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arXiv:2208.09246 · Physical review. B./Physical review. B

S=1 dimer system K2Ni(MoO4)2 : A candidate for magnon Bose-Einstein condensation

Benjamin Lenz, B. Koteswararao, Silke Biermann, P. Khuntia, M. Baenitz, Swarup Kumar Panda

Published Nov 29, 2022• 5 citations
arXivHTMLPDF

Abstract

Dimerized quantum magnets provide a unique possibility to investigate the Bose-Einstein condensation of magnetic excitations in crystalline systems at low temperature. Here, we model the low-temperature magnetic properties of the recently synthesized spin $S=1$ dimer system ${\mathrm{K}}_{2}\mathrm{Ni}{({\mathrm{MoO}}_{4})}_{2}$ and propose it as a candidate material for triplon and quintuplon condensation. Based on a first-principles analysis of its electronic structure, we derive an effective spin dimer model that we first solve within a mean-field approximation to refine its parameters in comparison to experiment. Finally, the model is solved by employing a numerically exact quantum Monte Carlo technique which leads to magnetic properties in good agreement with experimental magnetization and thermodynamic results. We discuss the emergent spin model of ${\mathrm{K}}_{2}\mathrm{Ni}{({\mathrm{MoO}}_{4})}_{2}$ in view of the condensation of magnetic excitations in a broad parameter regime. Finally, we comment on a geometrical peculiarity of the proposed model and discuss how it could host a supersolid phase upon structural distortions.

DOI
10.1103/physrevb.106.l180408

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Dimerized quantum magnets provide a unique possibility to investigate the Bose-Einstein condensation of magnetic excitations in crystalline systems at low temperature. Here, we model the low-temperature magnetic properties of the recently synthesized spin S=1S=1S=1 dimer system K2Ni(MoO4)2{\mathrm{K}}_{2}\mathrm{Ni}{({\mathrm{MoO}}_{4})}_{2}K2​Ni(MoO4​)2​ and propose it as a candidate material for triplon and quintuplon condensation. Based on a first-principles analysis of its electronic structure, we derive an effective spin dimer model that we first solve within a mean-field approximation to refine its parameters in comparison to experiment. Finally, the model is solved by employing a numerically exact quantum Monte Carlo technique which leads to magnetic properties in good agreement with experimental magnetization and thermodynamic results. We discuss the emergent spin model of K2Ni(MoO4)2{\mathrm{K}}_{2}\mathrm{Ni}{({\mathrm{MoO}}_{4})}_{2}K2​Ni(MoO4​)2​ in view of the condensation of magnetic excitations in a broad parameter regime. Finally, we comment on a geometrical peculiarity of the proposed model and discuss how it could host a supersolid phase upon structural distortions.
An asymmetric Bose-Einstein condensation (BEC) dome was observed in a recent experiment on the quantum dimer magnet Yb2Si2O7e{\mathrm{Yb}}_{2}{\mathrm{Si}}_{2}{\mathrm{O}}_{7}\mathrm{e}Yb2​Si2​O7​e [G. Hester et al., Phys. Rev. Lett. 123, 027201 (2019)], which is modeled by a ``breathing'' honeycomb lattice Heisenberg model with possible anisotropies. We report a remarkable agreement between key experimental features and predictions from numerical simulations of the magnetic model. Both critical fields, as well as critical temperatures of the BEC dome, can be accurately captured, as well as the occurrence of two regimes inside the BEC phase. Furthermore, we investigate the role of anisotropies in the exchange coupling and the ggg tensor. While we confirm a previous proposal that anisotropy can induce a zero-temperature phase transition at magnetic fields smaller than the fully polarizing field strength, we find that this effect becomes negligible at temperatures above the anisotropy scale. Instead, the two regimes inside the BEC dome are found to be due to a nonlinear magnetization behavior of the isotropic breathing honeycomb Heisenberg antiferromagnet. Our analysis is performed by combining the density matrix renormalization group (DMRG) method with the finite-temperature techniques of minimally entangled typical thermal states (METTS) and quantum Monte Carlo (QMC).
Besides being an ancient pigment, BaCuSi2O6{\mathrm{B}\mathrm{a}\mathrm{C}\mathrm{u}\mathrm{S}\mathrm{i}}_{2}{\mathrm{O}}_{6}BaCuSi2​O6​ is a quasi-2D magnetic insulator with a gapped spin dimer ground state. The application of strong magnetic fields closes this gap, creating a gas of bosonic spin triplet excitations. The topology of the spin lattice makes BaCuSi2O6{\mathrm{B}\mathrm{a}\mathrm{C}\mathrm{u}\mathrm{S}\mathrm{i}}_{2}{\mathrm{O}}_{6}BaCuSi2​O6​ an ideal candidate for studying the Bose-Einstein condensation of triplet excitations as a function of the external magnetic field, which acts as a chemical potential. In agreement with quantum Monte Carlo numerical simulations, we observe a distinct lambda anomaly in the specific heat together with a maximum in the magnetic susceptibility upon cooling down to liquid helium temperatures.
We study properties of magnetic field-induced Bose-Einstein condensate of triplons as a function of temperature and the field within the Hartree-Fock-Bogoliubov approach including the anomalous density. We show that the magnetization is continuous across the transition, in agreement with the experiment. In sufficiently strong fields the condensate becomes unstable due to triplon-triplon repulsion. As a result, the system is characterized by two critical magnetic fields: one producing the condensate and the other destroying it. We show that nonparabolic triplon dispersion arising due to the gapped bare spectrum and the crystal structure has a strong influence on the phase diagram.
Dimerized quantum magnets provide a useful arena for novel quantum states and phases transitions with the singlet-triplet type of triplon excitations. Here we study the triplon physics and the Bose-Einstein condensation in two isostructural dimerized antiferromagnets AAACu(SeO3_33​)2_22​ (AAA = Hg, Cd). With the systematic measurements, we demonstrate a dimer singlet ground state in HgCu(SeO3_33​)2_22​ with a triplon gap ∼\sim∼ 7.9 K and a triplon Bose-Einstein condensation with an antiferromagnetic order in CdCu(SeO3_33​)2_22​ below 4.4 K. We further adopt the bond-operator technique and show that the elemental replacement preserves the Hamiltonian and allows the study in a unified theoretical framework with tunable interdimer and intradimer interactions on the opposite sides of the quantum critical point. With the peculiar Cu2_22​O8_88​ dimer configuration and effective ferromagnetic interdimer interaction, AAACu(SeO3_33​)2_22​ is distinguished from other SSS = 1/2 dimerized antiferromagnets. Our results represent a global understanding of the magnetic ground states as well as the magnetic transitions in the dimerized magnets of this unusual crystal structure.
The recent experimental advances in the field of quantum spin materials have led to well-controlled systems which can be used in order to simulate complex quantum models in a clean fashion. Here we discuss how fascinating effects normally known from bosonic systems such as the Bose-Einstein condensation can be investigated with the help of such materials. We discuss as an example how a crossover between an effectively one-dimensional geometry described by a Luttinger liquid to a three-dimensional Bose-Einstein condensation can be induced. Additionally, we point out how more complex phases as the Bose-glass phase could be realized in these quantum magnets. Introduction Although it can seem paradoxical, the quantum magnetic states found in insulators offer an interesting route to study Bose-Einstein condensation (BEC) and more generally phenomena related to itinerant, interacting bosonic systems. In many materials, the repulsion between the electrons causes the ground state to be a Mott insulator with one electron localized per site. In such a case, the charge degrees of freedom are completely locked by large charge gaps (usually of the order of tens of electron volts). However, one can study the fascinating physics of the spin degrees of freedom. As was shown a long time ago, the localized spins are coupled by a so-called superexchange which may be ferro- or antiferromagnetic. The properties of the exchange coupling between the spins depend mainly on the underlying atomic structure of the material. The resulting physics is extremely rich and such materials can have a host of phases ranging from ordered magnetic phases to so-called spin-liquid phases in which spin–spin correlations decay extremely fast with distance. The field of research concerning these materials, dubbed quantum magnetism, is thus an extremely active field in its own right [1]. Additionally, one can exploit the formal mapping that exists between spin operators and bosonic ones, as will be described in the next section, to connect the magnetic materials to itinerant bosonic systems with interactions between the bosons. This opens the way to use such quantum spin systems as quantum simulators. A quantum simulator means that the experimental system can be employed in order to “solve” in a controlled way a problem/Hamiltonian known from a different less controlled physical realization, e.g., inspired by fundamental many-body physics, quantum information or computational applications.
Using the quantum Monte Carlo method, we study, under external magnetic fields, the ground state phase diagram of the two-dimensional spin S=1/2 dimer model with an anisotropic intraplane antiferromagnetic coupling. With the anisotropy 4 greater/approximately Delta greater/approximately 3, a supersolid phase characterized by a nonuniform Bose condensate density that breaks translational symmetry is found. The rich phase diagram also contains a checkerboard solid, an antiferromagnet in the z axis, and a superfluid phase formed by S(z)= +1 spin triplets which has a finite staggered magnetization in the in-plane direction. As we show, the model can be realized as a consequence of including the next nearest neighbor coupling among dimers and our results suggest that spin dimer systems may be an ideal model system to study the supersolid phase.