Mossbauer Studies in Spin 3/2 Iron Complexes BY H. H. WICKMAN AND A. M. TROZZOLO Bell Telephone Laboratories Incorporated Murray Hill New Jersey Received 16th October 1967 A series of penta-coordinate bis(N,N-dialkyldithiocarbamato) iron (111) halides have been prepared in which the ground iron (111) term is an orbital singlet and spin quartet. The quartet ground term results from the low symmetry (C2”) local environment of the iron. The Mossbauer technique was employed to study several homologues closely related to the basic unit bis(N,N-diethyldithiocarbamato) iron (111) chloride which exhibits a ferromagnetic ordering at low temperatures (T‘ = 25°K). While the paramagnetic character of the ground quartet remains independent of small structural changes no new magnetically ordered systems were found.However low-temperature Mossbauer data show that the small zero-field splitting of the quartet manifold is markedly affected by the halo-constituent of the penta-coordinate complex. Effects of a small external polarizing field on the Mossbauer spectra of these complexes is also considered. A number of recent investigations of the bis(N,N-dialkyldithiocarbamato) iron (111) halides have shown that the ground electronic term of the trivalent iron is an orbital singlet and spin Martin White and Hoskins have reported FIG. 1.-Structural formula and local iron sym- metry in Fe(S2CNEt2)2CI after Hoskins Martin and White.’ 81s (N N - DIETHYLDIT~(IOCARBAMATO) IRON~CHLORIDE \ C 2 7 I I 2 2 6 the crystal structure of the diethyl-chloro derivative together with room and nitrogen temperature susceptibility and e.p.r.data for several homologues. The structural formula and local iron environment of the Fe(S2CNEt2),Cl complex are shown in fig. 1. The chemical similarities of all of the related complexes prepared to date 21 22 SPIN 3/2 IRON COMPLEXES indicate that the iron environment is qualitatively similar in different species.,Y The point group symmetry at the iron (111) is therefore assumed to be CZv and the ligand fields have rhombic symmetry. A magnetic investigation of the diethyl-chloro derivative has shown a ferro- magnetic ordering of the iron at 2.5"K3 Single crystal e.p.r. measurements within one of the Kramers levels of the S = 3/2 multiplet of the paramagnetic diisopropyl-chloro complex have shown the zero field splitting of the two Kramers levels to be approximately 5 cm-I.The later data are consisent with early Mossbauer studies of relaxation effects in this complex.6 In the following synthetic methods were employed to obtain several compounds representing the minimal structural changes that are possible starting with the basic unit Fe(S,CNEt,),Cl. A methyl group has been added to or subtracted from the alkyl constituent and a bromide ion has replaced the chloro group. Bulk d.c. and a.c. susceptibility data shown that with any of these substitutions the magnetic ordering property is lost. However the paramagnetic character of the ground quartet remains substantially independent of structural changes. The difference in magnetic properties among the compounds appears as a change in sign of the splitting of the lowest quartet level on substitution of a bromo for a chloro group ; low-temperature Mossbauer effect (ME) data illustrate this effect.The effect of an external magnetic field on the Mossbauer patterns in these complexes is also investigated. LO W-TEMPERATURE MOSSBAUER EXPERIMENTS The Mossbauer effect in the four derivatives mentioned above has been observed with sample temperatures from 300 to 1.2%. At temperatures in the range 2-10°K complex relaxation effects have been observed in the chloro derivatives;3* a full discussion of these spectra will be given elsewhere. With the exception of Fe(S,CNEt,),CI the samples showed no magnetic orderings. These results were also confirmed by d.c. susceptibility data to 1.4"K and by a.c. susceptibility data to 0.3"K. The four homologues have effective moments derived from d.c.suscepti- bility data which show no marked dissimilarities and are in good agreement with the theoretical effective moment of 3-88 B.M. predicted for S = 3/2 and g = 2 ~ 0 0 . ~ Information concerning the magnetic hyperfine interactions within the quartet level is best derived from low-temperature data where relaxation times z are often long enough to allow a well-resolved paramagnetic h.f.s. In fig. 2 we give the Mossbauer absorption at 1 *2"K of (a) Fe(S2CNEt2)2Br (b) Fe(S,CN(i-propyl),),Cl (c) Fe(S2CNEt2)2Cl and (d) Fe(S,CNMe,),Cl. The nuclear parameters consistent with these data may be found in table 1. The prominant features of the spectra are summarized as follows. (a) Fe(S2CNEt,),Br. A simple quadrupole doublet is observed from 300 to 1.2"K. No appreciable temperature dependence was found ; at 1~2°K the splitting is 0.288 0.004 cmlsec.(b) Fe(S2CN(i-propyl)2)2C1. A typical multiline pattern is found. The data are consistent with a paramagnetic hyperfine field He, together with a large electric field gradient (EFG) with major axis perpendicular to the direction of He,,. In table 1 8 and 4 are conventional spherical polar co-ordinates defining the orientation of the EFG tensor with respect to He,,. (c) Fe(S,CNEt,),Cl. This spectrum is similar to that of (b). In the latter case however the sample is paramagnetic while here the material is ferromagnetically ordered T = 2.5"K. The parameters characterizing the data are given in table 1 ; 23 the similarity of these parameters with those of the paramagnetic homologue (b) is striking.The data reported here give the polycrystalline absorption in the ordered state at 1.2"K. In the earlier work the absorber was composed of larger crystallites H H. WICKMAN AND A. M. TROZZOLO FIG. 2.-Mossbauer effect at 1-2"K in poly- crystalline absorbers of (a) Fe(SzCNEt2)2Br (6) Fe( S2 CN( i - p r ~ p y l ) ~ ) ~ CI (c) Fe( S2CNEt 2)Z C1 and (d) Fe(SzCNMe2)2Cl. 1 I t " ' I ' ' I ' -0'8 0.6 -0'4 - 0 2 0 0 ' 2 0 ' 4 3.6 0.8 cm/sec TABLE 1 .-NUCLEAR SPIN-HAMILTONIAN PARAMETERS WHICH REPRODUCE THE MOSS BAUER SPECTRA OF FIG. 2 complex nuclear hyperfine data (a) Fe(SzCNEt2)zBr AE(1.2"K) = 0.288 f0.004 cm/sec = e q ~ / 2 4 1 +v2i3 (b) Fe( S 2CN( i-pr~pyl)~) ,C1 Heff = 334 f5 kOe eqQ/2 = 0.268 f0-003 cmlsec. y = 0*16f0.01 4 = 0 0 = 90". ( c ) Fe( S CNEt 2 ) C1 He€€ = 333 f 5 kOe eq&/2 =0*268 f0.004 cmlsec = 0.15 f o .o i 4 = 0 e = goo. z 0.15,4 = 0 e = goo. (d) Fe( S &NMe2) 2Cl Heff = 338 &lo kOe ; eqQ/2 E 0.266 cmlsec. which have a tendency to pack in such a way that a geometrically polarized absorber was produced. The relative intensities of fig. 2(c) and those in ref. (3) fig. 4 are slightly different for this reason. ( d ) Fe(S2CNMe,),Cl. In this system a fairly well-defined magnetic h.f.s. is observed. The material is paramagnetic and the broadening of the lines arises from electronic relaxation among the electronic levels. The estimated field If,,, 24 SPIN 3 / 2 IRON COMPLEXES and EFG are similar to those in (b) and (c). The shorter relaxation times are probably mainly due to decreased iron-iron separations in this compound which is the smallest homologue studied.A small transverse (with respect to the pray directions) polarizing field of 7 kOe was applied to the absorbers in the helium temperature range. The effect on the paramagnetic chloro-derivatives was generally small for temperatures where well resolved magnetic 1i.f.s. was observed (7 % o; I). For regions of intermediate relaxation times (z,-o;~) the effect of the field was to decrease relaxation times. However no striking features (aside from relative intensity changes and apparent line broadening occurring because polycrystalline absorbers were used) developed in the spectra of these derivatives. The effect in the ferromagnetic derivatives is more complicated and will not be discussed in detail here. 95 t L 9d I I I I I J 1 -4 -3 -2 -4 0 'I a 2 *3 -4 cmlsec FIG.3.-Mossbauer effect in Fe(S2CNEt2)Br with an external polarizing field of 7 kOe. In the di-ethyl-bromo derivative an interesting pattern was observed at 3-O"K and is shown in fig. 3. Similar patterns were found at higher temperatures but the doublet triplet character was most pronounced at about 4°K. This type of behaviour is indicative of the combined effect of a large randomly-oriented magnetic hyperfine field together with a quadrupole interaction. DISCUSSION The ground electronic term in the present series of complexes is an orbital singlet and spin quartet. The magnetic properties of the iron ion are therefore to good approximation ascribed entirely to the four levels of the S = 3/2 manifold. The interpretation of the Mossbauer magnetic h.f.s. requires knowledge of the magnetic interaction between the quartet levels and nucleus.In orbitally non-degenerate iron states such as Fe3+ 6S or the present case the interaction with the nucleus is primarily due to the isotropic contact interaction arising from core polarization. The standard procedure under these circumstances is first to characterize the electronic levels with a spin Hamiltonian S = 3/2 and then perturb these levels with the isotropic hyperfine interaction. The spin Hamiltonian parameters for one of the paramagnetic homologues have been determined from e.p.r. data and we begin by summarizing these results. H. H. WICKMAN AND A. M. TROZZOLO 25 Single crystal e.p.r. data have been reported for the Fe(S,CN(i-propyl),),Cl deri~ative.~ These results may be described by the spin Hamiltonian appropriate to rhombic symmetry with S = 3/2 and g = 2.00.The experimentally determined parameters D and iZ=E/D were 4.0°+0.5"K and 0.036+0*003 respectively. In the absence of an external field the quartet manifold is split into two Kramers doublets spaced by I 2 0 J m I . For simplicity? we assume that A = 0 (i.e.? E = O) so that the two doublets are I Ms = &3/2) and I Ms = 1/2). When D is negative the I Ms = &3/2) level is lower lying and positive D reverses the ordering? as shown in fig. 4. At low temperature 2% 1°K < I 2 0 1 only the ground doublet will be responsible for the Mossbauer magnetic h.f.s. FIG. 4.-Representation of crystal field and exchange splitting in the spin quartet state. Owing to a combination of (i) intrinsically different effective hyperfine interactions and (ii) markedly different relaxation rates specific Mossbauer patterns are expected depending on whether the I +3/2) or I & lf2) level is lowest lying i.e.whether D is negative or positive. For example under similar low-temperature circumstances in high spin Fe3+ 6S ions with an I S = 5/2 M = & 1/2) level lowest lying effective paramagnetic relaxation times and local perturbing fields preclude well-defined paramagnetic h . f . ~ . ~ In this fast relaxation limit one is left with a quadrupole doublet described by the nuclear spin Hamiltonian for the excited FeS7 level Completely analogous arguments apply to the present case of the I S = 3/2 Ms = + 1/2> doublet ; again a simple quadrupole splitting is expected when this is the ground doublet. No accurate description of the origin of the large EFG in these complexes is presently available.On the other hand when the I S = 3/2 Ms = +3/2) level lies lowest effective relaxation times z are long (zc% cu; l ) at low temperatures and a well-defined effective 26 SPIN 3/2 IRON COMPLEXES magnetic field is expected.s The resulting Mossbauer pattern is described by the nuclear spin Hamiltonian (for the excited state of FeS7 I = 3/2) the EFG tensor is expressed with respect to its principal axis system. The combined electric and magnetic interactions in this case lead to a multi-line pattern of normally six or more lines. Experimental data given below and appropriate to this case have been analyzed using a computer programme whose output are polycrystalline absorp- tion patterns for the Hamiltonian of eqn.(3). The general methods used to compute the spectra have been described 9 9 1 0 and in the present case all of the pertinent matrix elements have been given in closed form by Matthias Schneider and Steffen.' In the latter authors' work the spherical polar co-ordinates 4 and 8 are denoted a and p respectively. Except for this notational change the data of fig. 2 were analyzed with the conventions of ref. (11) and are summarized in table 1. The ground term in the S = 3/2 complexes is an orbital singlet so the hyperfine field arises from the core polarization interaction with S = 3/2. In the ground doublet 1 Ms = -&3/2) Hc is given by where (S,} = *3/2. Comparing eqn. (5) and (3) we find He, = -&*(a/glpN) ; it is easily shown that both " polarities '' yield the same Mossbauer pattern.By analogy with high spin Fe3+ 6S ions the core polarization term a is assumed negative. This description suffices to interpret the observed Miissbauer data in the para- magnetic complexes Fe(S2CNMe2)2CI Fe(S2CN(i-propyl),),Cl and Fe(S2CNEt,),Br. In the former two complexes the ME shows a many-line pattern a well-defined magnetic field (within the limit of relaxation broadening) and we conclude that the spin Hamiltonian parameter D is negative in these cases. This result is consistent with the e.p.r. data in the di-isopropyl derivative. The similarity of the spectra of (b) and (d) suggest that the zero-field splittings in these two complexes do not differ greatly. On the other hand the quadrupole doublet in the Fe(S,CNEt,),Br strongly suggests that D is positive ; the I S = 3/2 Ms = -& 1/2) level is lowest lying.The Mossbauer data while consistent with positive D in Fe(S,CNEt,)Br do not establish this result unambiguously. For example if the zero field splitting was extremely small I D Ilk< 1.2"K one would expect fast relaxation and only a quadrupole doublet independent of the sign of D. In the most general case then there are two possible explanations for the doublet of fig. 2(a); (i) very small I D I or (ii) comparatively large I D I and D> 0. In principle these two possibilities may be distinguished by a single crystal e.p.r. experiment at relatively large fields and low temperatures. In case (i) the small zero field splitting would not be expected to affect greatly the isotropic g = 2-0 resonance of the spin quartet level especially for large external fields.In case (ii) a resonance with gmaxN4*0 similar to that of Fe(S2CN(i-propyl),)Cl is expected. Unlike the latter case where the resonant doublet is an excited doublet the e.p.r. singal would be strongest at lowest tempera- ture for D> 0. E.p.r. experiments (24 Gc) at 4-2 and 1~4°K were therefore per- formed using a single crystal of Fe(S,CNEt,),Br. The magnetic symmetry axes H. H. WICKMAN AND A. M. TROZZOLO 27 of the crystal were not known prior to the experiment. The sample showed a single strong resonance whose intensity increased with decreasing temperature and which was characterized by g = 4.0+0.2 and gmin = 2.7+0.3. No resonance near g = 2 was found. This result argues for case (ii) a large (>2"K) and positive sign of D.The halo-constituent therefore appears crucial in determining the sign of the zero field splittings of the S = 3/2 manifold. The description of the h.f.s. of the Fe(S2CNEt2)2CI derivative is different as this complex undergoes a magnetic transition at 2-5"K3 The zero field splitting in this system has not yet been determined not is the mechanism of the collective ordering known in detail. Both dipole and exchange effects undoubtedly contribute to the ordering; we refer to these interactions collectively as the exchange field Hexch. Depending on the relative strengths of the crystal field and exchange field conplicated behaviour may occur. As a start however we will assume that the zero field splitting in Fe(S2CNEt,)2C1 is similar to that in the closely related Fe(S,CN(i-propyl),),C1 derivative.Because the ordering occurs at 2*5"K the magnetic character of the ion is mainly determined by the ground doublet i.e. the I Ms = +3/2) level. Here the relations I (S,) I = 3/2 (S,} = (S,,) = 0 are valid. The exchange inter- action may then be represented in the Weiss molecular field approximation by a field Hexch directed along the z-axis of the spin Hamiltonian of eqn. (1). Under these conditions a relatively simple level scheme is found. As shown in fig. 4 the exchange splitting simply removes the degeneracy of the I +3/2) level. The transition temperature of 2.5"K is a reasonable estimate of the separation of the two levels at the experimentai conditions of 1-2"K; the upper state populations are sufficiently low to be neglected entirely. When relaxation times are long (2 % C O ~ l) the I Ms = +3/2) and 1 Ms = -3/2) levels separately contribute identical Moss- bauer spectra and the observed spectrum is a Boltzman sum of these two spectra.The Mossbauer pattern of a polycrystalline absorber is (neglecting polarization of the y-rays) indistinguishable from the magnetic h.f.s. from the unsplit I M = &3/2> doublet. (If polarization of the y-rays were observed the two could often be dis- tinguished i.e. the transitions in a paramagnetic ion with {S,) = 0 are unpolarized.) The great similarity of the Mossbauer h.f.s. in Fe(S2CN(i-propyl)2)2Cl and Fe(S2CNEt2),C1 offers substantial support for a simple exchange splitting of the ground doublet. Deviations from the model would in principle be shown primarily by differences between the observed core polarization fields He,,.The latter para- meter is proportional to (S,) in one of the lower two electronic levels of the ion; an exchange field at an angle to the z-axis of the electronic spin Hainiltonian would produce a mixing of the I Ms = 1 3/2) and I M = k 1/2) levels and thus change (S,) from the value found in paramagnetic case. In fact no experimental evidence evidence for such an effect was observed the fields He, in both the paramagnetic and ferromagnetic samples were essentially the same. The large quadrupole splittings in these compounds are not as easily interpreted as the magnetic interactions. Within two Kramers doublets arising from an orbital singlet and spin quartet level there is no temperature dependence to the EFG i.e. the net EFG at the nucleus does not change with the population of the two Kramers doublets.Because of this no direct determination of the ionic contribution to the EFG from the quartet term is possible. The relatively temperature independent quadrupole splitting is consistent with the absence of excited electronic terms within a few hundred cm-I of the ground state. We have noted previously that the levels of the lowest quartet term in octahedral symmetry 4T1 separately produce no EFG at the n u c l e ~ s . ~ The lattice contribution to the EFG may be large enough to account for the large splittings but it seems more likely that an appreciable gradient 28 SPIN 3/2 IRON COMPLEXES should arise from the ground quartet term. In this case the orbital level will be a mixture of states from different octahedral representations.A larger quadrupole splitting was observed in the bromo derivative than in the chloro-complexes; this effect could equally well be accounted for by a change in either the ionic or lattice contribution to the total gradient. In all of the chloro derivatives the EFG q was positive with the assumption that eQ is also positive. In earlier work6 it was shown that at higher temperatues where the main effect of relaxation is to broaden the quadrupole peaks the left peak is broadened more than the right peak. This results mainly from the fact that within the ground Kramers level the effective field fluctuates along the axis perpen- dicular to the principal axis of the EFG.12 For collinear EFG and effective internal field the right peak would be broadened. This may be seen qualitatively as follows.With the nuclear quantization axis along the 2'-direction (eqn. 3) the excited state nuclear wave functions are (with 7 = 0) I 1/2) and I & 3/2) and correspond with q> 0 to the left and right hand peaks in a pure quadrupole pattern when (Heff} = 0. These two levels may be described by eflectiue nuclear g factors with I' = 1/2 in each case. Their magnetic character is described by the respective g' tensors (9 = g; = 2gl ; gl = gl) and (9 = gi = 0 ; gi = 3g,). Hence the I & 1/2) level will respond more readily to transverse fluctuations of a magnetic field (the present case) while the I +3/2) is affected first when the effective field fluctuates along an axis parallel to the EFG principal axis. These considerations emphasize the result that it is not in general possible to deduce the absolute sign of an EFG from relaxation broadening of a quadrupole doublet without knowledge of the relative orientation of EFG principal axis and the magnetic hyperfine direction.Finally while the qualitative picture involving effective g values is useful in that it predicts correct features of the spectrum it is rigorously incorrect in that it assumes a static perturbing field while in fact the fields are of a stochastic nature and models based on the ideas are generally required to give definitive answers relating to origins of broadening in Mossbauer spectra. In the bromo derivative where the I & 1/2) level is lowest and relaxation times very fast the effect of an external magnetic field is to induce an ionic moment in the paramagnetic ion and hence an internal field owing to the core polarization mechanism.For simplicity we assume that only the 1 f 1/2) ground doublet is occupied. Because little other information is available a main justification will lie in the agreement of this analysis with the experimental results. The ground doublet has 911 = 2 gl = 4 and (9) = g' = 2J3. An external field Hext will induce an internal magnetic field given by where 3 P H e x t (9;;") 2 k T ' (Sz}ion = - tanh - - - - J3 2 for P H I k T d . In the present case of Hext = 7 kOe T = 3.0°K it follows that Hint E -42 kOe. Because Hi, is oppositely directed to Ifext the net hyperfine field is -35 kOe. Calculations of the broadening of quadrupole lines induced by a random magnetic field have been made by Gabriel and Ruby,9 and C01lins.l~ Comparison of their computed spectra allow us to estimate 1 He, 1 from fig.3 to be 34+5 kOe. This result is in good agremeent with the estimate made using the single Kramers level H. H. WICKMAN AND A. M. TROZZOLO 29 approximation. In the present experiment the large internal field was produced by a relatively small external field. This method differs from the situation for which the calculations of Gabriel and Ruby and Collins l3 were intended namely where the large magnetic field was produced externally by a superconducting magnet. Finally the agreement of the approximation used to interpret the present data sug- gests that the splitting between the two Kramers doublets is greater than 6°K. B. F. Hoskins R. L. Martin and A. H. White Nature 1966 211 627. R. L. Martin and A. H. White Inorg. Chem. 1967 6 712. H. H. Wickman A. M. Trozzolo H. J. Williams G. W. Hull and F. R. Merritt Physic. Rev. 1967 155 563. H. H. Wickman and F. R. Merritt Chem. Physics Letters 1967 I 117. H. H. Wickman and A. M. Trozzolo Znorg. Chem. in press. 1966 16 162. ' H. H. Wickman and A. M. Trozzolo Physic. Rev. Letters 1965 15 156 ; Physic. Rev. Letters ' G. K. Wertheim and J. P. Remeika Physics Letters 1964 10 14. * H. H. Wickman M. P. KIein and D. A. Shirley Physic. Rev. 1966 152 345. J. R. Gabriel and S. L. Ruby Nucl. Instr. Methods 1965 36 23. lo H. H. Wickman and G. K. Wertheim Physic. Rev. 1966,148 211. l1 E. Matthias W. Schneider and R. M. Steffen Arkiv Fysik 1963 24,97. M. Blume Physic. Rev. Letters 1965 14 96. l3 R. Collins J. Chem. Physics 1965 42 1072,