Magnetic Ordering in the SpinIce Candidate Ho2Ru2O7

1
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. Savici2, Y. J. Uemura2, I.
Swainson6, Y. Qui4, and J. Copley4 1Department
of Physics and Astronomy, McMaster University,
Hamilton, ON, L8S 4M1 Canada 2Department of
Physics, Columbia University, New York, New York,
10027, USA 3Department of Physics, Brookhaven
National Laboratory, Upton, New York, 11973-5000,
USA 4NIST Center for Neutron Research,
Gaithersburg, Maryland, 20899-5682,
USA 5Department of Chemistry, University College
London, 20 Gordon Street, London, WC1H 0AJ,
UK 6NPMR, NRC, Chalk River Laboratories, Chalk
River, Ontario, K0J 1J0, Canada

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

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
(2) Strong lt111gt single ion anisotropy (trigonal
crystal field effect from rare earth moments such
as Ho3)
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
Dy2Ti2O7 specific heat
To date there are only 3 pyrochlore systems
discovered which have this unusual behaviour
These form two interpenetrating corner-shared
tetrahedra sublattices
S R (ln (2J 1) - (1/2) ln (3/2))
Ho2Ti2O7, Dy2Ti2O7, Ho2Sn2O7
It has been reported that the Ru S1 moments
order at 95 K What effect does a small
internal field have upon the spin ice state?
J is the spin angular momentum quantum number (J
is effectively ½ for Ising-like spins such as
Ho3 and Dy3)
(3/2) N/2 degeneracy of spin configurations
The only magnetic species is on the rare earth
site (Ti4 and Sn4 have no magnetic moment)
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
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)
(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)
The combination of these two effects give rise to
a two-in two-out low T spin configuration upon
each tetrahedra
Experimental signature specific heat C T(dS/dT)

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

Macroscopic entropy release at the ice transition
temperature
Elastic Neutron Scattering
Inelastic Neutron Scattering
Inelastic neutron scattering experiments were
completed with the Disc Chopper Spectrometer at
NIST.
Powder samples of Ho2Ru2O7 were prepared by the
following Ho2O3 2 Ru 2 O2 ? Ho2Ru2O7 (2
firings (1) 850º C for 24 h (2) 1125º C for
48 h)
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
Proposed Magnetic Structure below 95 K
Ho2Ru2O7 magnetic sublattice 2 interpenetrating
tetrahedral networks (red is Ho, blue is Ru)
This is akin to the Zeeman effect (Ru moments
order, an internal magnetic field develops and
the electronic energy levels change slightly)
Curie-Weiss law Effective moment 9.6(1) µB
(dominated by Ho3) T -4.0(5) K

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

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.
We completed elastic neutron scattering
experiments using the DualSpec spectrometer (C2)
at Chalk River using 1.31 and 2.37 Angstrom
neutrons.
Taking cuts through Q-space, we can investigate
the temp. dependance of these excitations
Expected results (1) Magnetic Bragg peaks at
95 K from Ru4 moments (2) Diffuse scattering
from short-ranged order on Ho3 moments
F
Ru4 ordered moment 1.17(17) µB (_at_ 20
K) Spin-ice like arrangement of moments
Proposed Magnetic Structure below 1 K
(Rosencranz et al , J. Appl. Physics, 87, 9,
(2000))
G
Conclusions, Acknowledgements and Future Work

• From size of Bragg peaks, and specific heat
  anomaly, it is assumed that Ru4 (S1) moments
  are ordering at 95 K.
• Subsequent experiments below 1 K show that the
  Ho3 moments order, and cause the Ru4 moments to
  rotate slightly.
• 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.
• 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.
• An interesting shift in the Ho3 crystal field
  levels has been observed at the Ru4 ordering
  temperature
• Future work
• (1) Correlate these results with µSR experiments
• Specific heat measurements
• Propose a crystal field scheme

Preliminary µSR results slowing down of
moments below 95 K. Dilution fridge work is
needed to investigate the Ho3 ordering
Ru4 ordered moment 1.82(56) µB (_at_ 100 mK) More
colinear arrangement of moments (under influence
of Ho3) Ho3 ordered moment 6.34(23)
µB Spin-ice like arrangement
(Kadowaki et al PRB, 65, 144421, 2002)
Ho2Ru2O7, our work
This work is supported by NSERC and the CIAR. We
are grateful for the assistance of the staff at
Chalk River, TRIUMF, and NIST