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Unravelling Multipole Order with RXS


How electrons organise themselves to form the abundance of states of matter found in nature, such as magnets, superconductors, ferroelectrics, metals, insulators etc., is of fundamental importance in contemporary condensed matter physics. It also underpins advances in technology and associated industry. A deeper understanding of collective phenomena may be obtained through investigations of how states form and transform into one another, or become critical, under external constraints such as temperature, applied magnetic and electric fields, pressure or through selective doping.

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Long range order does not come for free. The entropy cost is balanced by a lowering of potential energy and, at criticality, many possible electron states compete with one another. The final configuration, as expressed at the microscopic level by its quantum mechanical state, frequently exhibits some form of collective alignment, or phase coherence, on macroscopic space-time scales. This is characterised by introduction of an order parameter.

As a simple example, ferromagnetic order arises from the mutual, parallel alignment, of electronic magnetic moments. More sophisticated configurations, such as 'up' 'down' 'up' 'down' antiferromagnetic and more slowly twisting helical states of the moments also occur. It is important to note that, whilst ferromagnetism yields a macroscopic moment, as exploited since 4000 BC by Chinese navigators, the signatures of the more subtle antiferromagnetic states have required the development of scattering techniques. Currently, a veritable 'zoo' of diverse dipole magnetic structures have been discovered and classified by X-ray and neutron diffraction. Moreover, the familiar magnetic dipole is not alone; higher order geometric constructs, generically known as multipoles, may compete with the dipolar couplings and, in some instances, become the primary order parameter.

A powerful new microscope of both magnetic and multipole order is provided by resonant X-ray scattering (RXS). As a pertinent example of its use, we focus on the mysterious, unknown, order parameter of 'Phase IV' which occurs in Ce0.7La0.3B6 below a critical temperature, Tc, of 1.5 K.

The phase coherence is crucial to the order parameter on account of the entropy. It is often strongest at low temperature. Therefore, a microscopic probe that can be used under cryogenic conditions is central to investigate the underlying order. Recent experiments at the XMaS beamline [1], the success of which has hinged crucially on the implementation of a compact low temperature cryostat [2], have revealed a new state of compound electronic order in this compound below Tc. The results indicate that at 1.0 Kelvin, the polarisation of the 4f states exhibits octupole symmetry, which coexists with dipole magnetic order of the 5d levels, as shown in Figure 1.

schematic representation of the Ce ion order within the Ce0.7La0.3B6 crystal cell

Fig. 1: A schematic representation of the Ce ion order within the Ce0.7La0.3B6 crystal cell, in the Phase IV. The 5d dipole magnetic moment, coupled antiferromagnetically between adjacent (111) planes (dashed line), is represented by the red arrows. The octupole symmetry motif of the 4f electrons is represented by the blue triangles with the same alternating order. The detailed octupole structural model is described in reference [1].


The inherent element and electron shell selectivity of the RXS technique permits separation of the electronic phase coherence occurring in both the Ce 4f and 5d orbitals. A dramatic difference is found in the temperature dependence of Ce 4f and 5d order as shown in Figure 2. Moreover, the spatial correlation lengths are also quite distinct as shown in the insert, where the contrasting sharp 4f and the broad 5d response correspond to long and short range order respectively. The azimuth and polarisation dependence confirm that the 5d electron moments order with dipole magnetic symmetry whilst the 4f response is uniquely explained by the presence of octupole order [1]. In this manner we have been able to elucidate and study the microscopic properties of the elusive 'Phase IV' revealing it to be a novel state of dipole-octupole electronic order parameter segregation at low temperature.

The low temperature X-ray resonant scattering response

Fig. 2: The low temperature X-ray resonant scattering response separated into two orthogonal polarisation channels where the photon electric field vector is respectively un-rotated, , and /2 rotated, , with respect to the incident beam. A dramatic difference is observed in the thermal and spatial (see insert) responses from the 4f and 5d electronic states. The figure supplies crucial evidence establishing the presence of low temperature electronic order parameter segregation at the mesoscopic level in Phase IV.

[1] D. Mannix, Y. Tanaka, D. Carbone, N. Bernhoeft and S. Kunii, Physical Review Letters 95, 117206 (2005).
[2] D. Mannix, P. Thompson, S. Brown, L. Bouchenoire and P. Canfield, Physica B. 353, 121 (2004).

D. Mannix, ESRF