# Quantum magnetism

#### Molecular quantum magnetism in LiZn_{2}Mo_{3}O_{8}

A quantum dominated state of magnetism on a two dimensional lattice with just one spin per unit cell has been sought for decades. An influential paper by Anderson in 1973 showed a superposition of singlets is energetically competitive with conventional Neel ordering for spin-1/2 degree of freedom on the triangular lattice. Subsequent numerical work has however, shown that the spin-1/2 Heisenberg model on the triangular lattice does form Neel order.

Tyrel McQueen of IQM has introduced a different type of triangular lattice antiferromagnet. In LiZn_{2}Mo_{3}O_{8} electronic spins occupy triangular molecules rather than atoms. The extended nature of the spin [see the ab-initio calculation of the spin density in (a)] may give rise to interactions beyond the Heisenberg model that favor inter-molecular singlet formation. Thermo-magnetic data indicate a dynamic critical state among 1/3 of the spin degrees of freedom, the remaining 2/3 of the spins engaged in some form of high energy non-magnetic singlet formation.

Magnetic neutron scattering is complicated by the spatially extended nature of the spin (a) which suppresses all but the lowest wave vector transfer magnetic scattering. The ARCS spectrometer at SNS was used to look for high energy magnetic scattering associated with the vanishing 2/3 of the spins. The data shown in frame (c) do show the flat modes of phonons anticipated for a molecular solid. However, no difference in the inelastic neutron scattering cross section that can be attributed to magnetism was found when comparing data for LiZn_{2}Mo_{3}O_{8} to the non-magnetic analogue Zn_{2}Mo_{3}O_{8}. Normalization of these data and comparison to the magnetic resonance scattering associated with breaking an isolated singlet excludes such a mode and suggest a broad and so far undetectable spectrum of magnetic excitations is associated with the hidden 2/3 of the spins in LiZn_{2}Mo_{3}O_{8}.

Looking at 100 times lower energy transfer using the MACS spectrometer at NIST a ridge of magnetic scattering however, comes into view (a). The wave vector dependence of this scattering is consistent with it arising from breaking singlets that are formed between nearest and next nearest pairs of triangular Mo_{3}O_{13 }molecules. The gapless spectrum is consistent with a resonating valence bond state but might also arise from a static random singlet state. The experiment indicates that molecular cluster magnets offer exciting opportunities to realize spin systems where quantum coherence transcends the atomic scale. The experiment also shows that modern high efficiency neutron scattering instrumentation can be used to probe magnetism associated with extended molecular orbitals in these systems.

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#### “Meson” bound states in a quasi-one-dimensional quantum magnet

The one dimensional Ising spin chain is a paradigmatic example of an interacting quantum many body system. Using crystals synthesized by the IQM crystal grower Seyed Koohpayeh, postdoctoral fellow Chris Morris (Armitage group) has studied bound state spin excitations in the one-dimensional ferromagnetic Ising chain compound CoNb_{2}O_{6} through time-domain terahertz spectroscopy in zero applied transverse magnetic field. When antiferromagnetic interchain order develops at low temperature, nine spin flip bound states become visible. Their energies can be modeled exceedingly well by the Airy functions, exact solutions to a 1D Schrödinger equation in a linear confining potential. This sequence of “meson” bound states terminates at a threshold energy near two times the lowest bound state energy. Above this energy scale we observe a broad feature consistent with the onset of the two-particle continuum. At energies just below this threshold we observe a prominent excitation that we interpret as resulting from a novel bound state of bound states on neighboring chains. This assignment has been corroborated by graduate student Anirban Ghosh (theory group), whose calculations show evidence for a stable such excitation at energies below the 4 kink continuum. A manuscript describing this work has been accepted for publication in Physical Review Letters: arXiv:1312.4514.

#### New antiferromagnet on a triangular lattice

John Scheckelton, a graduate student in McQueen’s group, has synthesized a new frustrated antiferromagnet LiZn_{2}Mo_{3}O_{8} with spins 1/2 on a triangular lattice. This is the first of a new class of inorganic materials where magnetic moments arise from the spin of electrons in molecular orbitals of Mo_{3}O_{13} clusters, rather than on individual ions. This prevents Jahn-Teller distortions and orbital ordering that often spoil the perfect symmetries of the triangular lattice. Inelastic neutron scattering from powder specimens of LiZn_{2}Mo_{3}O_{8}, conducted by postdoc Martin Mourigal and graduate student Wes Fuhrman (Broholm group), provides evidence for interactions between these molecular spins. ESR, Li NMR, and μSR studies uncover the presence of short-range magnetic correlations at low temperatures, but show no evidence of long-range magnetic order. This antiferromagnet, with spin interactions of the order of 180 K, remains in a quantum-disordered state down to a temperature *T* = 0.07 K. The lack of order even at extremely low temperatures makes LiZn_{2}Mo_{3}O_{8} a candidate for a quantum spin liquid. A paper reporting the remarkable properties of this antiferromagnet has been recently published in Nature Materials. Two more manuscripts are under review: arXiv:1309.1165 and arXiv:1312.0955.