Interplay between transition-metal K-edge XMCD, slight structural distortions and magnetism in a series of trimetallic (Co_xNi_(1−x))₄[Fe(CN)₆]_3/8 Prussian blue analogues

Abstract

The magnetic properties of a series of trimetallic (Co,Ni)Fe Prussian blue analogues (PBAs) were investigated by SQUID magnetometry and X-ray magnetic circular dichroism (XMCD) at the three transition metal (TM) K-edges. In turn, the PBA trimetallic series was used as a tool in order to better understand the information contained in TM K-edge XMCD and particularly the chemical nature of the probed species (extended sub-lattice or localized entities). The results show that the magnetic behavior of the compounds is dictated by competing exchange interactions between the Co–Fe and Ni–Fe pairs, without spin frustration. They also show that XMCD at the TM K-edge is a local atomic probe of the element at the N side of the cyanide bridge and a local probe of the absorbing atom and its first magnetic neighbors on the C side of the bridge. At last, XMCD at the TM K-edge turns out to be highly sensitive to very small structural distortions.

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Introduction

X-ray magnetic circular dichroism (XMCD) at the transition metal (TM) K-edge is less frequently used than XMCD at the TM L_2,3 edges as a local magnetic probe. Indeed, in contrast to XMCD at the L_2,3 edges of TMs, for which quantitative information can be extracted from the sum rules^1–3 and the spectra can be well-reproduced by crystal field multiplet calculations,⁴ the interpretation of the XMCD signals at the TM K-edge remains unsatisfactory despite many efforts towards the quantitative interpretation and the reproduction of the signals.^5–15 Yet, XMCD at the TM K-edge is the preferred technique to probe magnetism under pressure for instance.^16–21 The literature on XMCD at the TM K-edge mostly deals with the study of metals,²² metal alloys²³ and intermetallics,^24,25 while works dealing with the study of molecular compounds are scarcer.

Most studies of molecular compounds by XMCD at the TM K-edge deal with the investigation of Prussian blue analogues (PBAs). Noticeably, in the search for room-temperature molecular-based magnets, Verdaguer and his team used this technique in the 90's as a probe of the exchange interactions in PBAs: they related the sign of the TM K-edge XMCD signal to the orientation of the magnetic moment carried by the absorbing atom with respect to the applied magnetic field.^26–33 Since then, only qualitative information has been extracted from these signals.

Therefore, we are engaged in the project aiming at disentangling the physical effects at the origin of the TM K-edge XMCD signals. We have been developing an original experimental approach aiming at making TM K-edge XMCD a real quantitative tool for molecular chemists.^34–38 Our strategy, presented in previous works,^35–38 uses the versatile chemistry of PBAs exhibiting the well-known face-centered cubic (fcc) structure, the unit cell of which is shown in Fig. 1 (for p = 4 and q = 8/3) and the chemical composition per unit cell is given by A_p[B(CN)₆]_q·nH₂O, where A and B are two TM ions. The large variety of TM ions that can thus be combined in isostructural compounds allow for the independent variation of the magnetic orbitals on both A and B sites. This enables the analysis of the effect of a change of each of them on both TM K-edge XMCD signals. Thus, the analysis of the TM K-edge XMCD signals of two series of PBAs of chemical formula A^II₄[Fe^III(CN)₆]_3/8·nH₂O (A²⁺ = Mn²⁺, Co²⁺, Ni²⁺, Cu²⁺) and A^II₄[Cr^III(CN)₆]_3/8·nH₂O (A²⁺ = Mn²⁺, Fe²⁺, Co²⁺, Ni²⁺) showed that TM K-edge XMCD was very sensitive to orbital symmetry and allowed us to relate the main 1s → 4p contribution of the XMCD signal to the electronic structure and the magnetic behavior of (i) the probed ion on the N side of the cyanide bridge and (ii) the probed ion and its magnetic neighbors on the C side. Furthermore, an expression for the intensity of this main 1s → 4p contribution was unprecedently derived for the sixteen XMCD signals (at both TM K-edges of the eight PBAs) of the two series.^36,38 This study also showed that XMCD at the TM K-edge can provide both original local structural and magnetic information, which, combined with macroscopic magnetic measurements, allowed for an unprecedented in-depth analysis of the magnetic behaviors of the two bimetallic series of PBAs.

Fig. 1 Scheme of the unit cell of a Prussian blue analogue with the chemical formula A₄[B(CN)₆]_2.7·xH₂O. Yellow circles stand for the B³⁺ ion, light grey circles the A²⁺ ions, dark grey the carbon atoms, blue the nitrogen atoms, and red the oxygen atoms. The hydrogen atoms of the water molecules bonded to the A²⁺ ions as well as the zeolitic water molecules are omitted for clarity.

In this work, we now focus on a series of trimetallic PBAs. Twenty-five years ago, trimetallic PBAs generated interest because of their intriguing magnetic behaviors and particularly magnetic pole inversions due to competitive exchange interactions between the TM ions^39–47 and also, later on, some photo-switching properties;^48–50 their magnetic properties were essentially investigated by SQUID magnetometry at the macroscopic level. In our on-going commitment to promote TM K-edge XMCD as a regular local probe of TM magnetic moment in molecular compounds, these systems offer the opportunity to go ahead. On the one hand, such study of trimetallic PBAs is an opportunity to test the relevancy of TM K-edge XMCD for the study of the magnetic properties of more complex systems than bimetallic PBAs. On the other hand, with the aim to better understand the information contained in the XMCD signals, one can analyze the effect on the XMCD signal at the three TM K-edges of the replacement of one ion by another in varying amounts in the same sublattice of one PBA; this should provide information on the nature of the species probed (extended on a sublattice level or localized at the atomic scale). Among trimetallic PBAs, the series of chemical formula (Co_xNi_(1−x))₄[Fe(CN)₆]_8/3·nH₂O (where x is the mole fraction of Co ions on the A site of the alkali cation free NiFe PBA), called the Co_xNi_(1−x)Fe series in the following, has been chosen. The preparation of the samples and their characterization are given in the experimental part and the ESI† (S1–S3). For this study, K-edge XMCD has a great advantage compared with L-edge XMCD, which is yet a direct local probe of the 3d levels: the former is bulk sensitive like SQUID magnetometry and therefore little sensitive to surface effects. Surface effects, which are yet poorly understood in PBAs, can be detected by surface sensitive techniques such as L-edge XMCD. Thus, the parent Rb-containing photo-switchable RbCoFe PBA of chemical formula Rb₂Co₄[Fe(CN)₆]_3.3·11H₂O was already studied by L-edge XMCD.⁵¹ This study revealed weak ferromagnetic interaction at the surface of the ferrimagnetic photoexcited state of RbCoFe.⁵¹ The addition to the XMCD signal of yet poorly understood surface effects could blur the information being sought here, making K-edge XMCD the most appropriate choice for this study. At last, it has also to be mentioned that neither experimental nor theoretical studies on the relative orientation of the magnetic moments on the A and B sites of the Co_xNi_(1−x)Fe series are available in the literature.

Results

Magnetic measurements

The magnetization curves versus the magnetic field at 4 K, temperature at which the XMCD measurements were performed, are shown in Fig. 2 for the samples of the Co_xNi_(1−x)Fe series.

Fig. 2 Magnetic field dependence of the magnetization at 4 K of CoFe (green), Co_0.7Ni_0.3Fe (pink), Co_0.56Ni_0.44Fe (red), Co_0.35Ni_0.65Fe (blue), and NiFe (black).

The field cooled (FC) and zero field cooled (ZFC) magnetization curves, as well as the temperature dependence of the inverse of magnetic molar susceptibilities, are given in S2 and S3 (ESI†). The magnetic ordering temperature T_C/N was determined as the temperature of a minimum in the derivative of the FC magnetization curve (dM_FC(T)/dT; S2, ESI†). The Weiss (θ) magnetic constant was extracted from the plots of the inverse of the molar susceptibility versus temperature by fitting a Curie–Weiss law to the curves (S3, ESI†). All these magnetic data as well as the coercive field (H_C) at 4 K and the magnetization value at 4 K and 4 T are gathered in Table 1.

Table 1 Macroscopic magnetic parameters of CoFe, Co_0.7Ni_0.3Fe, Co_0.56Ni_0.44Fe, Co_0.35Ni_0.65Fe, and NiFe

	T C/N (K)	θ (K)	H c (×10^−4 T)	M (4 T) (NμB)	M sat calc powder mixture (NμB)	M sat calc (NμB)
CoFe	14	−9	1240	8.3	9.3	9.3
Co0.7Ni0.3Fe	12	−0.25	500	8.9	9.7	3.3
Co0.56Ni0.44Fe	12	8.3	250	9.7	9.9	0.5
Co0.35Ni0.65Fe	16	14	750	9.4	10.2	3.7
NiFe	22	32	2000	10.1	10.7	10.7

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The FC/ZFC magnetization curves (S2, ESI†) show the classical profile of PBA magnets and they show that at 4 K, temperature at which the XMCD signals were recorded, all compounds are in a magnetically ordered state. The single X-ray diffraction peak for each reflection (S1), the unique minimum exhibited by the dM_FC(T)/dT curve (S2, ESI†) and the profile of the magnetic field dependence of the magnetization (Fig. 2) show that all compounds are made of a homogeneous PBA phase mixing the Ni²⁺ and Co²⁺ ions at the atomic scale. The presence of several phases richer in one or the other ion can be excluded.

As a first approximation, for TM ions of the first row, magnetic moments are considered originating from the spin angular momentum only. In the magnetically ordered states of PBAs, the orientation of the magnetic moments with regard to an applied external magnetic field can thus generally be predicted from the total spin quantum number of the ions and from the sign of J. In bimetallic PBAs, the magnetic moment of the ion with the largest total spin quantum number aligns in the direction of the magnetic field and the second one is parallel (J > 0) or antiparallel (J < 0) to the former depending on the sign of J. In such compounds where exchange interactions prevail, the sign of θ directly gives the sign of J. Thus, CoFe is a ferrimagnet: the magnetic moment carried by the Co²⁺ ion aligns in the direction of the applied magnetic field and the one of the Fe³⁺ ion in the opposite direction (Fig. 3a).³⁶ In contrast, NiFe is a ferromagnet: the magnetic moments carried by both the Ni²⁺ and the Fe³⁺ ions align in the direction of the applied magnetic field (Fig. 3b).³⁶

Fig. 3 Scheme of the orientation of the magnetic moment borne by the TM ions in an applied magnetic field H for (a) CoFe, (b) NiFe and (c) the Co_xNi_(1−x)Fe series by considering the same magnetic behavior as in the Mn_xNi_(1−x)Cr series.^39–42 (d) Experimental magnetization value at 4 K and 4 T (red circle) for the Co_xNi_(1−x)Fe series and M_sat values as a function of x calculated from eqn (1) (white diamond) and for the corresponding mixture of the CoFe and NiFe PBA powders (white circle).

In trimetallic PBAs containing two different metal ion pairs with different nature of exchange interactions (antiferro- and ferromagnetic) between them, the situation is more complex. As mentioned in the introductory part, several examples of magnetic studies of trimetallic PBAs exist in the literature and especially the PBA series of chemical formula (Mn_xNi_(1−x))₄[Cr(CN)₆]_8/3·nH₂O,^39–42 called the Mn_xNi_(1−x)Cr series in the following. This trimetallic PBA series is comparable to our series as the extreme compounds MnCr and NiCr are also respectively ferrimagnet and ferromagnet. For this Mn_xNi_(1−x)Cr series, the saturation magnetization was well predicted along the series by considering the same exchange interaction as in the extreme bimetallic compounds between the same pairs of ions. In the same way, we tried to predict the saturation magnetization value for one unit cell for the compounds of the Co_xNi_(1−x)Fe series by considering the same exchange interaction as in the bimetallic extreme PBAs between the same ion pairs (Fig. 3c) using eqn (1) in Nμ_B units, where N is the Avogadro constant, μ_B the Bohr magneton and g the electron g-factor (g = 2) and which is equivalent to the equation used in ref. 39–42:

M_sat calc = g|4(xS_Co − (1 − x)S_Ni) − 8/3S_Fe| (1)

The calculated values (M_sat calc) are given in Table 1 and plotted as a function of x in Fig. 3d, where they are compared to the experimental magnetization values at 4 T and the values calculated for the corresponding mixture of the CoFe and NiFe PBA powders. Even if the saturation is not reached at 4 T, Fig. 3d clearly shows that eqn (1) fails to predict the experimental saturation magnetization in our Co_xNi_(1−x)Fe series. The magnetic behavior of our Co_xNi_(1−x)Fe series is therefore different from that of the Mn_xNi_(1−x)Cr one described in ref. 39–42. To get a better insight into this original magnetic behavior, the compounds of the Co_xNi_(1−x)Fe series were investigated by XMCD at the Co, Ni and Fe K-edges to probe the local magnetic moment on each TM ion.

XMCD at the Co and Ni K-edges

The XMCD signals at the Co and Ni K-edges for the Co_xNi_(1−x)Fe series are shown in Fig. 4a and b respectively.

Fig. 4 XMCD signals of CoFe (green), Co_0.7Ni_0.3Fe (pink), Co_0.56Ni_0.44Fe (red), Co_0.35Ni_0.65Fe (blue), and NiFe (black) (a) at the Co K-edge, (b) at the Ni K-edge and (c) at the Fe K-edge.

The Co and Ni ions occupy the same site of the fcc PBA structure, called the A site above and in ref. 36. For this A site, the contributions to the signal over the edge and pre-edge regions were already assigned and discussed in ref. 36 and 38. For all compounds, over the pre-edge and edge regions, the XMCD signal exhibits one main contribution (γ) and two other contributions of significantly smaller intensity (α and β), all situated at the same energies along the series. The α contribution can be assigned to the electric-dipole forbidden 1s → 3d transitions and explained by the low symmetry of the site and associated 3d–4p orbital mixing. The β contribution can be assigned to the 1s → t_1uCNπ* transitions. The two latter contributions will not be further discussed here. The main contribution to the XMCD signal (γ) at the Co K-edge (Fig. 4a) and at the Ni K-edge (Fig. 4b) can be assigned to the electric-dipole allowed 1s → 4p transitions. For one given K-edge, its intensity is very close from one compound to the other and very close to that of the corresponding bimetallic PBA, except the one of Co_0.35Ni_0.65Fe, which is significantly higher at both edges (blue curves). It is now well established that the sign of the main contribution to the XMCD signal in PBAs is directly related to the nature of the exchange interaction between the TM, i.e. to the direction of the magnetic moment of the probed atom with regard to the applied magnetic field.^{18,30,31,36,38} The same sign and the same intensity of the main contribution for CoFe, Co_0.7Ni_0.3Fe and Co_0.56Ni_0.44Fe at the Co K-edge on the one hand and for NiFe, Co_0.7Ni_0.3Fe and Co_0.56Ni_0.44Fe at the Ni K-edge on the other hand shows that the magnetic moment borne by the Co(Ni) ions as well as its direction is the same as that of the Co(Ni) ion in the corresponding bimetallic PBA, in line with the magnetic data. One can therefore conclude that, as in the corresponding bimetallic PBA, the magnetic moment of the Co(Ni) ions is aligned in the direction of the magnetic field.

The intensity of the main contribution to the XMCD signal of Co_0.35Ni_0.65Fe is significantly higher (25–30%) than that of all other compounds at both the Co and Ni K-edges. This different behavior of Co_0.35Ni_0.65Fe arises from different local features of the Co and Ni ions in this compound. The magnetic measurements do not reveal neither a different electronic structure of the Co²⁺ and Ni²⁺ ions in Co_0.35Ni_0.65Fe nor a discontinuity in the macroscopic magnetic properties of this compound along the series. Nevertheless, structural strains and slight distortions of the ion coordination sphere could arise from the different sizes of the Co²⁺ and Ni²⁺ ions associated in the same A site of the PBA structure. The XRD patterns (S1) show that all compounds crystallize with the same fcc PBA structure and only the lattice constant varies. The variation of the lattice constant value with the percentage of Co²⁺ ions in the A site (Co%) is shown in Fig. S4 (ESI†). The lattice constant varies linearly with Co% for CoFe, Co_0.70Ni_0.30Fe and Co_0.56Ni_0.44Fe, indicating that up to the replacement of 44% of Co²⁺ ions by the smaller Ni²⁺ ones, the PBA structure accommodates both ions by a decrease of the lattice constant. Nevertheless, one can also see that the lattice constant of NiFe deviates from this linear variation as well as that of Co_0.35Ni_0.65Fe. When the Co% reaches a certain threshold between 56 and 35%, the replacement of Co²⁺ ions by the Ni²⁺ ones can no more be compensated by a single lattice constant decrease. The size of both cations being different, one too small (Ni²⁺) and the other one too large (Co²⁺) for the ideal face centered cubic lattice, the structural distortion would be local and different for both ions. Network strains likely develop, slightly distorting the coordination spheres of the Co²⁺ and Ni²⁺ ions and enhancing the deviation from the pure O_h symmetry of the local structure of the ions either with a slight displacement of the ion from the crystallographic site and/or a slight tilt of the coordination polymer. Such a local distortion of the A site, by reinforcing the intra-site 3d–4p orbital mixing, could explain the higher intensity of the main contribution to the XMCD signal of Co_0.35Ni_0.65Fe at the Co and Ni K-edges.

XMCD at the Fe K-edge

The XMCD signals of the Co_xNi_(1−x)Fe series at the Fe K-edge are shown in Fig. 4c. All the spectra exhibit the same contributions. Over the pre-edge and edge regions, the α and γ contributions can be assigned to the 1s → 3d and the 1s → 4p transitions respectively.³⁸ It is striking that the intensity of the γ contribution at the Fe K-edge varies strongly with the Co%. We already showed in ref. 38 that the γ contribution at the TM K-edge at the B site is sensitive to the nature of the ion in the A site, on the contrary to the A site, which is not sensitive to the ions in the B site; this difference between both sites is explained by the different symmetries of the sites.³⁸ In ref. 38, we showed that the intensity of the main contribution to the XMCD signal at the Fe K-edge is well reproduced by eqn (2).

I^Fe = (1 ± S_A) × (1/3) × P_exp (2)

where S_A is the total spin quantum number of the ion in the A site, the sign in front of S_A depends on the nature of the exchange interaction between the Fe ion and the TM ion in the A site (–(+) for an antiferromagnetic (ferromagnetic) exchange interaction), and P_exp is a constant, which depends on the experimental conditions (temperature, magnetic field, and the circular polarization rate of light). Under our experimental conditions, P_exp is equal to 0.012.^36,38Eqn (2), in which ±S_A is replaced by ((1 − x)S_Ni − xS_Co), is given by eqn (3).

I^Fe = (1 + (1 − x)S_Ni − xS_Co) × (1/3) × P_exp (3)

Eqn (3) has been used to predict the experimental intensity of the γ peak for our Co_xNi_(1−x)Fe series. The plot of the experimental (I_exp) versus the calculated (I_calc) intensity using eqn (3) is shown in Fig. 5, where the plot of I_expversus I_calc for the sixteen XMCD signals of the AFe PBAs (A²⁺ = Cu²⁺, Ni²⁺, Co²⁺, Mn²⁺) and the ACr PBAs (A²⁺ = Ni²⁺, Co²⁺, Fe²⁺, Mn²⁺) previously investigated and using the expressions for I_calc proposed in ref. 36 and 38 is also shown. Fig. 5 shows that the experimental intensity of the γ peak at the Fe K-edge is well reproduced by eqn (3) for all compounds of the Co_xNi_(1−x)Fe series. This result shows that the behaviour of the Fe³⁺ ion magnetic moment in the trimetallic compounds is the same as the latter in the extreme bimetallic compounds (CoFe and NiFe) weighted by the amount of Co²⁺ and Ni²⁺ ions; it is antiferromagnetically coupled with the Co²⁺ ions and ferromagnetically coupled with the Ni²⁺ ones, resulting in the distribution of its magnetic moment over the two orientations weighted by the percentage of both Co²⁺ and Ni²⁺ ions in the compound.

Fig. 5 Experimental (I_exp) versus calculated (I_calc) intensity using eqn (3) (blue open squares; error bar ±0.001) compared to I_expversus I_calc for the sixteen XMCD signals of the AFe PBAs (A = Cu²⁺, Ni²⁺, Co²⁺, Mn²⁺) and the ACr PBAs (A = Ni²⁺, Co²⁺, Fe²⁺, Mn²⁺) previously investigated in ref. 36 and 38 (black dots).

Discussion

Input of this work on the understanding of the magnetic properties of PBAs

The behavior of the magnetic moments carried by all three TM ions (Co²⁺, Ni²⁺ and Fe³⁺) can be proposed from the XMCD investigation at the three TM K-edges.

Very close main contributions to the XMCD signal at the Co and Ni K-edges for Co_0.70Ni_0.30Fe, Co_0.56Ni_0.44Fe, CoFe and NiFe indicate that the magnetic moments carried by both ions exhibit the same behavior as in the extreme bimetallic compounds CoFe and NiFe. This means that the magnetic moments of the Co²⁺ and Ni²⁺ ions are aligned in the direction of the applied magnetic field. This is in agreement with the experimental values of the magnetization at 4 T, significantly higher than those calculated using eqn (1) considering antiparallel magnetic moments for the Co²⁺ and Ni²⁺ ions, as was the case for the Mn²⁺ and Ni²⁺ ions along the Mn_xNi_(1−x)Cr series in ref. 39–42. The magnetic moments really borne by the Co²⁺ and Ni²⁺ ions are schematized as plain blue and plain green arrows in Fig. 6.

Fig. 6 Scheme of the proposed orientations of the magnetic moments for an octant of the fcc PBA structure. The Ni²⁺, Co²⁺ and Fe³⁺ ions are represented by green, blue and yellow spheres, respectively, and their magnetic moments by plain green, plain blue and dotted black arrows. The orientations of the magnetic moment with regard to the crystallographic axes are those proposed in ref. 38. The proposed alignment of the Fe magnetic moments along the 〈111〉 directions is in line with a slight trigonal distortion of the Fe(CN)₆ entities⁵² and a strong spin–orbit coupling. It has to be noted that the proposed spin-canted magnetic structure of the Fe ions remains a hypothesis or one of the possible models.

In the case of the Fe K-edge, the variation of the intensity of the main contribution to the XMCD signal is well reproduced by eqn (3). As mentioned above, this suggests that the behaviour of the Fe³⁺ ion magnetic moment in the trimetallic compounds is the same as that of the latter in the extreme bimetallic compounds, antiferromagnetically coupled with the Co²⁺ ions and ferromagnetically coupled with the Ni²⁺ ones but weighted by the amount of Co²⁺ and Ni²⁺ ions in the compounds. Such a magnetic situation could lead to spin frustration in the PBAs, especially since NiFe and CoFe present close strength of exchange interactions between the two ions in both ion pairs.‡⁵³ A frustration parameter given by f = |θ|/T_C/N has been introduced to evaluate the frustration degree and the condition |θ|/T_C/N > 10 has been proposed as a criterion for the presence of frustration.⁵⁴ This empirical criterion was proposed assuming that magnetic interactions are on an energy scale set by the exchange energy⁵⁴ and thus, without spin frustration, |θ| is expected to be close to the magnetic ordering temperature value. |θ| encompasses any deviation from the Curie law. In our case, deviation from the Curie law can reasonably be assigned to exchange interactions, but spin–orbit coupling can also play a non-negligible role. Assuming that neither NiFe nor CoFe exhibits spin frustration, the linear variation of the Curie–Weiss constant with the Co ion mole fraction percentage (x) along the series of compounds (Fig. S5, ESI†) shows that no significant effects other than those already operating in CoFe and NiFe are detectable along the series of compounds. Thus, along the Co_xNi_(1−x)Fe series, the linear variation of θ with x (Fig. S5, ESI†), the low value of the f parameter (f < 1.5) for all compounds, the classical profile of the FC and ZFC magnetization curves, as well as the orientation of each pair of spins consistent with the sign of the corresponding J constant, allow us to rule out the presence of spin frustration in the compounds of the series, as it was the case for the Mn_xNi_(1−x)Cr series previously studied.³⁹ From the variation of the intensity of the Fe K-edge XMCD signal (eqn (3)) along the Co_xNi_(1−x)Fe series, we propose an orientation of the magnetic moments carried by the Fe³⁺ ions with regard to that of the applied magnetic field dictated by the weighted amount of both the Ni²⁺ and Co²⁺ ions in the A sub-lattice, without spin frustration. The direction and orientation of the magnetic moment borne by the Fe³⁺ ions under the influence of Co²⁺ or Ni²⁺ ions are schematized as black doted arrows in Fig. 6.

The main difference between the comparable Mn_xNi_(1−x)Cr PBA series and our Co_xNi_(1−x)Fe series is that, in the former, the orientation of the magnetic moments at low temperature is directly dictated by the exchange interaction between the two ions in each pair (Ni–Cr and Mn–Cr). On the contrary, in our series the magnetic moments of the Co²⁺ and Ni²⁺ ions at the A site both align in the direction of the magnetic field despite the different nature of exchange interactions with the Fe³⁺ ion that they surround, and then, the orientation of the magnetic moment carried by the Fe³⁺ ions is dictated by the exchange interactions between the two ions in both pairs (Ni–Fe and Co–Fe), the average orientation being dictated by the relative amount of both Co²⁺ and Ni²⁺ ions. These different magnetic behaviors of the Mn_xNi_(1−x)Cr and Co_xNi_(1−x)Fe PBA series arise from different magnetic behaviors of the TM ions listed below. First, due to the higher number of unpaired electrons in the t_2g orbitals for the Cr³⁺ ions (3 against 1 for the Fe³⁺ ions), the exchange interactions with the surrounding ions (Mn²⁺ and Ni²⁺) are stronger in the Mn_xNi_(1−x)Cr series than in the Co_xNi_(1−x)Fe series. Second, due to the slightly different geometries of the M(CN)₆ entities, octahedral for Cr(CN)₆ and slightly trigonally distorted for Fe(CN)₆ with strong spin–orbit coupling (see ref. 38), the directions of the magnetic moments borne by the TM ion in these entities are different: aligned along the same 〈100〉 directions as those of the TM ions on the A site for the Cr(CN)₆ entities, while for the Fe(CN)₆ entities aligned along the 〈111〉 directions, different from those of the magnetic moments carried by the ions on the A site. Third, ref. 55 showing a comparable behavior of the Cu_0.73Mn_0.77[Fe(CN)₆]·zH₂O compound to those of the Mn_xNi_(1−x)Cr series, a stronger magnetic anisotropy of the Co²⁺ and Ni²⁺ ions in the Co_xNi_(1−x)Fe series than that of the Mn²⁺ and Ni²⁺ ions in the Mn_xNi_(1−x)Cr series can also be mentioned.³⁸ At last, one can also not exclude the role of the exchange interactions between TM second neighbors more important than those considered so far.

Input of this work on the understanding of XMCD at the transition metal K-edge for the study of molecular materials

1. Probed species. In a previous work,³⁶ we showed that the features of the main contribution to the XMCD signal at the TM K-edge of TM ions at the A site for the two AFe (A²⁺ = Cu²⁺, Ni²⁺, Co²⁺, Mn²⁺) and ACr (A²⁺ = Ni²⁺, Co²⁺, Fe²⁺, Mn²⁺) PBA series (i) do not depend on the nature of the TM ion at the B site and (ii) can be related to the electronic structure and magnetic behavior of the A²⁺ ion or of the A²⁺ ion sublattice: the shape of the signal to the filling of the 3d orbitals and the sign of the signal to the orientation of the magnetic moment with regard to that of the applied magnetic field; we also proposed an expression of its intensity as a function of the total spin quantum number S_A. The present study confirms the previous results and allows us to go a bit further concerning the species probed by XMCD at the A site of PBAs. As the intensity of the 1s → 4p XMCD contribution of CoFe at the Co K-edge is different from the one of NiFe at the Ni K-edge, the very close XMCD signals for the majority of the Co_xNi_(1−x)Fe series at the Co(Ni) K-edge show that the 1s → 4p contribution to the XMCD signal at the K-edge of the ions on the A site is sensitive neither to the replacement of one ion by the other in the A ions sublattice nor to the average distance between the same ions of the A ion sublattice. Hence, XMCD at the K-edge of TM ions on the A site of the molecular PBA compounds is not a probe of the sublattice or of a part of the sublattice of the ions on the A site. In that case, the contribution to the signal of each absorbing atom, encompassing either the contribution of all other ions of the sublattice (overlap of all 4p orbitals of the A²⁺ ions) or the contribution of all other same atoms of the sublattice (overlap of all 4p orbitals of the probed Co²⁺ or Ni²⁺ ions), would vary with the chemical composition of the sublattice, which is not observed. On the contrary, XMCD at the K-edge of TM ions on the A site of the molecular PBA compounds is a local probe of each absorbing atom without any influence from other ions and the XMCD signal at the K-edge of the ions on the A site is the average of all their contributions.

The case of the B site is different because our previous work showed that the 1s → 4p XMCD signal at the K-edge of the ions on the B site of PBAs contains not only information on the ions or the sublattice of the ions on the B site but also on the ions on the A site.³⁸ In order to determine whether XMCD at the K-edge of ions at the B site of PBAs is a local probe of the ion on the B site and its TM neighbors or a more extended probe, 50% of the Fe(CN)₆ entities were replaced by the Cr(CN)₆ ones in NiFe. This compound is called NiCr_0.50Fe_0.50 in the following and its X-ray diffraction pattern, FC-ZFC magnetization curves and magnetic field dependence of the magnetization at 4 K are shown in S6–S8. The XMCD signals of NiCr_0.50Fe_0.50 were compared to those of NiFe and the NiCr PBA (called NiCr) of chemical formula Ni₄[Cr(CN)₆]_8/3·17H₂O, the synthesis and characterization of which are both presented in ref. 36. Fig. 7a shows the XMCD signals at the Ni K-edge of NiFe, NiCr_0.50Fe_0.50 and NiCr. As expected, the signals are the same. XMCD at the TM ion on the A site of PBAs is a local probe of the ion, which is in a very close environment in the three PBAs, with definitely no influence from the TM ions in the B sites. Fig. 7b and c show the XMCD signals of NiCr_0.50Fe_0.50 compared to those of NiCr at the Cr K-edge and of NiFe at the Fe K-edge, respectively. The XMCD signal of NiCr_0.50Fe_0.50 is the same as that of NiCr at the Cr K-edge and the same as that of NiFe at the Fe K-edge. This result shows that, as at the K-edge of the TM ions on the A site, XMCD at the K-edge of the TM ions on the B site is not sensitive to the replacement of part of them and is therefore a local probe of the ion at the B site and its first metallic neighbors.

Fig. 7 (a) XMCD signals at the Ni-K edge of NiFe (black), NiCr_0.50Fe_0.50 (red) and NiCr (green) and XANES at the Ni K-edge of NiFe (black); (b) XMCD signals at the Cr K-edge of NiCr_0.50Fe_0.50 (red) and NiCr (green) and XANES at the Cr K-edge of NiCr_0.50Fe_0.50 (red); (c) XMCD signals at the Fe K-edge of NiCr_0.50Fe_0.50 (red) and NiFe (black) and XANES at the Fe K-edge of NiFe (black).

2. XMCD at the TM K-edge, a probe extremely sensitive to very slight structural distortions. Variable pressure XMCD measurements at the Ni and Fe K-edges of NiFe at 4 K already showed that XMCD at the TM K-edge is very sensitive to slight structural distortions.¹⁸ This high sensitivity arises from the symmetry dependent mixing of the 3d and 4p orbitals. As discussed above, the higher intensity of the 1s → 4p XMCD signal at the Co and Ni K-edges of Co_0.35Ni_0.65Fe is most likely caused by a slight distortion of the Co and the Ni sites due to network strains arising from the accommodation of ions of different sizes in the same sublattice of the PBA. No such effect is observed at the Fe K-edge of this compound. This is expected as the Fe(CN)₆ entity, in which the Fe³⁺ ion is low spin, is made of stronger and more covalent bonds than the Co²⁺ and Ni²⁺ high spin-to-ligand bonds. X-ray absorption near edge spectra (XANES) is a probe of the local structure around the absorbing atom. The XANES spectra of Co_0.35Ni_0.65Fe were recorded at the Co, Ni and Fe K-edges and compared to those of CoFe and NiFe; they are shown in Fig. 8. Fig. 8 shows that, whatever the K-edge, the XANES spectra of Co_0.35Ni_0.65Fe are very close to those of CoFe and of NiFe. The distortion of the Co²⁺ and Ni²⁺ sites is probably too small to be detectable on the XANES spectra at the TM K-edge. This therefore shows that XMCD at the TM K-edge could turn out to be an unprecedented tool to detect and analyze very slight distortions affecting magnetic sites.

Fig. 8 (a) XANES spectra at the Fe K-edge of Co_0.35Ni_0.65Fe (blue), CoFe (green) and NiFe (black); (b) XANES spectra at the Ni K-edge of Co_0.35Ni_0.65Fe (blue) and NiFe (black) (c) XANES spectra at the Co K-edge of Co_0.35Ni_0.65Fe (blue) and CoFe (green).

Experimental

A series of five (Co_xNi_(1−x))₄[Fe(CN)₆]_8/3·nH₂O PBAs (called Co_xNi_(1−x)Fe) were synthesized. EDS analysis, powder X-ray diffraction and magnetic measurements were performed using the devices of the ICMMO instrumentation platform. The syntheses and characterizations of the two extreme compounds CoFe and NiFe were presented in ref. 36.

Sample preparation

The three PBAs were synthesized by drop-by-drop addition of two precursors in aqueous solutions: a 400 mL aqueous solution of potassium hexacyanoferrate(III) K₃[Fe(CN)₆] (c = 2.5 × 10⁻³ mol L⁻¹) was added to a 100 mL aqueous solution of a mixture of Co(NO₃)₂ and Ni(NO₃)₂ salts (c_tot = 50 × 10⁻³ mol L⁻¹). The precipitates were washed with distilled water and centrifuged three times at 8000 rpm and finally allowed to dry in air at room temperature.

Energy dispersive spectroscopy (EDS) analysis

The chemical formulas of the three trimetallic PBAs were determined by EDS analysis, using an EDS spectrometer installed on a ZEISS Sigma HD microscope. Data processing was done using the IDFix EDS analysis software. The results are given in S1 (ESI†) for the Co_xNi_(1−x)Fe series.

Powder X-ray diffraction (XRD)

Powder XRD data were collected with a Philips X’Pert diffractometer (Cu Kα₁ radiation) at room temperature. All diagrams were recorded over the 10–70° 2θ angle range with steps of 0.01°. An aluminum sample holder was used for all measurements. The cell parameters were extracted by a Le Bail refinement procedure (using the Fullprof software), considering an Fm3m space group. The XRD patterns and corresponding cell parameters of the Co_xNi_(1−x)Fe series are given in S1 (ESI†).

SQUID magnetometry

Magnetic properties were investigated using a quantum device XL-7 SQUID magnetometer. 5.6 mg of PBA powder was placed in a capsule and 17 mg of eicosane were added to ensure that the particles would not move with the application of the magnetic field. Field cooled-zero field cooled (FC-ZFC) measurements were performed over the 2—100 K temperature range under a 30 Oe magnetic field (S2, ESI†). In order to determine the Weiss temperature (θ), the magnetization was measured as a function of temperature up to 300 K under a 5000 Oe magnetic field; the experimental curves were fitted using a Curie–Weiss law (S3, ESI†). Finally, the magnetic field dependence of magnetization was recorded at 4 K for a magnetic field varying between −40 000 Oe (−4 T) and 40 000 Oe (4 T).

Transition metal K-edge XAS

X-ray absorption spectra in the transmission mode were recorded for the Co_xNi_(1−x)Fe series at the three K-edges on the SAMBA beamline⁵⁶ at SOLEIL (Gif sur Yvette, France). We used a Si(220) monochromator and recorded the spectra in a continuous mode. Measurements were performed at room temperature on pellets. We carefully checked that no radiation damage occurred. Following the measurements, the spectra were energy-calibrated and conventionally normalized using the ATHENA software.⁵⁷

TM K-edge XMCD

Co, Ni and Fe K-edge X-ray absorption near-edge structure (XANES) spectra and XMCD signals were recorded in the transmission mode using the dispersive setup of the ODE beamline^58,59 at SOLEIL synchrotron (Gif sur Yvette, France). Detailed information is given about the measurements and normalization procedure in ref. 35, and so only the main ones are reminded here. The circular polarization rate is the same for all the edges. The Si(311) polychromator was chosen to achieve the highest possible resolution in the white line region of the spectra. Then, it is critical (i) to be well below the Curie temperature of the eight investigated PBAs, and (ii) to avoid any artifact in the intensity related to a change in the temperature, we carefully performed the measurements at 4 K. The largest external magnetic field (1.3 T) that can be reached when the cryostat was used was applied alternatively parallel and antiparallel to the direction of the photon beam. The samples were placed in a diamond anvil cell (DAC) and, to minimize the absorption of the beam while retaining a brilliant enough flux to be able to perform the measurements, the diamonds of the DAC were replaced by Plexiglas strips. No radiation damage occurred thanks to attenuators of appropriate thickness. A metallic foil was recorded at both edges for energy calibration. We normalized the XANES spectra and XMCD signals using the procedure described in ref. 35.

Conclusions

The study of the trimetallic Co_xNi_(1−x)Fe PBA series by TM K-edge XMCD at the Co, Ni and Fe K-edges and SQUID magnetometry shows that their magnetic structures can be explained by exchange interactions of the same sign as seen in the corresponding binary PBAs and spin frustration is not expected to occur.

Local structural distortions are likely to occur at certain compositions that cannot be detected by XAS but can be detected by XMCD, indicating that K-edge XMCD could be an extremely sensitive probe of slight structural distortions.

The use of the trimetallic Co_xNi_(1−x)Fe PBA series as a tool to better understand the TM K-edge XMCD in PBAs shows that K-edge XMCD is a local atomic probe of the TM atoms probed in this PBA series, despite the spatially extended character of the probed 4p orbitals. At the A site, TM K-edge XMCD is an atomic probe of only the probed element. At the B site, due to the deviation from centro-symmetry of the A site and the associated 3d–4p mixing,³⁸ XMCD at the TM K-edge is a local probe of the probed element but also of its first magnetic neighbors.

The Prussian blue analogues have been chosen as model compounds to better understand TM K-edge XMCD, because some electronic and structural parameters can be selectively varied and were successfully related to XMCD features. The next step will be to extend the interpretation of the TM K-edge XMCD signals of PBAs to (i) other molecular magnetic materials and (ii) materials whose electronic structures are well-described in terms of molecular orbitals. Another step will be to get direct experimental evidence of our hypothesis on the relative orientation of the magnetic moments and crystallographic axes (ref. 36 and 38 and this work). Resonant X-ray scattering using circularly polarized X-rays or neutron diffraction could be performed to get such evidence.

Author contributions

The authors are sad to specify that their colleague, co-author and friend, François Baudelet, passed away on January 28th, 2022. He carried out the experiments during two synchrotron beamtimes for the results presented here and was deeply involved in the interpretation of the data. The manuscript was written through the contribution of all other authors, who have given approval to the final version of the manuscript.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

Financial support was provided for the whole TM K-edge XMCD project and the PhD grant of A. N’Diaye by ANR MagDiDi (ANR-17-CE29-0011), Paris-Saclay University and the CNRS. The authors acknowledge SOLEIL for the provision of the synchrotron radiation facility on the ODE beamline through proposals 20190412 and 20201335 and on the SAMBA beamline through proposal 20180264.

Notes and references

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Footnotes

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d3cp04749k

‡ The absolute value of the ratio between the magnetic coupling constant between both NiFe (J_NiFe) and CoFe (J_CoFe) ions pairs can be estimated within the mean-field approach by considering dominant exchange interaction between neighboring TM ions.⁵³ Indeed, the proportional relationship between T_C/N, the magnetic ordering temperature, z the number of magnetic neighbors and J the magnetic coupling constant for a given PBA is given by: T_C/N ∝ zJ. The number of magnetic neighbors being the same in NiFe and CoFe, this approximation gives the value of 1.6 for |J_NiFe/J_CoFe|, indicative of exchange interactions with close strengths between both pairs of ions. Such close strength of exchange interactions of different nature in the same PBA network could give rise to spin frustration.

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