HALDANE CHAINS

In a number of quasi-one-dimensional magnets, transition metal ions obeying the motives of the crystal lattice can form chains of integer spins that are distant from each other, named Haldane chains. This paper provides a brief overview of the magnetic properties of Haldane chains and considers some compounds containing such chains. The main features of the S=1 spin chain are that it has an unordered ground state with a finite correlation length and a spin gap in the magnetic excitation spectrum. In this paper, the manifestation of these properties is considered on the example of some compounds containing chains of Ni2+ ions (S=1). The disappearance of the spin gap and the establishment of antiferromagnetic ordering can lead to inter-chain interaction (as is the case in CsNiCl3), as well as an external magnetic field (in the case of Ni(C5H14N2)2N3(ClO4)), in which the Zeeman splitting of the Haldane triplet state occurs. To date, PbNi2V2O8 is the only known compound, in which the long-range magnetic order is induced by non-magnetic dilution of S=1 chains. In contrast to the above-listed compounds, Y2BaNiO5 remains disordered down to 0.1 K. When the non-magnetic Y3+ ion in Y2BaNiO5 is replaced by the rare earth ion R3+, a three-dimensional magnetic ordering occurs in the system. However, the Haldane gap in the spectrum of magnetic excitations of nickel is preserved both in the paramagnetic region and in the ordered state. In the ordered state, there is a paradoxical coexistence of the Haldane phase and spin waves, and the ordering occurs in the rare-earth subsystem, while the nickel subsystem remains internally disordered.

New signatures of the spin gap in quantum point contacts

One dimensional semiconductor systems with strong spin-orbit interaction are both of fundamental interest and have potential applications to topological quantum computing. Applying a magnetic field can open a spin gap, a pre-requisite for Majorana zero modes. The spin gap is predicted to manifest as a field dependent dip on the first 1D conductance plateau. However, disorder and interaction effects make identifying spin gap signatures challenging. Here we study experimentally and numerically the 1D channel in a series of low disorder p-type GaAs quantum point contacts, where spin-orbit and hole-hole interactions are strong. We demonstrate an alternative signature for probing spin gaps, which is insensitive to disorder, based on the linear and non-linear response to the orientation of the applied magnetic field, and extract a spin-orbit gap ΔE ≈ 500 μeV. This approach could enable one-dimensional hole systems to be developed as a scalable and reproducible platform for topological quantum applications.