Magnetic interactions in Fe1−xMxSb2O4, M = Mg, Co, deduced from Mössbauer spectroscopy

Magnesium- and cobalt- substituted FeSb2O4, of composition Fe1−xMgxSb2O4 (x = 0.25, 0.50, 0.75) and Fe0.25Co0.75Sb2O4 have been examined by 57Fe Mössbauer spectroscopy. The complex spectra recorded from the magnetically ordered materials are interpreted in terms of models in which the dominant magnetic interactions occur along the rutile-related chains of FeO6 octahedra in the magnetic structure of FeSb2O4. In materials of the type Fe1−xMgxSb2O4, the diamagnetic Mg2+ ions have no magnetic moment and behave as non-magnetic blocks which disrupt the magnetic interactions in the chains along the c-axis forming segments of iron-containing chains separated by Mg2+ ions. In Fe0.25Co0.75Sb2O4 the spectra are composed of components from different configurations of neighbouring Fe2+ and Co2+ ions.


Introduction
The compound FeSb 2 O 4 occurs naturally as the mineral schafarzikite and is isostructural with the tetragonal form of Pb 3 O 4 [1,2]. Its structure, Fig. 1, consists of rutile-related chains of FeO 6 octahedra along the c-axis linked by trigonal pyramidal Sb 3+ cations which, being bound to three oxygen anions, possess a lone pair of electrons which can be regarded as a fourth ligand. The Fe-Fe distance within the chains (2.96Å) is shorter than the nearest Fe-Fe distance within the layers (6.07Å) and is consistent with some one-dimensional character in FeSb 2 O 4 . The material undergoes an antiferromagnetic transition around 45 K [3,4]. The 57 Fe Mössbauer spectrum of FeSb 2 O 4 at ca. 4.2 K is unusual, being the result of combined magnetic hyperfine and electric quadrupole interactions of comparable strength [5,6] and, together with data recorded above T N [7], has been used to determine the order of the t 2g orbital energy levels. The literature also documents some structurally related compounds of composition MSb 2 O 4 (M = Mn 2+ , Co 2+ , Ni 2+ , Cu 2+ , Zn 2+ , Mg 2+ ) [8][9][10][11][12][13].
Although an early attempt to substitute on the Sb site was not successful [14], we subsequently reported the synthesis of materials of composition FeSb 2−x Pb x O 4 [15]. We have also reinvestigated the Mössbauer spectra recorded from FeSb 2 O 4 and found that, in FeSb 2−x Pb x O 4 , the dominant intrachain magnetic exchange gives rise to situations where weakly coupled Fe 2+ ions coexist in a non-magnetic state alongside Fe 3+ ions in a magnetically ordered state [16]. We have also prepared new phases involving substitution on the M site. The magnetic moments deduced from neutron diffraction and magnetic susceptibility measurements in the series of composition Fe 1−x Co x Sb 2 O 4 suggested the existence of some short range correlations within the chains [17] whilst in materials of formulation Fe 1−x Mg x Sb 2 O 4 , the decrease in magnetic ordering temperature with increasing concentrations of magnesium was associated with non-magnetic Mg 2+ ions weakening the magnetic interactions between Fe 2+ ions [18]. An interesting feature of these materials has been the demonstration of their capacity to accommodate additional oxygen within their structures [19].
We report here on the examination of magnetic interactions in the materials  η is the asymmetry parameter (asymmetry of electric field gradient at nucleus); θ and are the polar and azimuthal angles that specify the direction of the magnetic field, H, with respect to the coordinates of the electric field gradient models in which the strongest magnetic interactions can be associated with Fe 2+ ions located along the c-axis in rutile-related FeO 6 octahedra but which differ according to the magnetic properties of Co 2+ and Mg 2+ . The purity of the phases was determined by X-ray powder diffraction at 298 K with a Bruker D8 diffractometer in transmission mode using Cu-K α1 radiation. 57 Fe Mössbauer spectra were recorded in constant acceleration mode using a ca. 25 mCi 57 Co source and a helium closed-cycle cryorefrigerator. All the spectra were computer fitted with those recorded at 16 K from Fe 0.5 Mg 0.5 Sb 2 O 4 , Fe 0.75 Mg 0.25 Sb 2 O 4 and Fe 0.25 Co 0.75 Sb 2 O 4 being fitted using the method of Kundig [20] in which the fitting variables contain not only the energy splitting of the magnetic hyperfine-and electric quadrupole-interactions but also the angle the hyperfine field makes with the principle axis of the electric field gradient. All the chemical isomer shift data are quoted relative to metallic iron at room temperature.  Table 1. The spectra shown in Fig. 2 have already been reported [18] but are reproduced here to assist this new discussion in terms of the magnetic interactions in these materials.  (Table 1, Fig. 2). In Fe 0,75 Mg 0.25 Sb 2 O 4 the three components required for a best fit to the spectrum (Fig. 2) at 16K all show magnetic splitting with hyperfine field values listed in Table 1.

Materials of composition
All features of the spectra are consistent with the magnetisation data reported in reference [18].

Fe 0.25 Co 0.75 Sb 2 O 4
Mossbauer spectra recorded at 298 K and 76 K showed only quadrupole split absorptions characteristic of paramagnetic Fe 2+ and consistent with the magnetic susceptibility data [17] which indicated a magnetic ordering temperature of ca 57 K. The 57 Fe Mössbauer spectra recorded from Fe 0.25 Co 0.75 Sb 2 O 4 at 298 K, 76 K and 16 K are shown in Fig. 3 with the 57 Fe Mössbauer parameters collected in Table 2. These spectra are best fitted with components with chemical isomer shifts characteristic of Fe 2+ .

Model of magnetism
The structure of the parent compound, FeSb 2 O 4 , consists of rutile-like chains of edge-linked FeO 6 octahedra along the c-axis linked by trigonal pyramidal Sb 3+ ions. The short Fe-Fe distance within the chains dominates the magnetic exchange interactions. Where the t 2g orbitals are partly filled, the strongest magnetic coupling involves direct overlap of these orbitals pointing at the linking octahedral edges. When the direct exchange is eliminated, for (t 2g ) 6 configurations, or is small because of poor orbital overlap, superexchange within the chains is significant and involves Fe-O-Fe pathways where the connecting oxygen ions are those of the joining edge between the FeO 6 octahedra. In FeSb 2 O 4 magnetic ordering occurs at ca. 45 K [3,4,15,18].
In this work we have probed changes in the magnetic behaviour when the cations Mg 2+ and Co 2+ are substituted on to the Fe 2+ sites. The analysis of the results aims to connect The Mg 2+ ion has no magnetic moment and thus behaves as a non-magnetic block to magnetic interactions along the c-axis. Thus the effect of Mg 2+ ions is to provide a mixture of iron-containing chains of different lengths along the c-axis separated by Mg 2+ ions.
We postulate here that the magnetic behaviour of a given iron-containing segment will depend on the number of iron ions in that segment. At a given temperature below the magnetic ordering temperature (T N , ca. 45 K [3,4,15,18]) isolated iron ions will be more likely to behave paramagnetically while long strings of iron ions will retain magnetic order. This model thus predicts different magnetic behaviour coexisting in the magnetically ordered temperature range because of the different segment lengths. The Mössbauer spectra reported here give insights into this potentially mixed magnetic state.
In the materials of composition Fe 1−x Mg x Sb 2 O 4 , the normalised relative probability that an iron ion is in a segment of n iron ions is p = n(1 − x) n / n(1 − x) n (n = 1, ..∞) where (1 − x) is the probability that any given cation site on the c axis is occupied by an Fe ion. Graphs of of p versus n for the iron concentrations (1 − x) = 0.25, 0.50 and 0.75 are shown in Fig. 4a, and we have used these to interpret, in a quasi-quantitative manner, the magnetic behaviour manifested in the Mössbauer spectra.
In Fe 0.25 Co 0.75 Sb 2 O 4 the minority Fe 2+ ions separate segments of Co 2+ . At the end points of this system FeSb 2 O 4 orders magnetically at 45 K in an A type configuration while CoSb 2 O 4 orders at 79 K in a C type configuration [17]. Thus Fe 2+ -Fe 2+ and Fe 2+ -Co 2+ magnetic interactions will shape the Fe 2+ Mossbauer spectrum and we attempt to interpret this via local environments.  Table 1.

Spectra of Fe 1−x Mg
The overall shape of the magnetic spectrum of Fe 0.75 Mg 0.25 Sb 2 O 4 at 16 K, while similar to that of the parent material FeSb 2 O 4 at ∼30 K, now requires three components for a good fit. Comparing the areas of fitted components of a spectrum with areas under the p(n) η is the asymmetry parameter (asymmetry of electric field gradient at nucleus); θ and are the polar and azimuthal angles that specify the direction of the magnetic field, H, with respect to the coordinates of the electric field gradient  Table 1 versus n curves of Fig. 4a we are able to establish the segment lengths (n) of Fe 2+ ions that give rise to each magnetic component in the spectrum. This is done by associating longer segment lengths with higher magnetic hyperfine fields, justified by assuming that the magnetic anisotropy energy required to reduce the mean spin value <S> by fluctuations is greater the longer length of coupled spins. Values of n, relating length of segment to each magnetic component in the fitted spectra are given in Fig. 4b Fig. 4a also apply to Fe 0.25 Co 0.75 Sb 2 O 4 where the majority magnetic ions are Co 2+ with the Fe 2+ ion segments being very short. In this distribution the probability, p, of an Fe 2+ ion having values n = 1, 2 and >2 are p = 56%, 28% and 16% respectively. These values correspond to the Fe 2+ ion having local environments along the c-axis of two Co 2+ neighbours, one Co 2+ and one Fe 2+ neighbour and two Fe 2+ neighbours respectively. Identifying these p values with the areas of the fitted components, listed in Table 2, with hyperfine fields of 16.4 T, 7.2 T and 2.6 T gives reasonable agreement suggesting that there is stronger magnetic coupling between Fe 2+ -Co 2+ than between Fe 2+ -Fe 2+ ions. This simple approach supports the picture that these Mossbauer spectra are largely shaped by the extreme local environment of the Fe 2+ ions.

Conclusions
The interpretation of the detailed features of the Mössbauer spectra recorded from magnetically ordered materials created by substitution of magnesium or cobalt ions into the parent material FeSb 2 O 4 are accounted for by a model in which the magnetic structure is quasi one dimensional with the dominant interactions along the c-axis of the rutile-related chains. Variations of detail arise from local configurations of cations within these rutile-related chains.