Possibility of a new order parameter driven by multipolar moment and Fermi surface evolution in CeGe

Abstract: Polycrystalline CeGe is investigated by means of DC and AC susceptibility, non-linear DC susceptibility, electrical transport and heat capacity measurements in the low temperature regime. This compound shows two peaks at low magnetic field approximately around 10.7 and 7.3 K due to antiferromagnetic ordering and subsequent spin rearrangement respectively. Investigation of non-linear DC susceptibility reveals a presence of higher order magnetization which results in the development of a new order parameter around 10.7 K. This leads to a lowering of symmetry of the magnetic state. The order parameter increases with decreasing temperature and stabilizes around 7.3 K. Consequently, the symmetry of the magnetic state is preserved below this transition. Heat capacity and resistivity results indicate the presence of a gap opening around 10.7 K on portion of Fermi surface, due to evolution of the Fermi surface. Magnetoresistance behavior and violation of Kohlers rule suggest that the evolution of Fermi surface changes the symmetry of magnetic state. The observation of new order parameter (which is of second order) is also confirmed from the Landau free energy theory.

• The paper identifies a novel quadrupole-driven order parameter in CeGe, demonstrated by distinct anomalies in magnetic susceptibility and non-linear magnetization responses.
• Using DC/AC susceptibility, heat capacity, and transport measurements, the study reveals a partial Fermi surface gap (~1.2 meV) that emerges concurrently with the new magnetic order.
• The work outlines a detailed magnetic phase diagram, elucidating the interplay between competing multipolar and dipolar interactions in correlated 4f-electron systems.

Emergence of a Multipolar-Driven Order Parameter and Fermi Surface Evolution in Polycrystalline CeGe

Introduction

This study presents a comprehensive investigation of the strongly correlated electron system CeGe, focusing on multipolar ordering phenomena, the consequent development of a new order parameter, and Fermi surface evolution. Through DC and AC susceptibility, non-linear magnetic response, transport, and heat capacity measurements, evidence is provided for complex low-temperature magnetic states, higher-order magnetization, and significant electronic reconstruction in CeGe. The work situates itself within the context of correlated $4f$-electron physics, specifically in Ce-based intermetallics where RKKY and Kondo interactions yield competitive magnetic ground states with potential for emergent multipolar order and associated Fermi surface topology changes.

Experimental Findings and Magnetic Phase Transitions

The structural analysis confirms single-phase orthorhombic CeGe, facilitating reliable investigation of intrinsic properties. Magnetic measurements reveal two pronounced anomalies at 10.7 K and 7.3 K in low-field DC susceptibility. The higher temperature feature corresponds to long-range antiferromagnetic order, as evidenced by a negative Curie-Weiss temperature and an effective moment consistent with Ce$^{3+}$ ions. The lower temperature anomaly is attributed to a spin rearrangement, absent in prior single-crystal studies, highlighting complexity in the polycrystalline system.

AC susceptibility further corroborates these two transitions and demonstrates field-dependent suppression of low-temperature features, indicating competing magnetic interactions. The negligible frequency dependence of the susceptibility peaks rules out glassy dynamics, affirming the collective nature of the magnetic ordering.

Isothermal magnetization displays notable hysteresis at temperatures below $T_N$, consistent with a weak ferromagnetic component superimposed on antiferromagnetic order. This component is rapidly quenched in fields exceeding 1 T, aligning with the suppression of irreversibility seen in DC susceptibility.

Higher-Order Magnetization and Novel Order Parameter

Non-linear susceptibility analysis uncovers a significant third-order response ($\chi_3$) developing below $T_N$, including a sign change that signals the onset of higher-order magnetization. The pronounced $\chi_3$ at low temperatures indicates quadrupolar correlations, implying a lowering of the magnetic state symmetry due to multipolar (quadrupolar) degrees of freedom. This observation is consistent with theoretical expectations for systems hosting excited quartet ground states with doublet admixture, generating a biquadratic order parameter through quadrupole–quadrupole coupling.

Landau free energy modeling confirms these findings. Arrott plot analysis reveals a shift from positive to negative slopes upon cooling below $T_N$, supporting a second-order phase transition associated with quadrupolar order. The temperature evolution of the Landau coefficients tracks the stabilization of the new order parameter as temperature decreases.

Fermi Surface Evolution: Gap Opening and Transport Signatures

Heat capacity measurements detect a clear jump at $T_N$, with exponential decay at low temperatures indicative of a gap in the excitation spectrum. Both heat capacity and DC susceptibility fits yield a gap magnitude of approximately 14–15 K ($\sim 1.2$ meV), confirming a partial gap opens on the Fermi surface concurrent with the development of multipolar order.

Resistivity displays a Kondo lattice-like maximum at low temperature and a distinct increase at $T_N$, consistent with coherent scattering off the emergent ordered state and Fermi surface reconstruction. Magnetoresistance is quadratic in field at low $H$, with deviations at higher fields attributed to non-linearities in magnetization stemming from enhanced antiferromagnetic exchange. Analysis of Kohler's rule reveals its breakdown above 5 K, indicating temperature-dependent restructuring of the carrier scattering mechanisms tied to the evolving Fermi surface, and its restoration below approximately $T_N/2$, where the reconstructed Fermi surface and associated order parameter stabilize.

Magnetic Phase Diagram and Electronic Phase Competition

The magnetic field–temperature phase diagram extracted from the data embodies the complexity of CeGe's ground state. Five distinct regions are demarcated: an intermediate phase with strong quadrupole–dipole competition and emergent order parameter; a stabilized quadrupolar phase with preserved symmetry; a dipolar-dominated regime; long-range antiferromagnetic order at high field; and a high-temperature paramagnetic phase. Notably, the order parameter driven by quadrupolar interactions manifests in low fields and is responsible for symmetry lowering, Fermi surface gapping, and the observed electron transport anomalies.

Implications and Future Prospects

This work establishes CeGe as a prototypical system for studying the interplay of multipolar ordering and Fermi surface evolution in $4f$ compounds. The unambiguous identification of a second-order, quadrupole-driven order parameter, and its correlation with Fermi surface reconstruction, frames CeGe within the broader context of hidden order, nematicity, and complex magnetic states in strongly correlated materials. The presence of higher order magnetization and its impact on electronic symmetry breaking suggests that similar mechanisms may be operative in related heavy fermion and Kondo lattice systems, with implications for unconventional superconductivity and non-Fermi liquid behavior.

Microscopically resolving the order parameter—e.g., via resonant x-ray scattering, field-dependent neutron diffraction, or NMR—remains an outstanding objective, which will further clarify the nature of the symmetry breaking and its coupling to electronic degrees of freedom. Theoretically, these findings motivate additional modeling of multipolar interactions and their impact on Fermi surface topology.

Conclusion

The polycrystalline CeGe compound exhibits clear signatures of higher-order magnetization below $T_N$, linked to the emergence of a quadrupole-driven order parameter and partial Fermi surface gap opening. The findings are substantiated by thermodynamic, transport, and non-linear susceptibility measurements, as well as Landau order parameter analysis. CeGe thereby provides a compelling example of symmetry-lowered, multipolar-ordered states driving electronic structure reconstructions. Further experimental and theoretical work targeting the microscopic nature of the new order parameter will deepen understanding of multipolar phenomena in correlated electron systems.