Magnetic Properties of the Distorted KagomÃ© Lattice Mn3(1,2,4-(O2C

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Magnetic Properties of the Distorted Kagomé Lattice Mn3(1,2,4(O2C)3C6H3)2 Richard A. Mole,*,†,‡ Stephen Greene,§ Paul F. Henry,⊥,# Simon M. Humphrey,§,∇ Kirrily C. Rule,† Tobias Unruh,∥,○ Gerald F. Weldon,§ Dehong Yu,† John A. Stride,†,‡ and Paul T. Wood*,§ †

Australian Nuclear Science and Technology Organisation, Locked Bag 2001, Kirrawee DC, NSW 2225, Australia Department of Chemistry, University of New South Wales, Sydney, NSW 2052, Australia § Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, U.K. ∥ Heinz Maier Leibnitz Zenturm, Technische Universitaet Muenchen, Lichtenbergstrasse 1, Garching 85747, Germany ⊥ Institut Laue-Langevin, CS 20156, F-38042 Grenoble Cedex 9, France # The ISIS Facility, STFC Rutherford Appleton Laboratory, Harwell Campus, Didcot OX11 0QX, U.K. ∇ Department of Chemistry, University of Texas at Austin, Welch Hall 2.204, 105E. 24th Street A5300, Austin, Texas 78712-1224, United States ○ Chair for Crystallography and Structural Physics, Physics Department, University of Erlangen-Nürnberg, 91058 Erlangen, Germany ‡

S Supporting Information *

ABSTRACT: Kagomé lattice types have been of intense interest as idealized examples of extended frustrated spin systems. Here we demonstrate how the use of neutron diffraction and inelastic neutron scattering coupled with spin wave theory calculations can be used to elucidate the complex magnetic interactions of extended spin networks. We show that the magnetic properties of the coordination polymer Mn3(1,2,4-(O2C)3C6H3)2, a highly distorted kagomé lattice, have been erroneously characterized as a canted antiferromagnet in previous works. Our results demonstrate that, although the magnetic structure is ferrimagnetic, with a net magnetic moment, frustration persists in the system. We conclude by showing that the conventions of the Goodenough−Kanamori rules, which are often applied to similar magnetic exchange interactions, are not relevant in this case.

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INTRODUCTION The study of the magnetic properties of coordination polymers and the associated structure−property relationships is a wellestablished field in chemistry. Work in this area has resulted in the discovery of new one-dimensional materials,1 frustrated materials, 2 and ferromagnetic materials.3 Many of the compounds reported are of interest to condensed matter physics, where they can be used as model materials to study quantum mechanics.4 One class of materials that has attracted intense research attention among both the chemistry and physics communities is that of the kagomé lattice systems.5 The ability to synthesize disorder-free, structurally perfect kagomé systems has been identified as a target for inorganic chemistry for years.6−9 Much of this intense research has been driven by the observation of unusal quantum effects10 and the potential relation to the resonating valence bond (RVB) phase postulated for superconducting cuprate ceramics.11 Inorganic chemistry has a key role to play, as the synthesis of new materials will widen the available range of materials to observe the physical properties resulting from frustration; it has also been extensively shown that synthetic inorganic chemistry can outperform mineralogical © 2017 American Chemical Society

samples, many of which are plagued by nonstoichiometry issues and structural differences or defects.5 Rather than focusing on the ideal kagomé lattice, we examined in detail the structure and magnetic properties of a highly distorted kagomé system. This is also an active field with other work looking at the distorted kagomé structure in volborthite,7 which shows a spin glass state and the effect of crystallographic disorder on the properties of perfect kagomé lattices in natural minerals. The study of the magnetic properties of novel molecule-based magnetic materials is frequently done using bulk properties such as susceptibility and specific heat. While these techniques are easily accessible, they do contain a limited quantity of information and are sometimes over and/or misinterpreted. Inelastic neutron scattering12 is a complementary technique that can directly access the energy scale as well as spatial information. Within the chemical sciences this is frequently used as a tool to determine the diffusion of molecular species,13 while within molecular magnetism it is common to determine the energy Received: March 6, 2017 Published: June 22, 2017 7851

DOI: 10.1021/acs.inorgchem.7b00597 Inorg. Chem. 2017, 56, 7851−7860

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Figure 1. (top left) Extended asymmetric unit of 1. (top right) Packing diagram showing the separation between layers. (lower left) Section within the layer showing only the metal ions and the carboxylate bridges. The exchange interactions are highlighted. In the two top figures the following color scheme is used: Mn red, O light blue, C dark blue, and H white, while in the lower figure Mn1 and Mn2 are distinguished by red (Mn1) and magenta (Mn2) coloring.

splitting of single molecule magnets in zero field14as well as the spatial variation being used to determine the nature of the magnetic wave functions.15 Similar analysis is possible on extended networks that undergo transitions to long-range magnetic order; however, this relies on the application of linear spin wave theory.16 Until recently the use of spin wave theories was more the domain of the solid-state physicist; however, software has now become available that makes these theoretical methods easy to calculate for arbitrary lattices with low symmetry.17 The advantage of this is that for molecule-based magnetic materials, which frequently have low symmetry due to the packing of the organic ligands, the spin wave spectrum can be calculated along high-symmetry directions, but more importantly it can be straightforwardly powder averaged and thus easily compared with experimental data. This can negate the need for significant investments in crystal growth efforts.18 Spin waves can be directly measured using inelastic neutron scattering. This has several practical advantages; first, it is typically measured in zero field, so the underlying Hamiltonian is much simpler, as all Zeeman terms can be omitted; second, the momentum transfer ensures that spatially relevant information is recorded. At the practical level this means that the specific length scales of interactions can be determined because of their observed Q dependence. The title compound has been reported previously19 along with some preliminary magnetic properties. The magnetic exchange topology has been identified as a distorted kagomé lattice; however, some of the originally reported magnetic

properties have little credence but have however been well-cited despite this. Here we report our own synthesis, structure, magnetic properties, neutron diffraction, and inelastic neutron scattering of Mn3(1,2,4-(O2C)3C6H3)2, 1.

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EXPERIMENTAL SECTION

A large powder sample of Mn3(1,2,4-(O2C)3C6H3)2 was prepared by the following method. MnCl2·4H2O (0.149 g, 0.753 mmol) was added to a solution of 1,2,4-benzenetricarboxylic acid (0.105 g, 0.500 mmol) in aqueous 0.3 M NaOH (5 cm3), water (2 cm3) was added, and the resulting solution was stirred and heated for 40 h at 180 °C under autogenous pressure. After it cooled for 6 h, Mn3(1,2,4-(O2C)3C6H3)2 (1) was isolated by filtration as small brown crystals (53 mg, 37%), before being washed with diethyl ether. This is similar to the synthesis reported elsewhere in the literature.19 Magnetic susceptibility data were measured using a Quantum Design MPMS 5 magnetometer; powder was packed into a gelatin capsule, and susceptibility data were acquired in the temperature range from 5 to 60 K using 50, 100, and 500 Oe measuring fields. Isothermal magnetization was also collected at 2 and 12 K. The samples were corrected for diamagnetism using Pascal’s constants.20 Neutron diffraction was measured on a 2.5 g sample using the instrument D20 at the Institut Laue-Langevin, France.21 Note that, for both this and the inelastic neutron scattering experiments, no attempt at deuteration was made, and a fully hydrogenous sample was used. A wavelength of 2.42 Å was used. The sample was held in a cylindrical vanadium can, placed in an “Orange” cryostat, and cooled to 1.8 K. Diffraction patterns were obtained at intermediate temperatures between 1.8 and 16 K. Data were analyzed using the GSAS suite of 7852


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K−1 and a Weiss constant of −47.3(1) K (Figure 2). The product χT reduces as the temperature is lowered, reaching a

programs,22 while the magnetic structures were calculated using the SARAh representational analysis software.23 Inelastic neutron scattering was measured on the same 2.5 g sample of 1. Initially data were collected using the multichopper time-of-flight spectrometer TOFTOF24 at the Maier Leibnitz Zentrum using 3 Å neutrons, giving a resolution of 0.47 meV at the elastic line, while further data were collected using the PELICAN crystal monochromator time-of-flight spectrometer25 at ANSTO using neutrons with wavelengths of 6 and 4.75 Å, which afforded resolutions at the elastic lines of 0.065 and 0.135 meV, respectively. In all cases the data had a measurement of an empty can subtracted and were normalized to a vanadium standard before being transformed to S(Q,ω). All data manipulations were performed using the Large Array Manipulation Program (LAMP).26 Data were collected at 4.4 and 20 K using the TOFTOF spectrometer, with additional data collected at 4.5 K using PELICAN. Calculations of the spin wave dispersion were performed using a semiclassical method using the SpinW software.17

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RESULTS Structure. The structure of 1 has been reported previously, and our own X-ray structure is in agreement with that already published;19 so, here we describe only those aspects of the structure that are of interest to understanding the magnetic behavior of 1. Compound 1 crystallizes in the space group P21/n and contains two crystallographically distinct Mn(II) ions. Mn1 lies on the general 4e Wyckoff position, while Mn2 is on the 2a site, which is a center of inversion. The coordination environment of Mn2 contains six oxygen atoms from the ligand in a slightly distorted octahedral geometry. Mn1 is also coordinated to six ligand oxygen atoms, but the distortion away from octahedral is much greater and is perhaps better described as distorted trigonal prismatic. The carboxylate in the 1-position chelates Mn1, while one oxygen is also bonded in an anti fashion to a different Mn1, and the other is bonded in an anti fashion to a Mn2, Mn1, and Mn1a, respectively. The carboxylate in the 4position bridges Mn1 and Mn2 in a syn−syn fashion. The packing is shown in Figure 1, and this shows that the Mn ions form buckled layers that are separated by the ligand. One layer is bonded to the 1- and 2-positions on the ligand, and the other is bonded to the 4-position. This results in a large inter-layer separation. Considering the structure within the layers, the carboxylates in the 1 and 2 positions provide single-atom oxygen bridges between all three of the Mn ions in the asymmetric unit, and these would be expected to provide the strongest exchange interactions. The magnetic topology considering only these interactions is shown in Figure 1 and forms a distorted kagomé lattice consisting of the Mn3 triangles with two Mn1 and one Mn2. Each side of the triangle is of different length (3.3500(9), 3.7929(13), and 4.0932(9) Å); the Mn−O−Mn bond angles are 97.93(15)°, 130.90(16)°, and 112.31(16)°. Thus, if the interactions between Mn ions are predominantly antiferromagnetic, the triangular motifs within the lattice would be expected to lead to geometric frustration. However, the scalene nature of these triangles is likely to lead to unequal interactions along each edge, and hence the degree of frustration would be lowered. Magnetic Susceptibility. The magnetic susceptibility is very similar to those reported previously. Given that we have come to significantly different conclusions to the original report, we present our results fully here, to complement those already in the literature. The magnetic behavior of 1 follows Curie−Weiss behavior down to ca. 50 K with a Curie constant of 14.0(3) cm3 mol−1

Figure 2. Temperature dependence of the inverse susceptibility of 1. The red line is a fit to the Curie−Weiss law.

minimum at 28 K, at which point its value is 6.31 cm3 K mol−1 (Figure 3). When cooled further, χT rises slowly at first and

Figure 3. Plot of χT vs T for 1 in varying fields.

more steeply below ca. 14 K. The field dependence of the magnetization shows a rapid increase on increasing the applied field from zero. Subsequent increases in the applied field cause only a moderate further increase in the magnetization, which reaches a value of 2300 Oe cm3 mol−1 by 5 T but does not saturate. This corresponds to a net moment of 4.1 μB mol−1. A small hysteresis is observed at 2 K, with a coercive field of 100 Oe (Figure 4). The Curie constant is close to the predicted value of 13.125 cm3 mol−1 K−1 for 3 × S = 5/2; alternatively, this could be interpreted as having g = 2.07, marginally above the range commonly observed for Mn(II) compounds. It is of note that this is significantly lower than that previously reported in the literature of g = 2.21, which would imply a much greater spin anisotropy. We interpret the negative Weiss constant as being indicative of antiferromagnetic coupling between spins, while the minimum in χT is consistent with the bulk properties being that of a ferrimagnet. Similarly the rapid increase is consistent 7853


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Figure 5. Rietveld refinement of the magnetic neutron diffraction of compound 1 obtained by subtracting the 16 K data from the 1.8 K data resulting in the removal of all structural Bragg reflections; the dip in the background at low 2θ is due to the loss of paramagnetic scattering on ordering. Red crosses are the observed data; the green line is the calculated diffraction pattern; the black tick marks indicate the calculated positions of the Bragg reflections; the magenta line is the difference between the observed and calculated diffraction patterns.

Figure 4. Isothermal magnetization curves for 1 in the low-field region. (inset) Expanded field range for the isothermal magnetization (color scheme, units, and axis labels the same for body and inset).

with either a ferro or ferrimagnetic behavior, while the moment of 4.1 μB mol−1 would be indicative of a ferrimagnetic behavior whereby the Mn atoms on the two different sites lie antiparallel to each other. Originally the hysteresis and reduced moment were interpreted as being typical of a canted antiferromagnet. This was an unusual interpretation given the size of the canted moment and that the hysteresis does not have the usual fieldsuppressed form of a conventional canted antiferromagnet; the interpretation as a ferrimagnet that we favor in this work appears more conventional. To a first approximation mean field theory (MFT) can be used to determine the average value of the exchange interactions. The appropriate form of MFT gives27

Θ=

Landau theory29 suggests that, since only one transition to longrange order is observed and both sites are anticipated to be isotropic, both Mn sites should order with the same propagation vector. Thus, only Γ1 and Γ3 need be considered. All possible combinations were however tried, and the best fit is when both sites have Γ3 symmetry. The best-fit magnetic difference pattern is shown in Figure 5. The orientation of the magnetic moments was optimized, and this showed that the magnetic moments preferred to align along a unique direction. Such behavior could be interpreted as a single ion anisotropy effecthowever, there is no relation between the orientation of the magnetic moment and the coordination environment of the magnetic ions. Examination of the magnetic structure (Figure 6) shows that the net structure is a ferrimagnet consistent with our interpretation of the magnetization. The spins lie broadly (but not exactly) perpendicular to the buckled kagomé layers; as there is no significant anisotropy of the Mn2+ ion, it is assumed that this structure is a compromise one, caused by the three-dimensional (3D) arrangement of the spins in the layer. Further evidence for this lies in the fact that the moment orientation is not related to that of the coordination sphere of the Mn ions. The structure is such that the interaction between Mn1 and Mn2 shows a clear antiferromagnetic alignment, while that between Mn1 and Mn1 shows a coparallel or ferromagnetic alignment. The net result is a ferrimagnet with one uncompensated Mn spin. Inelastic Neutron Scattering. The inelastic neutron scattering data are summarized in Figure 7. Initial inspection of the inelastic neutron scattering from TOFTOF data at 4.4 K revealed information-rich spectra, with excitations that varied as a function of both Q and energy but decreased in intensity as a function of Q. Such behavior is indicative of magnons, propagating magnetic excitations that are analogous to phonons in the case of vibrations. Data collected at 20 K (Figure 8), above the transition to long-range order, shows a large structureless feature, typical of a classical spin liquid. The PELICAN data were only collected at low temperature, but, as with the TOFTOF data, these displayed rich spectra, with numerous excitations observed in the two instrument configurations (which cover different energy and Q ranges and

2S(S + 1)zJ 3kB

Where S is the spin on the ion (S = 5/2 for octahedral Mn2+), z is the number of nearest neighbors, and J is the magnitude of the superexchange. This yields a coupling constant J = −2.02 K (for z = 4). This is certainly a very crude approach, as it neglects the structural anisotropy of the exchange lattice and averages the number of nearest-neighbor spins; however, it provides us with a magnitude for the coupling. Neutron Diffraction. Initial inspection of the data revealed additional peaks at 1.8 K, which were not observed at 16 K (Figure 5). Given the temperature and 2θ dependence, these were identified as magnetic Bragg peaks. The first temperature at which these were observed was 14.3 K, indicating that the rapid rise in χT at this temperature is actually a transition to long-range order. Attempts to solve the magnetic structure were made using representational analysis.22,28 The additional Bragg reflections could be indexed with a propagation vector of k = (0,0,0), meaning that the magnetic cell is the same size as the nuclear unit cell; antiferromagnetic structures are allowed, as there are two different Mn sites in the asymmetric unit. Group theory calculations show that there are four irreducible representations for the Mn1 site and two for the Mn2 site. The appropriate decomposition of the magnetic representation is then as follows: ΓMn(1) = 3Γ1 + 3Γ2 + 3Γ3 + 3Γ4 ΓMn(2) = 3Γ1 + 3Γ3 7854


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can wash out the Q dependent information, a signal highly dependent on both the hydrogen content and the sample geometry. However, the current experiments go further in displaying a complex spectrum with clear dispersion and Q dependence, despite the incoherent scattering contribution of six H atoms per formula unit. As such this again highlights that this technique is accessible to the inorganic chemist, and in this case with a large moment on the Mn2+ ion, there is no need for complex and time-consuming deuteration. It is relatively easy to obtain the inelastic data shown in Figure 7; however, calculating it has been fairly difficult and certainly a nonroutine process. In the current paper we use the freely available SpinW code,17 which is straightforward to use. The input parameters for the calculations are simply the atomic coordinates of the magnetic ions and the connectivity between those ions. The following general Hamiltonian was used for the spin wave calculation, and the magnetic exchange topology is shown in Figure 9: / = −∑ Si 1ijSj + i,j

∑ SiAiSi + B ∑ giSi i

i

In this Hamiltonian both isotropic and anisotropic exchange are included in the exchange tensor Jij, while the single-ion anisotropy is covered by the vector Ai. Any external field is given by the vector B. It is of note that neutron scattering does not require the application of a magnetic fieldnor typically does it preclude it. In the case of zero field (B = 0) measurements we are thus probing the simplest possible Hamiltonian. In the Supporting Information we include a step-by-step guide as to how the spin wave calculation was developed, starting from the position of the metal atoms and which terms could be included in the spin wave calculation. The exchange topology used is that of the distorted kagomé lattice from the original report, along with the possibility of anisotropic exchange for every exchange interaction and single ion anisotropy for each metal site. The first step in calculating the spin wave spectrum is to optimize the magnetic structure for the given exchange interactions. The orientation of the moment is highly dependent on the values of the exchange interactions. For the final values chosen the orientation of the magnetic moment agrees with that previously determined by neutron diffraction. Different values of the exchange interactions were tried systematicallynote that it is not possible to perform a least-squares refinement of the powder averaged dispersion curve to the observed parameters. The best reproduction of the data shown in Figure 7 (left-hand panels) convoluted with the appropriate resolution function for the data. A very good reproduction of the data (Figure 7, righthand panels) was obtained for J1 = J2 = −0.4 meV (= −4.6 K = −3.2 cm−1) and J3 = −0.1 meV (= −1.2 K = −0.8 cm−1), while no anisotropy term was required. The following are the key features of the calculated spectra that are well-reproduced in the observed data:

Figure 6. (top) Magnetic structure of 1 between the kagomé layers. (bottom) Magnetic structure of 1 within the kagomé layers. The red and purple circles represent Mn atoms on sites 1 and 2, respectively, while the black lines show the strongest expected exchange between Mn atoms. The box indicates the magnetic (and crystallographic) unit cell.

different resolutions). The description and modeling of this complex system is discussed in detail in the next section. In all cases rich spectra were observed; however, these can be reduced to four key features. At 6 Å and clearly shown in Figure 7 is a dispersive excitation that starts from the origin and extends to 1 meV. Second, there is a dispersive feature at 2 meV. Third, there is a higher energy excitation at 4 meV. Finally in all data sets the high Q regions shows a cluster of nondispersive modes between 1 and 2 Å−1.

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DISCUSSION First, note that both neutron diffraction and inelastic neutron scattering were performed on a fully hydrogenous sample. There are numerous reasons to do this varying from the expense of deuteration, as is the case here, to evidence that both physical and chemical properties can be modified on deuteration. Further, incomplete deuteration can lead to other issues such as crystallographic disorder. Such effects have been investigated in detail for neutron diffraction,30 while for the specific case of inelastic neutron scattering from single molecule magnets (SMMs)31 it was reported that the effect of hydrogenation

1. In the 3 Å TOFTOF data there is a large triangle-shaped mode with a vertex at Q = 1 Å−1, 2 meV energy transfer. Expanding to a horizontal edge at 4 meV energy transfer. 2. In both the 4.75 and 6 Å PELICAN data, a low-energy acoustic mode is observed, with a maximum at 1 meV. 3. In the 6 Å PELICAN data the high Q low-energy region is predicted to be two separate modes. 7855


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Figure 7. (top left) INS data from TOFTOF at 4 K, using 3 Å neutrons. (top right) Simulation of the model described in the text for the region covered by TOTOF with a 0.5 meV Gaussian resolution convoluted. (middle left) INS data from PELICAN with 4.75 Å neutrons at 4 K. (right) Same simulations covering the PELICAN accessible region with a 0.135 meV resolution. (bottom left) INS data from PELICAN with 6 Å neutrons at 4 K. (right) Same simulations covering the PELICAN accessible region with a 0.065 meV Gaussian resolution.

both spectrometers (Figure 10). The four peaks that can be seen in the model correspond to spin waves at the zone boundaries; the ones at 1 and 1.5 meV are well-reproduced, while that measured at 0.8 meV is predicted slightly lower in energy at 0.64 meV. The upper band at over 2 meV, only visible in the TOFTOF data, is well-reproduced, although we do not see a sharp peak in the data, this could be a lifetime broadening effect (see below). One clear difference between the data and the models presented in Figure 7 is that the highest-resolution data have features that are clearly broader in energy than the energy resolution. This is likely because the peaks are intrinsically broadened by the sample, as the energy width of the excitations is inversely proportional to the lifetime of the excitations. This

4. An intermediate energy acoustic mode gives rise to an arch between 1.5 and 2 meV. This is evident in the 4.75 Å PELICAN data. 5. At high Q (above Q = 1.5 Å −1) there is a flat mode at 1.5 meV, which is clearly observed in the 4.75 Å PELICAN data. 6. No intensity is predicted at Q = 1.2 Å−1, 1.75 meV in the 4.75 Å data and 3 Å TOFTOF data. 7. Between E = 0 and 1 meV at Q = 1.2 Å −1, there is a large, intense, structured feature. This is present to varying degrees in all of the reported data. The presentation of data in false color plots can be misleading, so we also integrated the model and the data in the Q range 1 < Q < 1.5 Å−1 and overlaid this with the data from 7856


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Figure 8. INS data at 20 K from TOFTOF using 3 Å neutrons. The excitations are clearly absent, and there is only a broad region of intensity typical of a classical spin liquid.

Figure 10. Comparison of inelastic neutron scattering data with the model, all data and models are integrated over the Q range 1 < Q < 1.5 Å−1: Black points, PELICAN data obtained using 6 Å neutrons. Blue data, TOFTOF data obtained using 3 Å neutrons. Red line model described in the text in the same Q range.

though the antiferromagnetic nature of all the exchange interactions indicates a degree of frustration must be present. Now that the value of these exchange interactions has been determined by spin wave theory, we are in a position to relate these back to the crystal structure and comment on the observed structure−property relationships. The final values of the exchange interactions along with the Mn−Mn distances and Mn−O−Mn angles are listed in Table 1. Table 1

J1 J2 J3

Figure 9. Magnetic exchange topology used to calculate the spin wave dispersion of 1. The structure is viewed along the crystallographic a axis for the unit cell in P21/c. Note that this is plotted in a different setting of the space group to the structural figures, as the spinW software does not allow for nonstandard space group settingsdetails are given in the Supporting Information.

Mn−Mn distance

Mn−O−Mn angle

J, meV

J, K

J, cm−1

3.3500(9) 3.7929(13) 4.0932(9)

97.93(15) 130.90(16) 112.31(16)

−0.4 meV −0.4 meV −0.1 meV

−4.6 K −4.6 K −1.2 K

−3.2 −3.2 −0.8

These highlight that there is no clear trend between Mn−Mn distance and Mn−O−Mn angle. The relative strength of superexchange interactions mediated via one-atom bridges are often analyzed using the Goodenough−Kanamori rules. It is worth noting here that these results go against this logic, where one anticipates the closer to 90° the angle is, the stronger the antiferromagnetic character. The results of linear spin wave theory show that in this case of exchange mediated via a oneatom carboxylate bridge, this trend is not followed. Though such a simple analysis ignores the fact that the coordination geometries of the two Mn ions are very different, to fully account for the changes in superexchange as a function of both the bridging modes and the coordination environment would require a calculation of the electronic structure, which is beyond the scope of the current paper. As the spin wave spectrum gives spatial information, the predicted spectrum is very sensitive to which exchange interaction is which, so if a more conventional arrangement of J1 = −0.4 meV, J2 = −0.1 meV, and J3 = −0.4 meV is used a very different spectrum is predicted. To prove the sensitivity of the technique we also calculated the spin wave spectrum for the case of J3 = +0.1 meV, which would remove the requirement for frustration. Again, a completely different spin wave spectrum is then predicted. We also investigated the inclusion of anisotropy; this has two effects. First, to obtain the

means that the excitations are short-lived relative to the resolution. As spin waves are known to vary in lifetime throughout the Brillouin zone, it would be very difficult to model this with the current data. To extract this information a single-crystal sample would be required. To confirm that this model is correct we performed additional simulations, where anisotropic exchange, single-ion anisotropy, or ferromagnetic exchange interactions were introduced. In all cases this resulted in at least one of the above not being reproduced in the model (see details below). Thus, on the basis of the magnetization, the neutron diffraction results, and the inelastic neutron scattering experiment, we are confident that there is no evidence of a Dzialozhinsky−Moriya (DM) interaction and that the behavior can be described by an isotropic spin with three antiferromagnetic exchange interactions; the unequal magnitude of these gives rise to the ferrimagnetic structure observed with neutron diffraction, 7857


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Inorganic Chemistry predicted structure, the anisotropy axis must be chosen to be exactly that predicted by the magnetic structure; this in itself is questionable. Second, in the inelastic spectrum a gap is predicted at the point where the acoustic modes meet the elastic line. No such gap is observed, even with the highestresolution data obtained using 6 Å neutrons with a resolution at the elastic line of 0.065 meV. A gap could potentially be obscured by nonmagnetic effects such as phonons or a weak quasielastic (QENS) signal, although comparing the elastic line width at Q = 0.5 Å−1, free from Bragg reflections with the Q = 1 Å−1 position, broadened due to phonons originating from Bragg reflections, allows an upper limit of 0.09 meV to be placed on the anisotropy. These additional calculations are all summarized in Figure 11. The fact that all three exchange interactions are antiferromagnetic and any anisotropy is beyond the resolution of the current measurements allows us to comment on the observation of frustrated behavior in this material. A highly frustrated material has been, slightly arbitrarily, defined as one that has a degree of frustration f = θ/Tn > 10.32 The original alternating current (ac) susceptibility revealed a strong dynamic response below the ordering temperature. The original discussion19 of this was related to the DM term and the possibility of having umbrella modes, as have been seen in potassium iron jarosite. However, our comprehensive investigation of the Hamiltonian using inelastic neutron scattering has shown that this is an isotropic system with partially compensated frustration. Thus, the most likely cause of this unusual out-of-phase behavior is probably due to enhanced spin fluctuations below the long-range ordering transition temperature. The latter is raised due to the partial compensation of the frustration. These ideas are outside the scope of the current paper and will be covered in further work. Of the many key results of this investigation, one is that the predicted magnetic structure is ferrimagnetic, but also that all three exchange interactions are antiferromagnetic. Thus, the weak overall magnetic moment can be explained, while the fundamental requirements for magnetic frustration persist.

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CONCLUSIONS We have shown that 1 is a complex magnetic material worthy of further study. The current paper has highlighted the limitations of simple techniques such as susceptibility to determine complex magnetic behavior. We have also shown that inelastic neutron scattering is a key tool to be able to study these complex magnetic materials. In the current work we studied the relatively straightforward Mn2+ ion, which can often be treated in a semiclassical fashion. The conclusion that 1 is actually a ferrimagnet could be made from the susceptibilityhowever, we have shown that in this case with very simple modeling techniques we can accurately probe a complex Hamiltonian. As the Hamiltonian used is as generic as possible this work highlights that this method could readily be transferred to more complex ions such as octahedral Co2+, which often have complex, yet highly intriguing, magnetic properties. There are several key conclusions of this work. In contrast to previous reports of the compound being a canted antiferromagnet, we have shown that it is in fact a ferrimagnet. The original rationale for canting was due to anisotropy caused by the distorted coordination environments of the two Mn2+ sites giving rise to a DM term. We have shown that this is not the case; in particular, a good reproduction of the inelastic neutron scattering data can be made without including any single-ion anisotropy or anisotropic exchange interactions.

Figure 11. (top) Calculated S(Q,w) for the final values J1 = −0.4 meV, J2 = −0.4 meV, J3 = −0.1 meV. Second row, for the unfrustrated system J1 = −0.4 meV, J2 = −0.4 meV, J3 = 0.1 meV. Third for the similar arrangement J1 = −0.4 meV, J2 = −0.1 meV, J3 = −0.4 meV. (bottom) For the arrangement J1 = −0.4 meV, J2 = −0.4 meV, J3 = −0.1 meV, D = −0.01 meV.

This has one important consequence for coordination chemists looking for magnetostructural correlations; even though the Mn2+ ion is distorted it does not give rise to significant anisotropy. In addition significant care should be taken when considering applying exotic models to rationalize the susceptibility. 7858


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Inorganic Chemistry

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However, the original conclusion that this complex may be of interest as a kagomé antiferromagnet still holds. Short-range magnetic correlations are observed up to 20 K, significantly above the magnetic ordering temperature. The exact nature of these correlations will be covered in a further publication. Finally we have shown that inelastic neutron scattering has come of age for the magnetochemist; this work did not involve a large, deuterated single crystal but a modest quantity of hydrogenous powder. The analysis is readily accessible to any chemist with knowledge of the structure of the material at hand. The general nature of the model applied means that the limiting cases of models that are often applied (Kambe vector coupling etc.) have removed these restrictions and that genuine structure−property relationships can be extracted.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.7b00597. Spin wave calculations using spinW, illustrated structures, spin wave dispersion plot, power averaged spectrum (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. (R.A.M.) *E-mail: [email protected]. (P.T.W.) ORCID

Richard A. Mole: 0000-0001-5018-4221 Simon M. Humphrey: 0000-0001-5379-4623 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS R.A.M. acknowledges UNSW for a visiting fellowship. J.S. acknowledges the John Yu Fellowship. R.A.M., G.F.W., and S.M.H. acknowledge the U.K. EPSRC for funding. All authors thank the Australian Centre for Neutron Scattering, the Institut Laue-Langevin, and the Maier Leibnitz Zentrum (MLZ) for access to neutron scattering facilities and technical help. Access to neutron scattering at the MLZ was funded via the European Commission under the seventh Framework Program through the “Research Infrastructures” action of the “Capacities” Program, Contract No. CP-CSA_INFRA-2008-1.1.1 No. 226507-N MI3.

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REFERENCES

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Magnetic Properties of the Distorted KagomÃ© Lattice Mn3(1,2,4-(O2C

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