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arXiv:2306.07389

Field-induced bound-state condensation and spin-nematic phase in SrCu$_2$(BO$_3$)$_2$ revealed by neutron scattering up to 25.9 T

Ellen Fogh, Mithilesh Nayak, O. Prokhnenko, Maciej Bartkowiak, Koji Munakata, Jian-Rui Soh, Alexandra A. Turrini, Mohamed Zayed, Ekaterina V. Pomjakushina, Hiroshi Kageyama, Hiroyuki Nojiri, Kazuhisa Kakurai, Bruce Normand, Frédéric Mila, Henrik Moodysson Rønnow

Published Jun 12, 2023• 0 citations
arXivHTMLPDF

Abstract

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 SrCu$_2$(BO$_3$)$_2$ , 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 SrCu$_2$(BO$_3$)$_2$ 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 $S = 2$ 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 SrCu$_2$(BO$_3$)$_2$ 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.

DOI
10.48550/arxiv.2306.07389

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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.
Abstract In quantum magnetic materials, ordered phases induced by an applied magnetic field can be described as the Bose-Einstein condensation (BEC) of magnon excitations. In the strongly frustrated system SrCu2(BO3)2, no clear magnon BEC could be observed, pointing to an alternative mechanism, 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(BO3)2 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 = 2 bound states into a spin-nematic phase, including the gradients of the one-magnon branches 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(BO3)2 is best understood as a condensate of bosonic Cooper pairs.
Low dimensional quantum magnets which display a collective singlet ground state and a gap in their magnetic excitation spectrum provide a framework for much exotic phase behavior in new materials, with high temperature superconductivity being the best appreciated example. Neutron scattering techniques can be applied to study a wide variety of problems in condensed matter physics. These techniques are particularly useful as applied to understanding the magnetic properties of quantum magnets that display exotic phases. SrCu2(BO3)2, is a rare example of a two-dimensional quantum magnet for which an exact theoretical solution describing its ground state is known to be a collective singlet. Previous high resolution neutron scattering measurements identified the most prominent features of the spin excitation spectrum in SrCu2(BO3)2, including the presence of one and two triplet excitations and weak dispersion characteristic of subleading terms in the spin Hamiltonian. The resemblance between the spin gap behavior in the Mott insulator SrCu2(BO3)2 and that associated with high temperature superconductors motivated the consideration of the significance of doping in order to understand the properties of this quantum magnetic system. For this reason, a series of neutron scattering studies on doped SrCu2(BO3)2 were initiated. These series of investigations began with the performance of neutron scattering measurements on a SrCu(2-x)Mgx(BO3)2 single crystal in order to introduce magnetic vacancies to the system. These results revealed the presence of new spin excitations within the singlet-triplet gap of this system. Application of a magnetic field induces Zeeman-split states associated with un-paired spins which exist as a consequence of doping with quenched non-magnetic impurities. Additional substantial broadening of both the one and two triplet excitations is observed in the doped system as compared to the pure system. Theoretical calculations are shown to qualitatively account for these features. These studies were extended to neutron scattering measurements on Sr(1-x)LaxCu2(BO3)2, with an aim of introducing charged carriers into this system. The broadening of the one and two triplet excitations is observed and compared to the thermally induced finite lifetime of the pure system. The temperature dependence of this broadening in Sr(1-x)LaxCu2(BO3)2 is different compared to that observed in both SrCu2(BO3)2 and SrCu(2-x)Mgx(BO3)2. It has also been suggested that there is a relation between the spin-lattice interaction in SrCu2(BO3)2 and the magnetic dynamics at low temperatures and high magnetic fields. For this reason there has been increased interest in the study of the crystalline structure and vibrational modes of SrCu2(BO3)2. In order to investigate the role of the lattice in the formation of the singlet ground state in SrCu2(BO3)2, a series of low and high energy neutron scattering measurements were carried out on this system to study both the crystalline structure as well as the normal modes of vibration of the lattice, the transverse acoustic and optical phonons. Transverse acoustic phonons with energies comparable to and higher than the onset of the two triplet continuum show substantially increased lifetimes on entering the singlet ground state below ~ 10 K. This may indicate the removal of the decay channel for the phonons due to the gapping of the spin excitation spectrum in SrCu2(BO3)2 at low temperatures. In high energy inelastic neutron scattering we observe broadening of optic phonons in the ~ 52 to 65 meV region on entering the low temperature singlet ground state. Additionally, the magnetic properties of CuMoO4, which is a triclinic quantum magnet system based on S=1/2 moments at the Cu2+ site, were studied using elastic and inelastic neutron scattering experiments. This material exhibits a first order structural phase transition at ~ 190 K as well as a magnetic phase transition at ~ 1.75 K. We were primarily interested in the low temperature magnetic properties of this material. Magnetization and heat capacity measurements as well as elastic and inelastic neutron scattering measurements were conducted on this system within the low temperature ordered phase. These studies confirm that this material has a magnetic phase transition at ~ 1.7 K. Neutron scattering results indicate that this magnetically ordered phase is characterized by a doubling of the a axis. Inelastic neutron scattering measurements revealed a gapped magnetic excitation spectrum in zero magnetic field, which could be filled in by the application of magnetic fields approaching 7 T.
Abstract Under magnetic fields, quantum magnets often undergo exotic phase transitions with various kinds of order. The discovery of a sequence of fractional magnetization plateaus in the Shastry-Sutherland compound SrCu 2 (BO 3 ) 2 has played a central role in the high-field research on quantum materials, but so far this system could only be probed up to half the saturation value of the magnetization. Here, we report the first experimental and theoretical investigation of this compound up to the saturation magnetic field of 140 T and beyond. Using ultrasound and magnetostriction techniques combined with extensive tensor-network calculations (iPEPS), several spin-supersolid phases are revealed between the 1/2 plateau and saturation (1/1 plateau). Quite remarkably, the sound velocity of the 1/2 plateau exhibits a drastic decrease of -50%, related to the tetragonal-to-orthorhombic instability of the checkerboard-type magnon crystal. The unveiled nature of this paradigmatic quantum system is a new milestone for exploring exotic quantum states of matter emerging in extreme conditions.
We present inelastic neutron-scattering data on the quantum paramagnet AgVOAsO4{\mathrm{AgVOAsO}}_{4}AgVOAsO4​ that establish this system as a S=1/2S=1/2S=1/2 alternating spin chain compound and provide a direct measurement of the spin gap $\mathrm{\ensuremath{\Delta}}=1.2\phantom{\rule{0.16em}{0ex}}\mathrm{meV}$. We also present experimental evidence for two different types of field-induced magnetic order between ${\ensuremath{\mu}}_{0}{H}_{c1}=8.4\phantom{\rule{0.16em}{0ex}}\mathrm{T}$ and ${\ensuremath{\mu}}_{0}{H}_{c2}=48.9\phantom{\rule{0.16em}{0ex}}\mathrm{T}$, which may be related to Bose-Einstein condensation (BEC) of triplons. Thermodynamic measurements in magnetic fields up to 60 T and temperatures down to 0.1 K reveal a $H\ensuremath{-}T$ phase diagram consisting of a dome encapsulating two ordered phases with maximum ordering temperatures of 3.8 and 5.3 K, respectively. This complex phase diagram is not expected for a single-$\stackrel{P\vec}{Q}$ BEC system and therefore establishes AgVOAsO4{\mathrm{AgVOAsO}}_{4}AgVOAsO4​ as a promising multi-$\stackrel{P\vec}{Q}$ BEC candidate capable of hosting exotic vortex phases.
We study the ground state and the magnetization process of a spin-1∕21∕21∕2 ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ model with a plaquette structure by using various methods. For small interplaquette interaction, this model is expected to have a spin gap and we computed the first and the second excitation energies. If the gap of the lowest excitation closes, the corresponding particle condenses to form magnetic orders. By analyzing the quintet gap and magnetic interactions among the quintet excitations, we find a spin-nematic phase around ${J}_{1}∕{J}_{2}\ensuremath{\sim}\ensuremath{-}2$ due to the strong frustration and the quantum effect. When high magnetic moment is applied, not the spin-1 excitations but the spin-2 ones soften and dictate the magnetization process. We apply a mean-field approximation to the effective Hamiltonian to find three different types of phases (a conventional BEC phase, ``striped'' supersolid phases, and a 1∕21∕21∕2 plateau). Unlike the BEC in spin-dimer systems, this BEC phase is not accompanied by transverse magnetization. Possible connection to the recently discovered spin-gap compound (CuCl)LaNb2O7(\mathrm{Cu}\mathrm{Cl})\mathrm{La}{\mathrm{Nb}}_{2}{\mathrm{O}}_{7}(CuCl)LaNb2​O7​ is discussed.
Field-Induced Spin Excitations in the Spin-1/2 Triangular-Lattice Antiferromagnet CsYbSe2_22​
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.