Magnetic ordering and exchange interactions in the rare-earth gallium compoundsRGa2

Magnetic ordering and indirect exchange interactions were studied in the series of hexagonal rare-earth intermetallic compounds $R{\mathrm{Ga}}_2$, where $R$ denotes Ce, Pr, Nd, Gd, Tb, Dy, Ho, and Er. The magnetic susceptibility ($\chi$) of polycrystalline samples was measured at low fields, from 1.5 K to about 300 K; the magnetization ($M$) versus applied magnetic field ($H$) of these polycrystalline samples and a Ho${\mathrm{Ga}}_2$ single crystal was measured up to 80 kOe at low temperatures; the resistivities ($\rho$) of Ce${\mathrm{Ga}}_2$, Gd${\mathrm{Ga}}_2$, Dy${\mathrm{Ga}}_2$, and Ho${\mathrm{Ga}}_2$ were measured from about 1.5 K to about 300 K, at zero field. The $\chi \mathrm{}\left(T\right)\mathrm{}$ and $M\left(H\right)\mathrm{}$ results indicated that the samples order antiferromagnetically, with ordering temperatures $T_N$ ranging from 6.4 K for Dy${\mathrm{Ga}}_2$ to 14.8 K for Tb${\mathrm{Ga}}_2$. $M\left(H\right)\mathrm{}$ results for single-crystal Ho${\mathrm{Ga}}_2$ show that the [100] direction is the easy direction and the [001] direction is the hard direction. High-temperature $\chi \mathrm{}\left(T\right)\mathrm{}$ results were fitted to the Curie-Weiss formula and the resulting effective moments are in good agreement with those expected for trivalent rare-earth ions. The paramagnetic Weiss temperatures ($\Theta$) are positive for all the samples measured except Gd${\mathrm{Ga}}_2$. The effects of magnetic ordering were observed below $T_N$ in the resistivity results. Letting the spin-disorder part of the resistivity ${\rho }_s$ be proportional to $T^n$, $n$ was determined to be about 2.0, 4.3, and 3.3 for Ho${\mathrm{Ga}}_2$, Gd${\mathrm{Ga}}_2$, and Dy${\mathrm{Ga}}_2$, respectively. In view of the theory of Mannari for ${\rho }_s$, these differences may be connected with differences in the spin structures of these compounds. Ruderman-Kittel-Kasuya-Yosida (RKKY) sums have been calculated for these compounds. The negative sign of the sum is in agreement with the anitiferromagnetic properties observed in various measurements. For Ho${\mathrm{Ga}}_2$, the dressed moment, due to polarization of conduction electrons, has been estimated. The theory of Nagamiya was applied to three of the compounds which can be considered as a layer compound with long-range ferromagnetic intralayer coupling and antiferromagnetic coupling between a layer and its nearest-neighbor layers. With one possible exception, the data are consistent with the theory which contains three exchange coefficients. Crystal-field-induced anisotropy appears to be important in determining the spin structures of these compounds.