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The effect of pressure and chemical substitution on the Kitaev Heisenberg system alpha-RuCl3

Periodic Reporting for period 1 - PRESS-CHESS-KHS (The effect of pressure and chemical substitution on the Kitaev Heisenberg system alpha-RuCl3)

Reporting period: 2018-06-01 to 2020-05-31

In magnetic materials, magnetic moments carried by the electrons interact with each other and their collective behavior accounts for the magnetic properties of materials, leading to a large variety of magnetic phenomenon. Frustrated magnets are materials, where not all magnetic interactions can be simultaneously satisfied. The magnetic frustration gives rise to the competition between various magnetic phases. Among them the quantum spin liquid state attracts much attention due to possible applications for topological quantum computation. In this phase a strong quantum entanglement and fractionalized excitations occurs, while long-range magnetic order is absent down to zero temperature.

In this project we focused on one particular frustrated magnet, i.e. alpha-RuCl3. The magnetism in this material is close to the Kitaev model: An exactly solvable theoretical model, which harbors a quantum spin liquid state as magnetic ground state with fractionalized Majorana-fermion quasiparticle as excitations . In this model, Ising-like magnetic interactions named Kitaev interactions couple for two neighboring magnetic moments the spin component parallel to the link/bond between the two neighboring magnetic moments to each other.

α-RuCl3 is a Mott insulator with a 2D layered structure of edge-sharing RuCl6 octahedra arranged in a honeycomb lattice. The spin and orbital moment of the ruthenium sites are strongly coupled by the spin-orbit interaction leading to the formation of so-called isospins Jeff=1/2. α-RuCl3 is close to the realization of the Kitaev model, since a ferromagnetic Kitaev interactions is the strongest magnetic interaction in this system, however, other magnetic interactions are present as well: Heisenberg interactions and off-diagonal couplings. Despite the proximity to the Kitaev model, alpha-RuCl3 orders magnetically at a temperature TN=7.5 K. However, this long-range magnetic order can be suppressed by the application of a magnetic field within the honeycomb plane at the critical field Hc ~ 7 T. While magnetic fields much higher than Hc = 7 T induce a field-polarized state, the occurrence of a field-induced quantum spin liquid state in a narrow field interval remains under debate.

In this research project, the Kitaev magnet alpha-RuCl3 was tuned by the application of hydrostatic pressure and by chemical substitution and intercalation. The aim was to test the stability of the magnetic order and to probe the different magnetic states such as quantum spin liquid states, which compete with this magnetic order and can be induced by these modifications of alpha-RuCl3.
Magnetization measurements under hydrostatic pressure were used to investigate the effect of pressure on the Kitaev magnet alpha-RuCl3. The design of the pressure cell for such measurements was optimized during this project. As a result, the resolution of magnetization measurements under pressures up to 4.5 GPa was enhanced both via an enlargement of the maximal sample dimensions and via a reduction of the background signal from the pressure cell.

We discovered a pressure-induced structural phase transition in alpha-RuCl3 under the application of a hydrostatic pressure of 0.2 GPa [1]. The high-pressure phase was further characterized via x-ray diffraction studies under hydrostatic pressure and quantum chemistry calculations in collaboration with the TU Dresden and the theory department of the IFW, respectively. We found that the honeycomb lattice is contracted along one direction and the Ru ions build pairs called dimers with a strong antiferromagnetic interaction within the dimer at this phase transition. As a consequence, the magnetization is strongly reduced and the Kitaev magnetic interaction is not the dominant magnetic interaction anymore in alpha-RuCl3. This pressure-induced state is named a valence bond solid.

Another route to tune the magnetic interactions in alpha-RuCl3 undertaken in this project, is the partial substitution of the magnetic ion Ru3+ by another magnetic ion Cr3+ or by non-magnetic ions Rh3+, Ir3+ and Ru2+. The last example of mixed Ru3+ and Ru2+ ions was obtained via the intercalation of K+ ions between the honeycomb layers.
We found that the introduction of the magnetic ions Cr3+ destabilizes the magnetic ground state of alpha-RuCl3 into a spin-glass state for a substitution rate of x=0.1 Cr ions per formula unit [2]. The chemical substitution of Ru3+ by non-magnetic ions Rh3+ and Ir3+ destabilize also the antiferromagnetic ground state. However, no signature of a spin-glass state has been observed despite its theoretical prediction and the nature of the state induced by chemical substitution remains unclear. Contrary to the chemical substitution of Ru3+ ions by non-magnetic ions Rh3+ and Ir3+, the introduction of Ru2+ by chemical intercalation of K+ ions allows displacement of the magnetic ions via hopping of electrons for temperature higher than 200K . This leads to the formation of a regular pattern of magnetic ions Ru3+ upon slow cooling from 300K. For the composition K0.5RuCl3 our results indicate the magnetic structure changing from a honeycomb structure for alpha-RuCl3 to a triangular-lattice antiferromagnet, which is very valuable since the realizations of triangular-lattice of 4d magnetic ions are rare. The formation of a long-range magnetic order on this triangular lattice was also detected at TN = 2.1K.

[1] G. Bastien, G. Garbarino, R. Yadav, F. J. Martinez-Casado, R. Beltrán Rodríguez, Q. Stahl, M. Kusch, S. P. Limandri, R. Ray, P. Lampen-Kelley, D. G. Mandrus, S. E. Nagler, M. Roslova, A. Isaeva, T. Doert, L. Hozoi, A. U. B. Wolter, B. Büchner, J. Geck, and J. van den Brink, Phys. Rev. B 97, 241108(R) (2018).
[2] G. Bastien, M. Roslova, M. H. Haghighi, K. Mehlawat, J. Hunger, A. Isaeva, T. Doert, M. Vojta, B. Büchner and A. U. B. Wolter, Phys. Rev. B 99, 214410 (2019).
To conclude, the work performed within this project revealed a broad variety of physical phenomena and magnetic phases which can be induced in alpha-RuCl3 by slight modifications of the system. This work emphasizes that the frustrated magnet alpha-RuCl3 is not only close to the Kitaev model and the realization of a quantum spin liquid state but also close to other phases, such as the valence bond crystal. In addition, the introduction of disorder brings new phases into play, such as the spin-glass state. The elucidation of this competition between various magnetic phases paves the way for the search of new magnetic materials for the realization of quantum spin liquid states and more generally for their applications in the future.