We propose novel triple-${\bm q}$ multipole orders as possible candidates for the two distinct low-temperature symmetry broken phases in quadrupolar system PrV$_2$Al$_{20}$. An analysis of the experiment under [111] magnetic fields indicates that the {\it ferro} octupole moments in the lower temperature phase arise from the {\it antiferro} octupole interactions. We demonstrate that the triple-${\bm q}$ multipole orders can solve this seemingly inconsistent issue. Anisotropies of quadrupole moments stabilize a triple-${\bm q}$ order, which further leads to the second transition to a coexisting phase with triple-${\bm q}$ octupole moments. The cubic invariant of quadrupole moments formed by the triple-${\bm q}$ components and the characteristic couplings with the octupole moments in their free energy play important roles. We analyze a multipolar exchange model by mean-field approximation and discuss the temperature and magnetic field phase diagrams. Many of the microscopic results, such as the number of phases and the magnitudes of critical fields in the phase diagrams, are qualitatively consistent with the experiments in PrV$_2$Al$_{20}$.
Electronic states and quadrupole orders in the 1-2-20 systems PrT2Al20 (T=Ti, V) are investigated on the basis of the first-principles band calculation. As the de Haas-van Alphen experiments reveal that the Pr-4f electrons in the systems are sufficiently localized and irrelevant for the Fermi surface, we derive the low-energy effective tight-binding models consists of 196 orbitals of conduction electrons so as to reproduce the first-principles electronic structures of LaT2Al20 (T=Ti, V) without contribution from the 4f electrons. Based on the effective models, we calculate the Ruderman-Kittel-…
Electronic states and quadrupole orders in the Pr 1-2-20 systems PrT2Al20 (T=Ti, V) are investigated on the basis of the first-principles calculations. The effective 196 orbital model is derived to reproduce the first-principles electronic structures of LaT2Al20 (T=Ti, V) without contribution from the Pr 4f electrons which are considered to be well localized and is employed to calculate the Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions between quadrupole and octupole moments of the Pr ions. Within the random phase approximation for the RKKY Hamiltonian, the most divergent susceptibility is…
We develop a microscopic theory of multipole interactions and orderings in 5$d^2$ transition metal ion compounds. In a cubic environment, the ground state of 5$d^2$ ions is a non-Kramers $E_g$ doublet, which is nonmagnetic but hosts quadrupole and octupole moments. We derive pseudospin one-half Hamiltonians describing various spin-orbital exchange processes between these ions. Direct overlap of the $t_{2g}$ orbitals results in bond-dependent pseudospin interactions similar to those for $e_g$ orbitals in manganites. The superexchange process via oxygen ions generates new types of pairwise inter…
The quantum mechanical position operators, and their products, are not well-defined in systems obeying periodic boundary conditions. Here we extend the work of Resta who developed a formalism to calculate the electronic polarization as an expectation value of a many-body operator, to include higher multipole moments, e.g., quadrupole and octupole. We define $n$-th order multipole operators whose expectation values can be used to calculate the $n$-th multipole moment when all of the lower moments are vanishing (modulo a quantum). We show that changes in our operators are tied to flows of $n-1$-…
Diffraction from Ordered States of Higher Multipoles
可能的识别方法进行了讨论的电子秩序的更高的多极，如八极和十六极。一个特别有效的方法是利用四极共振过程（称为E2）的共振X射线散射（RXS）。Ce $_{0.7}$ La $_{0.3}$ B $_6$的特征方位角依赖性被解释为反铁八极序的证据。对于PrRu $_4$ P $_{12}$，如果其金属-绝缘体转变是十六极序的结果，则预测了八重斑图对方位角的影响.在非共振超晶格布拉格散射中，由于没有四极分量，也可以识别十六极贡献。
The modern theory of electric polarization has recently been extended to higher multipole moments, such as quadrupole and octupole moments. The higher electric multipole insulators are essentially topological crystalline phases protected by underlying crystalline symmetries. Henceforth, it is natural to ask what are the consequences of symmetry breaking in these higher multipole insulators. In this work, we investigate topological phases and the consequences of symmetry breaking in generalized electric quadrupole insulators. Explicitly, we generalize the Benalcazar-Bernevig-Hughes model by add…
