mineralogy inspires physics - anl.gov
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Mineralogy Inspires Physics
Michael Norman
Materials Science Division – Argonne National Lab
Tulane – Oct. 22, 2018
Rev. Mod. Phys. 88, 041002 J. Magn. Magn. Matls. 452, 507 Phys. Rev. B 98, 054421
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Introduction to Frustrated Magnetism and Kagome Physics
Ryu et al., PRB (2007)
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Yildirim and Harris, PRB (2007)
Near neighbor Heisenberg model on a kagome latticeCertain rotations of spins cost no energy
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Sindzingre & Lhuillier, EPL (2009)
square triangular Kagome
Exact diagonalization studies of NN Heisenberg modelindicate a very different eigenvalue spectrum for the kagome case
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Topology and Fractionalization in Spin LiquidsSpinons and Visons
Vison pair at a and b
Free spinon (yellow arrow)
Ground state degeneracy& topological sectors
Balents, Nature (2000)Misguich & Lhuillier, arXiv (2012)He, Sheng, Chen, PRB (2014)
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Yan, White, Huse, Science (2011)Hwang, Huh, Kim, PRB (2015)
DMRG studies from 2011 are consistent with a gapped Z2 spin liquidthat appears to be a melted version of a diamond valence bond solid
but other studies claim either a U(1) Dirac or a chiral spin liquid
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Herbertsmithiterare mineral first identified from a mine in Chile
(hydrothermal synthesis by Dan Nocera’s group ~ 180 C)
Shores et al, JACS (2005)
Herbertsmithite
(photo courtesy of Bruce Kelley)
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Shores et al., JACS (2005)
Herbertsmithite - ZnCu3(OH)6Cl2 with copper on a kagome lattice
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Shores et al, JACS (2005)Lee et al, Nature Matls (2007)Mendels & Bert, JPSJ (2010)
Cu4 → ZnCu3Canted AF → spin liquid
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Helton et al., PRL (2007)
Specific heat indicates gapless behavior with quasi-linear T behavior
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But, there is a large spin defect concentrationEstimate is that roughly 1 in 6 Zn atoms are replaced by a Cu
Bert et al., PRB (2007)
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NMR indicates a decreasing c below 50 K for the kagome spins, despite the diverging behavior of
the bulk c due to impurity interlayer spins
Mendels & Bert, JPSJ (2010)
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INS data indicate a divergent response below 1 meV withquantum critical scaling as also observed in heavy fermions
Helton et al., PRL (2010)
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INS data on single crystals indicate a continuum ofspin excitations, with a dynamic structure factor consistent
with near neighbor dimers and of the form S(q,w) = f(q) f(w)
Han et al., Nature (2012)
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But INS data below 1 meV indicate AF interactions betweendefect copper spins sitting on the Zn intersites
Han et al., PRB (2016)
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INS data are a sum of impurity and kagome spin contributions(with the kagome spins having a spin gap)
Specific heat can be fit assuming a relaxational form for impurity c(w)
Han et al., PRB (2016)
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Mazin et al., Nature Comm. (2014)Guterding et al, Sci. Rep. (2016)
Can one “dope” herbertsmithite by replacing Zn2+ by 1+ or 3+ ions?Prediction of Dirac points (electron doping),flat bands (hole doping), and f-wave pairing
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Lithium intercalated HerbertsmithiteInsulating, but with indications for a Cu non-integer valence
Kelly et al., PRX (2016)
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Herbertsmithite has a much larger gap than a cuprate
Puphal et al., J Mater Chem C (2017)Pustogow et al., Phys Rev B (2017)
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There are many relatives of herbertsmithiteSeveral of these are polymorphs
Norman, Rev Mod Phys (2016)
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Zn-doped Barlowite exists, with 19F NMR indicating spinons
Feng et al, Chin Phys Lett (2017)
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Bobkingite – a possible D chain material
Hawthorne et al, Mineral. Mag. (2002)
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Copper Tellurium Oxides, Hydroxides, and Hydroxychlorides
Christy et al., Mineral. Mag. (2016)Norman, J. Magn. Magn. Matls. (2018)
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Quetzalcoatlite – a perfect Kagome latticebut with super-superexchange
Burns et al., Amer. Mineral. (2000)
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CuTeO4 - Monoclinic distorted CuO2 square netCuO6 quasi-octahedral, Cu-O-Cu bond angles 122.5°& 126.1°
Botana & Norman, PRB (2017)
CuTeO4 - Falck et al., Acta Cryst. B (1978)grown hydrothermally at 650 C
but Cu3TeO6 more thermodynamically stable
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Vondechenite, CaCu4Cl2(OH)8(H2O)4 - ortho distorted Cu square netCu-O-Cu bond angles 114.5°& 115.2°
Schluter et al, J. Min. Geochem. (2018)
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Averievite was found in a volcano in KamchatkaIt was first synthesized by Wendy Queen by
solid state reaction (~ 700 C)
Starova et al, Mineral. Mag. (1997)Wendy Queen, thesis (2009)
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Cu5O2(VO4)2(CsCl)
(Wendy Queen, thesis)
One kagome Cu3O2Cl plane
Two honeycomb CuVO3 planesOne triangular CsO2 plane
Cu3O2Cl
CuVO3
CsO2
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Cu5V2O10(CsCl), averievite, has a Cu kagome layer and Cu-Vhoneycomb layers separated by CsO2 layers (a pyrochlore slab)
Botana et al, PRB (2018)
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Jennifer Zheng (John Mitchell’s group) has synthesized it as wellSusceptibility data indicate J ~ 200K, as predicted from LDA+USubstitution by Zn leads to behavior similar to herbertsmithite
Botana et al, PRB (2018)
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Specific heat reveals a Neel transition at 24K (QCW/TN ~ 8)No transition is seen in a Cu4Zn doped version
Botana et al, PRB (2018)
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Botana et al, PRB (2018)
Substitution of Cu-honeycomb in the parent phase (left) by Znisolates the kagome planes (middle); Substitution of V5+ by Ti4+
dopes it and leads to a large increase in the bandwidth (right)
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Summary
• The synthesis of herbertsmithite led to a new era in the study of quantum spin liquids
• Low energy behavior controlled by disorder (orphan spins), as also seen in other spin liquid candidates
• Attempts to dope herbertsmithite leads to insulating behavior (polarons? – recent PRL of Zunger’s group)
• Several variants of herbertsmithite have been recently discovered, with others yet to be explored
• Charge transfer behavior and stability could be enhanced by looking for oxides rather than hydroxychlorides
• Averievite is a copper oxide, and a potential spin liquid
• Mineralogy space is vast, so many surprises await us