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Register a new userThe Fermi volume as a probe of hidden order
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We demonstrate that the volume of the Fermi surface, measured very precisely using de Haas-van Alphen oscillations, can be used to probe changes in the nature and occupancy of localized electronic states. In systems with unconventional ordered states, this allows an underlying electronic order parameter to be followed to very low temperatures. We describe this effect in the field-induced antiferroquadrupolar (AFQ) ordered phase of PrOs4Sb12, a heavy fermion intermetallic compound. We find that the phase of de Haas-van Alphen oscillations is sensitively coupled, through the Fermi volume, to the configuration of the Pr f-electron states that are responsible for AFQ order. In particular, the beta-sheet of the Fermi surface expands or shrinks as the occupancy of two competing localized Pr crystal field states changes. Our results are in good agreement with previous measurements, above 300 mK, of the AFQ order parameter by other methods. In addition, the low temperature sensitivity of our measurement technique reveals a strong and previously unrecognized influence of hyperfine coupling on the order parameter below 300 mK within the AFQ phase. Such hyperfine couplings could provide insight into the nature of hidden order states in other systems.
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In contrast to magnetic order formed by electrons dipolar moments, ordering phenomena associated with higher-order multipoles (quadrupoles, octupoles, etc.) are more difficult to characterize because of the limited choice of experimental probes that can distinguish different multipolar moments. The heavy-fermion compound CeB6 and its La-diluted alloys are among the best-studied realizations of the long-range-ordered multipolar phases, often referred to as hidden order. Previously the hidden order in phase II was identified as primary antiferroquadrupolar (AFQ) and field-induced octupolar (AFO) order. Here we present a combined experimental and theoretical investigation of collective excitations in the phase II of CeB6. Inelastic neutron scattering (INS) in fields up to 16.5 T reveals a new high-energy mode above 14 T in addition to the low-energy magnetic excitations. The experimental dependence of their energy on the magnitude and angle of the applied magnetic field is compared to the results of a multipolar interaction model. The magnetic excitation spectrum in rotating field is calculated within a localized approach using the pseudo-spin presentation for the Gamma8 states. We show that the rotating-field technique at fixed momentum can complement conventional INS measurements of the dispersion at constant field and holds great promise for identifying the symmetry of multipolar order parameters and the details of inter-multipolar interactions that stabilize hidden-order phases.
Broken symmetries in solids involving higher order multipolar degrees of freedom are historically referred to as hidden orders due to the formidable task of detecting them with conventional probes. Examples of such hidden orders include spin-nematic order in quantum magnets, and quadrupolar or higher multipolar orders in various correlated quantum materials. In this work, we theoretically propose that the study of magnetostriction provides a powerful and novel tool to directly detect higher-order multipolar symmetry breaking $-$ such as the elusive octupolar order $-$ by examining its scaling behaviour with respect to an applied magnetic field $h$. As an illustrative example, we examine such key scaling signatures in the context of Pr-based cage compounds with strongly correlated $f$-electrons, Pr(Ti,V,Ir)$_2$(Al,Zn)$_{20}$, whose low energy degrees of freedom are composed of purely higher-order multipoles: quadrupoles $mathcal{O}_{20,22}$ and octupole $mathcal{T}_{xyz}$. Employing a symmetry-based Landau theory of multipolar moments coupled to lattice strain fields, we demonstrate that a magnetic field applied along the [111] direction results in a length change with a distinct linear-in-$h$ scaling behaviour, accompanied by hysteresis, below the octupolar ordering temperature. We show that the resulting magnetostriction coefficient is directly proportional to the octupolar order parameter, providing the first clear access to this subtle order parameter. Along other field directions, we show that the field dependence of the magnetostriction provides a window into quadrupolar orders. Our work provides a springboard for future experimental and theoretical investigations of multipolar orders and their quantum phase transitions in a wide variety of systems.
Solids with strong electron correlations generally develop exotic phases of electron matter at low temperatures. Among such systems, the heavy-fermion semi-metal URu2Si2 presents an enigmatic transition at To = 17.5 K to a `hidden order state whose order parameter remains unknown after 23 years of intense research. Various experiments point to the reconstruction and partial gapping of the Fermi surface when the hidden-order establishes. However, up to now, the question of how this transition affects the electronic spectrum at the Fermi surface has not been directly addressed by a spectroscopic probe. Here we show, using angle-resolved photoemission spectroscopy, that a band of heavy quasi-particles drops below the Fermi level upon the transition to the hidden-order state. Our data provide the first direct evidence of a large reorganization of the electronic structure across the Fermi surface of URu2Si2 occurring during this transition, and unveil a new kind of Fermi-surface instability in correlated electron systems
We report angle-resolved photoemission spectroscopy (ARPES) experiments probing deep into the hidden order (HO) state of URu2Si2, utilizing tunable photon energies with sufficient energy and momentum resolution to detect the near Fermi surface (FS) behavior. Our results reveal: (i) the full itinerancy of the 5f electrons; (ii) the crucial three-dimensional (3D) k-space nature of the FS and its critical nesting vectors, in good comparison with density-functional theory calculations, and (iii) the existence of hot-spot lines and pairing of states at the FS, leading to FS gapping in the HO phase.
Shubnikov-de Haas measurements of high quality URu2Si2 single crystals reveal two previously unobserved Fermi surface branches in the so-called hidden order phase. Therefore about 55% of the enhanced mass is now detected. Under pressure in the antiferromagnetic state, the Shubnikov-de Haas frequencies for magnetic fields applied along the crystalline c axis show little change compared with the zero pressure data. This implies a similar Fermi surface in both the hidden order and antiferromagnetic states, which strongly suggests that the lattice doubling in the antiferromagnetic phase due to the ordering vector QAF = (0 0 1) already occurs in the hidden order. These measurements provide a good test for existing or future theories of the hidden order parameter.
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