Discontinuous quantum and classical magnetic response of the pentakis dodecahedron*

Abstract

The pentakis dodecahedron, the dual of the truncated icosahedron, consists of 60 edge-sharing triangles. It has 20 six-fold and 12 five-fold coordinated vertices, with the former forming a dodecahedron, and each of the latter connected to the vertices of one of the 12 pentagons of the dodecahedron. When spins mounted on the vertices of the pentakis dodecahedron interact according to the nearest-neighbor antiferromagnetic Heisenberg model, the two different vertex types necessitate the introduction of two exchange constants. As the relative strength of the two constants is varied the molecule interpolates between the dodecahedron and a molecule consisting only of quadrangles. The competition between the two exchange constants, frustration, and an external magnetic field results in a multitude of ground-state magnetization and susceptibility discontinuities. At the classical level the maximum is ten magnetization and one susceptibility discontinuities when the 12 five-fold vertices interact with the dodecahedron spins with approximately one-half the strength of their interaction. When the two interactions are approximately equal in strength the number of discontinuities is also maximized, with three of the magnetization and eight of the susceptibility. At the full quantum limit, where the magnitude of the spins equals 1 2 , there can be up to three ground-state magnetization jumps that have the z-component of the total spin changing by ΔS z = 2, even though quantum fluctuations rarely allow discontinuities of the magnetization. The full quantum case also supports a ΔS z = 3 discontinuity. Frustration also results in nonmagnetic states inside the singlet-triplet gap. These results make the pentakis dodecahedron the molecule with the largest number of magnetization and susceptibility discontinuities from the quantum to the classical level, taking its size also into account.

Competition between magnetic frustration and spin dimensionality in the ground state of the classical antiferromagnetic $n$-vector model with arbitrary $n$

“…The calculations were done numerically [15,[31][32][33][34][35][36][37][38][39][40]. Each spin s i being a classical unit vector in n dimensions is defined by n − 2 polar angles varying from 0 to π and an azimuthal angle varying from 0 to 2π.…”

“…The two corresponding exchange constants are parametrized as cosω and sinω. The zero-field ground state has been calculated for d = 3, along with the magnetization response both at the classical and quantum level [40]. Figure 10 shows the reduced ground-state energy per bond of Hamiltonian (1) as a function of ω for d = 1 to 4.…”

Energy Scale Deformation on Regular Polyhedra

“…Ground-state properties of the S = 1/2 antiferromagnetic Heisenberg model on these lattices have been known for the uniform case Ĥ(N) 0 . [47][48][49][50][51][52][53][54] In this article, we introduce the modulated part Ĥ(N)…”

Classical magnetization of a four-dimensional Platonic solid

“…The two molecules are dual of one another, and they have been shown to possess a similar low-energy spectrum. Fullerenes with different symmetries have also been found to exhibit rich magnetic behavior [17][18][19] , while the next-bigger icosahedral fullerene dual, the pentakis dodecahedron, shows a very rich magnetization response as a function of the relative strength of its two symmetrically unique exchange constants 20 .…”

“…The lowest-energy configuration of Hamiltonian ( 1) is a result of the competition for minimization between the exchange and the magnetic energy, with the frustrated connectivity of the 600-cell playing a central role. Minimization of the Hamiltonian gives the lowest-energy spin configuration as a function of h 12,13,15,[18][19][20][22][23][24][25][26][27][28] .…”