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Quantum magnetism
NaxCoO2 – Nano-patterning and control of properties
The variety of properties such as good thermopower, unexpected three dimensional magnetism, superconductivity when hydrated, and electrochemical control of sodium concentration in sodium cobaltate, NaxCoO2, has attracted wide interest in the condensed matter community. Increasingly it was realised that the affect of the sodium concentration in the sodium layers was to control these properties. Our work in collaboration with the CEA in Saclay, Universities of London, Oxford and Liverpool, has focussed on understanding the underlying role of the sodium ions via neutron and x-ray diffraction (HZB and ISIS) and modelling this with Monte Carlo calculations (Roger et al. 2007, Morris et al. 2009). We have shown that minimising Coulomb energy between sodium ions causes clusters of vacancies to form which then order over long range (fig. 1) giving rise to superstructure peaks in the diffraction data (fig. 2). This nano-pattering of sodium ions imprints onto the Coulomb energy landscape of the cobalt layer, therefore controlling magnetism and explaining why water is required in the superconducting material in order to reduce pair-breaking potentials. Buckling of the cobalt layer creates cages around the vacancy cluster allowing the sodium ion(s) inside to rattle therefore absorbing phonons whilst not reducing electrical conductivity; improving thermoelectric properties. This system provides a possible control mechanism for industrially important applications such as thermopower.
Fig. 1: Vacancy clusters order long range in the sodium layer. Two different sodium environments are shown in red and blue.
References:
M. Roger et al. Nature 445, 631-634 (2007)
D.J.P. Morris et al. Phys. Rev. B 79, 100103 (R) (2009)
Dy2Ti2O7 - Spin-ice
Spin-ice materials undergo a freezing transition into a disordered ground state similar to water ice. The spins on the lattice are analogous to the protons in water, with two spins pointing into (out of) the tetrahedra compared to short (long) H-O bond lengths in water ice tetrahedra. The only constraint on neighbouring tetrahedra is that the total spin equals zero (2in-2out) and so these neighbours can be uncorrelated. Zero field experiments on 162Dy2Ti2O7 agree with this freezing into the spin-ice structure at low temperature (fig. 4). Recent theoretical predictions have opened up the possibility of magnetic monopoles existing at either end of ‘Dirac string’ of spins in such pyrochlore spin-ice materials (Castelnovo, Moessner and Sondhi 2008). With experiments here at HZB and in collaboration with Instituto de Fisica de Liquidos y Sistemas Biologicos (Argentina), University of St. Andrews (UK), and PTB (Berlin) improving our understanding of the microscopic behaviour of spins, the search for monopoles has become possible. Diffraction experiments are providing limits for the strings, whilst heat capacity, thermal transport and magnetometry tell us about the nonequilibrium spin dynamics. Using high accuracy squid magnetometry direct signs of the monopoles are searched for. Therefore Dy2Ti2O7 is an ideal system to test theoretical understanding of the highly frustrated spins on the pyrochlore lattice.
Fig. 3: Spin-ice coordination in a single tetrahedral.
[note: this is from commons.wikimedia.org/wiki/File:Spinice.png]
Fig. 4: E2, HZB, experimental data in the (0.42,k,l) plane showing qualitative agreement with the spin-ice correlation function.
Reference:
C. Castelnovo, R. Moessner and S.L. Sondhi. Nature 451, 42-45 (2008)
Azurite - The Blue Magnet
In addition to being useful as a painting pigment, the natural mineral, azurite is also a curious low-dimensional quantum magnet. Azurite comprises a diamond chain arrangement of spin-½ Cu2+ atoms and is considered a candidate for the first system to exhibit spin-1/3 excitations. This material exhibits a plateau in magnetization at one-third of its saturation value (Kikuchi et al.2005) in which one third of the copper spins are polarised.
Fig. 5: The diamond chain arrangement of copper atoms in azurite. In zero field two-thirds of the copper spins are coupled into dimers.
Fig. 6: For magnetic fields (|| chain) between (approx.) 11 and 30T azurite exhibits a plateau in magnetization. In this phase 1/3 of the copper spins are believed to be polarised.
Using the triple axis spectrometer, FLEX here at HZB, we have been able to investigate the spin excitation spectrum of azurite in magnetic fields both above and below the onset of the plateau phase, revealing unexpected excitations in this system. The results facilitated a determination of magnetic exchange couplings in this system (Rule et al. 2008).
References:
Kikuchi et al. Phys. Rev.Lett. 94, 227201 (2005)
Rule et al. Phys.Rev.Lett. 100, 117202 (2008)
