Hirokazu Tsunetsugu’s research while affiliated with The University of Tokyo and other places

We numerically study orders of planer type ( x y , x 2 − y 2 ) quadrupoles on a triangular lattice with nearest-neighbor isotropic J and anisotropic K interactions. This type of quadrupole possesses unique single-ion anisotropy proportional to a third order of the quadrupole moments. This provides an unconventional mechanism of triple- q orders which does not exist for the degrees of freedom with odd parity under time-reversal operation such as magnetic dipoles. In addition to several single- q orders, we find various orders including incommensurate triple- q quasi-long-range orders with orbital moiré and a four-sublattice triple- q partial order. Our Monte Carlo simulations demonstrate that the phase transition to the latter triple- q state belongs to the universality class of the critical line of the Ashkin-Teller model in two dimensions close to the four-state Potts class. These results indicate a possibility of realizing unique quadrupole textures in simple triangular systems. Published by the American Physical Society 2024

We numerically study orders of planer type $(xy,x^2-y^2)$ quadrupoles on a triangular lattice with nearest-neighbor isotropic J and anisotropic K interactions. This type of quadrupoles possesses unique single-ion anisotropy proportional to a third order of the quadrupole moments. This provides an unconventional mechanism of triple-q orders which does not exist for the degrees of freedom with odd parity under time-reversal operation such as magnetic dipoles. In addition to several single-q orders, this system exhibits various orders including incommensurate triple-q quasi-long-range orders and a four-sublattice triple-q partial order. Our Monte-Carlo simulations demonstrate that the phase transition to the latter triple-q state belongs to the universality class of the critical line of the Ashkin-Teller model in two dimensions close to the four-state Potts class. These results indicate a possibility of realizing this unique quadrupole textures in simple triangular systems.

We study Γ3 quadrupole orders in a face-centered cubic lattice. The Γ3 quadrupole moments under cubic symmetry possess a unique cubic invariant in their free energy in the uniform (q=0) sector and the triple-q sector for the X points q=(2π,0,0),(0,2π,0), and (0,0,2π). Competition between this cubic anisotropy and anisotropic quadrupole-quadrupole interactions causes a drastic impact on the phase diagram both in the ground state and at finite temperatures. We show details about the model construction and its properties, the phase diagram, and the mechanism of the various triple-q quadrupole orders reported in our preceding letter [J. Phys. Soc. Jpn. 90, 043701 (2021)]. By using a mean-field approach, we analyze a quadrupole exchange model that consists of a crystalline-electric field scheme with the ground-state Γ3 non-Kramers doublet and the excited singlet Γ1 state. We have found various triple-q orders in the four-sublattice mean-field approximation. A few partially ordered phases are stabilized in a wide range of parameter space and they have a higher transition temperature than single-q orders. With lowering temperature, there occur transitions from these partially ordered phases into further symmetry broken phases in which previously disordered sites acquire nonvanishing quadrupole moments. The identified phases in the mean-field approximation are further analyzed by a phenomenological Landau theory. This analysis reveals results qualitatively consistent with the mean-field results and also shows that the cubic invariant plays an important role for stabilizing the triple-q states. The present mechanism for the triple-q states also takes effect in systems with different types of quadrupoles, and we discuss its implications for recent experiments in a few f- and d-electron compounds.

We study $\Gamma_3$ quadrupole orders in a face-centered cubic lattice. The $\Gamma_3$ quadrupole moments under cubic symmetry possess a unique cubic invariant in their free energy in the uniform (q=0) sector and the triple-q sector for the X points $q=(2\pi,0,0),(0,2\pi,0)$, and $(0,0,2\pi)$. Competition between this cubic anisotropy and anisotropic quadrupole-quadrupole interactions causes a drastic impact on the phase diagram both in the ground state and at finite temperatures. We show details about the model construction and its properties, the phase diagram, and the mechanism of the various triple-q quadrupole orders reported in our preceding letter [J. Phys. Soc. Jpn. 90, 43701 (2021), arXiv:2102.06346]. By using a mean-field approach, we analyze a quadrupole exchange model that consists of a crystalline-electric field scheme with the ground-state $\Gamma_3$ non-Kramers doublet and the excited singlet $\Gamma_1$ state. We find various triple-q orders in the four-sublattice mean-field approximation. A few partial orders of quadrupoles are stabilized in a wide range of parameter space at a higher transition temperature than single-q orders. With lowering the temperature, these partial orders undergo phase transitions into further symmetry broken phases in which nonvanishing quadrupole moments emerge at previously disordered sites. The obtained phases in the mean-field approximation are investigated by a phenomenological Landau theory, which clearly shows that the cubic invariant plays an important role for stabilizing the triple-q states. We also discuss its implications for recent experiments in a few f- and d-electron compounds.

We have developed a microscopic theory on phonon energy dispersion in chiral crystals within a harmonic approximation. One of the main issues is about the splitting of sound velocity of acoustic phonons with opposite ``crystal'' angular momentum. We have shown that the splitting must be zero even in chiral crystals and the difference starts from the order of at least $k^2$ or higher in their energy dispersion. Splitting is evident for chiral optical phonons, and we have derived a formula for their k-linear splitting. Another important finding is about possible interactions of atomic displacements in microscopic models. We have found that antisymmetric interactions of $\mathbf{D} _{ij} \cdot (\mathbf{d} _i \times \mathbf{d} _j)$ type are not allowed in microscopic Hamiltonians for chiral phonons in compatible with the stability against the Nambu-Goldstone mode. We have identified that the splitting in both acoustic and optical modes arises from the harmonic potentials with the electric toroidal quadrupole of $G_{u}$-type symmetry. These constraint are important for modeling real materials. Most of our microscopic calculations have been performed for (quasi-)one-dimensional systems with a trigonal crystal symmetry including Te, but these results generally hold also for other chiral phonon systems.

We theoretically study low-temperature properties of the antiferromagnetic Heisenberg model with half-integer spin S on the Kagome lattice with large trimerization. We have derived a low-energy effective model for general S in terms of spin and nematicity operators in triangular units, and studied their low-temperature correlations for S=3/2 by classical Monte Carlo simulations. The previous study for the S=1/2 case [M. Ferrero et al., Phys. Rev. B 68, 214431 (2003)] reported a spin liquid state at low temperatures driven by a glassy behavior of isolated dimers and trimers of nematicities. The results for S=3/2 show that nematicity dimers and trimers are connected by weak links to form a defective planar network. At very low temperatures, nematicities show glassy slow dynamics, and cluster spins continue to fluctuate in a nonperiodically frozen background of nematicities. The characteristic time of glassy dynamics scales with temperature following a power law.

We theoretically study electric quadrupole orders in f-electron systems on the fcc lattice. Qudrupole degrees of freedom $O_{20}$ and $O_{22}$ originate in the non-Kramers doublet ground state $\Gamma_3$ of ion with $f^2$ electron configuration. For discussing quadrupole orders, we use a minimal model with isotropic (J) and anisotropic (K) nearest-neighbor interactions, and determine the phase diagram using a four-site mean-field approximation at zero and finite temperatures. Quadrupoles couple the $\Gamma_3$ doublet to the singlet excited state $\Gamma_1$, and its effects on canting antiferro orders are examined in detail. We found that this coupling leads to a rich phase diagram including two- and four-sublattice antiferro phases, and that two phases show a partial order of quadrupoles at finite temperatures.