1. Magnetization and heat capacity of a ferromagnet: Consider a ferromagnet with spin S > 1/2. Orbital angular momentum is quenched. (a) Show that the magnetization M just below To in zero or a very weak magnetic field is given by M(T 10(5+1)3(TC-T) M(0) 3[(5+1)2+52]TC where M(0) the magnetization value at 0 K. (b) Show that there is a discontinuity in the heat capacity at Tc given by (25+1)2-1 AC = =nkB (25+1)2+1 where AC is the jump in the heat capacity at Te in zero external magnetic field. (c) Plot the heat capacity vs temperature at a small constant magnetic field (d) How will the magnetic entropy vary as a function of temperature? (Hint : You can make use of following approximation for the Brillouin function for small magnetic fields Bs(x) = (25+1)2-1]x (25+1)*-11 x (25)2 3 (25)4 45 + 0(x5) fory