Topology Meets Correlation: Neutron Scattering from Correlated Topological Materials

Recent theoretical predictions and experimental realizations of exotic quasiparticles and topological excitations in condensed matter have led to tremendous research interest in topological quantum materials. With the help of widely available material synthesis capacities, efficient experimental probes that can disentangle the fine details of electron band structures, such as ARPES, as well as the recently developed topological quantum chemistry theory, the non-trivial topology of single-electron band structures has been well established as a new paradigm for quantum materials with large spin-orbit coupling like that found in topological insulators and Weyl semimetals. These topologically non-trivial phases are characterized by topological invariants, for instance, the Chern number for topological band structures. A new trend is to look into correlated topological materials, in which the non-trivial topology of single-electron band structures meets electronic correlation, for even more exotic electronic and magnetic phenomena. A natural approach is thus to add various ingredients of correlated electron physics, for instance, magnetism, flat bands and density-wave phenomena, etc., to topological semimetals and insulators. This represents a large class of interesting materials that includes magnetic Dirac and Weyl semimetals and intrinsic magnetic topological insulators. Another approach is to look into non-trivial topology in a bosonic system, such as a system of magnonic excitations, since the band topology can be treated independently from the statistical nature of the particles. Meanwhile, topological order, different from topological band structures, can emerge in the enigmatic quantum spin liquid state that is characterized by fractionalized excitations and non-local quantum entanglement. As a unique microscopic probe for studying magnetic structures and excitations, neutron scattering matches the entire range of length and time scales relevant to those novel quantum phenomena; it is therefore ideally suited to studies of correlated topological materials.

In the two-dimensional, antiferromagnetic (AFM) Dirac semimetal EuMnBi₂, an intricate interplay between multiple magnetic sublattices and relativistic Dirac fermions was suggested. A comprehensive study of the AFM structures of the Eu and Mn magnetic sublattices as well as the interplay between Eu and Mn magnetism in this compound, using both polarized and non-polarized single-crystal neutron diffraction, has been carried out by us [1], as shown in Figure 1. Furthermore, the spin-flop (SF) phase transition of the Eu moments in an applied magnetic field along the crystallographic c axis is observed to take place at a critical field of Hc ≈ 5.3 T. The AFM exchange interaction and magnetic anisotropy parameters are determined based on a subsequent quantitative analysis of the SF transition. Strong evidence for the existence of a direct coupling between Eu and Mn magnetism has also been obtained. Such an interplay between two magnetic sublattices could bring new possibilities to tune Dirac fermions via changing magnetic structures by applied fields in this class of magnetic topological semimetals.

Figure 1. Magnetic structures and spin-flop transition in the Dirac semimetal EuMnBi₂. (a)–(d): Polarized neutron diffraction patterns obtained at the polarized instrument DNS (MLZ, Garching). (e): The refined magnetic structure of EuMnBi₂ at 3 K based on the single-crystal neutron diffraction data taken at HEIDI (MLZ, Garching). (f): The refined magnetic structure of the spin-flop phase in EuMnBi₂ at 1.5 K with 11.5-T magnetic field applied along the crystallographic c axis, based on the neutron diffraction data taken at D23 (ILL, Grenoble). The figure is reproduced from the work by Zhu et al. [1] with permission from the American Physical Society.

Bosonic analogs of topological insulators have been proposed in numerous theoretical works, but their experimental realization is still very rare, especially for spin systems. Recently, two-dimensional (2D), honeycomb-lattice, van der Waals (vdW) ferromagnets have emerged as a new platform for topological spin excitations. Via a comprehensive inelastic neutron scattering study and theoretical analysis of the spin-wave excitations, a new family of topological magnon insulators has been realized in 2D-vdW compounds CrXTe₃ (X = Si, Ge) by us [2], as shown in Figure 2. The nontrivial nature and intrinsic tunability of the gap opening at the magnon band-crossing Dirac points are confirmed, while the emergence of the corresponding in-gap topological edge states is demonstrated theoretically. The realization of topological magnon insulators with intrinsic gap-tunability in this class of remarkable 2D materials will undoubtedly lead to new and fascinating technological applications in the domain of magnonics and topological spintronics.

Figure 2. Inelastic neutron scattering from the two-dimensional van der Waals ferromagnet CrSiTe₃. (a)–(c): Energy- and momentum-resolved neutron scattering intensity maps of magnons in CrSiTe₃ along the high-symmetry directions measured at the thermal neutron triple-axis spectrometer PUMA (MLZ, Garching) and IN8 (ILL, Grenoble) and at the cold neutron triple-axis spectrometer IN12 (ILL, Grenoble), respectively. The gap opening at the magnon band-crossing Dirac K and K’ points can be clearly seen. The black solid lines are the linear spin-wave theory (LSWT) calculated magnon dispersion curves based on the parameters of a Heisenberg-DM model. The inset in (b) is a contrast-adjusted plot of the dashed-rectangle part to make the acoustic branch easy to see. The inset in (c) shows the exact scan paths in reciprocal space. (d)–(f) The LSWT calculated magnon spectra for (a)-(c), respectively. The figure is reproduced from the work by Zhu et al. [2] with permission from Science Advances.