b. d. gaulin- frustrated and satisfied ground states in pyrochlore magnets
TRANSCRIPT
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Frustrated and Satisfied Ground States in
Pyrochlore Magnets
Neutron and X-ray Scattering from Exotic Magnets
Spin liquid and Ordered Ground States in the PyrochloreAntiferromagnet Tb2Ti2O7
Spin Ice Ground State in Ho2Ti2O7
Structural Fluctuations within the Spin Liquid State of Tb2Ti2O7
B. D. Gaulin
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Collaborators
J.P.C. Ruff
K.A. Ross
S.R. Dunsiger
K.C. Rule
J.P. Clancy
M.J. Lewis McMaster University
A.J. Berlinsky
H.A. Dabkowska
C. Kallin J.E. Greedan
C.P. Adams St. Francis Xavier University
M.J.P. Gingras University of Waterloo
R.F. Kiefl University of British Columbia
J.S. Gardner
Y. Qiu NIST J.R.D. Copley
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??
Geometrical Frustration:
Antiferromagnetism + Triangles and Tetrahedra
2D Triangular Lattice: G.H. Wannier Phys. Rev. 79, 357, 1950.
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Ground State of the Ising AF on a
Triangular Lattice
Entropy at T=0 is finite ~ 0.34 R
No LRO at any temperature
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Geometrical Frustration:
Mean Field Theory predicts a phase transition near T=| QCW | ,but materials remains disordered to much lower temperatures
Spin Liquid
-QCW QCW
c-1
Temperature
Spin Liquid Paramagnet
Non-generic!
eg: Noncollinear AF
Spin glass
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Frustration in three dimensions:
The cubic pyrochlore structure;
A network of corner-sharing tetrahedra
Low temperature powder
neutron diffraction from
Tb2Ti2O7
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mSR Studies of Magnetic Ground States in:Tb2Ti2O7
Tb2Mo2O7Y2Mo2O7
Tb2Ti2O7 :Spin Liquid
Y2Mo
2O
7 :Spin Glass
Tb2Mo2O7 :Spin Liquidand Spin Glass
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+/- |4>
~ 175 K
~ 20 K
~ 125 K
+/- |5>
Inelastic neutron scattering on polycrystalline Tb2Ti2O7
( D : Ho2Ti2O7 ~ 240 K ; Dy2Ti2O7 ~ 380 K)
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Rare Earth moments:
Strong [111] anisotropy
Ferromagnetic exchange:
Spin Ice : 2 in 2 out
Harris, Bramwell et al, PRL, 79, 2554, 1997
Antiferromagnetic exchange:
All in - All out
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B.C. den Hertog and M.J.P. Gingras, PRL, 84, 3430, 2000.
Tb2Ti2O7
Ho2Ti2O7
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2-Axis Diffraction
T=9 K
TOF scattering
T=0.4 K
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Outstanding Questions:
Why is Tb2Ti2O7 disordered as low as 0.02 K (in H=0, P=0)?
S(Q) at low T is (perhaps naively)incompatable with Ising (111)
anisotropy. What is going on?
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Ordered phases appear on application of H // 110
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Low field (002) phase persists
to very high T > 25 K
High field (112) phase exists
on expected TN ~ 2 K
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Application of weak
[1-10] magnetic fieldbreaks system up intoa and b chains.Polarizable a-[1-10]chains (parallel to field)
Perpendicular b-[110]chains
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Application of weak
[1-10] magnetic fieldbreaks system up intoa and b chains.Polarizable a-[1-10]chains (parallel to field)
Perpendicular b-[110]chains
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a-chains polarized along the [1,1,0] Direction
P
P
P
P
P
P
P
P
P = Paramagnetic Site
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Field Aligned, Local AFM
+ +
+
+
++
+
+
-
--
-
-
-
- -
+ / - Denotes Z-Component
3 in 1 out local structure
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Canted AFM, Moments not respecting Ising 111 axes.
(Magnetization is ~11% of saturation along [110])
+ / - Denotes Z-Component
- +
-+
-
+
-
-
+-
+
-
++
-
+
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One Transition in Zero Field
Five Transitions in Non-Zero Field
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Spin Ice Ground State in Ho2Ti2O7
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Ho2Ti2O7 vs Tb2Ti2O7Static Spin Ice vs Dynamic Spin Liquid (H=0)
Magnetic Structure Factors appear complementary
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Ferro-ordering ofa-chains1D-correlations alongb-chains
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Spin Ice Ground State in Ho2
Ti2
O7
is static
Spin Liquid Ground State in Tb2Ti2O7is dynamic
High Resolution X Ray Scattering from Tb Ti O
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High Resolution X-Ray Scattering from Tb2Ti2O7Ruff et al., cond-mat/0707.1682, PRL to appear
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Conclusions:
New neutron scattering infrastructure leads to New Science
DCS has been a tremendous success in elucidating exotic magnetism
New time-of-flight neutron infrastructure at SNS, JSNS, 2TS@ISIS
Antiferromagnetic Pyrochlore Tb2Ti2O7:
Spin Liquid State in H=0 comes to order in small(ish) fields
Dispersive collective spin excitations observed in ordered states
evidence for continuous spin symmetry
Structural fluctuations characteristic of cooperative Jahn-Tellerphase transition accompany appearance of spin liquid state in Tb2Ti2O7
Ferromagnetic Pyrochlore Ho2Ti2O7:
Static Spin Ice Ground State