Critical behavior and critical endpoints of FeCl2·2H2O and CoCl2·2H2O in an applied magnetic field

Fe${\mathrm{Cl}}_2$·2${\mathrm{H}}_2$O and Co${\mathrm{Cl}}_2$·2${\mathrm{H}}_2$O represent metamagnets with two discontinuities in the magnetization at low temperatures. An antiferromagnetic (AF) phase at low fields is followed by a ferrimagnetic phase at intermediate fields and a paramagnetic ($P$) phase at high fields. These three phases meet at one point at a higher temperature. By means of neutron-diffraction experiments, we have investigated the properties of the systems in the vicinity of this point. For Fe${\mathrm{Cl}}_2$·2${\mathrm{H}}_2$O, this point is shown to be a critical endpoint ($H_{\mathrm{CEP}}=4.329\mathrm{}\pm 0.007$ T; $T_{\mathrm{CEP}}=11.20\mathrm{}\pm 0.05$ K), i.e., an endpoint of a $\lambda$ line of continuous transitions emanating from the Néel point and ending on a first-order transition line. In zero field, we find the critical exponent for the sublattice magnetization to be $\beta =0.30\mathrm{}\pm 0.01$; near the critical endpoint (CEP) we find ${\beta }_{\mathrm{CEP}}=0.29\mathrm{}\pm 0.02$, i.e., no crossover on the whole $\lambda$ line. For Co${\mathrm{Cl}}_2$·2${\mathrm{H}}_2$O, we find a triple point ($H_{\mathrm{TP}}=3.972\mathrm{}\pm 0.009$ T; $T_{\mathrm{TP}}=9.53\mathrm{}\pm 0.01$ K). The critical exponent $\beta$ in zero field is observed to be ${\beta }_3=0.32\mathrm{}\pm 0.01$ for ${\epsilon }_T=\frac{(T_N-T)}{T_N}<6\mathrm{}\times {10}^{-3\mathrm{}}$ but ${\beta }_1=0.18\mathrm{}\pm 0.01$ for $6\times {10}^{-3\mathrm{}}<{\epsilon }_T<6\mathrm{}\times {10}^{-2\mathrm{}}$; this is interpreted as crossover in effective spatial dimensionality. Under applied fields, the $d=3\mathrm{}$ behavior disappears on the AF-$P$-phase boundary at $H_t=4.00\mathrm{}\pm 0.01$ T; $T_t=10.0\mathrm{}\pm 0.1$ K. Here we find an exponent ${\beta }_t=0.130\mathrm{}\pm 0.005$. We discuss in detail whether this may be understood as a tricritical point at ($H_t$, $T_t$) or whether the triple point ($H_{\mathrm{TP}}$, $T_{\mathrm{TP}}$) should be characterized as a critical endpoint as in Fe${\mathrm{Cl}}_2$·2${\mathrm{H}}_2$O, so excluding the existence of a tricritical point: The issue cannot be fully resolved.