# Presentation: 201440

## Low Temperature Heat Capacity of the Frustrated Pyrochlore Magnets Gd2Hf2O7 and Gd2Zr2O7 

- Alice Durand
- Professor L.R. Corruccini
- Peter Klavins
- University of California, Davis

## Introduction

- Theoretically, pyrochlore lattices with isotropic anti-ferromagnetic exchange exhibit no magnetic order as temperature nears 0 K
- We use the isotropic Heisenberg Hamiltonian to model the nearest neighbor interactions for such pyrochlores
- (equation)
- So far, the closest model systems have been Gd2Ti2O7 and Gd2Sn2O7 – both pyrochlores order magnetically at about 1/10 of the Curie-Weiss temperature. Even though these materials have identical crystal structures, they have different ground states.
- 	These systems have been studied extensively by previous groups.

## Pyrochlore Lattice Diagram

- Black dots    = Gadolinium atoms

## Heat Capacity of Gd2Ti2O7 

- From P. Bonville et al.

## Heat Capacity of Gd2Sn2O7 

-  P. Bonville et al., J. Phys.: Condens. Matter 15 (2003) 7777

## Introduction Continued

- The long range order peaks in all of these materials implies that we need to take into account further-neighbor and dipole-dipole (potentially important for frustrated systems) interactions for the Hamiltonian.
- Gd2Hf2O7 and Gd2Zr2O7 are a potentially useful third model system to study.
- By measuring the heat capacity for Gd2Hf2O7 and Gd2Zr2O7, we discovered evidence of long-range ordering near 0.75 K in both the hafnium and zirconium pyrochlores.

## Magnetic Susceptibility for Gd2Hf2O7 and Gd2Zr2O7

- Χ(t) yields a magnetic moment μ = 7.86μB, which is close to the free-ion value of μ = 7.94μB

## Lattice Constants

- We can compare:
- Gd2Hf2O7 : a = 10.515 Å
- Gd2Zr2O7 : a = 10.522 Å
- Curie-Weiss constant: θW ≈ -7 K (for both materials)
- Gd2Ti2O7 : a = 10.184 Å
- Gd2Sn2O7 : a = 10.460 Å
- Curie-Weiss constant: θW ≈ -9 K (for both materials)
- The Zr(+4) ion is ~1% bigger than the Hf(+4) ion, which accounts for the slightly larger lattice constant in the zirconate.

## Heat Capacity for Gd2Hf2O7 

## Heat Capacity for Gd2Hf2O7 

- The sharp peak at TC ≈ 0.77 K is consistent with long-range magnetic order.
- This peak is superimposed on the broad maximum centered at about 1 K, the latter indicating short-range order.
- The peak maximum is about 17 J/mol-K, which is within 18% of the mean field prediction for a 2nd order magnetic phase transition for S = 7/2.
- This magnitude of the heat capacity maximum for this material resembles Gd2Ti2O7 more closely than Gd2Sn2O7, where the transition is largely first-order with a peak amplitude that is roughly an order of magnitude higher, at ~100 J/mol-K.
- θW /TC ~ 10 (similar to the stannate and titanate pyrochlores)

## Entropy for Gd2Hf2O7 

- The entropy of Gd2Hf2O7 approaches Rln(8)/mol at high temperatures.
- Picture

## Heat Capacity for Gd2Zr2O7 

## Heat Capacity for Gd2Zr2O7

- The sharp peak is at TC ≈ 0.77 K, which is nearly identical to the hafnate and again consistent with long-range magnetic order.
- Our results disagree with earlier measurements of the same material by S. Lutique et al., which showed no long-range order peak.
- 	The difference is probably due to a longer annealing schedule for our samples.
- The peak amplitude is larger than that of the hafnate, and is superimposed on a broad maximum whose amplitude is lower than in the hafnate.
- The peak maximum is about 24 J/mol-K, which is again close to the mean field prediction for the 2nd order magnetic phase transition.
- This heat capacity is qualitatively distinct from both the titanate and the stannate.

## Entropy for Gd2Zr2O7

- The entropy of Gd2Zr2O7 approaches Rln(8)/mol at high temperatures.
- Picture

## Comments

- One surprising result for our heat capacity measurements is that the long-range order peak maximum for the Gd2Zr2O7 is much larger than that of the Gd2Hf2O7 , even though other investigators have associated greater crystalline disorder with the zirconate lattice
- Rietveld refinements of both zirconium and hafnium pyrochlores give results consistent with some degree of cation disorder – at least 8% in Gd2Zr2O7
- The differences between Gd2Zr2O7 and Gd2Hf2O7 are likely due to the 1% smaller radius of the Hf4+ ion – Gd3+ and Zr4+ are closer in size than Gd3+ and Hf4+.

## Conclusions

- These materials resemble the titanate and the stannate in the degree of frustration present, but their heat capacities are distinct.
- The nature of the ordered ground state for the hafnate and the zirconate remains to be determined