TABLE 36.3 The Occurrence of Ferromagnetism omic number 25 262728 64 1.631.821.971.57 Ferromagnetic moment/mass (Am2/kg) 2177516154.390 Curie point, e K Neel temp, e,K have positive susceptibility. All atoms are diamagnetic by virtue of their having electrons. Some atoms are also paramagnetic as well, but in this case they are called paramagnetic since paramagnetism is roughly a hundred times stronger than diamagnetism and overwhelms it. Faraday discovered that paramagnetic are attracted by magnetic field and move toward the region of maximum field, whereas diamagnetic are repelled and move wara a s The total magnetization of both paramagnetic and diamagnetic materials is zero in the absence of an app ld, i. e, they have zero remanence. Atomic paramagnetism is a necessary condition but condition for ferro- or ferrimagnetism, i.e., for materials having useful magnetic properties not a suffici Ferromagnetism and Ferrimagnetism To develop technologically useful materials, we need an additional force that ensures that the spins of the outermost(or almost outermost)electrons are mutually parallel. Slater showed that in iron, cobalt, and nickel this could happen if the distance apart of the atoms(D)was more than 1. 5 times the diameter of the 3delectron shell(d).(These are the electrons, near the outside of atoms of iron, cobalt, and nickel, that are responsible for the strong paramagnetic moment of the atoms. Paramagnetism of the atoms is an essential prerequisite for ferro-or ferrimagnetism in a material. Slater's result suggested that, of these metals, iron, cobalt, nickel, and gadolinium should be ferromagnetic at room temperature, while chromium and manganese should not be ferromagnetic. This is in accordance with experiment. Gadolinium, one of the rare earth elements, is only weakly ferromagnetic in a cool room. Chro mium and manganese in the elemental form narrowly miss being ferromagnetic. However, when manganese is alloyed with copper and aluminum( Cu Mn2 Als)to form what is known as a Heusler alloy [Crangle, 1962 it becomes ferromagnetic. The radius of the 3d electrons has not been changed by alloying, but the atomic e. ing has been increased by a factor of 1.53/1.47. This small change is sufficient to make the difference ween positive exchange, parallel spins, and ferromagnetism and negative exchange, antiparallel spins, and antiferromagnetism. For all ferromagnetic materials there exists a temperature(the Curie temperature)above which the thermal disordering forces are stronger than the exchange forces that cause the atomic spins to be parallel. From Table 36.3 we see that in order of descending Curie temperature we have Co, Fe, Ni, Gd. From Fig. 36.4 we find that this is also the order of descending values of the exchange integral, suggesting that high positive values of the exchange integral are indicative of high Curie temperatures rather than high magnetic intensity in ferromagnetic materials. Negative values of exchange result in an antiparallel arrangement of the spins of adjacent atoms and in antiferromagnetic materials(Fig. 36.3). Until 5 years ago, it was true to say that antiferromagnetism had no practical application. Thin films on antiferromagnetic materials are now used to provide the bias field which is used to linearize the response of some magnetoresistive reading heads in magnetic disk drives. Ferrimag- netism, also illustrated in Fig. 36.3, is much more widely used. It can be produced as soft, i.e., low coercivity ferrites for use in magnetic recording and reading heads or in the core of transformers operating at frequencies up to tens of megahertz. High-coercivity, single-domain particles(which are discussed later )are used in very large quantities to make magnetic recording tapes and flexible disks - O, and cobalt-impregnated iron oxides and to make barium ferrite, the most widely used material for permanent magnets. e 2000 by CRC Press LLC© 2000 by CRC Press LLC have positive susceptibility. All atoms are diamagnetic by virtue of their having electrons. Some atoms are also paramagnetic as well, but in this case they are called paramagnetics since paramagnetism is roughly a hundred times stronger than diamagnetism and overwhelms it. Faraday discovered that paramagnetics are attracted by a magnetic field and move toward the region of maximum field, whereas diamagnetics are repelled and move toward a field minimum. The total magnetization of both paramagnetic and diamagnetic materials is zero in the absence of an applied field, i.e., they have zero remanence. Atomic paramagnetism is a necessary condition but not a sufficient condition for ferro- or ferrimagnetism, i.e., for materials having useful magnetic properties. Ferromagnetism and Ferrimagnetism To develop technologically useful materials, we need an additional force that ensures that the spins of the outermost (or almost outermost) electrons are mutually parallel. Slater showed that in iron, cobalt, and nickel this could happen if the distance apart of the atoms (D) was more than 1.5 times the diameter of the 3d electron shell (d). (These are the electrons, near the outside of atoms of iron, cobalt, and nickel, that are responsible for the strong paramagnetic moment of the atoms. Paramagnetism of the atoms is an essential prerequisite for ferro- or ferrimagnetism in a material.) Slater’s result suggested that, of these metals, iron, cobalt, nickel, and gadolinium should be ferromagnetic at room temperature, while chromium and manganese should not be ferromagnetic. This is in accordance with experiment. Gadolinium, one of the rare earth elements, is only weakly ferromagnetic in a cool room. Chro￾mium and manganese in the elemental form narrowly miss being ferromagnetic. However, when manganese is alloyed with copper and aluminum (Cu61Mn24Al15) to form what is known as a Heusler alloy [Crangle, 1962], it becomes ferromagnetic. The radius of the 3d electrons has not been changed by alloying, but the atomic spacing has been increased by a factor of 1.53/1.47. This small change is sufficient to make the difference between positive exchange, parallel spins, and ferromagnetism and negative exchange, antiparallel spins, and antiferromagnetism. For all ferromagnetic materials there exists a temperature (the Curie temperature) above which the thermal disordering forces are stronger than the exchange forces that cause the atomic spins to be parallel. From Table 36.3 we see that in order of descending Curie temperature we have Co, Fe, Ni, Gd. From Fig. 36.4 we find that this is also the order of descending values of the exchange integral, suggesting that high positive values of the exchange integral are indicative of high Curie temperatures rather than high magnetic intensity in ferromagnetic materials. Negative values of exchange result in an antiparallel arrangement of the spins of adjacent atoms and in antiferromagnetic materials (Fig. 36.3). Until 5 years ago, it was true to say that antiferromagnetism had no practical application. Thin films on antiferromagnetic materials are now used to provide the bias field which is used to linearize the response of some magnetoresistive reading heads in magnetic disk drives. Ferrimag￾netism, also illustrated in Fig. 36.3, is much more widely used. It can be produced as soft, i.e., low coercivity, ferrites for use in magnetic recording and reading heads or in the core of transformers operating at frequencies up to tens of megahertz. High-coercivity, single-domain particles (which are discussed later) are used in very large quantities to make magnetic recording tapes and flexible disks g-Fe2O3 and cobalt-impregnated iron oxides and to make barium ferrite, the most widely used material for permanent magnets. TABLE 36.3 The Occurrence of Ferromagnetism Cr Mn Fe Co Ni Gd Atomic number 24 25 26 27 28 64 Atomic spacing/diameter 1.30 1.47 1.63 1.82 1.97 1.57 Ferromagnetic moment/mass (Am2 /kg) At 293 K — — 217.75 161 54.39 0 At 0 K — — 221.89 162.5 57.50 250 Curie point, Qc K — — 1,043 1,400 631 289 Néel temp., Qn K 475 100 — — — —