Insulators occur in more than one guise, a recent finding was a class of topological insulators, which host a conducting surface juxtaposed with an insulating bulk. Here we report the observation of an unusual insulating state with an electrically insulating bulk that simultaneously yields bulk quantum oscillations with characteristics of an unconventional Fermi liquid. We present quantum oscillation measurements of magnetic torque in high purity single crystals of the Kondo insulator SmB 6 , which reveal quantum oscillation frequencies characteristic of a large three-dimensional conduction electron Fermi surface similar to the metallic rare earth hexaborides such as PrB 6 and LaB 6 . The quantum oscillation amplitude strongly increases at low temperatures, appearing strikingly at variance with conventional metallic behaviour.Kondo insulators, a class of materials positioned close to the border between insulating and metallic behaviour, provide fertile ground for unusual physics [1,2,3,4,5,6,7,8,9,10,11,12,13,14]. This class of strongly correlated materials is thought to be characterised by a 1 arXiv:1507.01129v1 [cond-mat.str-el] 4 Jul 2015

The physics of spin ice materials is intimately connected with the pyrochlore lattice, composed of corner-sharing tetrahedra. On the corners of these tetrahedra reside rare-earth magnetic moments J i , which, as a consequence of the strong crystal electric field, are constrained to point along their local trigonal axes z i , and behave like Ising spins. The magnetic interactions are composed of nearestneighbour exchange J and dipolar interactions between spins i and j separated by a distance r ij (ref. 7):wherenn ), µ 0 is the permeability of free space, g J is the Landé factor of the magnetic moment, µ B is the Bohr magneton and r nn is the nearest-neighbour distance between rareearth ions. The nearest-neighbour spin ice Hamiltonian is obtained by truncating the Hamiltonian (1), yielding:When the effective interaction J eff = (−J + 5D)/3 is positivethat is, when the dipolar term overcomes the antiferromagnetic exchange-a very unusual magnetic state develops, known as the spin ice state. The system remains in a highly correlated but disordered ground state where the local magnetization fulfils the so-called 'ice rule': each tetrahedron has two spins pointing in and two spins pointing out (see Fig. 1a), in close analogy with the rule which controls the hydrogen position in water ice 8 . The extensive degeneracy of this ground state results in a residual entropy at low temperature which is well approximated by the Pauling entropy for water ice 9 . Such highly degenerate states, where the organizing principle is dictated by a local constraint, belong to the class of Coulomb phases 5,10,11 : the constraint (the ice rule for spin ice) can be interpreted as a divergence-free condition of an emergent gauge field. This field has correlations that fall off with distance like the dipolar interaction 12,13 . In reciprocal space, this power-law character leads to bow-tie singularities, called pinch points, in the magnetic structure factor. They form a key experimental signature of the Coulomb phase physics. They have been observed by neutron diffraction in the spin ice materials Ho 2 Ti 2 O 7 and Dy 2 Ti 2 O 7 , in excellent agreement with theoretical predictions 14,15 . Classical excitations above the spin ice manifold are defects that locally violate the ice rule and so the divergence-free condition: by reversing the orientation of a moment, 'three in-one out' and 'one in-three out' configurations are created (see Fig. 1b). Considering the Ising spins as dumbbells with two opposite magnetic charges at their extremities, such defects result in a magnetic charge in the centre of the tetrahedron, called a magnetic monopole, that give rise to a non-zero divergence of the local magnetization 4 . Recently, theoreticians have introduced the concept of magnetic moment fragmentation 6 , whereby the local magnetic moment field fragments into the sum of two parts, a divergence-full and a divergence-free part (see Fig. 1c): for example, a monopole in the spin configuration m = {1, 1, 1, −1} on a tetrahedron can be written m = 1/2{1, ...

We present an experimental study of the pyrochlore coumpound Nd2Zr2O7 by means of neutron scattering and magnetization measurements down to 90 mK. The Nd 3+ magnetic moments exhibit a strong local 111 Ising anisotropy together with a dipolar-octupolar nature, different from the standard Kramers-doublet studied so far. We show that, despite the positive Curie-Weiss temperature, Nd2Zr2O7 undergoes a transition around 285 mK towards an all-in−all-out antiferromagnetic state. We establish the (H, T ) phase diagram in the three directions of the applied field and reveal a metamagnetic transition around 0.1 T. The strongly reduced ordered magnetic moment as well as the unexpected shape of the magnetization curves demonstrate that Nd2Zr2O7 is not a standard Ising antiferromagnet. We propose that the peculiar nature of the Nd doublet combined with competing interactions explain these findings.