“…Multipoles can also be defined in an extended scale over several atomic sites and such cluster-type extensions have recently garnered great attention as a source of intriguing phenomena [3][4][5][6][7][8][9][10][11]. For instance, a magnetic toroidal dipole induces the second harmonic generation in LiCoPO 4 [12], and the magnetocurrent effect in UNi 4 B [6,13] and Ce 3 TiBi 5 [14], a magnetic octupole plays a crucial role in the anomalous Hall effect [7,15], the anomalous Nernst effect [16], and the magneto-optical Kerr effect [17] in Mn 3 Sn, and a magnetic quadrupole causes the magnetoelectric effect in A(TiO)Cu 4 (PO 4 ) 4 (A=Ba, Sr, and Pb) [18][19][20][21]. Thus, it is useful to identify relevant multipoles for predicting the electronic, magnetic, transport, and optical properties.…”