Spin-orbit effects in Na$_4$Ir$_3$O$_8$, a hyper-kagomé lattice antiferromagnet

Details Spin-orbit effects in Na$_4$Ir$_3$O$_8$, a hyper-kagomé lattice antiferromagnet Spin-orbit effects in Na$_4$Ir$_3$O$_8$, a hyper-kagomé lattice antiferromagnet

2008-06-10

arxiv.org/abs/0806.1573v3

Phys. Rev. B 78, 094403 (2008)

Physics

Condensed Matter

Strongly Correlated Electrons

22 pages, 15 figures. submit to prb. New references are added

Scientific paper

10.1103/PhysRevB.78.094403

We consider spin-orbit coupling effects in Na$_4$Ir$_3$O$_8$, a material in which Ir$^{4+}$ spins form an hyper-kagom\'{e} lattice, a three-dimensional network of corner-sharing triangles. We argue that both low temperature thermodynamic measurements and the impurity susceptibility induced by dilute substitution of Ti for Ir are suggestive of significant spin-orbit effects. Because of uncertainties in the crystal-field parameters, we consider two limits in which the spin-orbit coupling is either weak or strong compared to the non-cubic atomic splittings. A semi-microscopic calculation of the exchange Hamiltonian confirms that indeed large antisymmetric Dzyaloshinskii-Moriya (DM) and/or symmetric exchange anisotropy may be present. In the strong spin-orbit limit, the Ir-O-Ir superexchange contribution consists of unfrustrated strong symmetric exchange anisotropy, and we suggest that spin-liquid behavior is unlikely. In the weak spin-orbit limit, and for strong spin-orbit and direct Ir-Ir exchange, the Hamiltonian consists of Heisenberg and DM interactions. The DM coupling is parametrized by a three component DM vector (which must be determined empirically). For a range of orientation of this vector, frustration is relieved and an ordered state occurs. For other orientations, even the classical ground states are very complex. We perform spin-wave and exact diagonalization calculations which suggest the persistence of a quantum spin liquid in the latter regime. Applications to Na$_4$Ir$_3$O$_8$ and broader implications are discussed.

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