Local magnetism and spin correlations in the geometrically frustrated cluster magnet ${\text{LiZn}}_{2}{\text{Mo}}_{3}{\text{O}}_{8}$

Local magnetism and spin correlations in the geometrically frustrated cluster magnet ${LiZn}_{2} {Mo}_{3} O_{8}$

J. P. Sheckelton, F. R. Foronda, LiDong Pan, C. Moir, R. D. McDonald, T. Lancaster, P. J. Baker, N. P. Armitage, T. Imai, S. J. Blundell, and T. M. McQueen

Phys. Rev. B 89, 064407 – Published 11 February 2014

Abstract

${LiZn}_{2} {Mo}_{3} O_{8}$ has been proposed to contain $S = ½$ ${Mo}_{3} O_{13}$ magnetic clusters arranged on a triangular lattice with antiferromagnetic nearest-neighbor interactions. Here, microwave and terahertz electron spin resonance, ${}^{7}{Li}$ nuclear magnetic resonance, and muon spin rotation spectroscopies are used to characterize the local magnetic properties of ${LiZn}_{2} {Mo}_{3} O_{8}$ . These results show the magnetism in ${LiZn}_{2} {Mo}_{3} O_{8}$ arises from a single isotropic $S = ½$ electron per cluster and that there is no static long-range magnetic ordering down to $T$ = 0.07 K. Further, there is evidence of gapless spin excitations with spin fluctuations slowing down as the temperature is lowered. These data indicate strong spin correlations, which, together with previous data, suggest a low-temperature resonating valence-bond state in ${LiZn}_{2} {Mo}_{3} O_{8}$ .

Received 25 September 2013

DOI:https://doi.org/10.1103/PhysRevB.89.064407

Authors & Affiliations

J. P. Sheckelton^1,2, F. R. Foronda³, LiDong Pan², C. Moir⁴, R. D. McDonald⁵, T. Lancaster⁶, P. J. Baker⁷, N. P. Armitage², T. Imai^8,9, S. J. Blundell³, and T. M. McQueen^1,2,*

¹Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
²Institute for Quantum Matter and Department of Physics and Astronomy, The Johns Hopkins University, Baltimore, Maryland 21218, USA
³Department of Physics, Oxford University, Clarendon Laboratory, Parks Road, Oxford, OX1 3PU, United Kingdom
⁴National High Magnetic Field Laboratory, Florida State University, 1800 E. Paul Dirac Drive, Tallahassee, Florida 32310, USA
⁵National High Magnetic Field Laboratory, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
⁶Department of Physics, Durham University, South Road, Durham, DH1 3LE, United Kingdom
⁷ISIS Facility, STFC Rutherford Appleton Laboratory, Harwell Oxford, Didcot, OX11 0QX, United Kingdom
⁸Department of Physics and Astronomy, McMaster University, Hamilton, Ontario L8S4M1, Canada
⁹Canadian Institute for Advanced Research, Toronto, Ontario M5G1Z8, Canada

^*mcqueen@jhu.edu

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Vol. 89, Iss. 6 — 1 February 2014

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Figure 1
ESR spectra of ${LiZn}_{2} {Mo}_{3} O_{8}$ at different applied frequencies and fields in (a) the terahertz electromagnetic range and (b) the microwave range (offset for clarity). (c) The extracted $g$ factor for this range of fields and applied EM radiation are in good agreement with each other and are consistent with an isotropic $g$ factor from a single $S = ½$ magnetic electron per formula unit. The magnetic electron is delocalized over a ${Mo}_{3} O_{13}$ cluster, shown in the inset with the corresponding molecular orbital diagram [20].
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Figure 2
(a) A schematic representation of ${LiZn}_{2} {Mo}_{3} O_{8}$ crystal structure. Differently colored circles represent four distinct crystallographic, mixed Li/Zn sites. Gray boxes represent ${Mo}_{3} O_{8}$ layers. (b) ${}^{7}{Li}$ NMR FFT lineshapes taken at $μ_{o} H$ = 5.36 T and point-by-point frequency scan obtained by spin echo integration at $T$ = 4.2 K (offset for clarity). The spectra indicate four distinct lithium magnetic environments (a–d), consistent with four lithium crystal sites. (c) Spin-lattice relaxation rate as a function of temperature for each NMR peak. The data remain approximately constant as the temperature is lowered, lacking any evidence of the opening of a spin gap.
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Figure 3
Example $μ SR$ spectra [the asymmetry function $A (t)$ ] for ${LiZn}_{2} {Mo}_{3} O_{8}$ measured at (a) $T$ = 120 K and (b) $T$ = 0.07 K in zero field and various longitudinal fields. The fits assume Kubo-Toyabe relaxation with an additional electronic relaxation included (see text). (c) The temperature dependence of $Δ$ , measured in zero field. (d) The temperature dependence of $λ$ measured in a longitudinal field of $μ_{o} H$ = 10 mT.
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Figure 4
(a) NMR spin-lattice relaxation rate [of peak “a,” see Fig. 2 (b)] divided by temperature, ${(T_{1} T)}^{- 1}$ , a measure of electron spin relaxation scales with $μ SR$ $λ T^{- 1}$ . Both data sets are compared to the previously reported bulk magnetic susceptibility, shown as a gray line. The data are self-consistent and indicate gapless, short-range spin-spin correlations. The characteristic measurement frequencies for each technique are approximately $ω_{o} = 8 \times 10^{6}$ Hz for $μ SR$ at $μ_{o} H = 10$ mT and $ω_{o} = 9 \times 10^{7}$ Hz for ${}^{7}{Li}$ NMR at $μ_{o} H = 5.36$ T. (b) The bulk susceptibility divided by NMR ${(T_{1} T)}^{- 1}$ and $μ SR$ $λ T^{- 1}$ , a measure of relaxation rate as compared to inelastic neutron scattering data [33]. The data show a slowing of spin fluctuations as the temperature is lowered, in agreement with the electron spin relaxation rate ( $Γ$ ) extracted from inelastic neutron scattering (blue diamonds). The red line is a guide to the eye, calculated by fitting to the NMR data the exponential $0.004 (\frac{e . m . u . \cdot s \cdot K^{0.71}}{Oe \cdot mol f . u .}) T^{0.29}$ . The error bars on the $μ SR$ data were calculated by propagating errors on both the bulk susceptibility and $μ SR$ datasets.
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Figure 5
Two possible microscopic origins of the valence-bond state in the cluster-based triangular lattice antiferromagnet ${LiZn}_{2} {Mo}_{3} O_{8}$ . (a) Dynamic octahedral cluster rotations as proposed in Ref. [50]. (b) Proximity to a metal-insulator transition. A triangular lattice Heisenberg antiferromagnet has a 120° magnetic ground state in the fully localized limit. As the electron wavefunction becomes more delocalized, a valence-bond state, such as what we observe in ${LiZn}_{2} {Mo}_{3} O_{8}$ , becomes energetically more favorable [34].
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Physical Review B

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Local magnetism and spin correlations in the geometrically frustrated cluster magnet ${LiZn}_{2} {Mo}_{3} O_{8}$

J. P. Sheckelton, F. R. Foronda, LiDong Pan, C. Moir, R. D. McDonald, T. Lancaster, P. J. Baker, N. P. Armitage, T. Imai, S. J. Blundell, and T. M. McQueen

Phys. Rev. B 89, 064407 – Published 11 February 2014

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Physical Review B

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Local magnetism and spin correlations in the geometrically frustrated cluster magnet LiZn2Mo3O8

J. P. Sheckelton, F. R. Foronda, LiDong Pan, C. Moir, R. D. McDonald, T. Lancaster, P. J. Baker, N. P. Armitage, T. Imai, S. J. Blundell, and T. M. McQueen

Phys. Rev. B 89, 064407 – Published 11 February 2014

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Local magnetism and spin correlations in the geometrically frustrated cluster magnet ${LiZn}_{2} {Mo}_{3} O_{8}$