Dipolar-octupolar correlations and hierarchy of exchange interactions in Ce 2 Hf 2 O 7

High-resolution neutron spectroscopy on <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:msub> <a:mi mathvariant="normal">Ce</a:mi> <a:mn>2</a:mn> </a:msub> <a:msub> <a:mi mathvariant="normal">Hf</a:mi> <a:mn>2</a:mn> </a:msub> <a:msub> <a:mi mathvariant="normal">O</a:mi> <a:mn>7</a:mn> </a:msub> </a:math> reveals a correlated state characterized by distinct dipolar scattering signals—quasielastic and inelastic contributions consistent with ‘photon’ and ‘spinon’ excitations in quantum spin ice. These signals coexist with weak octupolar scattering. Fits of thermodynamic data using numerical methods indicate a dominant octupolar exchange, <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:msub> <e:mi>J</e:mi> <e:mi>x</e:mi> </e:msub> </e:math> or <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:msub> <f:mi>J</f:mi> <f:mi>y</f:mi> </f:msub> </f:math> , with substantial dipolar <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:msub> <g:mi>J</g:mi> <g:mi>z</g:mi> </g:msub> </g:math> and minute dipole-octupole <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:msub> <h:mi>J</h:mi> <h:mrow> <h:mi>x</h:mi> <h:mi>z</h:mi> </h:mrow> </h:msub> </h:math> couplings. The <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"> <i:msub> <i:mi>J</i:mi> <i:mrow> <i:mi>x</i:mi> <i:mi>z</i:mi> </i:mrow> </i:msub> </i:math> value is corroborated by an independent fit of the neutron scattering amplitude balance between dipolar and octupolar ‘photon’ contributions, highlighting its importance to understand neutron scattering results in this family. <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"> <j:msub> <j:mi mathvariant="normal">Ce</j:mi> <j:mn>2</j:mn> </j:msub> <j:msub> <j:mi mathvariant="normal">Hf</j:mi> <j:mn>2</j:mn> </j:msub> <j:msub> <j:mi mathvariant="normal">O</j:mi> <j:mn>7</j:mn> </j:msub> </j:math> enriches the landscape of dipole-octupole pyrochlore physics, and reveals a ‘quantum multipolar liquid’ where hybrid correlations involve multiple terms in the moment series expansion, opening questions regarding their intertwining and hierarchy in quantum phases.