Daniel
Jezierski
*a,
Zoran
Mazej
*b and
Wojciech
Grochala
*a
aCenter of New Technologies, University of Warsaw, 02089 Warsaw, Poland. E-mail: d.jezierski@cent.uw.edu.pl; w.grochala@cent.uw.edu.pl
bDepartment of Inorganic Chemistry and Technology, Jožef Stefan Institute, Jamova cesta 39, 1000 Ljubljana, Slovenia. E-mail: zoran.mazej@ijs.si
First published on 26th April 2024
We present a new compound in the silver–cobalt-fluoride system, featuring paramagnetic silver (d9) and high-spin cobalt (d6), synthesized by solid-state method in an autoclave under F2 overpressure. Based on powder X-ray diffraction, we determined that AgIICoIIIF5 crystallizes in a monoclinic system with space group C2/c. The calculated fundamental band-gap falls in the visible range of the electromagnetic spectrum, and the compound has the character of charge-transfer insulator. AgCoF5 is likely a ferrimagnet with one predominant superexchange magnetic interaction constant between mixed spin cations (Ag–Co) of −62 meV (SCAN result). Magnetometric measurements conducted on a powdered sample allowed the identification of a transition at 128 K, which could indicate magnetic ordering.
The family of heterobimetallic AIIBIIIF5 compounds, although limited in number, demonstrates remarkable diversity (see Section I. in ESI‡).1,9–16 These includes pentafluorides with two transition metals, such as: CrTiF5,1 CrVF5,1 MnCrF5,17 CdMnF5.9 All known examples of pentafluorides with two paramagnetic sites are limited to early transition metals, late transition metal pentafluorides have not been reported.
To date, no pentafluorides with a paramagnetic transition metal (TM) ion in the trivalent state (TMIII) have been documented within the AgIITMF5 series. Only AgAuF5, which exhibits Au in its low-spin diamagnetic trivalent state (AuIII), has been postulated18 to be isostructural with the triclinic CuAuF5 homolog. Further investigation of Ag–TM–F phases identified four compounds that may exhibit magnetic interactions between divalent silver (AgII) and transition metals (TM). These compounds include AgMnIVF6,19 which is characterized by a Curie–Weiss constant of −66 K, and others such as AgRhIVF6,20 AgRuVF721 and AgIrVF7.21 However, the exact crystal structures of the Mn and Rh analogs and a detailed elucidation of the magnetic behavior of all compounds are still unresolved. This knowledge gap has initiated theoretical investigations of the magnetic coupling mechanisms between Ag and paramagnetic transition metals in possible fluoride systems.22–24 Remarkably, significant inter-metal magnetic superexchange constants of −45.9 meV for Ag–CuII and −33.3 meV for Ag–NiII22 systems have been calculated in theoretical AgTMF4 models (with TM = Cu or Ni). The question naturally arises whether other TM/AgII systems with even stronger magnetic interactions can be prepared.
In this study, we present a new member of the mixed-valence transition dimetal fluorides – AgCoF5. The precursors of this compound – AgF2 and CoF3, exhibit antiferromagnetic behavior below 163 K25 and 460 K,26 respectively. AgF2 is a 2D antiferromagnet,27 while CoF3 has a G-type antiferromagnetic structure.26,28 Of these two binary fluorides, AgF2 is recognized as a high temperature superconductor (HTSC) precursor,27,29,30 which has recently led to extensive investigations into its possible doping.31–38
In this paper, the crystal structure, magnetic, and electronic properties of AgCoF5 are described and supported by theoretical analysis.
AgF2 + CoF3 → AgCoF5 | (1) |
In our next experimental approach, we investigated the potential for the formation of a structure with mutual miscibility at the positions of metal atoms, similar to the observed behavior in AgF2/CuF2 mixtures.24 To investigate this, we started the synthesis with a mixture of AgF2 and CoF2 at a molar ratio of 0.7:0.3 under the same conditions as in the first approach (eqn (1)). Upon XRD analysis, we identified the presence of two distinct phases in the final product: AgCoF5 and AgF2 (sample S2), with the respective near equimolar ratio (0.44:0.56) determined by Rietveld refinement (see Fig. SI2 in the ESI‡). Crucially, our measurements revealed no change in the Néel temperature (TN) for AgF2, which remained at 163 K.
Given that the volume of the phases identified as AgCoF5 and AgF2 in the second approach practically coincides with the volume assigned in the first experiment (eqn (1), and also refer to Table SI1 in the ESI‡), we assume that solubility of the cations or partial mutual substitution at the corresponding cation sites24 is unlikely under these conditions. This assertion is also supported by the large differences in atomic radii between CoIII (R = 88.5 pm) and AgII (R = 108 pm).
Fig. 1 Powder XRD pattern for S1 (black line): mainly AgCoF5 (96%) with traces of AgF2 (4%), next to the refined model (red) and the fitted background (as black dashed line). The black markers indicate reflex positions for the AgF2 and AgCoF5 model phases for the Co Kα1 line. The differential profile is marked in orange (see also Fig. SI1 in ESI‡). |
Formula | AgCoF5 |
Crystal system | Monoclinic |
Space group (number) | C2/c (15) |
a, b, c [Å] | 7.274414 (2), 7.627744 (2), 7.529471 (2) |
α = γ, β [°] | 90, 115.976(4) |
Z | 4 |
V [Å3] | 375.580 (19) |
Temperature, radiation type, range | 298 K, Co Kα, 7°–100° of 2Θ |
Fit parameters | GOF = 1.66%, Rp = 1.12%, wRp = 1.68% |
Considering the final structure of AgCoF5, we also performed comparative analysis between space group C2/c (Z = 4) and its counterpart C2/m (Z = 2). The presence of a two-fold axis (C2) is observed in both groups. However, the distinct structural variations emerge from the different orientation of the symmetry plane in relation to this axis. In particular, in the monoclinic C2/c space group, the symmetry plane is oriented perpendicular to the binary axis. In the C2/m space group, on the other hand, the arrangement is such that the symmetry plane is aligned parallel to the two-fold axis. The result of this orientation of the symmetry plane is the presence of Co–F–Co chains without any tilting (bond angle of 180 degrees), with larger interatomic distances of the metal sites along the c axis compared to the C2/c type (check Fig. SI4 in ESI‡). This symmetry is quite uncommon, as none of the AIIBIIIF5 compounds exhibit it (see Section I. in ESI‡). Nevertheless, a comparative analysis of both structural forms was performed to clarify the final structure of AgCoF5. The structure of AgCoF5 in both proposed structural solutions is detailed in the ESI,‡ where a comprehensive analysis of its features is also provided.
We have also performed a comparative computational analysis of the ground state (GS) energies and dynamic stability for both structural solutions. Our calculations demonstrate that the C2/c space group is energetically more favorable, with an energy lower by 4.51 meV per f.u. compared to C2/m (DFT+U).
Moreover, the latter displays dynamic instability, evidenced by three imaginary phonon branches, while the former has no imaginary phonons (see ESI‡ for detailed information).
Indeed, if the C2/m space group is assumed for the Rietveld refinement procedure using the experimental diffraction pattern, it proves to be insufficient for the description the AgCoF5 structure. First, it leads to absence of several reflections – in particular at 45.7, 52.1, 52.7, 58.2 of 2θ, which are observable in the experimental data (but present for the C2/c space group), and (2) the fitting parameters are much worse to those obtained for the C2/c model (see Table SI5 and Fig. SI3 in the ESI‡). This led us to conclude that the C2/c space group accurately represents the crystal structure of the AgCoF5 compound.
The key structural information of AgCoF5 (C2/c) from the Rietveld refinement is presented in the Table 1. Further details are provided in Table SI2.‡
The experimentally determined parameters of the AgCoF5 unit cell were compared with the theoretical values from calculations, and the data are shown in Table SI3.‡ The best agreement between the Rietveld method and the theoretical values is observed for the DFT+U (UAg = 5 eV) and HSE06 methods, where calculations slightly underestimate and overestimate AgCoF5 volume by 0.07% and 0.34%, respectively. For DFT+U (U = 8 eV), the volume of the unit cell is underestimated more – by 1.36%. However, the largest discrepancy is observed with the SCAN method – the volume is by 1.87% larger than experimental data.
The intermetallic distances between the paramagnetic centers are defined by the lattice vectors. Specifically, the interatomic Ag–Co distance along the a-axis is determined to be 3.814(10) Å, while the corresponding distance along the b-axis is 3.637(10) Å. The nearest Co–Co and Ag–Ag contacts oriented along [100], appear as 3.765(10) Å (more detailed and theoretical data are explained in Table SI4‡). The fluorine atoms are the completing elements of the structure. They act as important bridging elements linking metal ions, thus creating a distinct network of metal–fluorine bonds and playing a crucial role in the magnetic properties of the compound.
A salient structural motif in the C2/c AgCoF5 framework comprises alternating Co–F–Co chains and Ag–F–Ag rectangles aligned along the c-axis – [001] direction (Fig. 2) in the (010) plane. The bond angles in these Co–F–Co chains are less than 180° and the tilt is determined to be 162.0(3)°. In contrast, there are no chain-like Ag–F–Ag connections. Along the c crystallographic axis, the Ag–F bonds are generally the longest, as shown in Fig. 4B. The Ag⋯Ag connections are bridged by two fluorine atoms along [001] and form a rectangle with an Ag–F–Ag angle of 107.6(5)°. These fluorine atoms simultaneously form covalent bonds with cobalt atoms, creating a composite structural network. Orthogonal to the Co–F–Co chains is a rectangular lattice of paramagnetic centers – silver and cobalt (001), which are bridged by fluorine atoms. The Ag–F–Co bonds have a corrugated arrangement; their angles are 158.9(12)° along the [010] direction and 127.9(8)° along the [100] direction (Fig. 2 and 3). All angles determined using theoretical and experimental methods are summarized in Table SI4 in the ESI.‡
Fig. 2 Structure of AgCoF5. Color code: grey for silver, blue for cobalt and green for fluorine atoms. |
Fig. 3 Projections of the AgCoF5 structure, from left: along c axis (001), centre – along the b axis (010) and right – along the a axis (100). Colour code: grey for silver, blue for cobalt and green for fluorine atoms. For further details see Table SI4 in the ESI.‡ |
Fig. 4 The first coordination sphere for (A) cobalt and (B) silver, both with CN = 6. The M–F bonds lengths are expressed in Å, following Rietveld refinement. |
The first coordination sphere of cobalt forms a distorted octahedral configuration (CN = 6), as presented in Fig. 4A. Such as distortion is also observed in CoF3 and can be attributed to the Jahn–Teller effect, which applies to the high-spin d6 electronic configuration.28 This distortion in AgCoF5 is manifested by the presence of three distinct sets of Co–F bond lengths: 2 × 1.827(16) Å, 2 × 1.905(6) Å, and 2 × 1.921(13) Å. The elongation of these bonds is aligned along specific crystallographic axes, with the longest Co–F bond along the [100] direction, the second longest along [001], and the shortest along the [010] b-axis. A comparative analysis of the computational data, derived from density functional theory augmented with Hubbard U (DFT+U), and the Rietveld refinement results reveal a general agreement with the observed trend (ESI, Table SI4‡).
In the primary coordination environment, the silver atoms exhibit a configuration that deviates strongly from the ideal octahedral symmetry (CN = 6), as can be seen in Fig. 4B. This distortion, which is similar to that found in pure AgF2, is primarily attributed to the pronounced Jahn–Teller effect, which is a characteristic feature of the d9 electron configuration of divalent silver.25 The manifestation of this effect is evident in the three distinct categories of Ag–F bond lengths within the coordination sphere: two bonds with a length of 2.052(16) Å [010], two others of 2.090(16) Å [100] and the last pair with 2.562(16) Å [001]. The computational methods provide closely matched results with a maximum deviation of 1.77% between experimental and theoretical Ag–F bond lengths in the (001) plane (HSE06 functional; for all methods see Table SI4‡).
The structural properties of AgCoF5 described above have a profound influence on the vibrational spectra of this compound (phonons) as well as its magnetic and electronic properties. Let us take a look at the phonons.
Fig. 5 shows comparison of the experimental IR and Raman spectra for AgCoF5 (lines) with the theoretical positions of the bands (dashed). The assignment of the observed band positions in the spectra shown (Fig. 5), along with their theoretical positions and symmetry (based on DFT+U calculations), is presented in Table SI6 in the ESI.‡
Fig. 5 The Raman spectrum (red line) and the infrared absorption spectrum (black line) together with the positions of the phonon vibrations based on DFT+U calculations (red and black dashes) (for exact positions see Table SI6‡). An extended range for Raman spectroscopy measurement is shown in the upper right corner of the image. |
In general, we find a very good agreement between the vibrational positions for the AgCoF5 lattice as predicted by computational methods and the positions in the experimental spectra. This is evidenced by a high correlation coefficient R2 = 0.9976 (Fig. 6). In addition, the wavenumbers of the translational (acoustic) modes are calculated with an error of ±2 cm−1, suggesting that the positions of other vibrations may have similarly small deviations (Table SI6‡). Overall, we succeeded to assign 12 out of 15 Raman-active modes (with the exception of one Ag vibration calculated at 534 cm−1 and two low-frequency modes that fall below our bottom experimental range). Also, we assigned 9 out of 12 IR-active modes (with two absent Bu vibrations calculated at 303 cm−1 and 165 cm−1, and one falling below our experimental range). Their absence in the spectra could be due to the low intensity of the corresponding bands or/and too much background noise.
Fig. 6 Correlation between experimental and theoretical positions for bands observed in the spectra. For exact band positions from IR and Raman spectra, cf. Table SI6 in the ESI.‡ |
Fig. 7 Magnetic susceptibility χ of the sample at 10 kOe. For FC regime −dχ/dT vs. T shown in the inset. |
Fig. 7 displays the magnetic susceptibility χ(T) of the sample, measured from 2 to 300 K under both zero-field-cooled (ZFC) and field-cooled (FC) conditions at 10 kOe. The magnetic behavior of the sample is rather complex, however, based on the maximum value of −dχ/dT (FC) we determined three transition temperatures: two associated with AgCoF5, T1 = 128 K and T2 = 3–9 K (depending on the applied field, see Fig. SI5 in ESI‡) and one for AgF2 with TN = 163 K. Between the temperatures of 300 K and 163 K, a decrease in magnetization with temperature is observed. This could indicate the existence of short-range antiferromagnetic (AFM) ordering in AgCoF5 in this temperature range, similar to that observed in KAgF3.43 On the other hand, the ordering at T2 is unspecific, as it may originate from a minute amount of any ferromagnetic impurities.
Below the transition temperature (128 K), a noticeable divergence in the temperature-dependent behavior of the magnetic susceptibility between the zero-field-cooled (ZFC) and field-cooled (FC) regimes can be observed. A similar feature is seen in pure AgF2 samples (see Fig. SI6‡), where the weak ferromagnetism below the Néel temperature (TN) is related to the spin-canting of silver(II), due to the Dzyaloshinskii–Moriya interaction.44,45 A similar explanation for the weak ferromagnetism of AgCoF5 below 128 K can be postulated. It should be noted that the canting of Ag2+ is likely to be more pronounced than that of Co3+, as the former exhibits a stronger spin–orbit coupling. In the structure of AgCoF5, the magnetic interactions within the square spin lattice parallel to the (001) plane are limited to the silver and cobalt atoms. In contrast, the interactions along the [001] direction are predominantly limited to homoatomic contacts, especially between two silver sites, and are similar to interlayer contacts observed in AgF2 (Fig. 3).
In addition, the presence of AgF2 traces with AgCoF5 in S1 can be used for comparison purposes. Thus, a significant difference in the magnetic transition widths between AgF2 and AgCoF5 is evident (see inset in Fig. 7). The significantly wider transition in AgCoF5 in contrast to AgF2, could be due to the existence of additional magnetic transitions in AgCoF5 and/or to differences in the dimensionality of the magnetic ordering for both compounds. Silver(II) difluoride is identified as a two-dimensional (2D) antiferromagnet, exhibiting an exchange constant close to −70 meV in the [AgF4] layers;27,33 this leads to a sharp transition at 163 K, evidenced by a distinct peak in the −dχ/dT versus T plot (see inset in Fig. 7). In the following, we focus on the M(H) dependence of the sample (S1).
Fig. 8 shows the M(H) curve for sample S1. We observe hysteresis loops at temperatures of 1.8 K, 50 K, and 130 K. The coercivity (Hc) varies with temperature and reaches 1060 Oe at 1.8 K, 4132 Oe at 50 K, 2116 Oe at 100 K, 1402 Oe at 130 K and drops to 11 Oe at 180 K. Therefore, in the observed magnetic transition at 128 K (see Fig. 7 and Fig. SI5 in ESI‡), as evidenced by the broad feature in magnetic susceptibility, a nonzero coercivity is discernible above 128 K, particularly at 130 K, and the phenomenon disappears only at temperatures close to 180 K. Furthermore, the remanence magnetization is strongly temperature-dependent, with values of 12 emu mol−1 at 1.8 K, 24 emu mol−1 at 50 K, 22 emu mol−1 at 100 K, and approximately 10 emu mol−1 at 130 K. Beyond the last transition point observed in the M(T) dependence of the sample (163 K for AgF2 traces), the M(H) curve becomes linear without coercivity (measurements at 180 K and 250 K, see also ESI‡). These results agree with the magnetic susceptibility measurements and indicate a weak ferromagnetic character of the sample at low temperatures. However, since magnetic saturation was not reached even at lowest applied temperature under the maximum applied magnetic field of 70 kOe, this indicates that spin canting may be at the origin of weak ferromagnetism (as in AgF2) or ferrimagnetism.
Fig. 8 Magnetization curves at 1.8 K, 100 K, 130 K and 250 K for S1 as a function of the applied field for fields up to 1000 Oe. The curves for the extended temperature range and the applied magnetic fields are listed in the ESI.‡ |
The magnetic behavior of AgCoF5 may be related to that of structurally analogous compounds. Several mixed-valent paramagnetic transition metal pentafluorides with the C2/c structure have been documented1,2,9 (see Section I. in ESI‡). Homometallic compounds such as Mn2F5 and Cr2F5 have been shown to be antiferromagnets by magnetic susceptibility measurements below 53 K2 and 30 K,1 respectively. For the heteroatomic compound MnCrF5 an antiferromagnetic order below 6 K was observed.17 However, for CrTiF5 and CrVF5, the ferrimagnetism was observed below 26 K1 and 40 K,1 respectively. This is attributed to the 3d1 and 3d2 configurations for TiIII and VIII ions and to the simultaneous 3d4 configuration of CrII. Therefore, the different electronic configurations of 3d6 HS-CoIII and 4d9 AgII, suggest the possibility of ferrimagnetism of AgCoF5 (Table 2).
Compound | T t [K] | Magnetic nature/GSa |
---|---|---|
n.d. – not defined.a AF – antiferromagnetic, Fi – ferrimagnetic.b This work.c Depending on the field applied (ESI‡). | ||
Mn2F52 | 53.4 | AF |
Cr2F51 | 40 | AF |
CrTiF51 | 26 | Fi |
CrVF51 | 40 | Fi |
MnCrF517 | 6 | AF |
CdMnF59 | n.d. | n.d. |
AgCoF5b | T N = 128, T2 = 3–9c | Complex behavior (most likely Fi) |
The complex magnetic behavior of the AgCoF5 compound necessitates a more comprehensive characterization. Techniques such as muon spin resonance spectroscopy or neutron diffraction, supported by quantum mechanical calculations in a non-collinear model and with explicit inclusion of spin–orbit coupling, should be employed. While these measurements and calculations remain to be performed in the future, we have conducted a preliminary analysis of the magnetic superexchange (SE) constants.
The exchange coupling constants were calculated using the Heisenberg Hamiltonian formalism based on the energy calculations of the respective spin configurations (see Fig. SI8 in ESI‡) within the broken symmetry method. We have determined the five closest metal contacts – both between silver and cobalt (Jb1, Ja2, Jc4), as well as the homoatomic ones (Jc3, J5). A detailed description of the SE paths is shown presented in Fig. SI8 in ESI.‡ The determined values of the superexchange (SE) constants obtained from DFT+U calculations (for UAg = 5 and 8 eV), SCAN and HSE06 methods are listed in the table below. A negative value indicates antiferromagnetic ordering between the spins, while a positive values indicate ferromagnetic ordering. In the context of magnetic interaction strength, we mainly refer to the absolute values of the particular constant describing the interactions, denoted as |J|.
Analyzing the differences in the calculated values for relevant superexchange constants between diverse methods, the largest discrepancies are observed for Jb1(Co–Ag). This situation is likely not only a result of differences in the exchange–correlation functionals employed, but also stems from the variations in the geometry of the systems obtained during optimization by each method – specifically, the distances between the paramagnetic centers and the angle of the bond formed through fluorine. All these parameters together with the SE constants, are listed in Table 3 for all the methods used. Recently, however, we have shown that among various exchange–correlation (XC) functionals, the SCAN method provides the best agreement between experimental and theoretical J2D value for AgF2, with an error margin of only 4%.33 Therefore, we assume here −62 meV as a reliable value for Jb1(Co–Ag) and restrict ourselves to the SCAN results in the following analysis.
Direction | Parameter | DFT+U (UAg = 5 eV) | DFT+U (UAg = 8 eV) | SCAN | HSE06 |
---|---|---|---|---|---|
[010] | J b1(Co–Ag) [meV] | −47.7 | −39.3 | −62.0 | −39.5 |
d [Å] | 3.822 | 3.803 | 3.874 | 3.831 | |
Angle [°] | 158.9 | 158.6 | 164.1 | 159.6 | |
[100] | J a2(Co–Ag) [meV] | −6.5 | −6.5 | −4.8 | −6.7 |
d [Å] | 3.593 | 3.579 | 3.635 | 3.600 | |
Angle [°] | 127.9 | 127.7 | 130.1 | 129.1 | |
[001] | J c3(Co–Co) [meV] | −8.3 | −8.2 | −10.3 | −8.0 |
d [Å] | 3.768 | 3.754 | 3.793 | 3.763 | |
Angle [°] | 158.9 | 158.9 | 162.4 | 160.2 | |
[001] | J c4(Ag–Ag) [meV] | −1.1 | −0.4 | −1.3 | +0.7 |
d [Å] | 3.768 | 3.754 | 3.793 | 3.763 | |
Angle [°] | 107.9 | 108.4 | 109.1 | 106.9 | |
[101] | J 5(Ag–Co) [meV] | −1.2 | −1.4 | −1.9 | −0.5 |
d [Å] | 3.961 | 3.943 | 3.915 | 3.967 | |
Angle [°] | 121.3 | 121.1 | 120.7 | 121.3 |
According to all the theoretical methods used, the ground state of AgCoF5 is antiferromagnetic with a quasi-G-type magnetic structure (as illustrated in the Fig. 9), which means that the antiferromagnetic exchange occurs between all six corner-sharing metal centers. In addition, Cr2F5, which has the same crystal structure as the compound discussed in this work, has a magnetic structure identical to that determined here for AgCoF5, as previously suggested.46 However, the specific values of the superexchange constants (SE) for Cr2F5 have not yet been determined.
Fig. 9 The G-type antiferromagnetic structure, calculated as the magnetic ground state for AgCoF5. A comprehensive description of the superexchange paths and all spin configurations considered can be found in the Fig. SI8 in the ESI.‡ |
In the rectangular lattice along the ab plane, we identified two SE constants: Jb1 and Ja2, both for heteroatomic (Ag–Co) magnetic interactions. The most important SE constant, labelled as Jb1(Co–Ag), is related to the Co–Ag interaction along the b-axis [010] via an F bridge. Its value from the SCAN method is −62.02 meV (Table 3). Since the Co–F–Ag bond angle along [010] is 164.1° (SCAN), the observation of a relatively strong antiferromagnetic exchange along this SE path is rather expected in line with the GKA (Goodenough–Kanamori–Anderson) rules.47–49 This interaction encompasses the eg electrons of Co S = 4/2 (high-spin) and Ag S = 1/2 cations, since the magnetic moments for these paramagnetic sites have been computed as 3.22μB and 0.58μB (DFT+U), respectively (as for typical HS-Co3+28 and d9 Ag2+,33,50 see Table SI8 in ESI‡). The subsequent SE constant in the rectangular lattice within the (001) plane, which describes the strength of the Co–Ag interaction along the [100] direction (Ja2(Co–Ag)), appears to be considerably weaker than the dominant interaction. The SCAN method gives the value of −4.8 meV. The Co–F–Ag angle along the a-axis is 130.1° (SCAN) and thus deviates significantly from 180°, which considerably weakens the antiferromagnetic interaction.
For Co–F–Co chains along [001], the superexchange is stronger than for Co–F–Ag (−10.3 meV). The other two exchange constants, Jc4(Ag–Ag) and J5(Ag–Co), are significantly weaker and show negative values. Our results are similar to those for isostructural Cr2F5, where Monte Carlo simulations suggested that the three strongest superexchange (SE) constants should be negative, indicating of antiferromagnetic ordering between the spins, while the other two constants are significantly weaker.46
The study of the SE constants in AgCoF5 clearly shows a pronounced anisotropy of these interactions. It was demonstrated that the interaction characterized by Jb1(Ag–Co) is considerably more robust than the other two, which are described as Ja2(Co–Ag) and Jc3(Co–Co). To assess the extent of this anisotropy, one can calculate the ratio J′/J′′, where J′′ represents the constant with the highest absolute value – in this case Jb1(Ag–Co), and J′ as that of Ja2(Co–Ag) or Jc3(Co–Co). The most significant anisotropy is evident in the SCAN results. Considering the constant J′ as the constant describing the interaction between S = 4/2 (CoIII) and S = 1/2 (AgII), the ratio is 7.69 × 10−2 (J′ = Ja2(Co–Ag)). For the SE constant, which describes the interaction between two cobalt ions (both S = 4/2), the ratio is 1.66 × 10−1 (J′ = Jc3(Co–Co)). The results for all methods are shown in the Table 4.
Method | J′/J′′ ratio | |
---|---|---|
J′ = Ja2(Co–Ag) | J′ = Jc3(Co–Co) | |
DFT+U (UAg = 5 eV) | 1.37 × 10−1 | 1.73 × 10−1 |
DFT+U (UAg = 8 eV) | 1.66 × 10−1 | 2.09 × 10−1 |
SCAN | 7.69 × 10−2 | 1.66 × 10−1 |
HSE06 | 1.71 × 10−1 | 2.02 × 10−1 |
The J′/J′′ ratios calculated in our study are significantly higher than those typically found in nearly ideal 1D antiferromagnets. For instance, in FeF3(4,4′-bpy), where superexchange (SE) occurs along the Fe–F–Fe (S = 5/2) chains, the J′/J′′ ratio is less than 3.2 × 10−5.51 This tendency can also be observed for ternary compounds with AgII and F, such as KAgF3 (2.1 × 10−2).43 Additionally, a similar ratio was also found for the quasi-1D magnet Bi2Fe(SeO3)2OCl3, where J′/J′′ is equal to 8.0 × 10−2.52 It is important to note that in all these compounds the chains are either completely or quasi-isolated, in contrast to AgCoF5, which has a 3D network of metal–ligand–metal bonds.
All this together suggests that AgCoF5 does not exhibit characteristics of a canonical one-dimensional (1D) antiferromagnet, but rather should be classified as a quasi-three-dimensional (3D) antiferromagnet with significant magnetic anisotropy within the rectangular mixed spin lattice (along ab) (J′ and J′′ < J1D by around 10−1). In view of this, one can tentatively assign the observed transition at 128 K to the onset of antiparallel alignment of the Co and Ag spins along the crystallographic b-axis.
Analysis of spin density for the ground state magnetic solution (Fig. 10) shows that there is substantial spin polarization on F atoms, which constitute key intermediaries of the superexchange.
Fig. 11 Density of states for AgCoF5 calculated with the DFT+U method (UCo is equal to 5 eV). For orbital resolved DOS only the d states of Co are shown, for Ag – only d(x2−y2). |
AgIIF2 + MIIIF3 → AgIIMIIIF5 | (2) |
dG = GAgMF5 − GAgF2 − GMF3 | (3) |
dV = VAgMF5 − VAgF2 − VMF3. | (4) |
MIII | dG [eV mol−1] | dE [kJ mol−1] | dV [Å3] | Mag. mom. [μB] | |
---|---|---|---|---|---|
Ag | MIII | ||||
a Structure of CuF3 not known experimentally but provisionally assumed to be isostructural with that of FeF3, as suggested by recent calculations.4 | |||||
Ag | −0.09 | −8.21 | 6.24 | ±0.82 | ±0.49 |
Cua | −0.06 | −5.97 | 5.97 | ±0.54 | ±1.06 |
Co | −0.03 | −3.25 | 5.25 | ±0.58 | ±3.22 |
Fe | 0.06 | 5.83 | 4.71 | ±0.59 | ±4.32 |
Ni | 0.06 | 6.07 | 4.36 | ±0.65 | ±1.01 |
Ga | 0.12 | 11.89 | 4.96 | +0.51 | ±0.01 |
Al | 0.21 | 20.28 | 2.92 | ±0.65 | ±0.03 |
Sc | 0.26 | 24.63 | 2.00 | ±0.51 | ±0.03 |
Au | 0.26 | 25.40 | 3.08 | ±0.56 | ±1.01 |
We found that only in three cases, the enthalpy (eqn (3)) of bimetallic pentafluoride formation was negative: for the already mentioned AgCoF5 and for two hypothetical phases – AgCuF5 and AgIIAgIIIF5. In the case of AgCuF5, for calculations of eqn (3) and (4) we adapted theoretically predicted CuF3 structure.4 Moreover, the latest experimental approach in the HT solid state reaction of CuF2/AgF2 mixtures with F2 overpressure revealed in the formation of AgII/CuII–F solid solutions without oxidation to CuIII fluoride.24 For these reasons, the significance of this result is somewhat diminished.
However, the case of AgIIAgIIIF5 is exceptionally interesting for three reasons: (i) it contains two powerful oxidizers, AgII and AgIII, simultaneously in its structure; (ii) it has two paramagnetic centers – Ag2+(d9) and HS-Ag3+(d8) and (iii) a compound with this stoichiometry has already been prepared. However, the structure produced is not monoclinic but triclinic and it contains LS-AgIII.3
This raises the question of the relative energetic stability of these two polytypes – the hypothetical monoclinic C2/c and the synthesized triclinic P. Our preliminary DFT+U calculations indicate that the C2/c structure is slightly more energetically favorable by 21 meV per f.u. (including Zero-Point Energy, ZPE) compared to the (P) structure type. Moreover, the most significant superexchange (SE) constants between S = 1/2 (d9) and S = 1 (d8) silver sites (J2D) in the ab plane, calculated for the monoclinic AgIIAgIIIF5 structure are at −100 meV and for two AgIII sites around −93 meV (DFT+U, UAg = 5 eV). A further description of this new hypothetical polymorphic form of a known compound is beyond the scope of this paper and will be explored elsewhere. It suffices to say that the theory suggests the existence of an AgIIAgIIIF5 phase with HS-AgIII that is analogous to the prepared AgIICoIIIF5.
Finally, we experimentally verified the reactions between NiF2, GaF3, and FeF3 separately with AgF2. Under conditions corresponding to those of the successful synthesis of AgCoF5, no formation of new phases was observed – the powder contained only the unreacted substrates after annealing at high temperature. Therefore, the theory seems to accurately describe the lack of energetic preference for the formation of AgNiF5 (starting from NiF3), AgGaF5 and AgFeF5.
For an accurate description of the magnetic properties of the compound, the application of more sophisticated methods, such as muon and neutron techniques, would be essential. In addition, obtaining the compound in the form of single crystals would significantly improve the possibilities of determining the magnetic structure of the titled compound, especially for measurements related to specific crystallographic axes. Experiments to grow single crystals will be carried out in the future.
Furthermore, based on theoretical calculations, we have indicated the possibility of the existence of a mixed-valence compound AgIIAgIIIF5 with HS-AgIII (C2/c). Here, the calculated predominant SE constant J2D value is −100 meV (DFT+U). It is worthwhile to investigate this fascinating system by experiments.
The IR spectra were recorded with a Vertex 80v spectrometer from Bruker. A small amount of the powder was placed under dry argon between the HDPE windows and tightly closed in the measurement cell.
Footnotes |
† Dedicated to Prof. Boris Žemva in memoriam. |
‡ Electronic supplementary information (ESI) available: Overview of the AIIBIIIF5 fluoride family, structural and magnetochemical data, and phonon spectra for title compound. CCDC 2332918 (AgCoF5). For ESI and crystallographic data in CIF or other electronic format see DOI: https://doi.org/10.1039/d4dt00419a |
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