Bichalcogenide Model Systems for Magnetic Chains with Variable

Jun 25, 2019 - To develop an understanding of the magnetism on one-dimensional lattices, one of the great challenges is to identify novel model system...
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Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX

Bichalcogenide Model Systems for Magnetic Chains with Variable Spin Sizes and Optional Crystallographic Inversion Symmetry Martin Valldor* and Ryan Morrow

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Leibniz Institute for Solid State and Materials Research, Helmholtzstraße 20, DE-01069 Dresden, Germany ABSTRACT: To develop an understanding of the magnetism on onedimensional lattices, one of the great challenges is to identify novel model systems with enough chemical flexibility to design the magnetic interactions in measurable samples. To contribute to this endeavor, we present a number of bichalcogenides with similar trigonal packing of magnetic chains. These chains consist of 3d transition-metal (TM) ions that are 6-fold-coordinated by S or Se. Each TM coordination can be described as a trigonally distorted octahedron that shares faces with two neighboring octahedra. A unique ability with these model systems is that an entity with electric polarity can be introduced between the chains that causes the TM ions in the chains to shift to polar positions, thereby allowing for magnetoelectric coupling. By a comparison of the macroscopic data of polar and nonpolar chains with either S = 1 or S = 3/2, it is obvious that the magnetic properties are affected by the indirect electric polarity from the entity between the chains.

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THE CHALLENGE Experiments are done to simulate and understand processes in nature and how they depend on different physical parameters, such as temperature and pressure. With those fundamental experimental results, it is possible to discern trends and parameter proportionalities, which often can be described by mathematical functions. By manipulation of these functions, a manifold of theoretical predictions emerges. However, nature is usually more complex and only rarely allows any of its parameters to be tuned as variables in functions. Hence, to connect between theory and experiment, we rely on so-called “model systems” that (i) experimentally can be realized, (ii) possess several tunable parameters, and (iii) are as similar as possible to a theoretical situation. Magnetism in one-dimensional (1D) chains is one outstanding area for theoretical work on crystalline solid-state matter. The low dimension of the magnetic lattice makes the theoretical description relatively simple by assuming that no interactions are perpendicular to the chain, i.e., between chains. On a truly 1D magnetic lattice, there cannot be any long-range spin order above absolute zero, as stated by Mermin and Wagner,1 but there are other magnetic phenomena that reveal how nature acts when the number of parameters is narrowed down. In the simplest description of a magnetic chain, every link has only one unpaired electron (S = 1/2) because this allows for the assumption that the electron−electron interaction at each link in the theoretical description is subordinate; the interaction between links (along the chain) will be more important for macroscopic magnetic phenomena. There are a few S = 1/2 chain model systems in the literature, of which CuCl2(pyr)2 (pyr = pyridine),2 KCuF3,3 and Sr2CuO34 probably are most prominent. If the magnetic interaction (J) along the chain is strong enough, the typical Curie paramagnetic behavior is partly replaced by a broad, © XXXX American Chemical Society

domelike maximum in the temperature-dependent magnetic susceptibility. According to Bonner and Fisher, this maximum for S = 1/2 centers at a temperature that is proportional to J.5 Also, des Cloizeaux and Pearson were able to find a theoretical description of the spin excitation spectrum (dispersion) of the S = 1/2 spin chain,6 which was later extended for situations with external magnetic fields.7 Ideally, a spin chain should be a spin liquid, i.e., no long-range spin order but with residual magnetic entropy at T = 0 K. However, because of finite interchain magnetic couplings, almost all real cases deviate from spin-liquid behavior at lower temperatures. A deviation from high-temperature paramagnetic behavior of a magnetic S = 1/2 chain is also realized in CuGeO3, and below 14 K, structural details indicate a phase transition that turns a homogeneous S = 1/2 chain into spin dimers.8 This dimer formation of magnetic spins is called a spin-Peierls transition, named after theoretician Peierls,9 and consists of local singlets but without long-range spin order. By simply increasing the spin size to S = 1 (two unpaired electrons) at each link in the magnetic chain, the properties change drastically; at low temperatures, the magnetic state is described by thermal population of excited spin states, also without long-range spin order. These phenomena are included in the Haldane gap physics,10 which, in comparison to the S = 1 /2 chains, is describing gapped spin ground states without breaking translational symmetry, i.e., no dimer formation. Only very few compounds exhibit such magnetic behavior, for example, Ni(C2H8N2)2NO2(ClO4)11 and NiSpecial Issue: Paradigm Shifts in Magnetism: From Molecules to Materials Received: March 1, 2019

A

DOI: 10.1021/acs.inorgchem.9b00610 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry Table 1. List of Three Groups of Structurally Related Compounds Containing Similar 3d TM Chainsa general formula

composition

Niggli notation

oxidation state

S

a [Å]

c [Å]

space group

1

ref

La3WTMS3O6

La3WVS3O6 La3WCrS3O6 La3WMnS3O6 La3WFeS3O6 La3WCoS3O6 La3WNiS3O6 Ba3V2S4O3 Ba3VCrS4O3 La4MnS6O La4MnSe6O La4FeSe6O

La3[WO6]1∞[VS6/2] La3[WO6]1∞[CrS6/2] La3[WO6]1∞[MnS6/2] La3[WO6]1∞[FeS6/2] La3[WO6]1∞[CoS6/2] La3[WO6]1∞[NiS6/2] Ba3[VSO3]1∞[VS6/2] Ba3[VSO3]1∞[CrS6/2] La3[LaS3O]1∞[MnS6/2] La3[LaSe3O]1∞[MnSe6/2] La3[LaSe3O]1∞[FeSe6/2]

3+ 3+ 3+ 3+ 3+ 3+? 3+ 3+ 2+ 2+ 2+

1 3 /2 2 5 /2 0 3 /2? 1 3 /2 5 /2 5 /2 2

9.46076(3) 9.442(2) 9.493(1) 9.4896(6) 9.4710(6) 9.4996(7) 10.1661(1) 10.1374(2) 9.4766(6) 9.7596(3) 9.7388(4)

5.51809(2) 5.506(2) 5.518(1) 5.4918(6) 5.4721(7) 5.4518(8) 5.9306(4) 5.9268(2) 6.8246(6) 7.0722(4) 7.0512(5)

P63/m P63/m P63/m P63/m P63/m P63/m P63 P63 P63mc P63mc P63mc

yes yes yes yes yes yes no no no no no

21 22 22 22 22 22 23 24 25 25 25

Ba3VTMS4O3 La4TMCh6O

a

TM = transition metal in chain, Ch = chalcogen, Ox. = expected oxidation state of TM, S = the expected spin size without orbital contributions, a and c = hexagonal unit cell axes sizes, where a = the distance between chains and c/2 the distance between TMs.

(C5H14N2)2N3(PF6),12 because several of the claimed Haldane compounds possess intrinsic complications, including distorted spin chains and competing, nontrivial superexchange interactions. Obviously, an understanding of S = 1 magnetic chains also would benefit from further physical examples of compounds with a simpler lattice topology. Spin chains not only exhibit unique magnetic properties but also are ideal for investigating magnetic contributions to heat transport; in crystalline materials with spin chains magnons and spinon topological excitations might add significantly to the fundamental phonon heat conductivity in the direction of the spin chain (see, for example, ref 13). Theory has even predicted that, by energy current conservation, magnetic heat transport can be frictionless (or ballistic) in spin- 1 / 2 Heisenberg spin chains.14 This unconventional magnetic mode of heat transport was observed in the SrCuO 2 compound.15 To understand the influence of the spin size, S, on the magnetic behavior and thermal conductivity of a spin chain, we need a model system with chemical flexibility. Only a very few compounds allow for this flexibility without major, conjunctive changes in crystallography and more. One candidate model system is ATMMoO4 (A = Na, K, Cd, Pb; TM = Cu, Mn, Fe, Co, Zn),16 and its crystal structure has chains of octahedrally coordinated TM ions, where TM can be either Cu2+ (S = 1/2), Mn2+ (S = 5/2), Fe2+ (S = 2), Co2+ (S = 3/2), or diamagnetic Zn2+. Unfortunately, ATMMoO4 is not truly a 1D system because all reported compositions with magnetic ions exhibit long-range magnetic order at low temperatures,17 revealing significant interchain magnetic interactions. It should also be noted that local properties, like the distribution of electrons among the d orbitals on a TM, add further complexity to the theoretical description by involving single-ion anisotropy18 and Jahn−Teller distortions.19 However, these local effects have not been taken into account in this brief introduction to the challenge at hand: to find a physical magnetic-chain model system having a favorably straightforward theoretical description.

chain, should be almost identical in all cases within the model system. However, the matrix around the chain might differ slightly as long as stacking of the chains remains the same and the interchain distance is similar in the related compounds and large enough to allow for the chains to be treated as single entities. To simplify the presentation of the following compounds, the Niggli notation20 will be used when writing the chemical formulas. In Table 1, a group of compounds are listed according to their general formulas, known compositions, respective Niggli notation, and further relevant parameters that can be used for further comparisons. In all listed compounds, the crystal structure is hexagonal and the magnetic ions (TMs) are situated on the unique axis: at (0, 0, z) and (0, 0, z + 0.5), thus constituting magnetic chains that are packed hexagonally (Figure 1). By symmetry, this magnetic chain is presented by a single TM position, making the theoretical description relatively simple. TM is always 6-fold-coordinated by S (or Se) in trigonally distorted octahedra (Figure 2), which share faces with the next two octahedra along the chain. Thus, each S (or Se) in the chain is shared by two TMs. The relatively large distance between the chains (equal to the hexagonal a axis) weakens the magnetic interchain interactions, and their trigonal stacking (pink triangles in Figure 1) allows for magnetic decoupling of the chains by geometric frustration, if the chain-to-chain interaction is antiferromagnetic. These three compound groups (Table 1) obviously exhibit advantageous chemical flexibilities, and there are still several unexplored compositions. The spin-to-spin interactions along the chains should be dominating the magnetic properties because the distances between the magnetic chains are sizable (at least 9 Å), and geometric frustration possibly decouples the magnetic chains. However, most importantly and uniquely, the magnetic chains can be designed to possess or lack inversion symmetry: P63/m is centrosymmetric, while P63 and P63mc are not. This has an influence on the position of the TM in the magnetic chain. In the centrosymmetric compound (P63/m), there is only one TM−S distance and TM is situated at the barycenter of the trigonal antiprism of S (Figure 2). Because of the electric polarity of the [VSO3] entity, having V5+ moved away from the coordination barycenter by the larger S2− compared to O2−, TM is slightly shifted in the opposite direction to compensate for the electric polarity in the crystal. Similarly, the [LaS3O] tetrahedron has one of its vertices pointing along the chain, invoking a strong electric polarity that is compensated for by TM in the chain. This results in two

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NOVEL BICHALCOGENIDE MAGNETIC-CHAIN SYSTEMS To find a novel 1D magnetic model system with vast chemical flexibility, knowledge about closely related bichalcogenide systems gives further possibilities. Important to remember during the search is that the wanted magnetic lattice, here the B

DOI: 10.1021/acs.inorgchem.9b00610 Inorg. Chem. XXXX, XXX, XXX−XXX

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Figure 1. Hexagonal packings of similar magnetic chains (face-sharing octahedra) in the three related compound groups (Table 1). Some Ba and La atoms have been omitted for clarity. The polyhedral entities between the chains are shown and account for the different space-group symmetries. The crystallographic unit cells are drawn with thin black lines, while the hexagonal a axis and geometric frustration between chains are marked in pink.

Figure 2. Side views of the magnetic chains (dashed line) of an example compound from each of the three compound groups. Emphasized is the nature of the interchain entity and its influence on the TM−S distances. The polar entities result in two different TM−S distances. Ch is either S or Se.

Figure 3. Temperature-dependent magnetic susceptibility of centrosymmetric compared to noncentrosymmetric magnetic chains of two different spin sizes. Lm is the measured “long moment”. The presented data originate from refs 21, 24, and 28.

TM−S distances that differ by about 0.3 Å (Figure 2), which is equal to the largest difference in the Ti−O distances in ferroelectric BaTiO3.26 Hence, TM coordination in the noncentrosymmetric compounds (Table 1) is very strongly polar. Any magnetic spin on TM is prone to couple to the polarity, i.e., the electric-field gradient, and a magnetoelectric coupling might evolve, as described by Dzyaloshinsky and Moriya.27 These effects add to the spin-to-spin interactions and cause preferences for noncollinear spin orientations, e.g., helices and spirals, with rare and complex spin excitation spectra. Naturally, the TM−TM distance (c/2) and the TM−S (Se)−TM angle along the chain are important for the spin-tospin direct and superexchange interactions, respectively. For the latter interaction, the centrosymmetric compounds have only a single angle, while the noncentrosymmetric compounds have two different angles. So far, strong antiferromagnetic interactions are observed along the chains, but a clear trend between the distances, angles, and magnetic properties can only be recognized when more data are at hand.

In most of the original publications on the compounds in Table 1, there are no magnetic data.22,23,25 However, in the more recent works, the magnetism has been studied.21,24,28 Some of the data are shown in Figure 3 as comparisons between magnetic chains of two different spin sizes (S = 1 and 3 /2) with (P63/m) and without (P63) inversion symmetry. First, only in one case (S = 1, P63/m) is a Curie-like paramagnetism present; all other data deviate from the paramagnetic behavior even at the highest temperatures (300 K), indicating strong spin−spin interactions already above room temperature. Corresponding specific heat measurements (not shown here) reveal no obvious phase transitions, neither structural nor magnetic, in the temperature range 2−300 K.21,24,28 Despite a lack of obvious phase transitions, several magnetic anomalies in temperature-dependent magnetic susceptibilities (Figure 3) can be described as very broad maxima, signaling strong magnetic interactions on lowdimensional lattices. Generally, all systems investigated so far by magnetometry seem to act as true magnetic chains with C

DOI: 10.1021/acs.inorgchem.9b00610 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

data (above 2 K) on this model system indicate true 1D magnetism because there is no long-range spin order.

strong intrachain magnetic interactions but without long-range spin orderings, at least above 2 K. To completely understand all magnetic anomalies of the magnetic chains, more data are required, preferably from local probes, such as NMR, muon spin resonance (μSR), and, if TM = Fe, Mö ssbauer spectroscopy. However, it is obvious that the presence or lack of crystallographic inversion symmetry does have an influence on the magnetic chain, underlining the importance of the here-presented model systems for further investigations.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Fax: +49-351-4659-313. ORCID

Martin Valldor: 0000-0001-7061-3492 Ryan Morrow: 0000-0001-9986-3049

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Author Contributions

NEAR-FUTURE INVESTIGATIONS Naturally, the chemical flexibility at the TM site has to be fully explored. Especially, a quantum spin (S = 1/2) system has to be found, like Cu2+, Ti3+, and Sc2+ or a low-spin state of Mn2+, Fe3+, or Co2+. The low-spin states are not far-fetched in these systems because a low spin of Co3+ (S = 0) was observed.24 Next to substitutions on the TM site, S can possibly be substituted for Se in the first and second compound groups, as was already successfully done in the third (Table 1). The choice of heavier chalcogen has a large influence on the bonding nature along the chain; Se will form more covalent bonding compared to S, which changes the magnetic coupling strength in the chain. Also, introducing Se might enhance the electronic conductivity and some of the magnetic moments could be lost due to delocalized electrons. In extreme cases, this might lead to metallic behavior and Pauli paramagnetism with weakly positive temperature-independent magnetic susceptibility. Although the local magnetic moments might be lost, a 1D metal is prone to exhibit interesting properties, but that belongs to another type of research area. Any successful single-crystal growth will be rewarding because the properties are expected to be strongly anisotropic as a consequence of the magnetic chains. Here, it is necessary to issue a warning: naturally grown crystals of the noncentrosymmetric compound are likely to contain inversion twin domains, which has to be taken into account when interpreting measured physical properties. However, if a singledomain single crystal of a noncentrosymmetric magnetic chain can be obtained, it would be possible to test the theoretical proposition that the magnetic part of the thermal conductivity exhibits a diode-like behavior as a result of broken inversion symmetry.29 That would be a first-time observation indeed. Even with a drastic change in the chemistry by substituting chalcogenide ion S2− for halogenide ion Cl−, it is possible to obtain the centrosymmetric compound but with completely empty chains in La3WO6Cl3 (P63/m, with Niggli notation La3[WO6]1∞[ΔCl6/2], where Δ = vacancy).30 Partial substitution of S for Cl might be a further possibility of these systems to increase their chemical flexibility and their adherence to material design. For further reading about magnetism on the 1D lattice, we recommend the review of Mikeska and Kolezhuk31 as well as that of Birgeneau and Shirane,32 with their excellent referencing of earlier works.

Both authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Xenophon Zotos for fruitful discussions on the thermal conductivity in 1D magnets. This work was financially supported by the German Science Foundation through Project VA831-4/1. R.M. acknowledges support from the Alexander von Humboldt Foundation.

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REFERENCES

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CONCLUSIONS A highly promising model system for 1D magnetism on chains has been identified, having also the unique ability to be designed with or without crystallographic inversion symmetry. That optional symmetry causes the chain to be either polar or nonpolar, which has a large influence on the behavior of the 1D magnetic lattice. So far, all magnetic and thermodynamic D

DOI: 10.1021/acs.inorgchem.9b00610 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry (15) Hlubek, N.; Ribeiro, P.; Saint-Martin, R.; Revcolevschi, A.; Roth, G.; Behr, G.; Büchner, B.; Hess, C. Ballistic heat transport of quantum spin excitations as seen in SrCuO2. Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 81, 020405. (16) Palache, C.; Berman, H.; Frondel, C. The System of Mineralogy; Dana, J. D., Dana, E. S., Eds.; Yale University: New Haven, CT, 1837−1890; John Wiley and Sons, Inc.: New York, 1951; Vol. 2, p 804. (17) Nawa, K.; Yajima, T.; Okamoto, Y.; Hiroi, Z. Orbital arrangements and magnetic interaction in the quasi-one-dimensional cuprates ACuMoO4(OH) (A = Na, K). Inorg. Chem. 2015, 54, 5566− 5570. (18) Meng, Y.-S.; Jiang, S.-D.; Wang, B.-W.; Gao, S. Understanding the magnetic anisotropy toward single-ion magnets. Acc. Chem. Res. 2016, 49, 2381−2389. (19) Halcrow, M. A. Jahn-Teller distortions in transition metal compounds, and their importance in functional molecular and inorganic materials. Chem. Soc. Rev. 2013, 42, 1784−1795. (20) Hornfeck, W. Quantitative crystal structure descriptors from multiplicative congruential generators. Acta Crystallogr., Sect. A: Found. Crystallogr. 2012, 68, 167−180. (21) Kim, J. K.; Ranjith, K. M.; Burkhardt, U.; Prots, Yu.; Baenitz, M.; Valldor, M. Impact of inversion symmetry on a quasi-onedimensional S = 1 system. Private communication ([email protected]). (22) Bryhan, D. N.; Rakers, R.; Klimaszewski, K.; Patel, N.; Bohac, J. J.; Kremer, R. K.; Mattausch, H. J.; Zheng, C. La3TWS3O6 (T = Cr, Mn, Fe, Co, Ni): Quinary rare earth transition-metal compounds showing a nonmagnetic/magnetic transition (T = Co) - Synthesis, structure and physical properties. Z. Anorg. Allg. Chem. 2010, 636, 74−78. (23) Calvagna, F.; Zhang, J.-H.; Li, S.-J.; Zheng, C. Synthesis and structural analysis of Ba3V2O3S4. Chem. Mater. 2001, 13, 304−307. (24) Kim, J. K.; Lai, K. T.; Valldor, M. Magnetism on quasi-1-D lattices in novel non-centrosymmetric Ba3CrVS4O3 and in centrosymmetric La3TMWS3O6 (TM = Cr, Fe, Co). J. Magn. Magn. Mater. 2017, 435, 126−135. (25) Ijjaali, I.; Deng, B.; Ibers, J. A. Seven new rare-earth transitionmetal oxychalcogenides: Syntheses and characterization of Ln4MnOSe6 (Ln = La, Ce, Nd), Ln4FeOSe6 (Ln = La, Ce, Sm), and La4MnOS6. J. Solid State Chem. 2005, 178, 1503−1507. (26) Merz, W. The electric and optical behavior of BaTiO3 singledomain crystals. Phys. Rev. 1949, 76, 1221−1225. Kwei, G. H.; Lawson, A. C., jr.; Billinge, S. J. L.; Cheong, S.-W. Structures of the ferroelectric phases of barium titanate. J. Phys. Chem. 1993, 97, 2368− 2377. (27) Dzyaloshinsky, I. A thermodynamic theory of “weak” ferromagnetism of antiferromagnetics. J. Phys. Chem. Solids 1958, 4, 241−255. Moriya, T. Anisotropic superexchange interaction and weak ferromagnetism. Phys. Rev. 1960, 120, 91−98. (28) Hopkins, E. J.; Prots, Yu; Burkhardt, U.; Watier, Y.; Hu, Z.; Kuo, C.-Y.; Chiang, J.-C.; Pi, T.-W.; Tanaka, A.; Tjeng, L. H.; Valldor, M. Ba3V2S4O3: A Mott insulating frustrated quasi one-dimensional S = 1 magnet. Chem. - Eur. J. 2015, 21, 7938−7943. (29) Takashima, R.; Shiomi, Y.; Motome, Y. Nonreciprocal spin Seebeck effect in antiferromagnets. Phys. Rev. B: Condens. Matter Mater. Phys. 2018, 98, 020401. (30) Brixner, L. H.; Chen, H.-Y.; Foris, C. M. Structure and luminescence of some rare earth halotungstates of the type Ln3WO6Cl3. J. Solid State Chem. 1982, 44, 99−107. (31) Mikeska, H.-J.; Kolezhuk, A. K. One-dimensional magnetism. Lect. Notes Phys. 2004, 645, 1−83. (32) Birgeneau, R. J.; Shirane, G. Magnetism in one dimension. Phys. Today 1978, 31, 32−43.

corrected, and the corrected version was reposted on July 1, 2019.

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NOTE ADDED AFTER ASAP PUBLICATION This paper was published on the Web on June 25, 2019, with errors in the space group column of Table 1. The Table was E

DOI: 10.1021/acs.inorgchem.9b00610 Inorg. Chem. XXXX, XXX, XXX−XXX