Naturally tuned quantum critical point in the $S=1$ kagom\'e ${\mathrm{YCa}}_{3}{(\mathrm{VO})}_{3}{({\mathrm{BO}}_{3})}_{4}$

Naturally tuned quantum critical point in the $S = 1$ kagomé ${YCa}_{3} {(VO)}_{3} {({BO}_{3})}_{4}$

Harlyn J. Silverstein, Ryan Sinclair, Arzoo Sharma, Yiming Qiu, Ivo Heinmaa, Alexander Leitmäe, Christopher R. Wiebe, Raivo Stern, and Haidong Zhou

Phys. Rev. Materials 2, 044006 – Published 26 April 2018

Abstract

Although $S = 1 / 2$ kagomé systems have been intensely studied theoretically, and within the past decade been realized experimentally, much less is known about the $S = 1$ analogs. While the theoretical ground state is still under debate, it has been found experimentally that $S = 1$ kagomé systems either order at low temperatures or enter a spin glass state. In this work, ${YCa}_{3} {(VO)}_{3} {({BO}_{3})}_{4}$ (YCVBO) is presented, with trivalent vanadium. Owing to its unusual crystal structure, the metal-metal bonding is highly connected along all three crystallographic directions, atypical of other kagomé materials. Using neutron scattering it is shown that YCVBO fails to order down to at least 50 mK and exhibits broad and dispersionless excitations. ${}^{11}B$ NMR provides evidence of fluctuating spins at low temperatures while dc magnetization shows critical scaling that is also observed in systems near a quantum critical point such as Herbertsmithite, despite its insulating nature and $S = 1$ magnetism. The evidence shown indicates that YCVBO is naturally tuned to be a quantum disordered magnet in the limit of $T = 0$ K.

Received 25 May 2017
Revised 9 February 2018

DOI:https://doi.org/10.1103/PhysRevMaterials.2.044006

Physics Subject Headings (PhySH)

Frustrated magnetism Magnetic susceptibility Spin liquid

Neutron scattering

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Harlyn J. Silverstein^1,2,3,*, Ryan Sinclair⁴, Arzoo Sharma⁵, Yiming Qiu⁶, Ivo Heinmaa⁷, Alexander Leitmäe⁷, Christopher R. Wiebe^1,5,8,9, Raivo Stern⁷, and Haidong Zhou^4,10

¹Department of Chemistry, University of Manitoba, Winnipeg, Canada R3T 2N2
²Department of Applied Physics, Stanford University, Stanford, California 94305, USA
³Geballe Laboratory for Advanced Materials, Stanford University, Stanford, California 94305, USA
⁴Department of Physics and Astronomy, University of Tennessee–Knoxville, Knoxville, Tennessee 37996-1220, USA
⁵Department of Chemistry, University of Winnipeg, Winnipeg, Canada R3B 2E9
⁶NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
⁷NICPB, National Institute of Chemical Physics and Biophysics, 12618 Tallinn, Estonia
⁸Department of Physics and Astronomy, McMaster University, Hamilton, Canada L8S 4M1
⁹Canadian Institute for Advanced Research, Toronto, Canada M5G 1Z7
¹⁰National High Magnetic Field Laboratory, Florida State University, Tallahassee, Florida 32306-4005, USA

^*harlynjs@stanford.edu

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Vol. 2, Iss. 4 — April 2018

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Figure 1
Structure of YCVBO contains rigid ${VO}_{6}$ (red octahedra) and ${BO}_{3}$ (green trimers) units. Y and Ca ions are denoted by the large spheres and occupy those sites randomly. The smaller light blue unit cell shows the typical gaudefroyite subcell and the larger black unit cell denotes the supercell of YCVBO formed by ${BO}_{3}$ stack ordering at the positions encircled. Atoms in the ${BO}_{3}$ units at the YCVBO unit cell origin are shown with half-circles, denoting that the positions of the trimers are statistically half-occupied rather than the positions of the atoms (for example, there are no BO or ${BO}_{2}$ units). The kagomé lattice is nearly perfect and is shown with red bonds. ${VO}_{6}$ octahedra are edge sharing along the crystal $c$ axis, with ${BO}_{3}$ units cross linking the infinite ${VO}_{6}$ chains that make up the kagomé network. Exchange pathways $J_{1}$ and $J_{2}$ as described in the text are indicated, but it should be noted that this is likely an oversimplification of the structure.
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Figure 2
(a) Magnetic signal at 50 mK can be isolated by subtracting off the data at 30 K, where phonon contributions dominate. This figure has been smoothed so that the broad excitation is better observed; (b) the raw signal at 50 mK with only an empty can subtraction is shown here. Phonons that are created by the incident neutrons can be observed; (c) the dynamic susceptibility is found through the process described in the text. The damped harmonic oscillator model used in [14] was used to fit the excitation at 50 mK as a guide to the eye; (d) no additional Bragg peaks or diffuse scattering are observed, even at 50 mK. The inset is a closeup view of a portion of the data. Error bars represent one standard deviation.
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Figure 3
(a) Scaling of the magnetization completely collapses onto the same curve in a remarkably similar manner to that of Herbertsmithite [16], which indicates the proximity of a quantum critical point; (b) approximating the dc susceptibility as the low frequency ac susceptibility, it can be seen that the scaling law holds here as well. The range of data shown is slightly beyond that for which the scaling law remains valid. The inset shows the dc susceptibility corrected for diamagnetism.
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Figure 4
${}^{11}B$ MAS NMR spectra of YCVBO as a function of temperature. These spectra are referenced to the resonance frequency of ${BF}_{3} {Et}_{2} O$ solution. The asterisks denote spinning sidebands, repeating the shift behavior of the central/isotropic line and determined in number and intensity just by the spinning rate at a given temperature. The inset shows the temperature dependence of the magnetic shift (in ppm from the reference) and linewidth (FWHM in ppm) of the line I.
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Figure 5
Temperature dependence of the magnetic susceptibility of YCVBO. The magnetic susceptibility was measured (PPMS-VSM) in an external field of 4.7 T, a close field to the one used for NMR. The full line (blue) represents the susceptibility curve where the Curie tail (red dash-dot line, corresponding to paramagnetic impurities per V ion of 7% of $V^{3 +}$ or 4% of $V^{2 +})$ is subtracted from the experimental data (small circles). The red stars denote ${}^{11}B$ Knight shift values (scale in the right); the dashed line is the theoretical function for the magnetic susceptibility for the 1D-HAF chain described in the text.
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Physical Review Materials

Naturally tuned quantum critical point in the S=1 kagomé YCa3(VO)3(BO3)4

Harlyn J. Silverstein, Ryan Sinclair, Arzoo Sharma, Yiming Qiu, Ivo Heinmaa, Alexander Leitmäe, Christopher R. Wiebe, Raivo Stern, and Haidong Zhou

Phys. Rev. Materials 2, 044006 – Published 26 April 2018

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Naturally tuned quantum critical point in the $S = 1$ kagomé ${YCa}_{3} {(VO)}_{3} {({BO}_{3})}_{4}$