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8/3/2019 T. Senthil, S. Isakov and Y.B. Kim- Ordering in Cs2CuCl4: is there a proximate spin liquid
http://slidepdf.com/reader/full/t-senthil-s-isakov-and-yb-kim-ordering-in-cs2cucl4-is-there-a-proximate 1/28
Ordering in Cs2CuCl4: is there a
proximate spin liquid?
T. Senthil (Indian Inst. of Sci./MIT)
S. Isakov (Toronto) and Y.B. Kim (Toronto)
8/3/2019 T. Senthil, S. Isakov and Y.B. Kim- Ordering in Cs2CuCl4: is there a proximate spin liquid
http://slidepdf.com/reader/full/t-senthil-s-isakov-and-yb-kim-ordering-in-cs2cucl4-is-there-a-proximate 2/28
Spin liquids and other exotica in quantummagnets
• Traditional quantum magnetism: Ordered ground states
(Neel, spin Peierls, …………)
Notions of broken symmetry
Modern theory (last 2 decades): Possibility of `spin liquid’ states
(well-known in d = 1, but also possible in any d).
Eg: Mott insulators with no broken symmetry
Excitations with fractional spin (spinons),
Emergent gauge structure, notion of `topological order’
Maturing theoretical understanding -
extensive developments in last few years
8/3/2019 T. Senthil, S. Isakov and Y.B. Kim- Ordering in Cs2CuCl4: is there a proximate spin liquid
http://slidepdf.com/reader/full/t-senthil-s-isakov-and-yb-kim-ordering-in-cs2cucl4-is-there-a-proximate 3/28
Hints from theory
• Frustrated quantum magnets
• ``Intermediate’’ correlation regime
Eg: Mott insulators that are not too deeply into the insulating regime
• More subtle: Intermediate scale physics of doped Mott insulators (incuprates?)
This and the next talk – focus on specific candidate materials.
But where are the spin liquids?No clear experimental sightings in d > 1 so far.
8/3/2019 T. Senthil, S. Isakov and Y.B. Kim- Ordering in Cs2CuCl4: is there a proximate spin liquid
http://slidepdf.com/reader/full/t-senthil-s-isakov-and-yb-kim-ordering-in-cs2cucl4-is-there-a-proximate 4/28
Hints from theory
• Frustrated quantum magnets
• ``Intermediate’’ correlation regime
Eg: Mott insulators that are not too deeply into the insulating regime
• More subtle: Intermediate scale physics of doped Mott insulators (incuprates?)
This and the next talk – focus on specific candidate materials.
But where are the spin liquids?No clear experimental sightings in d > 1 so far.
Thistalk
8/3/2019 T. Senthil, S. Isakov and Y.B. Kim- Ordering in Cs2CuCl4: is there a proximate spin liquid
http://slidepdf.com/reader/full/t-senthil-s-isakov-and-yb-kim-ordering-in-cs2cucl4-is-there-a-proximate 5/28
Hints from theory
• Frustrated quantum magnets
• ``Intermediate’’ correlation regime
Eg: Mott insulators that are not too deeply into the insulating regime
• More subtle: Intermediate scale physics of doped Mott insulators (incuprates?)
This and the next talk – focus on specific candidate materials.
But where are the spin liquids?No clear experimental sightings in d > 1 so far.
Thistalk
Nexttalk
8/3/2019 T. Senthil, S. Isakov and Y.B. Kim- Ordering in Cs2CuCl4: is there a proximate spin liquid
http://slidepdf.com/reader/full/t-senthil-s-isakov-and-yb-kim-ordering-in-cs2cucl4-is-there-a-proximate 6/28
Very promising candidate for exotica -Cs2CuCl4
• Transparent layered Mottinsulator
• Spin ½ per Cu site onanisotropic triangularlattice
8/3/2019 T. Senthil, S. Isakov and Y.B. Kim- Ordering in Cs2CuCl4: is there a proximate spin liquid
http://slidepdf.com/reader/full/t-senthil-s-isakov-and-yb-kim-ordering-in-cs2cucl4-is-there-a-proximate 7/28
J ≈ 0.375meV
J’ ≈J/3
J’’ ≈ 0.045 J (weak interlayer
exchange)
Known microscopic spin Hamiltonian
8/3/2019 T. Senthil, S. Isakov and Y.B. Kim- Ordering in Cs2CuCl4: is there a proximate spin liquid
http://slidepdf.com/reader/full/t-senthil-s-isakov-and-yb-kim-ordering-in-cs2cucl4-is-there-a-proximate 8/28
J ≈ 0.375meV
J’ ≈J/3
J’’ ≈ 0.045 J (weak interlayer
exchange)
Known microscopic spin Hamiltonian
Weak Dzyaloshinski-Moriya interaction along zigzag bonds
8/3/2019 T. Senthil, S. Isakov and Y.B. Kim- Ordering in Cs2CuCl4: is there a proximate spin liquid
http://slidepdf.com/reader/full/t-senthil-s-isakov-and-yb-kim-ordering-in-cs2cucl4-is-there-a-proximate 9/28
Ordering at low T
Magnetic long range spiral orderbelow T=0.62K with incommensurate wave vector
But many unusual phenomena en route!
8/3/2019 T. Senthil, S. Isakov and Y.B. Kim- Ordering in Cs2CuCl4: is there a proximate spin liquid
http://slidepdf.com/reader/full/t-senthil-s-isakov-and-yb-kim-ordering-in-cs2cucl4-is-there-a-proximate 10/28
Spin fluctuation spectrum
Low energy gapless magnon (as expected) – two dimensional dispersion
Large high energy continuum(not contained in spin wave theory)
8/3/2019 T. Senthil, S. Isakov and Y.B. Kim- Ordering in Cs2CuCl4: is there a proximate spin liquid
http://slidepdf.com/reader/full/t-senthil-s-isakov-and-yb-kim-ordering-in-cs2cucl4-is-there-a-proximate 11/28
Inelastic line shape – failure of spin wavetheory
Spin wavepeak
Broad inelasticbackgroundfrom 0.2 meVto 1 meV
Possibly power law, fit to estimate exponent.
8/3/2019 T. Senthil, S. Isakov and Y.B. Kim- Ordering in Cs2CuCl4: is there a proximate spin liquid
http://slidepdf.com/reader/full/t-senthil-s-isakov-and-yb-kim-ordering-in-cs2cucl4-is-there-a-proximate 12/28
Temperature dependence
Magnon shoots out of broadbackground on coolingbelow TN.
General qualitative similarityto antinodal ARPES inunderdoped cuprates.
8/3/2019 T. Senthil, S. Isakov and Y.B. Kim- Ordering in Cs2CuCl4: is there a proximate spin liquid
http://slidepdf.com/reader/full/t-senthil-s-isakov-and-yb-kim-ordering-in-cs2cucl4-is-there-a-proximate 13/28
General viewpoint on the experiments
Unstable fixed point controlsbroad continuum scattering.
??Nature and description??
General framework:
1. Two dimensional but anisotropic
2. Spin SU(2) invariant(DM small effect in this energy range)
3. Scale invariant?
8/3/2019 T. Senthil, S. Isakov and Y.B. Kim- Ordering in Cs2CuCl4: is there a proximate spin liquid
http://slidepdf.com/reader/full/t-senthil-s-isakov-and-yb-kim-ordering-in-cs2cucl4-is-there-a-proximate 14/28
Candidates (in order of increasing sophistication)
1. Decoupled 1d chains
2. Proximate quantum critical point
to gapped spin liquid
3. `Algebraic spin liquid’
(Gapless fermionic spinons coupled
to fluctuating gauge field)
4. Proximate quantum critical point todimer ordered (spin Peierls) state
5. Something even more exotic
8/3/2019 T. Senthil, S. Isakov and Y.B. Kim- Ordering in Cs2CuCl4: is there a proximate spin liquid
http://slidepdf.com/reader/full/t-senthil-s-isakov-and-yb-kim-ordering-in-cs2cucl4-is-there-a-proximate 15/28
Candidates (in order of increasing sophistication)
1. Decoupled 1d chains
2. Proximate quantum critical point
to gapped spin liquid
3. `Algebraic spin liquid’
(Gapless fermionic spinons coupled
to fluctuating gauge field)
4. Proximate quantum critical point todimer ordered (spin Peierls) state
5. Something even more exotic
8/3/2019 T. Senthil, S. Isakov and Y.B. Kim- Ordering in Cs2CuCl4: is there a proximate spin liquid
http://slidepdf.com/reader/full/t-senthil-s-isakov-and-yb-kim-ordering-in-cs2cucl4-is-there-a-proximate 16/28
8/3/2019 T. Senthil, S. Isakov and Y.B. Kim- Ordering in Cs2CuCl4: is there a proximate spin liquid
http://slidepdf.com/reader/full/t-senthil-s-isakov-and-yb-kim-ordering-in-cs2cucl4-is-there-a-proximate 17/28
Crossovers near phase boundary to spinliquid
T
g
8/3/2019 T. Senthil, S. Isakov and Y.B. Kim- Ordering in Cs2CuCl4: is there a proximate spin liquid
http://slidepdf.com/reader/full/t-senthil-s-isakov-and-yb-kim-ordering-in-cs2cucl4-is-there-a-proximate 18/28
Structure of spiral ordering
8/3/2019 T. Senthil, S. Isakov and Y.B. Kim- Ordering in Cs2CuCl4: is there a proximate spin liquid
http://slidepdf.com/reader/full/t-senthil-s-isakov-and-yb-kim-ordering-in-cs2cucl4-is-there-a-proximate 19/28
Topological defects in ordered state
8/3/2019 T. Senthil, S. Isakov and Y.B. Kim- Ordering in Cs2CuCl4: is there a proximate spin liquid
http://slidepdf.com/reader/full/t-senthil-s-isakov-and-yb-kim-ordering-in-cs2cucl4-is-there-a-proximate 20/28
Liberating spinons
8/3/2019 T. Senthil, S. Isakov and Y.B. Kim- Ordering in Cs2CuCl4: is there a proximate spin liquid
http://slidepdf.com/reader/full/t-senthil-s-isakov-and-yb-kim-ordering-in-cs2cucl4-is-there-a-proximate 21/28
Structure of the spin liquid
8/3/2019 T. Senthil, S. Isakov and Y.B. Kim- Ordering in Cs2CuCl4: is there a proximate spin liquid
http://slidepdf.com/reader/full/t-senthil-s-isakov-and-yb-kim-ordering-in-cs2cucl4-is-there-a-proximate 22/28
Spiral – spin liquid phase transition
8/3/2019 T. Senthil, S. Isakov and Y.B. Kim- Ordering in Cs2CuCl4: is there a proximate spin liquid
http://slidepdf.com/reader/full/t-senthil-s-isakov-and-yb-kim-ordering-in-cs2cucl4-is-there-a-proximate 23/28
Scaling of spin fluctuations
8/3/2019 T. Senthil, S. Isakov and Y.B. Kim- Ordering in Cs2CuCl4: is there a proximate spin liquid
http://slidepdf.com/reader/full/t-senthil-s-isakov-and-yb-kim-ordering-in-cs2cucl4-is-there-a-proximate 24/28
Useful future experiments
8/3/2019 T. Senthil, S. Isakov and Y.B. Kim- Ordering in Cs2CuCl4: is there a proximate spin liquid
http://slidepdf.com/reader/full/t-senthil-s-isakov-and-yb-kim-ordering-in-cs2cucl4-is-there-a-proximate 25/28
More dramatic consequence-enhanced O(4) symmetry
8/3/2019 T. Senthil, S. Isakov and Y.B. Kim- Ordering in Cs2CuCl4: is there a proximate spin liquid
http://slidepdf.com/reader/full/t-senthil-s-isakov-and-yb-kim-ordering-in-cs2cucl4-is-there-a-proximate 26/28
Detecting vector spin chirality fluctuations-polarized inelastic neutron scattering
(Maleyev’95, Isakov,TS,Kim,’05)
8/3/2019 T. Senthil, S. Isakov and Y.B. Kim- Ordering in Cs2CuCl4: is there a proximate spin liquid
http://slidepdf.com/reader/full/t-senthil-s-isakov-and-yb-kim-ordering-in-cs2cucl4-is-there-a-proximate 27/28
Expected result in quantum critical regime
8/3/2019 T. Senthil, S. Isakov and Y.B. Kim- Ordering in Cs2CuCl4: is there a proximate spin liquid
http://slidepdf.com/reader/full/t-senthil-s-isakov-and-yb-kim-ordering-in-cs2cucl4-is-there-a-proximate 28/28
Summary
• Concrete version of general idea that Cs2CuCl4is proximate to a spin liquid
Many testable consequences.
Wish-list for experiments:
1. Careful frequency scans at fixed wavevector
2. NMR relaxation3. Polarized inelastic neutron
Future theory: Direct second order spiral – dimer transition?