Elastic softening due to the quadrupole interaction and anomalous magnetic phase diagram under the magnetic field in HoRu2Al10

Quadrupolar Response from the Crystal Electric Field Level Scheme Consisting of Only Kramers Doublets in DyNiAl

“…Ultrasonic spectroscopy is a powerful tool for investigating the quadrupole interaction [15][16][17][18][19][20][21][22][23][24]. This is because a strain induced by ultrasound bilinearly couples to a corresponding quadrupole moment.…”

Magnetic transition due to the inter-singlet spin-exchange interaction and elastic softening by the interplay of electric quadrupoles in the distorted kagome lattice antiferromagnet Tb3Ru4Al12

“…In our recent works, it was clarified that a quadrupole interaction by electric quadrupoles under the hexagonal CEF plays an important role for understanding physical properties in the R 3 Ru 4 Al 12 system [19,20,22,24]. The ultrasonic technique is a powerful tool for investigating the quadrupole interaction because a strain induced by ultrasound bilinearly couples to a corresponding quadrupole moment [25][26][27][28][29][30][31][32][33][34][35]. Here, the transverse modulus C 66 (C 44 ) is the linear responses to the ε xy and ε xx − ε yy (ε yz and ε zx ) strains which couple to the quadrupoles O xy and O 2 2 (O yz and O zx ), respectively, in the hexagonal symmetry.…”

“…Here, the transverse modulus C 66 (C 44 ) is the linear responses to the ε xy and ε xx − ε yy (ε yz and ε zx ) strains which couple to the quadrupoles O xy and O 2 2 (O yz and O zx ), respectively, in the hexagonal symmetry. The CEF analyses based on the elastic properties in addition to the magnetic properties make the results more precise [20,22,24,33,34,36]. In this work, to clarify the 4 f -electronic state under the CEF and an influence of the quadrupole interaction in Tb 3 Ru 4 Al 12 , we measured the elastic moduli using ultrasonic technique at zero magnetic field and under fields, and determined the CEF level scheme and the H-T phase diagrams.…”