Among heavy fermion materials, there is a set of rare-earth intermetallics with non-Kramers Pr 3+ 4f 2 moments which exhibit a rich phase diagram with intertwined quadrupolar orders, superconductivity, and non-Fermi liquid behavior. However, more subtle broken symmetries such as multipolar orders in these Kondo materials remain poorly studied. Here, we argue that multi-spin interactions between local moments beyond the conventional two-spin exchange must play an important role in Kondo materials near the ordered to heavy Fermi liquid transition. We show that this drives a plethora of phases with coexisting multipolar orders and multiple thermal phase transitions, providing a natural framework for interpreting experiments on the Pr(TM)2Al20 class of compounds.The celebrated Doniach picture of Kondo materials captures their evolution from magnetically ordered phases of local moments to the eventual heavy Fermi liquid phase when the local moments get fully incorporated into the Fermi sea [1][2][3][4]. These systems provide a fertile ground for the emergence of novel electronic and magnetic ground states as well as exotic quantum phase transitions [5][6][7][8][9]. While magnetic ordering of a periodic array of local moments and its influence on Kondo physics has been studied extensively, subtler forms of broken symmetry such as multipolar orders remain less explored [10][11][12][13][14][15][16][17]. In this context, recent experiments on the rare-earth intermetallics Pr(TM) 2 Al 20 (TM=Ti,V) and PrIr 2 Zn 20 are significant, showing rich phase diagrams as a function of temperature, pressure, and magnetic field, exhibiting quadrupolar orders, non-Fermi liquid physics, and superconductivity (SC) [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32].In these systems, Pr 3+ ions have a non-Kramers ground state doublet, which acts as a pseudospin-1/2 degree of freedom on the diamond lattice [21,22]. As explained later, two components of this pseudospin carry a quadrupolar moment while the third component describes an octupolar moment, so their ordering would respectively correspond to time-reversal-even quadrupolar and time-reversal-odd octupolar symmetry breakings [33]. Such ordering is expected to be driven by a Kondo-coupling to conduction electrons arising from TM and Al in Pr(TM) 2 Al 20 (TM = Ti, V). Indeed, experiments suggest ferroquadrupolar (FQ) ordering in PrTi 2 Al 20 at T 1 ≈ 2K, well above the superconducting transition temperature T c ≈ 0.2K [18,19,21,27,32]. A recent series of experiments on PrV 2 Al 20 discovered two closely spaced consecutive thermal transitions, at T 1 ≈ 0.8K and T 2 ≈ 0.7K, again well above the superconducting T c ≈ 50mK, with evidence that the higher transition at T 1 is due to antiferroquadrupolar (AFQ) order [18,30,34]. Understanding such multipolar orders is important for clarifying the phase diagram of these heavy fermion systems, including the origin of SC.On general grounds, the Doniach phase diagram of heavy fermion materials suggests that the weak Kondo coupling regime ...

Recent experiments have examined the impact of a magnetic field on ferroquadrupolar orders in the intermetallic Kondo material PrTi 2 Al 20. Motivated by this, we use extensive Monte Carlo simulations to study a diamond lattice XY model of non-Kramers pseudospin-1/2 Pr 3+ moments which crucially incorporates three-spin interactions. This model supports a thermal Z 3 Potts ordering transition upon cooling from the paramagnetic phase into the ferroquadrupolar phase. An applied magnetic field along the [110] direction leads to a thermal Ising transition out of the quadrupolar ordered phase. A magnetic field along the [001] direction leads to only thermal crossovers, but supports a spinodal transition out of metastable domains which could be strongly pinned by coupling to elastic lattice deformations. We propose noise measurements as a potential probe to "hear" the spinodal transition. Our work highlights the importance of multispin interactions in Kondo materials near the small-to-large Fermi surface transition.

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