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, , USA
4NIST Center for Neutron Research, Gaithersburg, Maryland, , 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 <111> 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 S=1 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+) Θ = -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 F’and 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 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+ (S=1) 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 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, , 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