correlated defects in the kagome spin liquid herbertsmithite · 1 mev for the kagome layers, which...
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Correlated Defects in the KagomeSpin Liquid Herbertsmithite
Michael Norman
Materials Science Division – Argonne National Lab
NWU – Oct. 15, 2015
Harry Han, U Chicago & ANLYoung Lee, Stanford U
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Introduction to Kagome Physics
Ryu et al., PRB (2007)
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Sindzingre & Lhuillier, EPL (2009)
square triangular Kagome
Exact Diagonalization (36 sites)
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Yan, White, Huse, Science (2011)
Latest DMRG studies indicate a small spin gap
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The Universe is a String-Net Liquid
Zeeya Merali, New Scientist (15 March 2007)
Herbertsmithite
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Emily Nytko, thesis (2008)
Herbertsmithite is one member of an interesting class of cuprateswith kagome Cu(OH)2 layers stacked/connected in different manners
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(a) ABC stacking (clinoatacamite, herbertsmithite)(b) AA stacking (kapellasite, haydeeite)(c) AA stacking (claringbullite, barlowite)
Emily Nytko, thesis (2008)
Stacking sequences
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Shores et al., JACS (2005)
Herbertsmithite - ZnCu3(OH)6Cl2
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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
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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)kagome planes – pristine or not?
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Freedman et al, JACS (2010)
DANES at the Cu/Zn K edge indicate pristine kagome planeswith no Zn on Cu sites, but with Cu on Zn sites
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This is confirmed by NMR, which shows a decreasing c below 50 K for the kagome spins
despite the diverging behavior of the bulk c
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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Castro-Neto & Jones, PRL (1998)
vs
Schroeder et al, Nature (2000)
Is this novel quantum critical physics (left)OR
Is this a signature of random exchange (right)
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INS data on single crystals are consistent with NN dimers,but at low energies, the (HK0) pattern is more spot like
Han et al., Nature (2012)
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S(q,w) is relatively flat in energy,but upturns below 1 meV
Han et al., Nature (2012)
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(HK0)
Different S(q,ω) above and below
0.8 meV
New low energy INS data (Harry Han & Young Lee)
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Han & Lee, unpublished
A strong variation is seen along Lwith a peak at (0,0,3/2)
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The variation along 00L can be fit by NN AF correlationsbetween spins on different layers of the same type(triangular Zn-Zn or kagome Cu-Cu, but not Cu-Zn)
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Q=(0,0,3/2) magnetism for the Fe jarosites
Grohol et al, Nature Matls (2005)Ballou et al, JMMM (2003)
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Problem! Peaks are at (11L), not (00L)For the q=0 structure, the sum of the in-plane components
of the spins for a given kagome triangle vanish
Alternate – Ferro planes AF coupled along the c-axis
Implication – (00L) peaks arise from Cu defect spins sitting on the Zn intersites (triangular layers)
Kit Matan, thesis (2007)
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Calculated structure factor for interplanarAF coupling between Cu defect spins sitting on the Zn sites
(including the Cu form factor)
(HK0) (H0L) (HHL)
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Magnetic structure for clinoatacamiteIntersite-Kagome net coupling – Ferro
Intersite-Intersite (interplane) net coupling – AF
–
Lee et al, Nature Matls (2007)Kim et al, PRL (2008)Wills & Henry, JPCM (2008)
Kagome: blue – up; red – downIntersite: cyan – up; magenta – down
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Herbertsmithite (left) vs Clinoatacamite (right)
blue – kagomecyan – intersite
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Some evidence for a structural distortion from a peak in 35Cl NMR
Imai et al, PRL (2008)
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Low energy INS data are consistent with spin defects
Nilsen et al., JPCM (2013)
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Specific heat can be fit assuming a relaxational form for impurity c(w)
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Random Bond Heisenberg Modelgives a good description of the INS data
Kawamura et al., JPSJ (2014)
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Conclusions
• Latest NMR data indicate that there is a spin gap of about 1 meV for the kagome layers, which are likely defect free
• Divergent response below 1 meV due to spins from Cu defects sitting on the Zn intersites
• Quantum critical scaling of c consistent with a random bond Heisenberg model
• The defect spins polarize the surrounding kagome spins, and are in turn AF coupled along the c-axis
• Such magnetic correlations are reminiscent of the pure Cu analogue, clinoatacamite
• The implication is that the Cu defects locally distort the surrounding lattice, which could be tested by PDF, etc.