12.2.Magnetic Phenomena and Their Interpretation 229 FIGURE 12.4.(a)Schematic represen- Nucleus tation of electrons which spin around their own axis.A(para)mag- netic moment um results;its direc- tion depends on the mode of rota- tion.Only two spin directions are shown (called "spin up"and "spin down").(b)An orbiting electron is the source for electron-orbit para- (a) (b) magnetism. 12.2.2Para- Paramagnetism in solids is attributed to a large extent to a mag- magnetism netic moment that results from electrons which spin around their own axis;see Figure 12.4(a).The spin magnetic moments are gen- erally randomly oriented so that no net magnetic moment results An external magnetic field tries to turn the unfavorably oriented spin moments in the direction of the external field,but thermal agitation counteracts the alignment.Thus,spin paramagnetism is slightly temperature-dependent.It is generally weak and is ob- served in some metals and in salts of the transition elements. Free atoms(dilute gases)as well as rare earth elements and their salts and oxides possess an additional source of paramag- netism.It stems from the magnetic moment of the orbiting elec- trons;see Figure 12.4(b).Without an external magnetic field, these magnetic moments are,again,randomly oriented and thus mutually cancel one another.As a result,the net magnetization is zero.However,when an external field is applied,the individ- ual magnetic vectors tend to turn into the field direction which may be counteracted by thermal agitation.Thus,electron-orbit paramagnetism is also temperature-dependent.Specifically,para- magnetics often (not always!)obey the experimentally found Curie-Weiss law: X=。 (12.10) where C and 0 are constants (given in Kelvin),and C is called the Curie Constant.The Curie-Weiss law is observed to be valid for rare earth elements and salts of the transition elements,for ex- ample,the carbonates,chlorides,and sulfates of Fe,Co,Cr,Mn. From the above-said it becomes clear that in paramagnetic ma- terials the magnetic moments of the electrons eventually point in the direction of the external field,that is,the magnetic moments enhance the external field [see Figure 12.2(a)].On the other hand, diamagnetism counteracts an external field [see Figure 12.2(c)].Paramagnetism in solids is attributed to a large extent to a mag￾netic moment that results from electrons which spin around their own axis; see Figure 12.4(a). The spin magnetic moments are gen￾erally randomly oriented so that no net magnetic moment results. An external magnetic field tries to turn the unfavorably oriented spin moments in the direction of the external field, but thermal agitation counteracts the alignment. Thus, spin paramagnetism is slightly temperature-dependent. It is generally weak and is ob￾served in some metals and in salts of the transition elements. Free atoms (dilute gases) as well as rare earth elements and their salts and oxides possess an additional source of paramag￾netism. It stems from the magnetic moment of the orbiting elec￾trons; see Figure 12.4(b). Without an external magnetic field, these magnetic moments are, again, randomly oriented and thus mutually cancel one another. As a result, the net magnetization is zero. However, when an external field is applied, the individ￾ual magnetic vectors tend to turn into the field direction which may be counteracted by thermal agitation. Thus, electron-orbit paramagnetism is also temperature-dependent. Specifically, para￾magnetics often (not always!) obey the experimentally found Curie–Weiss law: $
T  C  (12.10) where C and  are constants (given in Kelvin), and C is called the Curie Constant. The Curie–Weiss law is observed to be valid for rare earth elements and salts of the transition elements, for ex￾ample, the carbonates, chlorides, and sulfates of Fe, Co, Cr, Mn. From the above-said it becomes clear that in paramagnetic ma￾terials the magnetic moments of the electrons eventually point in the direction of the external field, that is, the magnetic moments enhance the external field [see Figure 12.2(a)]. On the other hand, diamagnetism counteracts an external field [see Figure 12.2(c)]. 12.2 • Magnetic Phenomena and Their Interpretation 229 12.2.2 Para￾magnetism m m m e – e – e – Nucleus (a) (b) FIGURE 12.4. (a) Schematic represen￾tation of electrons which spin around their own axis. A (para)mag￾netic moment m results; its direc￾tion depends on the mode of rota￾tion. Only two spin directions are shown (called “spin up” and “spin down”). (b) An orbiting electron is the source for electron-orbit para￾magnetism.