In geometrically frustrated magnetic compounds, the ground state is the result of a subtle equilibrium between different energy terms. Exotic short range magnetic orders, like spin ices or spin liquids, may be stabilised, in the absence of any chemical disorder. Presently, many experimental and theoretical works are devoted to their understanding.
A crystal lattice where frustration plays an important role is the pyrochlore lattice. In pyrochlores with formula R2Ti2O7, the magnetic rare earth ions R3+ are located on tetrahedra linked by their summits. The local symmetry of the R site is threefold with respect to the <111> anisotropy axis joining one summit to the center in a given tetrahedron. In the presence of a magnetic field, the orientation and the magnitude of the magnetic moment of each rare earth ion is the result of a compromise between two energetic terms: the Zeeman term arising from the applied field and the crystal electric field term, which possesses its own anisotropy either parallel or perpendicular to the local axis.
How could the local magnetic susceptibility be measured? The difficulty comes from the fact that the 4 summits of a tetrahedron each have a different local <111> axis: the macroscopic susceptibility, obtained with a magnetometer, is thus an average over the 4 axes, even for a single crystal sample. The idea is to measure the susceptibility by polarised neutron diffraction, which increases the sensitivity in case the induced moments are weak (small magnetic field, high temperature). The relationship between moment and applied field is described by a susceptibility tensor which, for symmetry reasons, has only two components χ// and χ⊥. Simultaneous refinement of hundreds of diffraction peaks allows these quantities to be determined for each temperature, whatever the field direction.
Measurements done in 4 compounds (R=Ho, Tb, Yb, Er) showed that the anisotropy is either planar (Er, Yb) or axial (Tb, Ho). Most of the thermal variation of the susceptibility arises from the progressive population of the crystal field levels, the spacings of which have been determined independently par inelastic neutron scattering. In order to thoroughly explain the measured susceptibility, it is necessary to introduce an exchange and /or dipolar interaction, within a molecular field model. Rather surprisingly, it comes out also as a tensorial quantity, i.e. it is anisotropic. Even more surprising, in both cases (Er and Yb) presented here, the anisotropy seems to originate not from the dipolar coupling, which is rather classical, but from exchange itself, which is not at all classical. This new result will have to be taken into account by theorists !
Local susceptibility in Er2Ti2O7 (XY, AF) et Yb2Ti2O7 (XY, F) extracted from polarised neutron measurements in the paramagnetic phase; the dashed lines correspond to a calculation involving the crystal field alone, the solid lines the self-consistent calculations with molecular field.
1Laboratoire Léon Brillouin, CEA-CNRS, CE-Saclay, 91191 Gif-sur-Yvette, France
2Service de Physique de l'Etat Condensé, CEA-CNRS, CE-Saclay, 91191 Gif-Sur-Yvette, France
3Laboratoire de Physico-Chimie de l'Etat Solide, ICMMO, Université Paris-Sud, 91405 Orsay, France