Magnetic Ordering in the Spin-Ice Candidate Ho2Ru2O7 C.

Magnetic Ordering in the Spin-Ice Candidate Ho2Ru2O7 C.

Magnetic Ordering in the Spin-Ice Candidate Ho2Ru2O7
C. R. Wiebe1,2, S.-J. Kim1, G. MacDougall1, G. M. Luke1, J. S. Gardner3,4, A. S. Wills,5 P. L. Russo2, A. T.
2
2
6
4
4
Savici , Y. J. Uemura , I. Swainson , Y. Qui , and J. Copley
Department of Physics and Astronomy, McMaster University, Hamilton, ON, L8S 4M1 Canada
2
Department of Physics, Columbia University, New York, New York, 10027, USA
3
Department of Physics, Brookhaven National Laboratory, Upton, New York, 11973-5000, USA
4
NIST Center for Neutron Research, Gaithersburg, Maryland, 20899-5682, USA
5
Department of Chemistry, University College London, 20 Gordon Street, London, WC1H 0AJ, UK
6
NPMR, NRC, Chalk River Laboratories, Chalk River, Ontario, K0J 1J0, Canada
1

The dipolar spin ice arises in
systems which satisfy two
requirements:
(1) Weak ferromagnetic
interactions upon a pyrochlore
lattice (dipole interactions
become important)

(dipolar interactions are ~ 1 K for
rare earth
species these stabalize the
spin ice state. The
ferromagnetic interaction is to
favour a certain low temperature
spin configuration)

(2) Strong <111>
single ion anisotropy
(trigonal crystal field
effect from rare earth
moments such as
Ho3+)

This is analgous to the
situation in water
freezing: hydrogen
bonding constraints
require a two short,
two long bond
distance between
protons and oxygen in
a tetrahedral
arrangement

The combination
of these two
effects give rise to
a two-in two-out
low T spin
configuration upon
each tetrahedra

In both cases, there
is a highly
degenerate ground
state which is
determined by the
large number of
energetically
equivalent ways one
can arrange N units
of spin or protons

There is an entropy release at the transition
temperature which accounts for this
degeneracy:

By counting the number of ways one can
achieve these configurations, one arrives at
(3/2)N/2 for a sample containing N water
molecules

Macroscopic entropy release at the ice transition temperature

Dy2Ti2O7 specific heat:

Ho2O3 + 2 Ru + 2 O2 Ho2Ru2O7
(2 firings: (1) 850 C for 24 h
(2) 1125 C for 48 h)

Ho2Ru2O7 magnetic sublattice:
2 interpenetrating tetrahedral networks
(red is Ho, blue is Ru)

These form two
interpenetrating
corner-shared
tetrahedra sublattices

S ~ R (ln (2J +1) - (1/2) ln (3/2))
Ho2Ti2O7, Dy2Ti2O7, Ho2Sn2O7
J is the spin
angular
momentum
quantum number
(J is effectively
for Ising-like spins
such as Ho3+ and
Dy3+)

(3/2) N/2
degeneracy
of spin
configurations

It has been reported
that the Ru S=1
moments order at ~ 95
K

The only magnetic
species is on the rare
earth site (Ti4+ and Sn4+
have no magnetic
moment)

Experimental
signature: specific
heat C ~ T(dS/dT)

What effect does a
small internal field have
upon the spin ice state?

Bansal et al recently
reported that Ho2Ru2O7 is
another candidate for a
spin ice ground state:
Magnetic species lie on
both sites (Ho3+ and Ru4+
both have moments)

(A) Ramirez et. Al, Nature,
399, 333 (1999).
(B) B. C. den Hertog and
M.J.P. Gingras, PRL,
84, 3430 (2000).

Elastic Neutron Scattering
Powder samples of Ho2Ru2O7 were
prepared by the following:

To date there are only 3
pyrochlore systems discovered
which have this unusual
behaviour:

Inelastic Neutron Scattering
Inelastic neutron scattering
experiments were completed with
the Disc Chopper Spectrometer at
NIST.

Proposed Magnetic Structure below 95 K

There is a clear shift in the
position of these peaks as
one cools below the Ru
ordering transition at 95 K

This appears to be a shift in
the Ho3+ xtal field levels as
the Ru moments order

-1.5

Center of peak (meV)

-1.6

This is akin to the
Zeeman effect
(Ru moments order, an
internal magnetic field
develops and the
electronic energy levels
change slightly)

-1.7
-1.8
-1.9
-2.0
-2.1
-2.2
40

60

80

100

120

140

160

180

200

220

240

Temp (K)

Curie-Weiss law: Effective
moment: 9.6(1) B (dominated by
Ho3+) = -4.0(5) K
Expected results: (1) Magnetic Bragg
peaks at 95 K from Ru4+ moments
(2) Diffuse scattering from short-ranged
order on Ho3+ moments

Analogy with Ho2Ti2O7
Using Ho2Ti2O7 as a model
for the Ho3+ crystal field
levels, one can identify the
transitions as being Fand
G, between the A1g singlet
Eg and doublets.
The internal field from the
Ru4+ moments ordering
splits the doublets slightly,
and changes the energy
levels.

Taking cuts through Q-space, we can
investigate the temp. dependance of
these excitations
Ru ordered moment: 1.17(17) B (@ 20 K)
Spin-ice like arrangement of moments
4+

Proposed Magnetic Structure below ~ 1 K

Intensity (arbitrary units)

We completed elastic neutron
scattering experiments using the
DualSpec spectrometer (C2) at
Chalk River using 1.31 and 2.37
Angstrom neutrons.

(1) Dispersionless excitations observed
(crystal field levels)
(2) No clear spin waves forming

1

T = 220 K
T = 210 K
T = 150 K
T = 100 K
T = 85 K
T = 75 K
T = 70 K
T = 61 K
T = 50 K

F

0
-4

G

-2

E (meV)

(Rosencranz et al , J. Appl. Physics, 87, 9, (2000))

Conclusions, Acknowledgements and Future Work

(1) From size of Bragg peaks, and specific heat anomaly, it is assumed that
Ru4+ (S=1) moments are ordering at 95 K.
(2) Subsequent experiments below ~ 1 K show that the Ho3+ moments order,
and cause the Ru4+ moments to rotate slightly.
(3)The diffuse scattering shows qualitative agreement with what is expected for
a dipolar spin ice (short-ranged order on Ho3+ sites above 1 K).

Ho2Ru2O7, which was originally thought to be a spin-ice, has two
ordering transitions (T ~ 95 K and T ~ 1 K for Ru and Ho moments,
respectively, into Q = (0, 0, 0) structures). Subsequent powder
diffraction experiments on the dilution fridge confirm this result.

Preliminary SR results : slowing down of
moments below 95 K. Dilution fridge work is
needed to investigate the Ho3+ ordering
LF = 5 T

(Kadowaki et al PRB, 65, 144421, 2002)

Ho2Ru2O7, our work

Ru4+ ordered moment: 1.82(56) B (@ 100 mK)
More colinear arrangement of moments (under influence of Ho 3+)
Ho3+ ordered moment: 6.34(23) B
Spin-ice like arrangement

An interesting shift in the Ho3+ crystal field levels has been observed at
the Ru4+ ordering temperature
Future work:
(1) Correlate these results with SR experiments
(2) Specific heat measurements
(3) Propose a crystal field scheme

10
-1

Relaxation rate (s )

There is evidence for SRO upon the Ho moments until 1 K, but it
appears that the Ru4+ moments ordering are enough of a
perturbation upon the spin-ice state to drive the system to an ordered
state.

1

0.1

0.01
0

50

100

150

200

250

Temperature (K)

This work is supported by NSERC and the CIAR. We are grateful
for the assistance of the staff at Chalk River, TRIUMF, and NIST

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