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arXiv:2207.12445 · Physical review. B./Physical review. B

Investigating field-induced magnetic order in Han purple by neutron scattering up to 25.9 T

Stephan Allenspach, Alexander Madsen, Alun Biffin, Maciej Bartkowiak, O. Prokhnenko, Alsu Gazizulina, X. Liu, Robert Wahle, Sebastian Gerischer, Stephan Kempfer, P. Heller, Peter Smeibidl, Antonietta Mira, Nicolas Laflorencie, Frédéric Mila, Bruce Normand, Christian Rüegg

Published Sep 16, 2022• 2 citations
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Abstract

The material BaCuSi${}_{2}$O${}_{6}$ has a fascinating dual status as an ancient pigment (the original Terracotta Army was colored with Han purple) and as a quasi-two-dimensional quantum magnet at the modern frontier of research into unconventional quantum many-body phenomena. The HFM/EXED facility at the Helmholtz-Zentrum Berlin neutron source allowed the authors to investigate the field-driven quantum phase transition to magnetic order above 23 T by neutron diffraction and spectroscopy. They report their search for fingerprints of the exotic critical behavior predicted to appear in the two-dimensional regime.

DOI
10.1103/physrevb.106.104418

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Exotic excitations can emerge in the vicinity of a quantum phase transition. When the quantum critical point of the one-dimensional (1D) transverse field Ising model is perturbed by a longitudinal magnetic field, it was predicted that its massive excitations are precisely described by the exceptional E$_8$ Lie algebra. Here we show an unambiguous experimental realization of the massive E$_8$ phase in the quasi-1D antiferromagnetic material BaCo$_2$V$_2$O$_8$, via nuclear magnetic resonance and inelastic neutron scattering measurements, and detailed theoretical analysis. The large separation between the masked 1D and 3D quantum critical points of the system allows us to identify, for the first time, the full 8 single-particle E$_8$ excitations as well as various multi-particle states in the spin excitation spectrum. Our results open new experimental route for exploring the dynamics of quantum integrable systems and physics beyond integrability, and thus bridge key physics in condensed matter and statistical field theory.

•May 27, 2020•1 citation
The material BaCuSi2{}_{2}2​O6{}_{6}6​ has a fascinating dual status as an ancient pigment (the original Terracotta Army was colored with Han purple) and as a quasi-two-dimensional quantum magnet at the modern frontier of research into unconventional quantum many-body phenomena. The HFM/EXED facility at the Helmholtz-Zentrum Berlin neutron source allowed the authors to investigate the field-driven quantum phase transition to magnetic order above 23 T by neutron diffraction and spectroscopy. They report their search for fingerprints of the exotic critical behavior predicted to appear in the two-dimensional regime.
Bose Einstein Condensation of Magnons in BaCuSi2_{2}2​O6_{6}6​: An experimental perspective
Han Purple, a pigment first obtained in ancient China, is one of the earliest known synthetic pigments. Also naturally occurring, as a mineral, it is known as colinowensite (Cwn). Its chemical formula is BaCuSi2_{2}2​O6_{6}6​, and its structure is a layered cyclosilicate in which magnetic Cu2+^{2+}2+ ions (S = 1/2) form dimers arranged on a square lattice, making it also the first known synthetic metal dimer compound. Most interesting magnetic properties arise from a strong intradimer spin coupling, accompanied by weaker interdimer interactions within and between Cu-dimer layers. In zero or small magnetic fields, BaCuSi2_{2}2​O6_{6}6​ remains a quantum paramagnet. However, under high magnetic fields between 23 and 49 Tesla -- about a million times stronger than Earth's magnetic field -- it undergoes magnetic ordering at subliquid Helium temperatures into an almost ideal easy-plane (XY) antiferromagnetic state regarded as a realization of a Bose-Einstein condensate of magnons. Within this experimentally accessible field range, BaCuSi2_{2}2​O6_{6}6​ serves as an extraordinary playground for testing predictions of quantum many-body physics.
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.
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A layered triangular lattice with spin-1/2 ions is an ideal platform to explore highly entangled exotic states like quantum spin liquid (QSL). Here, we report a systematic in-field neutron scattering study on a perfect two-dimensional triangular-lattice antiferromagnet, CsYbSe2_22​, a member of the large QSL candidate family rare-earth chalcogenides. The elastic neutron scattering measured down to 70 mK shows that there is a short-range 120∘^{\circ}∘ magnetic order at zero field. In the field-induced ordered states, the spin-spin correlation lengths along the ccc axis are relatively short, although the heat capacity results indicate long-range magnetic orders at 3 T −-− 5 T. The inelastic neutron scattering spectra evolve from highly damped continuum-like excitations at zero field to relatively sharp spin wave modes at the plateau phase. Our extensive large-cluster density-matrix renormalization group calculations with a Heisenberg triangular-lattice nearest-neighbor antiferromagnetic model reproduce the essential features of the experimental spectra, including continuum-like excitations at zero field, series of sharp magnons at the plateau phase as well as two-magnon excitations at high energy. This work presents comprehensive experimental and theoretical overview of the unconventional field-induced spin dynamics in triangular-lattice Heisenberg antiferromagnet and thus provides valuable insight into quantum many-body phenomena.
Field-induced bound-state condensation and spin-nematic phase in SrCu2_22​(BO3_33​)2_22​ revealed by neutron scattering up to 25.9 T
Bose-Einstein condensation (BEC) underpins exotic forms of order ranging from superconductivity to superfluid 4 He. In quantum magnetic materials, ordered phases induced by an applied magnetic field can be described as the BEC of magnon excitations. With sufficiently strong magnetic frustration, exemplified by the system SrCu2_22​(BO3_33​)2_22​ , no clear magnon BEC is observed and the complex spectrum of multi-magnon bound states may allow a different type of condensation, but the high fields required to probe this physics have remained a barrier to detailed investigation. Here we exploit the first purpose-built high-field neutron scattering facility to measure the spin excitations of SrCu2_22​(BO3_33​)2_22​ up to 25.9 T and use cylinder matrix-product-states (MPS) calculations to reproduce the experimental spectra with high accuracy. Multiple unconventional features point to a condensation of S=2S = 2S=2 bound states into a spin-nematic phase, including the gradients of the one-magnon branches, the presence of many novel composite two- and three-triplon excitations and the persistence of a one-magnon spin gap. This gap reflects a direct analogy with superconductivity, suggesting that the spin-nematic phase in SrCu2_22​(BO3_33​)2_22​ is best understood as a condensate of bosonic Cooper pairs. Our results underline the wealth of unconventional states yet to be found in frustrated quantum magnetic materials under extreme conditions.
We synthesized single crystals of composition Ba2CuSi2O6Cl2{\mathrm{Ba}}_{2}{\mathrm{CuSi}}_{2}{\mathrm{O}}_{6}{\mathrm{Cl}}_{2}Ba2​CuSi2​O6​Cl2​ and investigated their quantum magnetic properties. The crystal structure is closely related to that of the quasi-two-dimensional (2D) dimerized magnet BaCuSi2O6{\mathrm{BaCuSi}}_{2}{\mathrm{O}}_{6}BaCuSi2​O6​ also known as Han purple. Ba2CuSi2O6Cl2{\mathrm{Ba}}_{2}{\mathrm{CuSi}}_{2}{\mathrm{O}}_{6}{\mathrm{Cl}}_{2}Ba2​CuSi2​O6​Cl2​ has a singlet ground state with an excitation gap of $\mathrm{\ensuremath{\Delta}}/{k}_{\mathrm{B}}=20.8$ K. The magnetization curves for two different field directions almost perfectly coincide when normalized by the ggg factor except for a small jump anomaly for a magnetic field perpendicular to the ccc axis. The magnetization curve with a nonlinear slope above the critical field is in excellent agreement with exact-diagonalization calculations based on a 2D coupled spin-dimer model. Individual exchange constants are also evaluated using density functional theory (DFT). The DFT results demonstrate a 2D exchange network and weak frustration between interdimer exchange interactions, supported by weak spin-lattice coupling implied from our magnetostriction data. The magnetic-field-induced spin ordering in Ba2CuSi2O6Cl2{\mathrm{Ba}}_{2}{\mathrm{CuSi}}_{2}{\mathrm{O}}_{6}{\mathrm{Cl}}_{2}Ba2​CuSi2​O6​Cl2​ is described as the quasi-2D Bose-Einstein condensation of triplets.
Exceptional E8_88​ symmetry in spin dynamics of quasi-one-dimensional antiferromagnet BaCo2_22​V2_22​O8_88​
Exotic excitations can emerge in the vicinity of a quantum phase transition. When the quantum critical point of the one-dimensional (1D) transverse field Ising model is perturbed by a longitudinal magnetic field, it was predicted that its massive excitations are precisely described by the exceptional E8_88​ Lie algebra. Here we show an unambiguous experimental realization of the massive E8_88​ phase in the quasi-1D antiferromagnetic material BaCo2_22​V2_22​O8_88​, via nuclear magnetic resonance and inelastic neutron scattering measurements, and detailed theoretical analysis. The large separation between the masked 1D and 3D quantum critical points of the system allows us to identify, for the first time, the full 8 single-particle E8_88​ excitations as well as various multi-particle states in the spin excitation spectrum. Our results open new experimental route for exploring the dynamics of quantum integrable systems and physics beyond integrability, and thus bridge key physics in condensed matter and statistical field theory.