March 2025 ESRFnews

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because its spins while localised on individual ions

can interact with each other Even more intriguing is

the cluster Mott insulator an emerging new class of

material that exhibits what could be called a local

delocalisation Here electrons are fully delocalised

over a dimer or another small collection of ions but

they cannot propagate from one dimer to another

This results in local magnetic moments residing not

on individual ions but on quasimolecular clusters

In contrast to the usual electron spin these cluster

moments are something that we can tailor by choosing

the ionic species cluster geometry electron count

pressure and so on,” says Grüninger.

In 2022, Grüninger and colleagues used their new

RIXS interferometry to unambiguously identify a

cluster Mott insulator for the first time. The ID20

data could directly reveal the presence of three electron

spins delocalised over an iridium dimer, creating a

cluster magnetic moment (Phys. Rev. B 106 155107) in a

compound that is a candidate for a quantum spin liquid.

The data also paved the way for a systematic exploration

of more complex compounds, for example with trimers

(Phys. Rev. B 111 085122) or tetramers, rather than

dimers. “Our results show that the trimers reside in an

unexpected parameter regime that promises non-trivial

magnetic moments,” says Grüninger. “They challenge

previous views on trimer physics, highlighting the

strength of RIXS interferometry.”

Cluster Mott insulators are exciting because of

their potential as microscopic, fine-tuned magnets, as

well as for their still-unexplored quantum properties.

They also have potential to realise quantum “spin

liquids”. First predicted by the US physicist and

Nobel laureate Philip Anderson back in the 1970s,

though experimentally elusive spin liquids excel by

the quantumdriven absence of magnetic order even

at temperatures close to absolute zero that defines

more conventional magnets They are characterised by

a quantumentangled network of strongly fluctuating

spins driven by competing interactions that cannot

be satisfied simultaneously A simplified example of

the situation is three spins on the vertices of a triangle

they may all want to align antiparallel to each other

but this is possible only for a pair of them not all three

simultaneously

According to Grüninger one can picture the electron

spins as musicians in a band In a ferromagnet the

EXOTIC MAGNETISM

FIGURE 1

S C I. A D V. 5 E A A V 4 0 2 0

Figure 1: (a) RIXS spectra of the iridium oxide Ba

3

CeIr

2

O

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measured at dif ferent momentum transfers q, corresponding to maxima (5Q, 7Q) and

minima (4Q, 6Q) of the intensity. As q changes, the peak energy remains the same, whereas the intensity varies periodically, the hallmark of

interference. This is the basis of RIXS interferometry, which can provide insights into the spatial delocalisation and entanglement of electrons

in novel magnetic materials. (b) An integration of the RIXS intensity (over the energy range highlighted by the blue box) yields the periodic

interference pattern as a function of q in units related to the lattice constant c or the intradimer Ir-Ir distance d = π/Q.

FIGURE 2

A R X I V:2 3 0 1.0 8 3 4 0

The integrated RIXS intensity (blue to red) of magnetic excitations in Na

2

IrO

3

is plotted as a function of momentum transfer along dif ferent crystallographic

directions and at dif ferent temperatures. (The q-space equivalent of the honey-

comb lattice is overlaid in black lines.) In a normal magnet, spin excitations would

be the same along the three equivalent bond directions. Here, the intensity varies

depending on the bond and its direction – one of the hallmarks of the Kitaev spin-

liquid model. Kitaev quantum spin liquids are desirable for their potential to host

Majorana fermions for quantum computing, among other applications.