Magnetization steps in the diluted Heisenberg layer materials ${\left({\mathrm{C}\mathrm{H}}_3{\mathrm{N}\mathrm{H}}_3\right)}_2{\mathrm{Mn}}_x{\mathrm{Cd}}_{1-x}{\mathrm{Cl}}_4$: Equilibrium data at 0.6 K

The magnetization $M$ of ${\left({\mathrm{C}\mathrm{H}}_3{\mathrm{N}\mathrm{H}}_3\right)}_2{\mathrm{Mn}}_x{\mathrm{Cd}}_{1-x}{\mathrm{Cl}}_4$, with $x$ from 0.025 up to 0.265, was measured at 0.6 K in a slowly varying magnetic field $B$ up to 17 T. The exchange interaction in these strongly diluted planar magnetic materials is antiferromagnetic. The in-plane cation structure is well approximated by a square lattice. The observed qualitative features, listed in the order that they appear in increasing $B$, are as follows: a fast rise of $M$, starting at $B=0$; a magnetization plateau (plateau of “apparent saturation”); a large magnetization step (MST), attributed to nearest-neighbor (NN) pairs; a second magnetization plateau; another large MST from NN pairs; and a third plateau that is not completed below the highest available $B$. These features are expected from the NN cluster model presented in the preceding paper. The magnetic fields at the two MST’s give $J_1∕k_{\mathrm{B}}=(-4.39\pm 0.10)\mathrm{K}$ for the NN exchange constant. This value is slightly lower than reported for the undiluted $(x=1)$ member of this series, ${\left({\mathrm{C}\mathrm{H}}_3{\mathrm{N}\mathrm{H}}_3\right)}_2\mathrm{Mn}{\mathrm{Cl}}_4$. A smaller $J_1$ when $x⩽0.265$ may be the result of an in-plane expansion with decreasing $x$, caused by the slightly larger ${\mathrm{Cd}}^{2+}$ ion compared to ${\mathrm{Mn}}^{2+}$. Analysis of the initial rise of $M$ at low $B$ indicates the presence of weak interactions that are not included in the NN cluster model. This conclusion is consistent with the observation (to be reported later) of a weak exchange interaction with a neighbor that is more distant than a NN. The apparent saturation value $M_s$, at the first magnetization plateau, was determined for all seven samples. There is a fair agreement with the values expected from a random distribution of the Mn ions over all cation sites. The largest deviation is for samples with $x⩾0.15$, where the measured $M_s$ is somewhat higher. In the same samples the magnetization jump $\Delta M$ at the MST’s from NN pairs is somewhat smaller than for a random Mn distribution. A proposed explanation of the discrepancies for $x⩾0.15$ postulates that the probability that a cation site is occupied by a ${\mathrm{Mn}}^{2+}$ is lowered by the presence of other ${\mathrm{Mn}}^{2+}$ ions at one or more NN cation sites.

Figure 1

Schematic of the crystal structure of ${\left({\mathrm{C}\mathrm{H}}_3{\mathrm{N}\mathrm{H}}_3\right)}_2\mathrm{Mn}{\mathrm{Cl}}_4$. Adapted from Knorr et al. (Ref. 11). Unlike the notation in Ref. 5, $a$ is one of the lattice constants of the tetragonal structure, not the distance between NN cations.

Figure 2

Magnetization curves for the seven MST samples at $T\approx 0.60\mathrm{K}$. The “chosen values” of $x$ (Table ) are 0.025 for sample A, 0.063 for B, 0.067 for C, 0.078 for D, 0.157 for E, 0.172 for F, and 0.265 for G. The SI unit ${\mathrm{Am}}^2∕\mathrm{kg}$ for the ordinate scale is equivalent to $\mathrm{emu}∕\mathrm{g}$.

Figure 3

Magnetic field dependence of the derivative $dm∕dB$ of the normalized magnetization $m=M\left(B\right)∕M\left(17\mathrm{T}\right)$ for five of the samples. These results were obtained numerically from the curves in Fig. 2.

Figure 4

Measured magnetization curves (solid lines) and the corresponding simulated magnetization curves (dashed lines) for samples A $(x=0.025)$, C $(x=0.067)$, and E $(x=0.157)$. The simulations use the NN cluster model at the actual experimental temperature, $T=0.6\mathrm{K}$.

Figure 5

The measured (solid) and simulated (dashed) magnetization curves for samples B $(x=0.063)$) and G $(x=0.265)$).

Figure 6

The measured (solid) and simulated (dashed) magnetization curves for samples D $(x=0.078)$ and F $(x=0.172)$.

Figure 7

Apparent saturation value $M_s$ as a function of $x$. The filled circles are the experimental values for the various samples, expressed in ${\mathrm{Am}}^2∕\mathrm{kg}$ (equivalent to $\mathrm{emu}∕\mathrm{g}$). The solid curve is the calculated $M_s$, assuming a random Mn distribution. The dashed curve is the saturation magnetization $M_0$.