Hyperfine Interactions in Fe2+ Salts BY C. E. JOHNSON Solid State Physics Division Atomic Energy Research Establishment Harwell Berks. Received 20th September 1967 Magnetic hyperfine field data for a number of Fez+ salts are summarized and discussed in terms of the theory of hyperfine interactions in solids. The qualitative agreement between theory and experiment is good and the relative importance of the contributions from the orbital and spin moment of the ion seems to be understood. The effects of covalency are considered and it appears that if they could be quantiatively interpreted the measurement of hyperfine fields could be a powerful as well as sensitive method for studying chemical bonding. The Mossbauer effect has become a valuable tool for the investigation of magnetic ions in crystalline solids and many applications to the study of ferrous salts have been made.In this paper we summarize the data on a number of high-spin ferrous salts and show that in most cases they may be understood qualitatively on a simple theory. Measurements of hyperfine fields are useful in determining the spin part of the ground-state wave function of the ion and in principle if the interpretation could be made quantitative would yield information on the degree of covalency of the ion. Of the sources of energy shifts in Mossbauer spectra the isomer shift and the quadrupole splitting are commonly interpreted in terms of and correlated with the chemical properties of the ion. The isomer shift which gives a measure of the electron charge density at the nucleus is clearly related to the covalency.By means of calculations of the effect at the nucleus of changes in the outer electrons of the ion a detailed interpretation may be attempted. The quadrupole splitting arises from the asymmetry of the distribution of the electronic charge of the ion and its surroundings and is only indirectly related to the covalency of the ion. Its great value lies in providing a method for determining the orbital ground state of the ion in the crystal and for finding the direction of the axes of the crystalline electric field. The hyperfine field i.e. the magnetic field internal to the ion which acts on the nucleus is a complicated quantity which depends upon both the spin and orbital magnetism of the ion. It is a tensor which may be analyzed into anisotropic terms arising from orbital (IfL) and spin dipolar (Hd) fields and an isotropic term (Hs) which is proportional to the electron spin density at the nucleus.The latter is sensitive to the degree of covalency of the ligands as is known from studies of the spherically symmetric ions Mn2+ and Fe3+ (see table 1) where it is the dominant contribution. In Fe2+ salts the anisotropic terms are comparably large and so it would be necessary to be able to subtract these out quantitatively in order to study chemical bonding from hyperfine field data. Many ferrous salts are antiferromagnets and from the Mossbauer spectrum measured well below their Nee1 temperatures the component of the hyperfine field tensor H along the direction of spin alignment may be directly determined. 7 8 HYPERFINE INTERACTIONS IN Fe2+ SALTS For salts which remain paramagnetic down to liquid helium temperatures and which also have fast electron spin relaxation rates (which is generally true for Fe2+ ions) magnetic hyperfine splitting may only be observed if an external magnetic TABLE 1 .-HYPERFINE FIELD DATA FOR Fe3+ SALTS co-ordination Hn (kG) ref.FeF3 6 F- 622 a Fe2(S0,)3 . (NH&S04 . 24H20 6 H20 584 b Fez03 6 02- 540 C FeC13 6 C1- 487 d a D. N. E. Buchanan and G. K. Wertheim Bull. Amer. Physic. Soc. 1962 I1 7,227. b L. E. Campbell and S. DeBenedetti Physics Letters 1966 20 102. c T. Nakamura and S. Shimizu Bull. Inst. Chem. Res. Kyoto Univ. 1964 42 299. d C. W. Kocher Physics Letters A 1967 24 93. field H is applied in order to produce an appreciable magnetization. In practice this requires fields of about 30kG or more at liquid helium temperatures and allows the components Hn1 of the hyperfine interaction tensor along all the principal axis directions i to be determined.The effective magnetic field at the nucleus is then where ( S ) / S is the fractional magnetization produced which may be calculated from the applied field the temperature and a knowledge of the spin-Hamiltonian of the ion. Hence from the measured values of He, the components of H, may be deduced. Heff = H+ ( ( S ) I W m HYPERFINE FIELDS AND MAGNETIC PROPERTIES OF THE Fe2+ ION IN CRYSTALS The theory of hyperhe interactions in solids is based largely on the work of Abragam and P ~ y c e . ~ The hyperfine field is made up of several contributions These contributions and their relation to other measured properties of magnetic ions have been discussed by Marshall and by Marshall and J o h n s ~ n .~ using unrestricted Hartree-Fock wave functions. The value they obtained for the free Fe2+ ion is -550 kG. By comparison with the data for Mn2+ and Fe3+ this value may be reduced in an actual solid because of covalency. The core polarization field H has been calculated by Watson and Freeman The field due to the orbital moment is given by H L i = 4B(r-3Xgi-22) where gr is the component of the electron g-factor so that the orbital moment is (gf -2)S and S = 2 for Fe2+. r is the position of the electron relative to the nucleus and { ) denotes the average taken over the 3d electron wave function. The dipolar field arises from the asymmetry of the electron spin density and is therefore closely related to the quadrupole splitting which arises from the asymmetry of the electron charge density.In fact Hd = Pq where q is the electric field gradient and where I 0) is the orbital wave function of the ion. H~~ =~P(~-~>(O[L~-~L(L+~)IO), C. E. JOHNSON 9 Summing together all the contributions 1 H = H + 4 p y 3 ) (& -2) +-(0 L; -2 *}I [ l4 = H + 4p( r - 3)Ri where 1 14 Qi =(gi-2)4-(o~L~-2~o). The Fe2+ ion has a 3d6 . 5D configuration i.e. there is a single d-electron outside a spherically symmetrical half-filled shell. In a solid the orbital angular momentum is quenched by the crystal field and we denote the orbital ground state by I O} and the excited states by I n ) with energies An. Measurement of the sign of the electric field gradient from Mossbauer effect spectra enables the ground state 1 O} to be determined and the temperature variation of the quadrupole splitting allows the energies A to be e~timated.~ When 10) has been determined the dipolar field tensor may be calculated.The fivefold spin degeneracy of the orbital ground-state is removed by the spin- orbit coupling acting together with the crystal field. This also partly restores some of the orbital moment. As an illustration we consider the case where the symmetry is high enough so that the only orbitals populated are dxy dvz and dzx and we assume that dxy is lowest in energy. This corresponds closely to the situation in several of the salts we shall discuss. Then the g-factors are where A is the spin-orbit coupling parameter (A = -104cm-l for the free Fez+ ion). In many salts the g-factors are known from magnetic susceptibility measure- ments.In others they may be estimated from the values of the A, deduced from the temperature variation of the quadrupole splitting. If the splittings are large compared with kT the electric field gradient at a temperature T is approximately whence the A the g-values and the orbital hyperfine fields may be calculated. In the special case where one orbital say dzx is much higher in energy than the other two the susceptibility has axial symmetry about the x-axis with g = gz = 2 and There are errors from e.g. the neglect of thermal expansion but in the absence of anything better this approach can be useful. INTERPRETATION OF HYPERFINE FIELD DATA FOR Fez+ SALTS Table 2 summarizes an analysis of the hyperfine fields measured in several Fe2f salts using the above simple theory.Two of the crystals FeSiF6. 6H20 and FeCl . 4H20 are paramagnetic at 4.2"K and the data were taken in an external magnetic field and the remainder are antiferromagnetic. The g-values were taken from susceptibility measurements except for FeF which has been studied by C. E. JOHNSON 9 Summing together all the contributions 1 H = H + 4 p y 3 ) (& -2) +-(0 L; -2 *}I [ l4 = H + 4p( r - 3)Ri where 1 14 Qi =(gi-2)4-(o~L~-2~o). The Fe2+ ion has a 3d6 . 5D configuration i.e. there is a single d-electron outside a spherically symmetrical half-filled shell. In a solid the orbital angular momentum is quenched by the crystal field and we denote the orbital ground state by I O} and the excited states by I n ) with energies An. Measurement of the sign of the electric field gradient from Mossbauer effect spectra enables the ground state 1 O} to be determined and the temperature variation of the quadrupole splitting allows the energies A to be e~timated.~ When 10) has been determined the dipolar field tensor may be calculated.The fivefold spin degeneracy of the orbital ground-state is removed by the spin- orbit coupling acting together with the crystal field. This also partly restores some of the orbital moment. As an illustration we consider the case where the symmetry is high enough so that the only orbitals populated are dxy dvz and dzx and we assume that dxy is lowest in energy. This corresponds closely to the situation in several of the salts we shall discuss. Then the g-factors are where A is the spin-orbit coupling parameter (A = -104cm-l for the free Fez+ ion).In many salts the g-factors are known from magnetic susceptibility measure- ments. In others they may be estimated from the values of the A, deduced from the temperature variation of the quadrupole splitting. If the splittings are large compared with kT the electric field gradient at a temperature T is approximately whence the A the g-values and the orbital hyperfine fields may be calculated. In the special case where one orbital say dzx is much higher in energy than the other two the susceptibility has axial symmetry about the x-axis with g = gz = 2 and There are errors from e.g. the neglect of thermal expansion but in the absence of anything better this approach can be useful. INTERPRETATION OF HYPERFINE FIELD DATA FOR Fez+ SALTS Table 2 summarizes an analysis of the hyperfine fields measured in several Fe2f salts using the above simple theory.Two of the crystals FeSiF6. 6H20 and FeCl . 4H20 are paramagnetic at 4.2"K and the data were taken in an external magnetic field and the remainder are antiferromagnetic. The g-values were taken from susceptibility measurements except for FeF which has been studied by C. E. JOHNSON 11 which confirms the basic correctness of the understanding of the orbital and dipolar fields. The anisotropy in the hyperfine field tensor in the paramagnetic crystals FeSiFs . 6H20 and FeCl . 4H20 is well accounted for. The approximate linear law found in fig. 1 shows that (r3) and H for the salts considered which are all hydrates do not vary greatly. For a qualitative interpretation of the data it would be necessary to take account of covalency which would be expected to reduce both 1 H J and {r3).The latter is associated with the observed reduction of the spin- orbit coupling parameter For salts which are considerably more covalent there is evidence for a greatly reduced isotropic hyperfine interaction. For example in (NMe,)FeCl where a Fe2+ ion is tetrahedrally co-ordinated to four chlorine ions the hyperfine field observed is only -38 kG,ll and in FeCl with co-ordination to six chlorine it is almost zero.12 Both these salts have quadrupole splittings which indicate that (r3) has not been drastically reduced. They also have large orbital fields but to get such small hypcrfine fields I H I must have been reduced perhaps to about 350 kG. It is evident that a systematic study of hyperfine fields in the more covalent Fe2+ compounds should be valuable in providing information on the effects of chemical bonding.As a method for investigating covalency they could if correctly inter- preted by more useful than isomer shift data as they are more sensitive to small changes . and has been discussed by several authors.g* lo L. R. Walker G. K. Wertheim and V. Jaccarino Physic. Rev. Letters 1961 6 98. J. S. van Wierengen Disc. Furaday Soc. 1955 19 118. A. Abragam and M. H. L. Pryce Proc. Roy. SOC. 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