Multiple Magnon Modes and Consequences for the Bose-Einstein Condensed Phase in BaCuSi 2 O 6
Christian Rüegg, MCMORROW Desmond Francis, Bruce Normand, Henrik Moodysson Rønnow, Suchitra E. Sebastian, I. R. Fisher, Cristian D. Batista, S. N. Gvasaliya, Ch. Niedermayer, Jochen Stahn
The compound BaCuSi2O6 is a quantum magnet with antiferromagnetic dimers of S=1/2 moments on a quasi-2D square lattice. We have investigated its spin dynamics by inelastic neutron scattering experiments on single crystals with an energy resolution considerably higher than in an earlier study. We observe multiple magnon modes, indicating clearly the presence of magnetically inequivalent dimer sites. The more complex spin Hamiltonian revealed in our study leads to a distinct form of magnon Bose-Einstein condensate phase with a spatially modulated condensate amplitude.
The compound BaCuSi2O6 is a quantum magnet with antiferromagnetic dimers of S=1/2 moments on a quasi-2D square lattice. We have investigated its spin dynamics by inelastic neutron scattering experiments on single crystals with an energy resolution considerably higher than in an earlier study. We observe multiple magnon modes, indicating clearly the presence of magnetically inequivalent dimer sites. The more complex spin Hamiltonian revealed in our study leads to a distinct form of magnon Bose-Einstein condensate phase with a spatially modulated condensate amplitude.
We present a 63,65Cu and 29Si NMR study of the quasi-2D coupled spin 1/2 dimer compound BaCuSi2O6 in the magnetic field range 13−−26T and at temperatures as low as 50mK. NMR data in the gapped phase reveal that below 90K different intradimer exchange couplings and different gaps $({\ensuremath{\Delta}}_{\mathrm{B}}∕{\ensuremath{\Delta}}_{\mathrm{A}}=1.16)$ exist in every second plane along the c axis, in addition to a planar incommensurate (IC) modulation. 29Si spectra in the field induced magnetic ordered phase reveal that close to the quantum critical point at Hc1=23.35T the average boson density n of the Bose-Einstein condensate is strongly modulated along the c axis with a density ratio for every second plane ${\overline{n}}_{\mathrm{A}}∕{\overline{n}}_{\mathrm{B}}\ensuremath{\simeq}5$. An IC modulation of the local density is also present in each plane.
Bose Einstein Condensation of Magnons in BaCuSi2O6: 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 BaCuSi2O6, and its structure is a layered cyclosilicate in which magnetic Cu2+ 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, BaCuSi2O6 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, BaCuSi2O6 serves as an extraordinary playground for testing predictions of quantum many-body physics.
The ground states of Bose-Einstein condensates (BECs) of spin-2 bosons are classified into three distinct phases (ferromagnetic, ``antiferromagnetic,'' and cyclic) depending on the s-wave scattering lengths of binary collisions for total-spin 0, 2, and 4 channels. Many-body spin correlations and magnetic response of the condensate in each of these phases are studied in a mesoscopic regime, while low-lying excitation spectra are investigated in the thermodynamic regime. In the mesoscopic regime, where the system is so tightly confined that the spatial degrees of freedom are frozen, the exact, many-body ground state for each phase is found to be expressed in terms of the creation operators of pair or trio bosons having spin correlations. These pairwise and trio-wise units are shown to bring about some unique features of spin-2 BECs such as a huge jump in magnetization from minimum to maximum possible values and the robustness of the minimum-magnetization state against an applied magnetic field. In the thermodynamic regime, where the system is spatially uniform, low-lying excitation spectra in the presence of magnetic field are obtained analytically using the Bogoliubov approximation. In the ferromagnetic phase, the excitation spectrum consists of one Goldstone mode and four single-particle modes. In the antiferromagnetic phase, where spin-singlet ``pairs'' undergo Bose-Einstein condensation, the spectrum consists of two Goldstone modes and three massive ones, all of which become massless when magnetic field vanishes. In the cyclic phase, where boson ``trios'' condense into a spin-singlet state, the spectrum is characterized by two Goldstone modes, one single-particle mode having a magnetic-field-independent energy gap, and a gapless single-particle mode that becomes massless in the absence of magnetic field.
We synthesized single crystals of composition Ba2CuSi2O6Cl2 and investigated their quantum magnetic properties. The crystal structure is closely related to that of the quasi-two-dimensional (2D) dimerized magnet BaCuSi2O6 also known as Han purple. Ba2CuSi2O6Cl2 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 g factor except for a small jump anomaly for a magnetic field perpendicular to the c 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 is described as the quasi-2D Bose-Einstein condensation of triplets.
Field-induced bound-state condensation and spin-nematic phase in SrCu2(BO3)2 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(BO3)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 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, 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(BO3)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.
Spin dynamics of the E8 particles
In this article, we report on inelastic neutron scattering measurements on a quasi-1D antiferromagnet BaCo2V2O8 under a transverse magnetic field applied along the (0,1,0) direction. Combining results of inelastic neutron scattering experiments, analytical analysis, and numerical simulations, we precisely studied the E8 excitations appearing in the whole Brillouin zone at Bc1D≈4.7 T. The energy scan at Q=(0,0,2) reveals a match between the data and the theoretical prediction of energies of multiple E8 excitations. Furthermore, dispersions of the lightest three E8 particles have been clearly observed, confirming the existence of the E8 particles in BaCo2V2O8. Our results lay down a concrete ground to systematically study the physics of the exotic E8 particles.