Hall effect of triplons in a dimerized quantum magnet

Abstract

SrCu 2 (BO 3 ) 2 is the archetypal quantum magnet with a gapped dimer-singlet ground state and triplon excitations. It serves as an excellent realization of the Shastry-Sutherland model, up to small anisotropies arising from Dzyaloshinskii-Moriya interactions. Here we demonstrate that these anisotropies, in fact, give rise to topological character in the triplon band structure. The triplons form a new kind of Dirac cone with three bands touching at a single point, a spin-1 generalization of graphene. An applied magnetic field opens band gaps resulting in topological bands with Chern numbers ±2. SrCu 2 (BO 3 ) 2 thus provides a magnetic analogue of the integer quantum Hall effect and supports topologically protected edge modes. At a threshold value of the magnetic field set by the Dzyaloshinskii-Moriya interactions, the three triplon bands touch once again in a spin-1 Dirac cone, and lose their topological character. We predict a strong thermal Hall signature in the topological regime.

Topological triplon modes and bound states in a Shastry–Sutherland magnet

“…A bosonic analogue of this result for the case when the band is thermally populated is the thermal Hall effect which, rather than depending on the Chern number and yielding a quantized response, instead depends on the magnitude of the Berry curvature in thermally occupied parts of the band 28,29 . A topological transition is visible as a kink in the Hall effect resulting from a spike in the Berry curvature at the touching point between topologically nontrivial bands with equal and opposite Chern numbers.For the idealized triplon model of Romhanyi et al 19 there exist only two topologically nontrivial triplon bands with Chern numbers C = +2 and C = −2 and a single finite field topological transition at the upper critical field B c = 1.4 T. At B c these bands touch at the point and, as expected, the thermal Hall effects shows a kink. For our refined model the situation turns out to be much richer.…”

“…At zero field, the gap to the triplons is roughly 3 meV, which is the scale of the nearest-neighbour isotropic exchange J . Instead of the predicted 19 spin-1 analogue of a Dirac point with an almost flat band crossing through this point we find that the modes are non-degenerate at zero field, indicative of a significant anisotropy in the system.…”

“…It turns out that only two of the three components of the inter-dimer DM exchange, D ⊥ and D , contribute. It is well known 19 that a dispersion in the single triplons coming from J (in the absence of DM interactions) arises only to sixth order in J /J . We neglect this lowest-order contribution to the triplon hopping.…”

“…Their role is therefore similar to that of spin-orbit coupling in electronic topological insulators. Based on a theoretical model of non-interacting triplons, Romhanyi et al 19 predicted that in a small magnetic field the triplon bands of SrCu 2 (BO 3 ) 2 acquire a nontrivial topological invariant, called a Chern number, which implies the existence of chiral magnetic edge states.…”

Topological thermal Hall effect in frustrated kagome antiferromagnets

“…This suggests that the DMI is not the primary source of topological spin excitations in frustrated magnets, which sharply differs from collinear magnets [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] and triplon excitations [44] in a magnetic field with zero scalar spin chirality. We note that scalar spin chirality plays a crucial role in different areas of physical interest.…”