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Review Report – Grant GR/L83677/02: Frustration in Pyrochlore Magnets

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Review Report – Grant GR/L83677/02: Frustration in Pyrochlore Magnets Review Report – Grant GR/L83677/02: Frustration in Pyrochlore Magnets O.A. Petrenko, University of Warwick, Department of Physics (I) Introduction The Grant “Frustration in Pyrochlore Magnets” was transferred to me after the unexpected departure from science of one of the two principal investigators, Mark Harris. At that stage approximately 2/3 of the project had been completed. Naturally, the change over at such a late stage in a project brought with it considerable difficulties. It took a significant effort to get the project back on track, but the efforts required have been generously rewarded. The unusual and, quite often, spectacular results of the project have generated an intense interest in our work by groups around the world. The success of the project is largely due to the excellent neutron scattering facilities available at the UK, along with millikelvin temperature and high magnetic field sample environments. In this report, I concentrate mostly on one aspect of the project, with which I have been directly involved, namely our studies of several high quality single crystals of the pyrochlore materials. I describe the motivation for, the methodology and the results of our neutron diffraction experiments on these materials. I also list the results of other neutron scattering experiments. The other aspects of this project, such as bulk property measurements and Monte Carlo simulation are omitted, as they have already been described in detail by Prof. Steven Bramwell, UCL, in his Review Report for the other half of this Grant. Prof. Bramwell’s report has been very highly rated by the Referee. As a result no additions or corrections to it are required. (II) The Spin Ice Concept Spin ice materials are magnetic substances in which the atomic magnetic moments obey the same ordering rules as the hydrogen atoms in ice, H2O. They provide a bridge between the simple statistical mechanics of ice-type models and the complex behaviour of frustrated magnets, with wider relevance to diverse areas of research such as high temperature superconductivity and neural networks. Furthermore, relatives of spin ice such as R2Ti2O7 (R= rare earth) are a current focus of attention for their interesting electronic properties. It is therefore important and desirable to establish the detailed physics of the simplest spin ice materials, which provide among the best model systems for the study of frustration and its broad consequences. Experiments on Ho2Ti2O7 provided the original motivation for the concept of spin ice. In Ho2Ti2O7, the magnetic Ho3+ ions occupy a cubic pyrochlore lattice, a corner-linked array of tetrahedra that is identical to the lattice formed by the mid-points of the oxygen-oxygen bonds of cubic ice. The ground state of Ho3+ is an effective Ising doublet of local <111> quantisation axis, with nearest neighbour Ho3+ moments experiencing an overall ferromagnetic coupling. Qualitatively, Ho2Ti2O7 approximates to the nearest neighbour spin ice model, in which ferromagnetically-coupled Ising spins on the pyrochlore lattice lie parallel to the local <111> axes that point towards the centres of the tetrahedra. The ground state of this model requires two spins pointing into and two pointing out of each tetrahedron. Then, if spins represent hydrogen atom displacement vectors, one obtains the ice rules that lead to Pauling's result for the extensive zero temperature entropy of the disordered ground state of ice. None of the measurements reported so far however, constitute a proof that the spin ice ground state exists in Ho2Ti2O7 or in a related material Dy2Ti2O7 in zero applied field. Moreover, a certain amount of confusion has recently arisen due to some contradictory observations: Siddharthan et al. suggested that the specific heat behaviour of Ho2Ti2O7 possibly indicates a transition to a partially ordered state at 0.8 K, in disagreement with the previous neutron scattering and muon-spin resonance results. It was only the neutron scattering data that unambiguously established the spin ice nature of the zero field spin correlations in Ho2Ti2O7 (Phys. Rev. Lett. 8704 7205 (2001)) and Dy2Ti2O7 (cond-mat/0107414). 1. Spin correlations in Ho2Ti2O7: A dipolar spin ice system Figure 1a shows the neutron scattering pattern from Ho2Ti2O7 at T~50 mK. One of the main features of the experimental data is the `four-leaf clover' of intense scattering around (000). There is also strong scattering around (003) and a broad region of slightly weaker scattering around (3/2,3/2,3/2). These intense regions are connected by narrow necks of intensity giving the appearance of bow-ties. The width of the intense regions indicates short-range correlations on the order of one lattice spacing. Qualitatively similar scattering has been observed in ice itself. For the near neighbour spin ice model the calculated pattern is shown in Fig. 1b. It successfully reproduces the main features of the experimental pattern, but there are differences, notably in the extension of the (000) intense region along (hhh) and the relative intensities of the regions around (003) and (3/2,3/2,3/2). Also, the experimental data shows much broader regions of scattering along the diagonal directions. Clearly, the experimental spin correlations do not reflect a completely disordered arrangement of ice-rule states, but some states are favoured over others. In the more complete dipolar spin ice model, the spin ice behaviour emerges from the dominant effect of the long-range nature of dipolar interactions. The calculated pattern for this model is shown in Fig 1c. It captures most details of the experimental pattern missed by the near neighbour spin ice model in Fig. 1b, such as the four intense regions around (000), the relative intensities of the regions around (003) and (3/2,3/2,3/2) and the spread of the broad features along the diagonal. Note also the low scattering intensity at (220), consistent with the experimental low intensity around at (220). Fig.1 (a) Experimental neutron scattering pattern of Ho2Ti2O7 in the (hhl) plane of reciprocal space at T~50 mK. Dark blue shows the lowest intensity level, red-brown the highest. (b) I(Q) for the nearest neighbour spin ice model at T=0.15J. (c) I(Q) for the dipolar spin ice model at T=0.6 K. The areas defined by the solid lines denote the experimental data region of (a). The difference between Figs. 1b and 1c shows that dipolar interactions, whilst inducing a low energy ice-rules manifold, do cause further correlations to emerge among the spins than those that are due to a nearest neighbour ferromagnetic interaction. This thermal bias towards certain ice-rule configurations in the dipolar model is consistent with mean field calculations. These results settle the question of the nature of the low temperature spin correlations in Ho2Ti2O7 for which contradictory claims have been made. 2. Field Induced Partial Order in the Spin-Ice Dysprosium Titanate Polycrystalline Dy2Ti2O7 was synthesised by a solid diffusion reaction starting from stoichiometric quantities of TiO2 and isotopically enriched Dy2O7. The single crystal sample of Dy2Ti2O7 was then grown by the floating zone method using infra-red image furnace. The absorption cross section of natural Dysprosium is 994 barn. Through isotopic enrichment, the absorption cross section was reduced by a factor of five to 208 barn. Neutron scattering was carried out at the ISIS facility on the indirect geometry spectrometer PRISMA configured in the diffraction mode. Rotation of the crystal allows a rapid mapping of a large section of reciprocal space, making PRISMA ideal for observing magnetic diffuse scattering. In the first experiment, the crystal was cooled by a 3He sorption refrigerator for measurements in zero applied magnetic field. It was aligned with [1-10] vertical, such that the (hhl) scattering plane included the three principal symmetry axes [100], [110] and [111]. In the second experiment, an Oxford instruments 7T vertical field cryomagnet, with dilution refrigerator insert, was used. For the applied field measurements two field orientations were studied: [1-10] as above and [100] corresponding to a (0kl) scattering plane. The data were normalised to vanadium and corrected for absorption. With [100] vertical, a map of reciprocal space was made at the base temperature (~70 mK) in zero field. The diffuse scattering maxima observed agree with those predicted in the (hhl) scattering plane for the dipolar spin ice model. On application of a field the diffuse scattering disappeared and was replaced by magnetic Bragg peaks at the Q=0 positions. A field of ~0.7 T was sufficient to saturate these peaks. This behaviour is readily explained as the applied field breaks the degeneracy of the six “two in, two out” spin configurations of the elementary tetrahedron. The pyrochlore lattice can be described as a face centred cubic lattice with a tetrahedral basis, and the degeneracy breaking means that every tetrahedron adopts the same “two in, two out” state with a net moment in the direction of the applied field, [100]. This non-collinear ferromagnetic structure allows the observed magnetic Bragg peaks at the Q=0 positions such as (200). Interestingly the experimental magnetisation did not develop smoothly, but in a series of steps. Hysteresis was observed on cycling the field. In Dy2Ti2O7 the [1-10] direction is a hard direction of magnetisation. In zero field, the magnetic scattering was observed to be diffuse, and characteristic of the disordered low temperature state of dipolar spin ice. Application of a small field (~0.1 T) in this direction again caused the appearance of the Q=0 Bragg peaks; however, unlike the [100] direction, the diffuse scattering features did not disappear. As the field was raised to 1.5 T the diffuse scattering sharpened around the Q=X positions such as (001) without becoming resolution limited.
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