FIG. 7: (Color online). Magnetic susceptibility as a function of temperature. (Solid line) The inverse molar magnetic susceptibility of BiMnO$_{3}$ measured in 1T [19] has been rescaled by its value at T = 101 K in order to obtain the dimensionless quantity. Dashed and dotted lines represent the respective calculated temperature variations of the magnetic susceptibility (28); we used the same parameter values as in Fig. 2. have sets of planes for each of the order parameters. Namely, we have the dependencies M 2 ( H$_{a}$ M , E$_{a}$ P ) , P 2 ( H$_{a}$ M , E$_{a}$ P $^{)}$. The plane which crosses point (0 , 0) corresponds to the phase transition temperature in zero field. A representative set of the Arrot planes is drawn in Fig. 8 for the magnetization. One can see that the transition temperature can be determined from the dependence ˜ M 2 vs e/ ˜ P , not only from ˜ M 2 vs h/ ˜ M ! From (3) and (4) after dividing both equations by the order parameter and solving the resulting system we obtain: where x$_{e}$ = e ˜ P and x$_{h}$ = h ˜ $_{M}$. From Eq. (29) one can also see that for T > T$_{RM}$ we still have a nonzero value of ˜ P (cf. Eq. (20)). Therefore, the Arrot planes P $^{2}$( H$_{a}$/M, E$_{a}$/P ) are not important, since T$_{f}$ > T$_{RM}$ . 13 ˜ P 2 = T 2 M T 2 $_{f}$( l − γ 2 $_{m}$)$^{(}$ x$_{e}$ − γ$_{m}$ T$_{f}$ T$_{M}$ ( 1 − T T$_{M}$ + x$_{h}$$^{)}$ + l T 2 f T 2 M ( 1 − T T$_{f}$$^{))}$ , (29) ˜ M 2 = x$_{h}$ + 1 − T T$_{M}$ − γ$_{m}$ l − γ 2 m T$_{M}$ T$_{f}$ ( x$_{e}$ − l T 2 f T 2 M $^{(}$T T$_{f}$ − 1$^{)}$ − γ$_{m}$ T$_{f}$ T$_{M}$ ( 1 − T T$_{M}$ + x$_{h}$$^{))}$ , (30)