The material a-RuCl₃ has been the subject of intense study for the past few years owing to the expectation that it exhibits competing uniaxial exchange interactions characteristic of what are now termed Kitaev materials [1]. coordinated Ru³⁺ ions form a honeycomb lattice with layers weakly bonded via van der Waals interactions. The ease of formation of stacking faults and domains has made a definitive determination of the low temperature crystallographic space group difficult since many possible arrangements of the layers are energetically similar. In the absence of a magnetic field single crystals with few stacking faults show a phase transition near a Neel temperature T_N = 7 K to an antiferromagnetic structure that has zigzag order in a single plane and a 3-fold out of plane periodicity [2,3]. The introduction of stacking faults results in a structure with a 2-layer periodicity with T_N = 14 K [2,3]. The phase diagram in the presence of external in-plane magnetic field perpendicular to a Ru-Ru bond has not been fully resolved, but some features are clear, including a transition to an ordered state with a different layered periodicity near 6 Tesla and the complete suppression of zigzag order above roughly 7.5 Tesla [4,5,6]. Substitution of non-magnetic Ir4+ for Ru3+ also suppresses the zigzag order [7].This talk discusses these results in the context of measurements of the magnetic excitations, and the possible presence of a quantized thermal Hall effect and other interesting phenomena.

[1] Takagi, H., Takayama, T., Jackeli, G., Khaliullin G., & Nagler,S.E. (2019). Nature Reviews Physics 1, 264. [2] Banerjee, A. et al. (2016), Nature Materials 15, 733.

[3] Cao, H.B. A. et al. (2016), Physical Review B 93, 134423.

[4] Banerjee, A. et al. (2018), NPJ Quantum Materials 3, 8.

[5] Balz, C. et al. (2019), Physical Review B 100, 060405(R).

[6] Balz, C. et al. (2021), Physical Review B 103, 174417.

[7] Lampen-Kelly P. et al. (2017), Physical Review Letters 119, 237203.

The research discussed here used resources at the High Flux Isotope Reactor and Spallation Neutron Source, DOE Office of Science User Facilities operated by the Oak Ridge National Laboratory.

A central line of inquiry in condensed matter science has been to understand how the competition between different states of matter give rise to emergent physical properties. Perhaps some of the most studied systems in this respect are the hole-doped LaMnO3 perovskites, with interest in the past three decades being stimulated on account of their colossal magnetoresistance (CMR). However, phase segregation between ferromagnetic (FM) metallic and antiferromagnetic (AFM) insulating states, which itself is believed to be responsible for the colossal change in resistance under applied magnetic field, has until now prevented a full atomistic level understanding of the orbital ordered (OO) state at the optimally doped level. Here, through the detailed crystallographic analysis of the hole-doped phase diagram of a prototype system, we show that the superposition of two distinct lattice modes gives rise to a striped structure of OO Jahn-Teller active Mn3+ and charge disordered (CD) Mn3.5+ layers in a 1:3 ratio. This superposition leads to a cancellation of the Jahn-Teller-like oxygen atom displacements in the CD layers only at the 3/8th doping level, coincident with the maximum CMR response of the manganties. Furthermore, the periodic striping of layers containing Mn3.5+, separated by layers of fully ordered Mn3+, provides a natural mechanism though which long range OO can melt, a prerequisite for the emergence of the FM conducting state. The competition between insulating and conducting states is seen to be a key feature in understanding the properties in highly correlated electron systems, many of which, such as the CMR and high temperature superconductivity, only emerge at or near specific doping values.

Orbital molecules are clusters of transition metal cations formed by orbital- and charge-ordering in systems with direct d-d interactions [1]. Vanadium oxides exhibit a particularly rich variety of orbital molecule states, notably the V-V dimerisation that accompanies the metal-insulator transition in VO₂ [2]. In vanadium oxide spinels such as AlV₂O₄ and GaV₂O₄ the 3D connectivity of V-V nearest neighbours allows larger orbital molecules to form, and these also persist into a hidden high-temperature disordered state [3].

Not all AV₂O₄ spinels have orbital molecule ground states, but as the formation of V-V bonds is associated with marked lattice distortions we have employed synchrotron X-ray powder diffraction and pair-distribution function analysis to determine the structural and electronic requirements for V-V bonding to be stabilised. Studying the Zn_xGa_1−xV₂O₄ family of materials revealed that, whilst the long-range order of orbital molecules in the ground state of GaV₂O₄ is highly sensitive to A-site substitution, local V-V bonding interactions are stable to x > 0.75 before the ground state of ZnV₂O₄, which is orbitally ordered but without V-V bonding, emerges [4]. Furthermore, we have found a monoclinic distortion coincident with the reported pressure-driven metal-insulator transition in LiV₂O₄ that suggests it to be the result of orbital-molecule formation [5]. Overall, we have determined that the formation and ordering of orbital molecules bonds in AV₂O₄ spinels is principally dependent on the V-V nearest-neighbour distance.

[1] Attfield, J. P. (2015). APL Mater. 3, 041510.

[2] Goodenough, J. B. (1971). J. Solid State Chem. 3, 490.

[3] Browne, A. J., Kimber, S. A. J. & Attfield, J. P. (2017). Phys. Rev. Mater. 1, 052003(R).

[4] Browne, A. J. & Attfield, J. P. (2020). Phys. Rev. B 101, 024112.

[5] Browne, A. J., Pace, E. J., Garbarino, G. & Attfield, J. P. (2020). Phys. Rev. Mater. 4, 015002.

Perovskites are one of the most prevalent classes of functional materials and are already known to exhibit a wide range of properties, including ferroelectricity, superconductivity and magnetism amongst others [1]. Many traditional perovskites have poor toxicity and sustainability; however, the inclusion of organic components could help alleviate these issues and provide greater structural diversity. Several examples of hybrid perovskites with interesting properties have already been reported with the inclusion of complex anions such as cyanides, formates and azides on the X site of the perovskite [2]. Whilst the oxalate ligand has already been extensively used in coordination polymers, its use in perovskite materials has only recently been reported in the compound KLi₃Fe(C₂O₄)₃ [3], the compound exhibits simultaneous 1:3 ordering on both the A and B sites of the perovskite (Figure 1). In order to gain a more detailed understanding of this structure type, a series of compounds with the general formula A^ILi₃M^II(C₂O₄)₃ where A = K⁺, Rb⁺, Cs⁺ and M = Fe²⁺, Co²⁺, Ni²⁺ have been synthesised and characterised [4].

Figure 1. Comparison of hypothetical cubic perovskite with 1:3 cation ordering at the A and B site (left) and the corresponding crystal structure of the perovzalates (right). Li octahedra blue, M octahedra brown and A cation purple.

1 J. P. Attfield, P. Lightfoot and R. E. Morris, Dalt. Trans., 2015, 44, 10541–10542.

2 G. Kieslich and A. L. Goodwin, Mater. Horizons, 2017, 4, 362–366.

3 W. Yao, Y. Guo and P. Lightfoot, Dalt. Trans., 2017, 46, 13349–13351.

4 R. Clulow, A. J. Bradford, S. L. Lee and P. Lightfoot, Dalt. Trans., 2019, 48, 14461–14466.

Keywords: Perovskite; Hybrid materials; Coordination polymers

We would like to thank the EPSRC for a doctoral studentship to R. Clulow (DTG012 EP/K503162-) and the University of St Andrews for a doctoral studentship to A. J. Bradford

The Aurivillius materials are well known for their ferroelectric properties[1] and associated structural distortions.[2] They form a class of layered perovskite-related phases with general formula Bi₂A_n-1B_nX_3n+3 (X is usually oxide, but halides are also known), with structures built up from alternating fluorite-like [Bi₂O₂]²⁺ layers and [A_n‑1B_nX_3n+1]^2- perovskite-like layers. The search for magnetoelectrics, with coupled magnetic and ferroelectric order, has motivated investigations to introduce magnetic ions into the B cation sites. However, this has been challenging and the concentrations of magnetic B cations in Aurivillius oxides is typically low.[3-5] Redirecting research away from oxides and towards mixed-anion systems, including Aurivillius oxyfluorides, opens up a wider compositional range, as well as the possibility of tuning structure and properties by anion order.[6, 7]

This presentation describes work on n = 1 Aurivillius oxyfluorides including Bi₂TiO₄F₂ and Bi₂CoO₂F₄. Our symmetry analysis[8] of possible anion-ordered structures highlights the challenges of packing polar heteroanionic units to break inversion symmetry, as well as means by which this might be achieved for Bi₂TiO₄F₂. We also explore methods to determine anion ordering in materials with anions with similar scattering lengths.[9]

Increasing the fluoride content in these oxyfluorides gives access to phases with lower oxidation states for B cations, and the report of Bi₂CoO₂F₄, with long-range magnetic order of the Co²⁺ sublattice,[10] motivated our investigation using neutron powder diffraction. We’ve explored its nuclear structure and in particular, the anion sublattice and structural distortions, and determined its magnetic structure.[11] This gives insight into its physical properties and opens the door to designing and preparing new multiferroics.

[1] de Araujo, C. A. P.; Cuchiaro, J. D.; McMillan, L. D.; Scott, M. C.; Scott, J. F., (1995), Nature 374, 627-629.

[2] Guo, Y. Y.; Gibbs, A. S.; Perez-Mato, J. M.; Lightfoot, P., (2019), Iucrj 6, 438-446.

[3] Keeney, L.; Downing, C.; Schmidt, M.; Pemble, M. E.; Nicolosi, V.; Whatmore, R. W., (2017), Scientific Reports 7.

[4] Giddings, A. T.; Stennett, M. C.; Reid, D. P.; McCabe, E. E.; Greaves, C.; Hyatt, N. C., (2011), Journal of Solid State Chemistry 184, 252-263.

[5] McCabe, E. E.; Greaves, C., (2005), Journal of Materials Chemistry 15, 177-182.

[6] Charles, N.; Saballos, R. J.; Rondinelli, J. M., (2018), Chemistry of Materials 30, 3528-3537.

[7] Kageyama, H.; Hayashi, K.; Maeda, K.; Attfield, J. P.; Hiroi, Z.; Rondinelli, J. M.; Poeppelmeier, K. R., (2018), Nature Communications 9.

[8] Campbell, B. J.; Stokes, H. T.; Tanner, D. E.; Hatch, D. M., (2006), J. Appl. Cryst. 39, 607-614.

[9] Giddings, A. T.; Scott, E. A. S.; Stennett, M. C.; Apperley, D. C.; Greaves, C.; Hyatt, N. C.; McCabe, E. E., (2021), in preparation.

[10] Vagourdi, E. M.; Mullner, S.; Lemmens, P.; Kremer, R. K.; Johnsson, M., (2018), Inorganic Chemistry 57, 9115-9121.

[11] Scott, E. A. S.; Vagourdi, E. M.; Johnsson, M.; John, F.; Cascos, V. A.; Pickup, D. M.; Chadwick, A. V.; Zhang, W.; Halasyamani, P. S.; McCabe, E. E., (2021), in preparation.

Heusler alloys close to stoichiometric Ni₂MnGa undergo a sequence of diffusionless, displacive phase transformations from parent cubic austenite to various martensitic or ferroelastic phases, modulated 10M and 14M (also marked 5M and 10M) and non-modulated (NM) tetragonal phase depending on composition. Often the cascade of intermartensitic transformations (10M-14M-NM) is observed with decreasing temperature or with increasing mechanical stress [1]. Owing to the ferromagnetic state and highly mobile twin boundaries in modulated phases, the relatively weak magnetic field can induce the reorientation of ferroelastic domains via twin boundary motion [2]. This results in giant magnetic-field-induced strain up to 12% in single crystal [3] called magnetic shape memory (MSM) effect. Although the martensitic transformation is relatively well understood, the nature of intermartensitic transformation (IMT) is still disputed. One reason is that even the character of modulated phases is not settled [4-6]. Understanding the IMT can provide some clue to the character of modulated phases and has also practical impact as the IMT limits the operational range of the MSM effect. Although many diffraction studies were performed on polycrystalline samples only little neutron research has been done on single-crystals. Regarding the complex nature of the modulated phases and continuing discussion about their character (nanotwinning v. harmonic modulation) [4-6], only single crystalline studies represent the proper way in attempt to understand the 10M-14M intermartensitic transformation. The neutron diffraction as bulk method is particularly suitable for direct comparison with magnetic [7] and transport measurements [6].

Here we present study of 10M-14M transformation by neutron diffraction using the D9 and D10 single-crystal four-circle diffractometers and CYCLOPS (neutron Laue single-crystal diffractometer) in ILL Grenoble. The Laue method allowed continuous tracing of the transition and broader survey of the reciprocal space with temperature, revealing any changes in crystal orientation and newly occurring twinning in transformed phase. Additional laboratory X-ray diffraction using rotating anode diffractometer provide further insight and better precision. The q-scans measured at different temperatures across the transition revealed the details of the modulation, pointing to its nanotwinning character. Fine features in the q-scans suggested the traces of 10M within 14M phase in the temperature well below the IMT. The structural changes indicated by the diffraction were related to the changes of magnetic properties. In presentation, we will also look on preference of the 14M phase in epitaxial thin films compared to bulk single crystals.

[1] Ullakko, K., Huang, J. K., Kantner, C. & Handley, R. C. O. (1996) Appl. Phys. Lett. 69, 1966–8.

[2] Kellis, D., Smith, A., Ullakko, K. & Müllner, P. (2012) J. Cryst. Growth 359, 64-68.

[3] Heczko, O., Kopecký, V., Sozinov, A. & Straka, L. (2014) Appl. Phys. Lett. 103, 198-211.

[4] Straka, L., et al. (2011) Acta Mater. 59, 7450–63.

[5] Seiner, H., Straka, L. & Heczko, O. (2013) J. Mech. Phys. Solids 64, 072405.

[6] Veřtát, P., et al. (2021) J. Phys.: Condens. Matter, accepted, https://doi.org/10.1088/1361-648X/abfb8f

[7] Ge, Y. et al., "Transitions between austenite and martensite structures in Ni₅₀Mn₂₅Ga₂₀Fe₅ thin foil", available at: http://dx.doi.org/10.2139/ssrn.3813433

This work was supported by Operational Programme Research, Development and Education financed by the European Structural and Investment Funds and the Czech Ministry of Education, Youth and Sports, project number SOLID21 CZ.02.1.01/0.0/0.0/16_019/0000760. P.V. thanks for the support by the Grant Agency of the Czech Technical University in Prague, grant number SGS19/190/OHK4/3T/14. We acknowledge the Institut Laue-Langevin and the project LTT20014 financed by the Ministry of Education, Youth and Sports, Czech Republic, for the provision of neutron radiation facilities.