Quadrupole Orders on the fcc Lattice

Triple-$q$ quadrupole-octupole order scenario for PrV$_2$Al$_{20}$

“…The appearance of the type V for K<0 is consistent with the result in Ref. [48]. Its domain structure is rather complex.…”

“…1(b) is O 22 type with a finite ferro QM. Such parasite ferro QMs emerge also in the previous studies 27,29,30,48 and are clearly observed in Re-double perovskite recently 55 . For P2, tQtO-V state emerges subsequently, since J o 2 is large.…”

“…For the fcc lattice model, it is shown that the third-order coupling similar to Eq. ( 1) leads to the conclusion that the first-order transition temperatures of the triple-q QOs are always higher than those for the single-q in a wide range of parameter space 48 . Thus, for the present cases with J 2 >|J 1 |, a similar triple-q QO can also emerge.…”

“…Following Ref. [48], we denote Γ 3 and Γ 1 states at the site i as (|u i , |v i ) and |s i , respcetively. In terms of these bases, the QM τ i =(τ u i , τ v i ) and OM t i are expressed as…”

Electronic Nematic Ordering Driven by Atomic-scale Multipoles

“…The electronic nematic states have been discussed in various contexts, such as the Pomeranchuk instability [4][5][6], spin nematic state [7][8][9][10][11][12][13][14], and charge/orbital nematic state [15][16][17][18][19][20][21], which have been observed in d-electron materials like Ba 2 MgReO 6 [22][23][24] and f -electron materials, such as CeB 6 [25][26][27][28], PrPb 3 [29][30][31], PrT 2 X 20 (T = Ir, Rh, X = Zn; T = V, X = Al) [32][33][34][35][36], and CeCoSi [37][38][39][40][41][42][43]. Recently, further exotic states coexisting spin and nematic orders have been suggested, such as the CP 2 skyrmion [44][45][46][47] and other multiple-Q states [48][49][50]…”