Hall effect studies have been performed in the compounds \ensuremath{\kappa}-(BEDT-TTF${)}_{2}$Cu[N(CN${)}_{2}$]X, where X=Cl and Br and BEDT-TTF is bis(ethylenedithio)tetrathiafulvalene, in the temperature range 100 to 10 K. Hall constant has been found to be temperature independent in the Br salt down to 55 K and equal to +2\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}8}$ ${\mathrm{m}}^{3}$/C. In the Cl salt the Hall constant is equal to +1.4\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}7}$ ${\mathrm{m}}^{3}$/C at 100 K and increases on cooling down to 70 K almost parallel to the resistance increase. Below \ensuremath{\sim}70 and \ensuremath{\sim}55 K in the Cl and Br, respectively, the magnetic field change has been found to produce long-term sample resistance relaxation. The relaxation phenomena change dramatically with temperature, reaching the maximum above magnetic ordering temperature in the Cl salt at 30 K, and then sharply dropping in magnitude in the magnetically ordered state. A similar relaxation is observed in the Br salt. These effects are considered to be due to the magnetic domain structure formation in the antiferromagnetically ordered state. Essential changes of the domain wall dynamics, appearing in the Br salt at 25 K, evidence the presence of the second magnetic transition in the Br salt, quite similar to the Cl salt. By studying the anisotropy of the relaxation phenomena within highly conducting plane in the Cl compound it is shown that domain walls are lying parallel to the a direction. A possible origin of the magnetic order in the salts is discussed.
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