Influence of order on magnetic properties R. Smoluchowski To cite this version: R. Smoluchowski. Influence of order on magnetic properties. J. Phys. Radium, 1951, 12 (3),pp.389- 398. 10.1051/jphysrad:01951001203038900. jpa-00234397 HAL Id: jpa-00234397 https://hal.archives-ouvertes.fr/jpa-00234397 Submitted on 1 Jan 1951 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. LE JOURNAL DE PHYSIQUE ET LE RADIUM. 1’OME 12, MARS 1~~1~ PAGE 389. INFLUENCE OF ORDER ON MAGNETIC PROPERTIES By R. SMOLUCHOWSKI. Sommaire. - Une nouvelle théorie de saturation magnétique dans les alliages binaires est présentée. Dans cette théorie on considère les fluctuations de concentration électronique dans tous les groupes équivalents des atomes. Dans le cas d’un réseau du cube centré ces groupes contiennent les premiers et les seconds voisins et la théorie est en accord avec les données expérimentales pour Fe-Co. Pour les alliages à faces centrées, comme Fe-Ni, on emploie un groupe contenant les premiers voisins. Cette théorie permet aussi de calculer l’influence d’ordre sur les propriétés magnétiques comme le moment de saturation et la magnétostriction et elle est en accord avec les expériences dans les cas connus. L’influence d’ordre sur la température de Curie, sur l’anisotropie magnétique, sur la force coercitive et sur la perméabilité est aussi discutée. Enfin l’influence de propriétés magnétiques sur les phénomènes d’ordre est considérée. 1. General characteristics. - a. The order- know that metallic bonding has a much more compli- disorder phenomena. - A brief summary of the cated origin and also that there are ordering reac- important features of the ordering phenomena may tions in which the average number of bonds of each not be out of place here. In many binary alloys, kind does not change at all. usually those which exhibit complete or nearly Finally, it should be pointed out that above the complete miscibility, at particular compositions critical temperature, T" the crystal exists in an there can exist below a critical temperature, T,., essentially random state. There is much good an « ordered » lattice. In the ordered lattice each evidence that at least near the temperature, T,, kind of atom occupies a specific kind of lattice site there is a tendency for atoms A to seek a B-rich in the unit cell. Ideally, at sufficiently low tempe- neighborhood, and vice-versa. This tendency, the ratures this « long range order » should extend so-called « short range order », is best described throughout each single crystal. However, at low as a general decrease in the probability of local temperature the ordering process is too slow and concentration fluctuations as compared to those in a at higher temperature the disturbing thermal agita- purely random solid solution. tion too large to allow the ideal condition ever to be attained. The ordered state in an actual single b. Saturation magnetizafion. - When considering crystal (or grain) should be imagined as consisting the influence of order on magnetic properties [ 1 ~, it is of many small volumes within which the order is very high but varying in a discontinuous manner at the boundary between these volumes. Each of these volumes can be thought of as separately nucleated during the transition from a random to an ordered solid solution. Clearly, the over-all degree of order in a crystal at equilibrium depends upon the size of these blocks of high order and it changes with temperature and with deviation from the stocchiometric composition which corresponds to an ideal complete order. For some time it was believed that the order- disorder transformation is a homogeneous trans- formation ; i. e., the two states cannot coexist in Fig. i. -- Saturation magnetization of transition elements equilibrium. Recently, mounting evidence [2] points and their alloys (after Pauling). to the conclusion that this is not true and that many, if not all, ordering reactions are heterogeneous necessary to know the dependence of saturation and similar to the conventional phase transitions. magnetization on the position of the elements in the The ordering process is very conveniently described periodic table and of the interpolated positions of in terms of a change in the number of nearest their binary alloys. This dependence is illustrated neighbors of each kind of atoms. The ordering in figure i where the saturation moment of several usually leads to a preferential formation of « mixed alloy series is plotted against the number of elec- bonds n, AB rather than AA or BB. The opposite trons in the combined 3 d and 4 s shells. The tendency leads to a separation of an A-rich and striking regularity of this diagram found an early a B-rich phase. This concept of bonds is intu’itively interpretation in the work of Pauling [3] which can and mathematically convenient, but it should not be expressed, according to Shockley [4], in terms be assigned much physical significance since we of band theory as follows : let us assume that the Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphysrad:01951001203038900 390 3 d band is split into two parts, the higher one of the R band reaches the highest occupied state in containing ~~.88 and the lower one ,~.I2 electrons. the L band. From here on proceeding to iron and Half of the states in each of these parts correspond beyond it towards manganese, the seaparation of to electrons which are parallel to each other and anti-parallel to the other half, and we imagine them occupying separate bands which we shall denote R (right) and L (left). In ferromagnetic metals due to the exchange interaction, the R and L bands are displaced with respect to each other, and thus an unbalance of R and L spins is produced. Accor- ding to this model, in a ferromagnetic metal the top of the band containing, the R spins say, is lower than the bottom of the upper part of the band ccntaining the L spins. Progressing from nickel towards iron, the electrons are gradually drained off from the upper L band, and thus the number cf unbalanced spins reaches a maximum value of 2.!~4 at about 8.2 electrons per atom. Further reductions of the total number of electrons lower the number of the R spins, and thus the unbalance OIGPLACEMENT OF BANDS ACCORDING TO THE DIRECTION OF SPIN. is now gradually reduced in accordance with 1. figure - Fig. 2. Schematic of filled bands This model, rather artificial and without presentation partly although in a ferromagnetic material. much additional support, is very convenient in correlating the properties of the various alloys. Perhaps a more satisfactory interpretation of the two halves will further decrease with increa- figare i is based on the differences of the 3 d shells sing and both halves will have unoccupied in the various atoms. Electrons in the 3 d band states. This causes a progressive decrease of the are far from free and, in fact, the identity of 3 d number of unpaired spins, if the separation decreases shells is to a great extent preserved. In the band linearly with Z, in accordance with experiment. , theory, the exchange interaction tends to separate the R and L bands, and this is counteracted by the increase of the Fermi energy The actual separation of the R and L bands is determined by a balance between these two tendencies which depends on many factors which in turn depend upon the position among the transition elements. One of the important factors is the fact that the increase of energy due to a transfer of an electron from the L to the R band is greater the greater is the width of the 3 d band. This width is greater for lower Z since then the lower charge of the nucleus allows the 3 d shell to expand more, and thus the overlap and interaction between neighboring 3 d shells is greater. In comparison with the change in the size of the 3 d shell, the interatomic distance remains constant for the transition elements in practically Fig. 3. - Density of electronic states the ferromagnetic group. This allows us to esti- in the 3 d band of copper (after Slater). mate how varies within the group of elements which are of interest here. The situation can be thus qualitatively understood in the following way, The above reasoning can be put into a very rough illustrated in figure 2. In nickel, all vacancies are quantitative form : let us make the assumption that in L, and the bands are widely separated since Slater’s calculations [5] of the 3 d band in copper the 3 d shell and the AEp are relatively small. apply qualitatively to other transition elements The unbalance of spins is thus equal to the number (fig. 3) when the proper change of the width of of missing electrons. In cobalt, the smaller number the band is taken into account. In other words, of electrons leaves a still larger number of unpaired the distribution n (E) of electronic states in the spins than in nickel. At an electron concentra- band remains the same although the vertical energy tion 8.2, however, the separation of the L and R scale changes.