M R. il? - UNCLASSIFIED ORNL og Sabi * . 296 re MO), 1. Y " R1 I ." 14 LITY . 42 . W MA 1. . . . 4 W 74 ... ORNL-P. 296 DTIES CONF-690-2-6459 SEF, 100 DIFFICULTIES IN APPLYING SEMIEMPIRICAL COUPLING RULES TO MAGNETIC STRUCTURES* M. K. Wilkinson Solid State Division, Oak Ridge National Laboratory Oak Ridge, Tennessee r INTRODUCTION Water Wocumc. de med bombone, por meya watu aydirme, mesa de G irona el where we town weder mange and now white wa TEGAL NOTICE As indicated previously in this series of lectures, the semiempirical rules for magnetic coupling have not received wide application in the analysis of magnetic structures by neutron diffraction. This does not iapply the inapplicability of the rules but merely the difficulties in applying them. In almost all magnetic structures there are competing mag- netic interactions which are responsible for the development of a particu- lar type of structure. The determinations of the types of interactions and the relative strengths of the interactions on the basis of orbital overlaps are very complicated, and in many structures such determinations are virtually impossible. Even for those symmetries in which the crystal field interactions are understood, quantitative calculations of the mag- netic interactions are not very accurate. Furthermore, a relatively small interaction between second or third neighbors can be influential in es- tablishing the magnetic otructure. The existence of several possible exchange interactions is found even in compounds with relatively simple crystal structures. This lecture will discuss investigations that have been made on rutile-type structures and on hexagonal layer-type structures in which complicated magnetic ordering *Research sponsored by the U. S. Atomic Energy Commission under contract with the Union Carbide Corporation. . . -2- has been observed. For both series of compounds molecular field analyses have furnished the most important information on the magnetic properties, and only minor attempts have been made to analyze them using the coupling rules. RUTILE-TYPE STRUCTURES One of the first neutron diffraction investigations of magnetic structures was made on a series of difluorides (MDF,, FeF2, Cof, and N1F,) with the rutile structure by Erickson. These compounds have the body-centered tetragonal crystal structure of Snog, and they were found to exhibit a simple type of antiferromagnetic order that could be analyzed in terms of the two-sublattice model of antiferromagnetism discussed. by Néel? and Van Vleck. In this structure, which is shown in Fig. 1 and corresponds to body-centered ordering of the first kind, the magnetic unit cell has the same dimensions as the chemical unit cell, and the moments of the magnetic fons at the lattice corners are antiparallel to the moments of the body-centered ions. This type of magnetic lattice has received a large amount of both experimental and theoretical investigation in recent years. This is par- ticularly true of MnF, which represents a very favorable case for the determination of exchange interactions by magnetic measurements. Good single crystal samples of Maf, are available for various experiments, and the theoretical analyses are not complicated by orbital contributions to the magnetic moment. Most of the early investigations suggested that the magnetic properties of MnF, could be accounted for with the assumption of a reasonable anisotropy field and nearest-neighbor interactions only. ! / L whi : .. " L LA ! L7 7. wote, AL WD RC ! . 2 " 1 . 'M . CA SUA NO C. . . -3- However, this explanation appears to have been just fortuitous, because more recent experimental observations“,5 on MnF, indicate that at least two exchange interactions are preeent. Furthermore, observacions on other rutile structures indicate that one interaction could not possibly account for the magnetic structures. In particular, neutron diffraction data by Ericksonº for Mno, showed that it did not have the saune simple antiferro- magnetic structure of MnF., and that the magnetic unit cell was seven is. times as large as the chemical unit cell along the c-axis. These data have been interpreted recently on the basis of theoretical calculations Act. by Yoshimort,' which showed that a helical arrangement of the magnetic 2. : A moments is stable in the rutile-type crystal for certain conditions of exchange interactions. With three different exchange interactions between magnetic cations, Yoshimori showed that three different types of anti- ferromagnetic structures are possible and that the relative stability is dependent on the relative magnitudes of the three exchange integrals. These are the MnFz-type structure, a structure suggested by Bizette, Erickson,' and Yosida, º in which the corner moments and body-center moments form uncorrelated antiferromagnetic sublattices, and the helical structure in which positive spins on the corner sites and negative spins on the body-center sites screw along the c-axis. Yoshimori's calculations were the first to indicate the stability of the now well-established helical magnetic structure, and he showed that the neutron diffraction results of Erickson could be explained by the structure shown in Fig. 2. Since at least three magnetic exchange interactions are required to sta- bilize such a magnetic structure, there 18 no doubt that several competing interactions can exist in structures of this type. i 1. . .. w 12V. ! IN 1" i :" w. A .. . ! . " ." . For cations in octahedral symetry the semiempirical coupling riles allow a unique role for magnetic ions with the a* electron configuration, because the two e, orbitals that are prominent in magnetic coupling have a different electron population. Consequently, the magnetic coupling between such cations was expected to be different from that between other transi- tion metal ions, and this was confirmed in the antiferromagnetic structures of MnFz, Limno, and KCrfz. Since the cations in the rutile structure are located at the center of a distorted octahedral arrangement of enions, it warl of interest to determine if the 304 configuration would also produce unique magnetic structures for this gymmetry. Both CrF, and crcı, have crystal structures similar to rutile but distorted from tetragonality, and neutron diffraction investigations were made on these compounds. CrF, was found to have the same antiferromagnetic structure as MnFy, which indi- cates that the 3a* configuration does not assume a unique role in the magnetic coupling. Moreover, Crci, was found to have a different type of magnetic structure in which there are ferromagnetic (011) planes with adjacent planes antiparallel. Both results suggest that the magnetic - - - E L . YŁ -7 ordering in these compounds is established by competing magnetic inter- actions and that the semi empirical rules can not be easily applied. HEXAGONAL LAYER-TYPE STRUCTURES Another class of compounds, which has received a large amount of theoretical and experimental attention, is one in which the magnetic atoms are arranged in hexagonal layers perpendicular to the principal crystal- lographic axis. Typical of these εtructures are the anhydrous dihalides of certain 3d transition metals, and in these structures the layers of 1 I . VI! S- t , Detec W 'la . mi * AK " 10 . MANY. WE 7--- metal atoins are separated by two layers of halide atoms. The bromides and iodidee have the car, structure, while the chlorides have the caci, structure. As indicated schematically in Fig. 3, these structures are similar, but there is a different stacking sequence of the MX, groups . 1. Dihalides of Fe and Co The umisual magnetic properties of the iron and cobalt compounds were first observed about forty years ago and led to their considera- tion as a special class of magnetic materials called "metamagnetics." Measurements of the specific heat and magnetic susceptibility for these compounds gave results which were not clearly associated with either ferromagnetism or antiferromagnetism. Consequently, there was considerable theoretical speculation on the type of magnetic order that developed at low temperatures and even on the existence of three- dimensional. 1:agnetic structures. Neutron diffraction measurements2 taken on the iron and cobali dibromides and dichlorides showed that they have magnetic transitions at temperatures ranging from 25°K to 11°K to antiferromagnetic layer strictures. In these magnetic struc- tures the atomic magnetic moments within a metal layer form ferro. magnetic sheets and the moments in adjacent sheets are antiparallel. In the Fe compounds the moments are oriented paralle). to the hexagonal c-axis and in the Co compounds the moment orientation is perpendicular to that axis. Small angle scattering measurements were made of the critical magnetic scattering from Feci, and Cock, and showed that the ferromagnetic coupling between moments within a layer is much stronger than the antiferromagnetic coupling between moments in adjacent .. . .. M2 cocina .. TE -6- . . S . . . < 2 layers. Recent theoretical analyses13,14 of this scattering from Feci, show that the ratio of these exchange interactions must be abcut twelve to one. Singie crystal neutron diffraction measurements on Feci, and Coci, in an external magnetic field showed that the large magnetiza- tion values that are produced in these compounds with moderate fields are undoubtedly achieved by overcoming only the weak interlayer interaction. This procedure would requtre that the moments within a layer are always aligned parallel and turn simultaneously with the application of the field. The procedures by which parallel moment alignment is accomplished are different in Coci, and in Fecig, but both mechanisms are predicted by Néel") from molecular-field calcu- lations based on a two sublattice model of an antiferromagnet. In Cocią, when a magnetic field is applied perpendicular to the c-axis, the moments first undergo a domain transformation to the domain in *:.. . which the antiferromagnetic axis is favored by the field direction, V . after which they flip to a direction perpendicular to the field and then are rotated into parallel alignment. In Feci, the field parallel to the c-axis is predominant in obtaining a net magnetization, and when this field exceeds a critical value, the moments antiparallel to the field become reversed in direction. Expressions based on a + . DRA TOK . Y 4 S * two-sublattice model may not be directly applicable to these magnetic 74 ! structures, but Néel's calculations show that they certainly predict i the correct behavior. . Although these are very simple types of magnetic structures, in A which the relative strengths of the two major coupling interactions i yir u . " :"1 are known, the specific mechanisms which produce the interactions are not understood. The ferromagnetic coupling between inoments within a metal layer may be caused by a direct exchange interaction between the 3d electrons of two neighboring magnetic atoms or by an indirect exchange mechanism through halide ions in the adjacent layers. Kanamori lº has pointed out that the latter is probable, because the orbital population of the cation d-orbitals that overlap the anion p-orbitals at a 90° angle would be favorable for a ferro- magnetic interaction. Of course, the distance between adjacent metal layers is sufficiently large that any exchange coupling be- tween these magnetic moments must be indirect via the intervening halide ions. Furthermore, since there are two layers of halide ions between metal layers, the exchange may take place through a two- anion indirect exchange mechanism. It is necessary that exchange i.nteractions exist between atoms in these layers, because the ob- served magnetic structures in the Fe compounds can not be stabilized by dipole forces. Dihalides of Mn Neutron diffraction experiments Vodooty have been performed on MnBrand MnIg, which possess the hexagonal cal, structure, and on Mncin, which has the rhombohedral structure characteristic of caci, All three compounds have very low temperature magnetic transitions (below 4°K) to complex antiferromagnetic systems which required single crystal investigations in an external magnetic field to determine the magnetic structures. .. opere diensten to the persones venta en AROME TO H 7 SW A .. it de N WY Jura CE . Manganous bromide was found to have a very sharp antiferro- magnetic transition at 2.16°K, which 18 really first order rather than the usual second order type, and very pronounced short-range order was observed at temperatures above the Néel transition. In the absence of a magnetic field, the antiferromagnetic structure appeared to have hexagonal symmetry, but this apparent symmetry was found to be associated with a structure-domain property. The true magnetic unit cell is orthorhombic as shc:n in Fig. 4, and this structure develops in domains along three equivalent crystal directions. In an external magnetic field an entire crystal of MnBr, can be trans- formed into one type of domain, and when the field is removed, most of the domain transformation is retained. As shown in the figure, the antiferromagnetic structure consists of sheets of like spins that are parallel to hexagonal (011) planes, and they are arranged in the sequence ++-- so that there are actually small ferromagnetic bands, two atoms wide, tilted with respect to the hexagonal c-axis. Since the manganese ions are well separated from each other, any magnetic exchange must be of an indirect type through two layers of bromide ions. The over-all picture of the coupling is obviously complicated, and only a few qualitative observations can be made. One of these is associated with the possibility of a two-anion indirect exchange along nearly linear Mn --Brº-Brº-Mn linkages. As shown in Fig. 4, each Mn ion has six of these linkages to ions in adjacent layers, five of which have antiparallel moments, while only one moment is parallel. This moment orientation suggests that this possible two- anion indirect exchange is antiferromagnetic. However, other 1. L'I . . 17 "Y! WWW .Y NNMENT WAY . 12 V nly. WW i i yon " . .. . . . . u 7221 1 o . VAM . . 2 AYAW 4. 40 + w . . . 449 lucu IN -9- significant contributions to the magnetic coupling would have to exist, because the most optimum structure for an antiferromagnetic exchange of this type would be an antiferromagnetic layer structure similar to that found in the Fe and Co compounds. Therefore, it would appear that some antiferromagnetic intra)ayer coupling is re- quired to stabilize this magnetic structure. The general magnetic properties of Mni, were founato to be very similar to those of MrBrg. A very sharp transition was observed at 3.40°K, and the antiferromagnetic structure below that temperature was found to develop as structure domains along equivalent crystal di.rections. However, the specific magnetic structure was different, and in fact, Mni, was found to possess a helical magnetic structure in which the moments are ferromagnetically aligned in (307) planes, are criented parallel to those planes, and rotate by 27/16 in sue- cessive planes. This structure was supported both by intensity e measurements of the antiferromagnetic reflections and by the domain transformations effected with an applied magnetic field. As men- tioned previously, helical structures can be stabilized by a minimum of three near-neighbor exchange interactions, and it is possible that even longer range interactions exist. In MnI, the helical axis assumes a direction which has no apparent correlations with the neigh- bors of the manganese ions. Consequently, it is virtually impossible to determine the magnetic interactions that exist in this structure. In Mncly, the magnetic ordering is even more complicated than tbat in MnBr, and MnIn, because this compound has two antiferromag- netic transitions at very low temperatures. At 1.96°K there is a ** , M W ' !* , ! " 11 . -10- transition from the paramagnetic state to one type of antiferromag- netic structure, while in a small temperature region around 1.82°K, there is a reorientation of the atomic moments into a different type of antiferromagnetic order. Both antiferromagnetic structures develop as structure domains along equivalent hexagonal directions with mag- netic unit cells which are similar but more complicated than the one that develops in Mnbry. The two structures of Mnci, are similar, and although neither closely resembles the structure o: MnBrg, both seem to have narrow ferromagnetic bands tilted at an angle to the hexagonal c-axis. The domains of both structures can be transformed by a magnetic field, and the transition from one structure to the other is depressed to lower temperatures when a magnetic field is applied.. > 3 3. Other Magnetic Structures in Layer-Type Compounds. It is apparent 9. . ' from the results on the Mn compounds that long-range magnetic inter- .--. IX- 4 actions exist in these hexagonal layer-type structures. Since the nature of the interactions and the neighbors involved can not be determined, there can be no attempt to apply the semiempirical coupling rules to structures of this type. Part of the complication in the Mn compounds undoubtedly arises because of competition between the very weak interactions that are involved. However, somewhat similar confusion is found in attempts to interpret the exchange sa_3 interactions in a series of anhydrous trihalides that have higher transition temperatures. These compounds have crystal structures A - which are very similar to the dihalides except that one third of * - - . - * the metal ion lattice positions are unoccupied. Although CrBr, * -' . s . .1l. 18 a ferroinagnet below 37°K and Crci, has a simple antiferromagnetic layer structure below 17°K, Peci, has a wignetic transition at about 150K to a complex antiferromagnetic system.21 The latter de- ve.lops structure domains along equivalent hexagonal axes and pos- sesses a helical magnetic structure in which the moments lie within (1450) planes and rotate by 2 T/15 in successive planes. Therefore, even in compounds with stronger exchange interactions than those in the dibalides of manganese, complex structures are observed which involve at least three significant magnetic interactions. CONCLUSION The semi empirical rules that have been developed for the analysis of indirect magnetic coupling between two magnetic cations have been justi- ried theoretically and they are generally accepted as correct. These rules have been thoroughly tested in certain compounds that possess magne- tic cations in octahedral lattice sites. In these compounds there is only one important magnetic interaction responsible for the magnetic ordering, and this interaction can be traced easily through the d-orbitals that re- sult from crystal field effects. The rules bave not received appreciable application in other types of compounds, The narrow application of these rules at the present time should not imply a lack of importance, because their development and application bave made very significant contributions to the present knowledge of indirect exchange. Furthermore, analyses of magnetic interactions in more compli- cated compounds by such rules can certainly be expected in the future. These analyses, although difficult, can help to provide more information NIKE ! -32- on the types of orbital overlap and on the relative strengths of the corresponding magnetic exchange interactions. It should also be expected that new sets of rules will be developed to account for new exchange pro- cesses that are discovered. One possible new process would be the two- anion indirect exchange that 18 suggested in the hexagonal layer-t: pe structures. With quantitative calculations of exchange interactions so exceedingly difficult, semiempirical rules of this type undoubtedly will continue to make valuable contributions to the understanding of the mecahnisms involved. -13. REFERENCES 1. R. A. Erickson, Phys. Rev. 20, 779 (1953). E. L. Néol, Ann. Phys. , 256 (1936). J. H. Van Vleck, J. Chem. Phys. 2, 85 (1941). 4. A. Okazaki and K. C. Turberfield, Phys. Ltrs. 8, 9 (1964). 5. D. Cribier and B. Jacrot, Inelastic Scattering of Neutrons in Liquids and solids, International Atomic Energy Agency, Vienna, Vol. II, D 309 (1963). 6. R. A. Erickson, unpublished. 7. A. Yoshimori, J. Phys. Soc. Japan 14, 807 (1959). 8. H. Bizette, J. Phys. Radium 12, 161 (1951). 9. R. A. Erickson, Phys. Rev. 85, 745 (1952). 10. K. Yosida, Progr. Theor. Phys. 8, 259 (1952). 11. Cable, Wilkinson, and Wollan, Phys. Rev. 118, 950 (1960). 12. Wilkinson, Cable, Wollan, and Koehler, Phys. Rev. 113, 497 (1959). 13. 0. ila gai, J. Phys. Soc. Japan 18, 74 (1963). 14. B. R. Heap, Proc. Phys. Soc. (London) - to be published. 15. 1. Néel, Report to 10th Solway Congress (1954); Suppl. Nuovo Cimento 6, 942 (1957). 16. J. Kanamori, J. Phys. Chem. Solids 10, 87 (1959). 17. Wollan, Koehler, and Wilkinson, Phys. Rev. 110, 638 (1958). 18. Cable, Wilkinson, Wollan, and Koehler, Phys. Rev. 125, 1860 (1962). 19. Wilkinson, Cable, Wollan, and Koehler, ORNL Report 2430, p 65 (1958); ORNL Report 2501, P 37 (1958). 20. Cable, Wilkinson, and Wollan, J. Phys. Chem. Solids 19, 29 (1961). 21. Cable, Wilkinson, Wollan, and Koehler, Phys. Rev. 127, 714 (1962). OF Fig. 1. Magnetic Structure of MnFz. W : A 32 . UNCLASSIFIED ORNL-DWG 64-6549 . 11 . ti . . WA 2. . es 3 < . . . 1 - VIL A 4 1 43 . WT Fig. 2. Helical Arrangement of Magnetic Moments in MnO2 V " . UNCLASSIFIED ORNL-LR-DWG 26689 METAL IONS O HALIDE IONS c A B co CdCI, -TYPE RHOMBOHEDRAL STACKING Cdly-TYPE HEXAGONAL STACKING Fig. 3 Schematic Representation of Colz and CdClz Layer-Type Structures. UWCLASSIFIED N - t ai32 in- 1 4 - [100] w d . - . 1 - - 3. 1 . " . 2 Mn 54 . Fig. 4. Magnetic Structure of MnBrz. . . N DATE FILMED 11/ 24 / 64 WY .. LEGAL NOTICE This roport mas prepared as an account of Govoromont sponsored work. Nolthor the United Mtatas, nor the Commission, nor any person aoting on behall of the Commission: A. Makes any warranty or representation, express or implied, with respect to the scou- ruoy, completeness, or wofulnous of the laformation contained in this roport, or that the use of any lalormation, apparatus, method, or process disoloned in the report may not latring privately owned richalos or B. Asmumos muy habilidas with roopoot to the wo of, or for damagoi rosulting from the um of any inforaation, apparatus, wethod, or procou diooloud in this roport. As wund in the abovo, "person notes on behall of the Commission" includes my on- ploys or contrmotor of the Commission, or employw of ouch contructor, to the extent that such employs or contractor of the Commission, or employs of uwoh coatractor properos, dienominatos, or provides socou to, any information pursuant to Mo onployment or contract with the Commission, or his employment with such contractor.