Neutron diffraction studies of nuclear and magnetic structures in the $S=1∕2$ square Heisenberg antiferromagnets ${\left({\mathrm{d}}_6\text{−}5\mathrm{CAP}\right)}_2\mathrm{Cu}{X}_4$ ($X=\mathrm{Br}$ and $\mathrm{Cl}$)

We report the neutron scattering studies of the nuclear and magnetic structures of deuterated samples of the model two-dimensional $S=1∕2$ Heisenberg antiferromagnets on a square lattice, ${\left({\mathrm{d}}_6\text{−}5\mathrm{CAP}\right)}_2\mathrm{Cu}{\mathrm{Cl}}_4$ and ${\left({\mathrm{d}}_6\text{−}5\mathrm{CAP}\right)}_2\mathrm{Cu}{\mathrm{Br}}_4$ (where 5CAP is 2-amino-5-chloropyridinium). Interest in these materials stems from the fact that they have relatively weak exchange between the magnetic ions, and it is therefore possible to perturb their magnetic structures and excitations significantly in experimentally accessible magnetic fields, and thereby access new quantum disordered states. We succeeded in growing fully deuterated single crystals and determined the nuclear and magnetic structures of the bromide at 10 and $1.8\mathrm{K}$, respectively, confirming the four-sublattice spin structure expected for systems, where both inter- and intraplane exchange interactions are antiferromagnetic. The determination of the full crystal structure of the bromide highlights the possibility that interlayer exchange may also propagate via hydrogen bonds to and through the 5CAP molecule. We also determined the critical exponents for the sublattice magnetization of the bromide and mapped out the $H\text{−}T$ phase diagram of the chloride up to $5\mathrm{T}$.

Figure 1

(Color online) Crystal and magnetic structures of the bromide viewed (a) parallel and (b) perpendicular to the $c$ axis. (c) shows the numbering scheme for atoms in the 5CAP molecule as used in Tables .

Figure 2

(Color online) Magnetic structure depicting the copper sites of the unit cell, with the moment direction indicated by the arrows. The nearest-neighbor intralayer coupling $J$ and interlayer coupling $J^{\prime }$ are indicated by the gray lines.

Figure 3

(Color online) (a) Dependence of $I\left(101\right)$ on temperature for (5CAP) copper (II) bromide in zero applied field. Data have been corrected for background scattering. The line is a fit to the standard power-law expression $I\left(T\right)=A{\epsilon }^{2\beta }$, where $\epsilon =[1-(T∕T_N)]$, yielding $T_N=5.18\left(1\right)\mathrm{K}$ and $\beta =0.23\left(4\right)$. (b) The same data in a log-log plot. (c) The derivative of the total integrated intensity, $-dI∕dT$, as a function of temperature showing a cusp at $T_N$.

Figure 4

(Color online) Dependence of $I\left(101\right)$ on temperature for (5CAP) copper (II) chloride in zero applied field. Data have been corrected for background. We deduce the transition temperature $T_N=754\left(5\right)\mathrm{mK}$.

Figure 5

(Color online) Variation of $I\left(101\right)$ for (5CAP) copper (II) chloride with applied field at selected temperatures denoted by the symbols: $30\mathrm{mK}$ (closed circles), $267\mathrm{mK}$ (open circles), $455\mathrm{mK}$ (closed triangles), and $670\mathrm{mK}$ (open triangles). The black lines are guides to the eye. Data were taken in $0.2\mathrm{T}$ steps up to and beyond the point where no scattering intensity was observed above the background.

Figure 6

(Color online) $H\text{−}T$ phase diagram for (5CAP) copper (II) chloride determined by neutron scattering and specific heat measurements. The solid points are the critical fields obtained by tracking the neutron scattering intensity $I\left(101\right)$ at fixed temperatures as a function of magnetic field applied along the $b$ axis (Fig. 4). The top panel shows the heat capacity, $C_p(T,H)$, as a function of temperature for three constant magnetic fields ($H=0$, 3, and $5\mathrm{T}$) applied perpendicular to the $b$ axis. $C_p(T,H)$ was measured in a temperature range $T=0.35–12\mathrm{K}$ for a total of 11 different fields, from which the color map of $C_p$ vs temperature and field was constructed. To allow direct comparison with the neutron scattering data, the magnetic-field scale for the $C_p$ data has been scaled by the $g$ factors (Ref. 21) $g_{ac}∕g_b=2.06∕2.22$. The peak in $C_p$ traces the phase transition to the antiferromagnetic phase in good accord with the neutron scattering data.

Figure 7

(Color online) Crystal structure of the bromide viewed (a) nearly parallel and (b) perpendicular to the $c$ axis along $\mathit{a}+\mathit{b}$, with closest Br–Br separations and shortest Br–D separations indicated by the dashed lines.