B. D. Gaulin- Frustrated and Satisfied Ground States in Pyrochlore Magnets

8/3/2019 B. D. Gaulin- Frustrated and Satisfied Ground States in Pyrochlore Magnets

1/31

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


2/31

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


3/31

?

??

Geometrical Frustration:

Antiferromagnetism + Triangles and Tetrahedra

2D Triangular Lattice: G.H. Wannier Phys. Rev. 79, 357, 1950.


4/31

Ground State of the Ising AF on a

Triangular Lattice

Entropy at T=0 is finite ~ 0.34 R

No LRO at any temperature


5/31

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


6/31

Frustration in three dimensions:

The cubic pyrochlore structure;

A network of corner-sharing tetrahedra

Low temperature powder

neutron diffraction from

Tb2Ti2O7


7/31

mSR Studies of Magnetic Ground States in:Tb2Ti2O7

Tb2Mo2O7Y2Mo2O7

Tb2Ti2O7 :Spin Liquid

Y2Mo

2O

7 :Spin Glass

Tb2Mo2O7 :Spin Liquidand Spin Glass


8/31

+/- |4>

~ 175 K

~ 20 K

~ 125 K

+/- |5>

Inelastic neutron scattering on polycrystalline Tb2Ti2O7

( D : Ho2Ti2O7 ~ 240 K ; Dy2Ti2O7 ~ 380 K)


9/31

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


10/31

B.C. den Hertog and M.J.P. Gingras, PRL, 84, 3430, 2000.

Tb2Ti2O7

Ho2Ti2O7


11/31

2-Axis Diffraction

T=9 K

TOF scattering

T=0.4 K


12/31

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?


13/31

Ordered phases appear on application of H // 110


14/31


15/31

Low field (002) phase persists

to very high T > 25 K

High field (112) phase exists

on expected TN ~ 2 K


16/31

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


17/31

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


18/31

a-chains polarized along the [1,1,0] Direction

P

P

P

P

P

P

P

P

P = Paramagnetic Site


19/31

Field Aligned, Local AFM

+ +

+

+

++

+

+

-

--

-

-

-

- -

+ / - Denotes Z-Component

3 in 1 out local structure


20/31

Canted AFM, Moments not respecting Ising 111 axes.

(Magnetization is ~11% of saturation along [110])

+ / - Denotes Z-Component

- +

-+

-

+

-

-

+-

+

-

++

-

+


21/31


22/31

One Transition in Zero Field

Five Transitions in Non-Zero Field


23/31

Spin Ice Ground State in Ho2Ti2O7


24/31

Ho2Ti2O7 vs Tb2Ti2O7Static Spin Ice vs Dynamic Spin Liquid (H=0)

Magnetic Structure Factors appear complementary


25/31

Ferro-ordering ofa-chains1D-correlations alongb-chains


26/31

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


27/31

High Resolution X-Ray Scattering from Tb2Ti2O7Ruff et al., cond-mat/0707.1682, PRL to appear


28/31


29/31


30/31


31/31

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

Documents

B. D. Gaulin- Frustrated and Satisfied Ground States in Pyrochlore Magnets