Quantum magnetism and frustrated magnets

Finite temperature tensor network algorithm for frustrated 2D quantum materials

We present a two-dimensional tensor network algorithm to study finite temperature properties of frustrated model quantum systems and real quantum materials. To obtain state-of-the-art benchmarking results, we explore the highly challenging spin-1/2 Heisenberg antiferromagnet on the Kagome lattice, a system for which we investigate the melting of the magnetization plateaus at finite magnetic field and temperature. Making a close connection to actual experimental data of real quantum materials, we go on to studying the finite temperature properties of Ca₁₀⁢Cr₇⁢O₂₈

P Schmoll, C Balz, B Lake, J Eisert, and A Kshetrimayum, Phys. Rev. B 109 (2024) 235119

Spin dynamics of the E8 particles

A quantum phase transition arises at zero temperature when the system is tuned by a non-thermal parameter. For a continuous quantum phase transition, novel physics with higher symmetry may emerge at the quantum critical point (QCP). As the system is driven away from the QCP with a relevant perturbation, exotic physics may further emerge. The transverse-field Ising chain is a paradigmatic model: when an Ising chain is perturbed by a longitudinal field parallel to the Ising direction, the quantum E₈ integrable model emerges — a massive relativistic quantum field theory containing eight massive E₈ particles.

Xiao Wang, K Puzniak, K Schmalzl, C Balz, M Matsuda, A Okutani, M Hagiwara, J Ma, J Wu, B Lake, Science Bulletin 69 (2024) 2974 (OA) 

Field-induced bound-state condensation and spin-nematic phase in SrCu₂(BO₃)₂

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.

E Fogh, M Nayak, O Prokhnenko, M Bartkowiak, K Munakata, J-R Soh, AA Turrini, ME Zayed, E Pomjakushina, H Kageyama, H Nojiri, K Kakurai, B Normand, F Mila, and HM Rønnow, Nature Commun 15 (2024) 442

See also the associated highlight report

Spinon Heat Transport in PbCuTe_2⁢O₆ 

Quantum spin liquids (QSLs) are novel phases of matter which remain quantum disordered even at the lowest temperature. They are characterized by emergent gauge fields and fractionalized quasiparticles. Here we show that the sub-Kelvin thermal transport of the three-dimensional S = 1/2 hyperhyperkagome quantum magnet PbCuTe₂⁢O₆ is governed by a sizeable charge-neutral fermionic contribution which is compatible with the itinerant fractionalized excitations of a spinon Fermi surface. We demonstrate that this hallmark feature of the QSL state is remarkably robust against sample crystallinity, large magnetic field, and field-induced magnetic order, ruling out the imitation of QSL features by extrinsic effects. Our findings thus reveal the characteristic low-energy features of PbCuTe₂⁢O₆ which qualify this compound as a true QSL material.

X Hong, M Gillig, ARN Hanna, S Chillal, ATMN Islam, B Lake, B Büchner, and C Hess, Phys Rev Lett 131 (2023) 256701, OA version

Quantum wake dynamics in Heisenberg antiferromagnetic chains

Traditional spectroscopy, by its very nature, characterizes physical system properties in the momentum and frequency domains. However, the most interesting and potentially practically useful quantum many-body effects emerge from local, short-time correlations. Here, using inelastic neutron scattering and methods of integrability, we experimentally observe and theoretically describe a local, coherent, long-lived, quasiperiodically oscillating magnetic state emerging out of the distillation of propagating excitations following a local quantum quench in a Heisenberg antiferromagnetic chain. This “quantum wake” displays similarities to Floquet states, discrete time crystals and nonlinear Luttinger liquids. We also show how this technique reveals the non-commutativity of spin operators, and is thus a model-agnostic measure of a magnetic system’s “quantumness.”

A Scheie, P Laurell, B Lake, SE Nagler, MB Stone, J-S Caux, DA Tennant, Nat Commun 13 (2022) 5796 (OA)

See also the associated highlight report

Spin liquid and ferroelectricity close to a quantum critical point in PbCuTe₂O₆

We report a comprehensive study of thermodynamic, magnetic and dielectric properties on single crystalline and pressed-powder samples of PbCuTe₂O₆, a candidate material for a 3D frustrated quantum spin liquid featuring a hyperkagome lattice. Whereas the low-temperature properties of the powder samples are consistent with the recently proposed quantum spin liquid state, an even more exotic behavior is revealed for the single crystals. These crystals show ferroelectric order at T_FE ≈ 1 K, accompanied by strong lattice distortions, and a modified magnetic response—still consistent with a quantum spin liquid—but with clear indications for quantum critical behavior

C Thurn, P Eibisch, A Ata, M Winkler, P Lunkenheimer, I Kézsmárki, U Tutsch, Y Saito, S Hartmann , J Zimmermann, ARN Hanna, ATM Islam, S Chillal, B Lake, B Wolf, and M Lang, npj Quantum Materials (2021) 6:9 (OA)

Weak three-dimensional coupling of Heisenberg quantum spin chains in SrCuTe₂O₆

We studied the magnetic Hamiltonian of the Heisenberg quantum antiferromagnet SrCuTe₂O₆ by inelastic neutron scattering above and below the magnetic transition temperatures at 8 and 2 K. The high-temperature spectra reveal a characteristic diffuse scattering corresponding to a multispinon continuum, confirming the dominant quantum spin chain behavior due to the third neighbor interaction. The low-temperature spectra exhibit sharper excitations at energies <1.25 meV, which can be explained by considering a combination of weak antiferromagnetic first nearest neighbor interchain coupling J₁ and even weaker ferromagnetic second nearest neighbor J₂. These results suggest that SrCuTe₂O₆ is a highly one-dimensional Heisenberg system with three mutually perpendicular spin chains coupled by a weak ferromagnetic J₂ in addition to the antiferromagnetic J₁.

S Chillal, ATMN Islam, P Steffens, R Bewley, B Lake, Phys Rev B 104 (2021) 144402, OA version

Magnetization Process of Atacamite

We present a combined experimental and theoretical study of the mineral atacamite Cu₂⁢Cl⁢(OH)₃. Density-functional theory yields a Hamiltonian describing anisotropic sawtooth chains with weak 3D connections. Experimentally, we fully characterize the antiferromagnetically ordered state. Magnetic order shows a complex evolution with the magnetic field, while, starting at 31.5 T, we observe a plateaulike magnetization at about M_sat/2. Based on complementary theoretical approaches, we show that the latter is unrelated to the known magnetization plateau of a sawtooth chain. Instead, we provide evidence that the magnetization process in atacamite is a field-driven canting of a 3D network of weakly coupled sawtooth chains that form giant moments.

L Heinze, HO Jeschke, II Mazin, A Metavitsiadis, M Reehuis, R Feyerherm, J-U Hoffmann, M Bartkowiak, O Prokhnenko, AUB Wolter, X Ding, VS Zapf, MC Corvalán, F Weickert, M Jaime, KC Rule, D Menzel, R Valentí, W Brenig, and S Süllow, Phys Rev Lett 126 (2021) 207201 (OA)

Signatures for Berezinskii-Kosterlitz-Thouless critical behavior

Neutron diffraction and muon spin rotation measurements on the spin-1 honeycomb antiferromagnet BaNi₂⁢V₂⁢O₈ in the critical regime, both below and above the ordering temperature T_N, characterize BaNi₂⁢V₂⁢O₈ as a two-dimensional (2D) antiferromagnet across the entire temperature range, displaying a series of crossovers from 2D XY to 2D XXZ and then to 2D Heisenberg behavior with increasing temperature. The extracted critical exponent of the order parameter reveals a narrow temperature regime close to T_N, in which the system behaves as a 2D XY antiferromagnet. Above T_N, evidence for Berezinskii-Kosterlitz-Thouless behavior driven by vortex excitations is obtained from the scaling of the correlation length.  

ES Klyushina, J Reuther, L. Weber, ATMN Islam, JS Lord, B Klemke, M. Månsson, S Wessel, and B Lake, Phys Rev B 104 (2021) 064402 (OA)

Witnessing entanglement in quantum magnets

We demonstrate how quantum entanglement can be directly witnessed in the quasi-1D Heisenberg antiferromagnet ${\mathrm{KCuF}}_3$. We apply three entanglement witnesses—one tangle, two tangle, and quantum Fisher information—to its inelastic neutron spectrum and compare with spectra simulated by finite-temperature density matrix renormalization group (DMRG) and classical Monte Carlo methods. We find that each witness provides direct access to entanglement. Of these, quantum Fisher information is the most robust experimentally and indicates the presence of at least bipartite entanglement up to at least 50 K, corresponding to around 10% of the spinon zone-boundary energy. We apply quantum Fisher information to higher spin-$S$ Heisenberg chains and show theoretically that the witnessable entanglement gets suppressed to lower temperatures as the quantum number increases. Finally, we outline how these results can be applied to higher dimensional quantum materials to witness and quantify entanglement.

A Scheie, P Laurell, AM Samarakoon, B Lake, SE Nagler, GE Granroth, S Okamoto, G Alvarez, DA Tennant, Phys Rev B 103 (2021) 224434 (OA)

See also the associated highlight report

Evidence for a three-dimensional quantum spin liquid in PbCuTe₂O₆

Quantum spin liquids are very rare and are confined to a few specific cases where the interactions between the magnetic ions cannot be simultaneously satisfied (known as frustration). Lattices with magnetic ions in triangular or tetra-hedral arrangements, which interact via isotropic antiferromagnetic interactions, can generate such a frustration. Three-dimensional isotropic spin liquids have mostly been sought in materials where the magnetic ions form pyrochlore or hyperkagome lattices. Here we present a three-dimensional lattice called the hyper-hyperkagome that enables spin liquid behaviour and manifests in the compound PbCuTe₂O₆. Using a combination of experiment and theory, we show that this system exhibits signs of being a quantum spin liquid with no detectable static magnetism together with the presence of diffuse continua in the magnetic spectrum suggestive of fractional spinon excitations.

S Chillal, Y Iqbal, HO Jeschke, JA Rodriguez-Rivera, R Bewley, P Manuel, D Khalyavin, P Steffens, R Thomale, ATMN Islam, J Reuther, B Lake, Nat Commun 11 (2020) 2348 (OA)

See also the associated highlight report

 

Follow-up publications:

ARN Hanna, ATMN Islam, R Feyerherm, K Siemensmeyer, K Karmakar, S Chillal, B Lake,
Phys Rev Materials 5 (2021) 113401, OA version

P Eibisch, C Thurn, A Ata, Y Saito, S Hartmann, U Tutsch, B Wolf, ATMN Islam, S Chillal, ARN Hanna, B Lake, M Lang, Phys Rev B 107 (2023) 235133, OA version

Dispersions of many-body Bethe strings

Complex bound states of magnetic excitations, known as Bethe strings, were predicted almost a century ago to exist in one-dimensional quantum magnets. The dispersions of the string states have so far remained the subject of intensive theoretical studies. By performing neutron scattering experiments on the one-dimensional Heisenberg–Ising antiferromagnet SrCo₂V₂O₈ in high longitudinal magnetic fields, we revealed in detail the dispersion relations of the string states over the full Brillouin zone, as well as their magnetic field dependencies. Furthermore, the characteristic energy, the scattering intensity and linewidth of the observed string states exhibit excellent agreement with our precise Bethe–ansatz calculations. Our results establish the important role of string states in the quantum spin dynamics of one-dimensional systems, and will invoke studies of their dynamical properties in more general many-body systems.

AK Bera, J Wu, W Yang, R Bewley, M Boehm, J Xu, M Bartkowiak, O Prokhnenko, B Klemke, ATMN Islam, JM Law, Z Wang, and B Lake, Nat Phys 16 (2020) 625, OA version

See also the associated highlight report

Order out of a Coulomb Phase and Higgs Transition in Nd₂Zr₂O₇

The pyrochlore material ${\mathrm{Nd}}_2{\mathrm{Zr}}_2{O}_7$ with an “all-in-all-out” (AIAO) magnetic order shows novel quantum moment fragmentation with gapped flat dynamical spin ice modes. The parametrized spin Hamiltonian with a dominant frustrated ferromagnetic transverse term reveals a proximity to a U(1) spin liquid. We studied the magnetic excitations of ${}_{\mathrm{Nd2Zr2O7}}$ above the ordering temperature ($T_N$) using high-energy-resolution inelastic neutron scattering. Our findings relate the magnetic ordering of ${\mathrm{Nd}}_2{\mathrm{Zr}}_2{O}_7$ with the Higgs mechanism and provide explanations for several previously reported experimental features.

J Xu, O Benton, ATMN Islam, T Guidi, G Ehlers, and B Lake, Phys Rev Lett 124 (2020) 097203 (OA)