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arXiv:1511.02483 · Physical Review B

Quantum phase transitions and decoupling of magnetic sublattices in the quasi-two-dimensional Ising magnet Co3V2O8 in a transverse magnetic field

Katharina Fritsch, Georg Ehlers, K. C. Rule, Klaus Habicht, M. Ramazanoglu, H. A. Dabkowska, B. D. Gaulin

Published Nov 5, 2015• 10 citations
arXivHTMLPDF

Abstract

The authors present the first example of a quasi-2D experimental realization of a transverse field Ising model, which is one of the canonical examples of a quantum phase transition driven by quantum mechanical fluctuations induced by a magnetic field applied perpendicular to the preferred direction of the magnetic moments. Experimental realizations of this model are rare, and include the prominently discussed quasi-1D Ising chain system CoNb${}_{2}$O${}_{6}$, and the 3D dipolar-coupled Ising ferromagnet LiHoF${}_{4}$, but the experimental realization of a quasi-2D system has been lacking until now.

DOI
10.1103/physrevb.92.180404

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The authors present the first example of a quasi-2D experimental realization of a transverse field Ising model, which is one of the canonical examples of a quantum phase transition driven by quantum mechanical fluctuations induced by a magnetic field applied perpendicular to the preferred direction of the magnetic moments. Experimental realizations of this model are rare, and include the prominently discussed quasi-1D Ising chain system CoNb2{}_{2}2​O6{}_{6}6​, and the 3D dipolar-coupled Ising ferromagnet LiHoF4{}_{4}4​, but the experimental realization of a quasi-2D system has been lacking until now.
The Ising model in transverse magnetic field is perhaps the simplest quantum spin model, yet the elements of site disorder, random magnetic fields, and tunable quantum fluctuations permit a rich array of ground states, and the rare ability to emphasize their classical or quantum character. We briefly review in this chapter experimental results from chains to crystals of spins, with magnetic, glassy, and spin liquid ground states. Singlet Ground State Magnets In a crystalline lattice, the crystal fields often take a form such that the ground states of magnetic ions are singlets separated from the higher lying spin multiplets. Sufficiently strong magnetic dipolar or exchange couplings between different sites can mix the singlets with the multiplets enough so as to induce non-zero expectation values for the magnetic dipoles at individual sites. Examples of this phenomenon are generally found among metals and insulators based on rare earths. Such metals were a subject of extensive research in the 1960's and 1970's, and the book by MacKintosh and Jensen [408] gives an excellent account of both the data as well as mean field approaches. With respect to insulating materials, LiTbF 4 emerged as a model system in the 1970's. It is an example of an ideal Ising dipolar coupled ferromagnet; here the long-range nature of the dipolar interactions leads to an upper critical dimension [149] (at which mean field theory with logarithmic corrections calculable using RG methods becomes an exact description of thermal phase transitions) of three rather than four. LiTbF 4 belongs to the LiREF 4 isostructural series of ionic salts. Li and F carry valences +1 and −1 respectively, leaving RE, which can be any rare earth atom or the nonmagnetic element Y, with a valence of +3. Figure 14.1 shows the body-centered tetragonal crystal structure for the family.
Abstract We report on high-resolution terahertz spectroscopic studies of quantum spin dynamics in the quasi-one-dimensional Ising-like ferromagnet CoNb2O6 and antiferromagnet BaCo2V2O8 as a function of an applied transverse magnetic field. In the ordered phases stabilized by inter-chain couplings, we reveal characteristics for confined spinon excitations, E 8 dynamical spectrum, and field-induced quantum phase transitions. The connections between these characteristic dynamical features are found in the field-dependent evolution of the excitation spectra.
Abstract Motivated by the recent surge of transverse-field experiments on quasi-one-dimensional (1D) antiferromagnets Sr(Ba)Co 2 V 2 O 8 , we investigate the quantum phase transition (QPT) in a Heisenberg–Ising chain under a combination of two in-plane inter-perpendicular transverse fields and a four-period longitudinal field, where the in-plane transverse field is either uniform or staggered. We show that the model can be unitary mapped to the 1D transverse-field Ising model (1DTFIM) when the x and y components of the spin interaction and the four-period field are absent. When these two terms are present, following both analytical and numerical efforts, we demonstrate that the system undergoes a second-order QPT with increasing transverse fields, where the critical exponents as well as the central charge fall into the universality of 1DTFIM. Our results naturally identify the 1DTFIM universality of 1D quantum phase transitions observed in the existed experiments in Sr(Ba)Co 2 V 2 O 8 with transverse field applied along either [ ] or [ ] direction. Upon varying the tuning parameters, a critical surface with 1DTFIM universality is determined and silhouetted to exhibit the general presence of the universality in a much wider scope of models than conventional understanding. Our results provide a broad guiding framework to facilitate the experimental realization of 1DTFIM universality in real materials.
We present experimental evidence for a quantum phase transition in the easy-axis S=3/2S=3/2S=3/2 anisotropic quasi-one-dimensional ferromagnet ${\mathrm{CoCl}}_{2}\ifmmode\cdot\else\textperiodcentered\fi{}2{\mathrm{D}}_{2}\mathrm{O}$ in a transverse field. Elastic neutron scattering shows that the magnetic order parameter vanishes at a transverse critical field ${\ensuremath{\mu}}_{0}{H}_{c}=16.05$(4) T, while inelastic neutron scattering shows that the gap in the magnetic excitation spectrum vanishes at the same field value, and reopens for H>HcH>{H}_{c}H>Hc​. The field dependence of the order parameter and the gap are well described by critical exponents $\ensuremath{\beta}=0.45\ifmmode\pm\else\textpm\fi{}0.09$ and $z\ensuremath{\nu}$ close to 1/21/21/2, implying that the quantum phase transition in ${\mathrm{CoCl}}_{2}\ifmmode\cdot\else\textperiodcentered\fi{}2{\mathrm{D}}_{2}\mathrm{O}$ differs significantly from the textbook version of a S=1/2S=1/2S=1/2 Ising chain in a transverse field. We attribute the difference to weak but finite three-dimensionality of the magnetic interactions.
The discovery of dynamical quantum phase transitions (DQPTs) has fundamentally challenged the traditional view that phase transitions only occur in thermal equilibrium. Experimental platforms and 1D numerical methods, like matrix product states (MPS), have made great progress. However, exploring true 2D DQPTs remains difficult due to finite-size limitations and the geometric biases of quasi-1D cylinder mappings. Here, we bypass these limitations by deploying a tree tensor network (TTN) approach. This allows us to directly compute the quench dynamics of the transverse-field Ising model (TFIM) on an open 2D square lattice. Because the TTN architecture naturally mirrors 2D lattice connectivity, we can extract the global Loschmidt echo. Our simulations reveal that while deep quenches yield standard DQPTs, quenching within the ferromagnetic phase produces an anomalous dynamical response. In this regime, the rate function exhibits sharp non-analytic peaks even as the macroscopic order parameter maintains its initial sign. This decoupled behavior strongly indicates that local spin excitations drive 2D DQPTs, rather than the macroscopic domain-wall motions seen in 1D chains. These results provide a quantitative numerical baseline for understanding non-equilibrium quantum matter in higher dimensions.
The Ising chain in a transverse field stands out as a paradigmatic example for a quantum phase transition. CoNb2_22​O6_66​ has been discussed as a material realization of this physics, but it was later realized that its magnetic exchange couplings are more complicated, taking the form of twisted Kitaev chains. Here we study a three-dimensional model for CoNb2_22​O6_66​, taking into account both Kitaev physics and frustrated interchain coupling, in applied magnetic field. Using semiclassical techniques at zero temperature, we map out the sequence of field-driven phases for arbitrary field direction; these include phases with commensurate and incommensurate interchain order. As a result of spin-orbit coupling, the phase diagram is extremely sensitive to small changes in the field angle. We compute static observables as well as magnetic excitation spectra in the various phases and connect our results to existing experimental data.