Weak ferromagnetism, metal-to-nonmetal transition, and negative differential resistivity in single-crystalSr2IrO4

${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ has the ${\mathrm{K}}_2{\mathrm{NiF}}_4$ structure and its ${\mathrm{Ir}}^{4+}$ ion ${(5d}^5)$ is in a low spin configuration $t_{2g}^5$ with $S$=$\frac{1}{2}$. In this paper, we report results of our study on single-crystal ${\mathrm{Sr}}_2{\mathrm{IrO}}_4.$ Magnetic susceptibility and isothermal magnetization display weak ferromagnetism below 240 K with an easy axis along the $a$ axis and a spin reorientation transition in low magnetic fields. Both the effective paramagnetic moment ${\mu }_{\mathrm{eff}}$ $(=0.5\mathrm{}{\mu }_B)$ and the saturation moment ${\mu }_S(=0.14\mathrm{}{\mu }_B)$ are found to be quite small, but the ratio of ${\mu }_{\mathrm{eff}}/{\mu }_S$ (=3.5) qualitatively fits the Rhodes-Wohlfarth plot. Resistivity, $\rho \mathrm{}\left(T\right),$ along two principal crystallographic directions is strongly anisotropic and shows a metallic behavior below 120 K. ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ exhibits strikingly nonlinear conductivity, i.e., a current-controlled negative differential resistivity for $2<~T<\mathrm{}300\mathrm{}$ K. The origin of the nonohmic behavior may be associated with charge-density-wave depinning. Unlike other systems such as ruthenates ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ appears to show no correlation between conductivity and magnetism.