CANCELLED or postponed: Sayak Dasgupta, Johns Hopkins University, Field theory of a hexagonal antiferromagnet with 3 sublattices

Date: Mon. March 16th, 2020, 12:45 pm-1:45 pm
Location: Rockefeller 221 (Les Foldy Room)

Field theory of a hexagonal antiferromagnet with 3 sublattices

Sayak Dasgupta, John’s Hopkins University, Department of Physics

We present a classical field theory of magnetization dynamics in a generic 3-sublattice antiferromagnet in 2 spatial dimensions exemplified by the Heisenberg model on the triangular [1] and kagome [2] lattices. In a ground state, spins from the 3 sublattices are coplanar and at angles of 120° to one another such that S₁+S₂+S₃=0. The six normal modes, shown in Fig. 1, either keep the spins in this plane (the a modes) or take them out of the plane (the b modes). The soft modes b_x, b_y, and a₀ respect the ground-state condition S₁+S₂+S₃=0 and are the Goldstone modes of the spontaneously broken SO (3) symmetry. The hard modes a_x, a_y, and b₀ generate a net magnetization and are hence energetically costly. They can be safely integrated out to generate kinetic energy for the soft modes.

The 3 Goldstone modes can be grouped into the trivial singlet a₀ and the irreducible doublet b = (b_x, b_y) of the point group D₃. The a₀ singlet obeys a simple scalar field theory. The field theory of the b doublet is reminiscent of the elasticity theory of a 2-dimensional isotropic solid with two distinct “speeds of sound” (longitudinal and transverse). Thus the 3 branches of low-frequency spin waves generally have 3 distinct velocities. The nearest-neighbor Heisenberg models on the triangular and kagome lattices are exceptional in that sense. The former exhibits an accidental degeneracy of the spin-wave velocities between the two b modes. The nearest-neighbor kagome model is similar to a two-dimensional solid with a vanishing shear modulus and thus a zero speed for the transverse part of the b doublet (the weather-vane mode) while the longitudinal part of the doublet is degenerate with the a₀ mode. The 3 speeds can be readily calculated for any lattice model. The hard doublet a = (a_x,a_y) plays an important role in mediating the coupling between external perturbations – such as an applied magnetic field – and the antiferromagnetic order parameter. We apply this field theory to the hexagonal antiferromagnet Mn₃Ge [3,4].

[1] A. V. Chubukov, S. Sachdev, and T. Senthil, “Large-S expansion for quantum antiferromagnets on a triangular lattice,” J. Phys.: Condens. Matter 6, 8891 (1999).

[2] A. B. Harris, C. Kallin, and A. J. Berlinsky, “Possible Néel orderings of the Kagomé antiferromagnet,” Phys. Rev. B 45, 2899 (1992).

[3] S. Nakatsuji, N. Kiyohara, and T. Higo, “Large anomalous Hall effect in a non-collinear antiferromagnet at room temperature,” Nature 527, 212 (2015).

[4] Y. Chen, J. Gaudet, S. Dasgupta, G. Marcus, J. Lin, Y. Zhao, W. C. Chen, M.B. Stone, O. Tchernyshyov, S. Nakatsuji, C. Broholm, “Antichiral spin order its Goldstone modes and their hybridization with phonons in the topological semimetal Mn3Ge”, arXiv: 2001.09495.

 

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