model of a spatially anisotropic triangular lattice within a single $bc$ layer in $\text{Cu}\left(\text{tn}\right){\text{Cl}}_2$. The layers are stacked along the $a$ direction. The full circles denote ${\text{Cu}}^{2+}$ ions.

Figure 2

Temperature dependence of the total specific heat, $C_{\text{TOT}}$, of $\text{Cu}\left(\text{tn}\right){\text{Cl}}_2$ in various magnetic fields. Solid lines represent data for $B=0$, 0.5, 0.75, 1, 1.5, 2, 2.5, 3, 3.5, and 4 T, while the dashed lines correspond to $B=5$, 6, 7, 8, and 9 T. The dot-dashed line represents the specific heat of the diamagnetic isomorph $\text{Zn}\left(\text{tn}\right){\text{Cl}}_2$.

Figure 3

Temperature dependence of the total specific heat of $\text{Cu}\left(\text{tn}\right){\text{Cl}}_2$ in $B=0$, 0.5, 0.75, 1, 1.5, 2, and 2.5 T. Inset: Temperature dependence of the difference $\Delta C=\left[C\left(T,B\right)-C\left(T,0\right)\right]$ between the total specific heat in finite and zero magnetic fields.

Figure 4

(Color online) Temperature dependence of the total specific heat of $\text{Cu}\left(\text{tn}\right){\text{Cl}}_2$ in various magnetic fields.

Figure 5

(Color online) Magnetic field dependence of isothermal ac susceptibility of $\text{Cu}\left(\text{tn}\right){\text{Cl}}_2$ at various temperatures. Inset: Magnetic field dependence of the normalized isothermal magnetization at 40 mK.

Figure 6

Magnetic field dependence of the value for the maximum of the $\text{Cu}\left(\text{tn}\right){\text{Cl}}_2$ magnetic specific heat, $C_{\text{max}}$, divided by the gas constant $R$ (open squares). The solid line is a guide for eyes. Magnetic field dependence of the temperature, $T_{\text{max}}$, denoting the position of $C_{\text{max}}$ (full squares). The broken line is a linear fit (see text).

Figure 7

$C_M{T}^2$ vs $T^4$ dependence for $\text{Cu}\left(\text{tn}\right){\text{Cl}}_2$ in $B=0$, 0.5, 0.75, 1, 1.5, 2, and 2.5 T. Inset: Magnetic field dependence of the coefficient $b$, Eq. (6). The solid line represents a linear fit.

Figure 8

Magnetic field dependence of the peak position, $T_{\text{p}}$, of the low temperature specific heat anomalies (full squares) in $\text{Cu}\left(\text{tn}\right){\text{Cl}}_2$. The theoretical prediction for the field induced BKT phase transition for the isotropic square lattice is denoted by the open squares and the broken line. Inset: Temperature dependence of the difference between the specific heat in finite and zero magnetic field. The solid lines represent $B=1$, 2, 3, 3.5, and 4 T, and the dashed lines correspond to $B=4.5$, 5, 5.5, 6, and 7 T.

Figure 9

(Color online) Extended magnetic phase diagram of $\text{Cu}\left(\text{tn}\right){\text{Cl}}_2$. The open squares represent the $T_{\text{max}}$ vs $B$ dependence, while the pluses $(+)$ correspond to the line constructed from the condition that ${\delta }_{T}S\left(T,B\right)-{\delta }_{T}S\left(T,0\right)=0$, see text. The theoretically predicted BKT transition and the experimental $T_{\text{p}}$ vs $B$ dependence are denoted by full triangles and full circles, respectively. Open circles correspond to the positions of the midpoints in the shoulders of ac susceptibility data. The star represents the $B_{\text{sat}}$ as extracted from an analysis of the specific heat data measured in 9 T and 14 T. The dotted and solid lines are guides for eyes. The regions of short-range order (SRO) and free or bound vortex (V) and antivortex (AV) pairs are identified. Detailed descriptions of each $B-T$ region are given in the text.