Landau theory of multipolar orders in Pr(TM)${}_2$X${}_{20}$ Kondo materials

Abstract

A series of Pr(TM)${}_2$X${}_{20}$ (with TM=Ti,V,Rh,Ir and X=Al,Zn) Kondo materials, containing non-Kramers Pr${}^{3+}$ $4f^2$ moments on a diamond lattice, have been shown to exhibit intertwined orders such as quadrupolar order and superconductivity. Motivated by these experiments, we propose and study a Landau theory of multipolar order to capture the phase diagram and its field dependence. In zero magnetic field, we show that different quadrupolar states, or the coexistence of quadrupolar and octupolar orderings, may lead to ground states with multiple broken symmetries. Upon heating, such states may undergo two-step thermal transitions into the symmetric paramagnetic phase, with partial restoration of broken symmetries in the intervening phase. For nonzero magnetic field, we show the evolution of these thermal phase transitions strongly depends on the field direction, due to clock anisotropy terms in the free energy. Our findings shed substantial light on experimental results in the Pr(TM)${}_2$Al${}_{20}$ materials. We propose further experimental tests to distinguish purely quadrupolar orders from coexisting quadrupolar-octupolar orders.

9 pages, 4 figs, PRB submission

References in corpus (10)

• Quantum Criticality in Heavy Fermion Metals
• Heavy Fermions and Quantum Phase Transitions
• Heavy Fermion Superconductivity in the Quadrupole Ordered State of PrV2Al20
• Selective measurements of intertwined multipolar orders: non-Kramers doublets on a triangular lattice
• Two-stage multipolar ordering in Pr(TM)${}_2$Al${}_{20}$ Kondo materials
• NMR Observation of Ferro-quadrupole Order in PrTi2Al20
• Classical Monte Carlo study for antiferro quadrupole orders in a diamond lattice
• Anomalous specific heat behaviour in the quadrupolar Kondo system PrV2Al20
• The effect of quenched bond disorder on first-order phase transitions
• Optical gyrotropy in quadrupolar Kondo systems

Cited by in corpus (31)

• Octupolar order in d-orbital Mott insulators
• Unveiling Hidden Orders: Magnetostriction as a Probe of Multipolar-Ordered States
• Multipolar magnetism in d-orbital systems: Crystal field levels, octupolar order, and orbital loop currents
• Magnetoelectric Effects and Charge-Imbalanced Solenoids: Antiferro Quadrupole Orders in a Diamond Structure
• Field-Induced Switching of Ferro-Quadrupole Order Parameter in PrTi2Al20
• Probing octupolar hidden order via Janus impurities
• Critical theory of non-Fermi liquid fixed point in multipolar Kondo problem
• Octupolar order and Ising quantum criticality tuned by strain and dimensionality: Application to $d$-orbital Mott insulators
• Field-induced Ferrohastatic Order in Cubic Non-Kramers Doublet Systems
• Channel-selective non-Fermi liquid behavior in the two-channel Kondo lattice model under a magnetic field
• Quadrupole Orders on the fcc Lattice
• Triple-$q$ quadrupole-octupole order scenario for PrV${}_2$Al${}_{20}$
• Eight-color chiral spin liquid in the $S=1$ bilinear-biquadratic model with Kitaev interactions
• Quadrupolar spin liquid, octupolar Kondo coupling and odd-frequency superconductivity in an exactly solvable model
• Emergent non-Fermi-liquid phenomena in multipolar quantum impurity systems
• Quadrupole partial orders and triple-$q$ states on the face-centered cubic lattice
• Multipolar superconductivity in Luttinger semimetals
• Unveiling Quadrupolar Kondo Effect in the Heavy Fermion Superconductor PrV${}_2$Al${}_{20}$
• Unconventional Superconductivity arising from Multipolar Kondo Interactions
• Non-Fermi liquid behavior and quantum criticality in cubic heavy fermion systems with non-Kramers multipolar local moments
• Evolution of non-Kramers Doublets in Magnetic Field PrNi${}_2$Cd${}_{20}$ and PrPd${}_2$Cd${}_{20}$
• Phonon-driven multipolar dynamics in a spin-orbit coupled Mott insulator
• Multipolar Skyrmion Crystals in Non-Kramers Doublet Systems
• Rise and Fall of Non-Fermi Liquid Fixed Points in Multipolar Kondo Problems
• Thermal and field-induced transitions in ferroquadrupolar Kondo systems
• Fate of multipolar physics in $5d^2$ double perovskites
• Nematic and time-reversal breaking superconductivities coexisting with quadrupole order in a ${\Gamma }_3$ system
• Intertwined Magnetic Dipolar and Electric Quadrupolar Correlations in the Pyrochlore Tb${}_2$Ge${}_2$O${}_7$
• Standard model of electromagnetism and chirality in crystals
• Pseudo-chiral phonon splitting from octupolar magnetic order
• L-point quadrupole order under magnetic field in cubic PrIr${}_2$Zn${}_{20}$