Session G55: 1D Magnetism

Uncovering new low-dimensional magnets: A computational toolbox and experimental results

A quantitative geometric predictor for the dimensionality of magnetic interactions has been released as a free searchable database. This predictor is based on networks of superexchange interactions and can be quickly calculated for crystalline compounds of arbitrary chemistry, occupancy, or symmetry. The resulting data are useful for classifying structural families of magnetic compounds. Starting with 42,520 compounds, we have classified and quantified compounds with 3d transition metal cations. The predictor reveals trends in magnetic interactions that are often not apparent from the space group of the compounds, such as triclinic or monoclinic compounds that are strongly 2D. We present specific cases where the predictor identifies compounds that should exhibit competition between 1D and 2D interactions, and how the predictor can be used to identify sparsely-populated regions of chemical space with as-yet-unexplored topologies of specific 3d magnetic cations. Use of the toolkit to identify new low-dimensional spin-1/2 materials will be discussed, along with the prospects for future applications to rare-earth systems.   

Spins, magnons, and phonons in the quasi-1D material MoI3

Quasi-1D materials are interesting for both basic and applied physics. MoI₃ has attracted special attention due to its strongly 1D character. In the Pmmn phase, each Mo atom is surrounded by 6 chalcogen atoms in distorted octahedral coordination forming dimerized chains. The chains are weakly coupled to neighboring chains in a triangular lattice.  Density functional theory calculations find an antiferromagnetic (AFM) ground state with an easy plane perpendicular to the chains, alternating spins along the dimerized chains, and a spin spiral texture from chain to chain. The calculated magnetic moments of ~3 μ_B per Mo ion are consistent with Mo³⁺ with 3 electrons in the t_2g ground state resulting from the octahedral crystal field splitting. Exchange coupling constants are extracted for a Heisenberg-type magnetic Hamiltonian, which is then solved for the magnon dispersion using linear spin wave theory. The phonon spectrum is determined, and the frequencies of the phonon and magnon spectra match well with measured Raman peaks [1]. The anisotropic thermal conductivity is also determined from the phonon Boltzmann transport equation.

[1] F. Kargar et al., arXiv preprint arXiv:2210.05081 (2022).

    

LT Scaling in Depleted Quantum Spin Ladders

Using a combination of neutron scattering, calorimetry, quantum Monte Carlo simulations, and analytic results we uncover confinement effects in depleted, partially magnetized quantum spin ladders. We show that introducing nonmagnetic impurities into magnetized spin ladders leads to the emergence of a new characteristic length L in the otherwise scale-free Tomonaga-Luttinger liquid (serving as the effective low-energy model). This results in universal LT scaling of staggered susceptibilities. Comparison of simulation results with experimental phase diagrams of prototypical spin ladder compounds bis(2,3-dimethylpyridinium)tetrabromocuprate(II) (DIMPY) and bis(piperidinium)tetrabromocuprate(II) (BPCB) yields excellent agreement.   

Experimental evaluation of quantum entanglement measures in spin chain systems

Fractionalized excitations in quantum magnets such as 1D Heisenberg S=1/2 systems (quantum spin chains) are known to present evidence of quantum entangled states. Conventionally, systems with larger angular momenta (S≥3/2) are closer to the classical limit and therefore quantum entanglement is less important. Some rare earth systems nevertheless exhibit S=1/2 physics due to the selection of ground-state Kramers doublets by strong spin-orbit coupling and crystal electric fields. Here we present analysis of inelastic neutron scattering experiments, aiming to evaluate how the prevalence of quantum collective behavior (multipartite entanglement) manifests itself in the effective S=1/2 case of a rare earth Yb ion. We turn to recent advances to the analysis of neutron spectra, which have shown it possible to calculate certain model-independent measures of multipartite entanglement. These entanglement measures, such as the quantum Fisher information, can place quantitative bounds on the degree of entanglement which may be present in a system. These have already been evaluated by others on KuCF₃ [1], a system of weakly coupled S=1/2 chains. Here, we analyze entanglement measures in a rare earth material YbAlO₃[2], which demonstrates clear two-spinon spectra characteristic of quantum spin chains and compare it with the case of a higher-spin transition metal system. Special attention is paid to the behavior of these entanglement measures at magnetic field and temperature points near known thermal and quantum phase transitions.

 

References:

[1] A. Scheie, Pontus Laurell, A. M. Samarakoon, B. Lake, S. E. Nagler, G. E. Granroth, S. Okamoto, G. Alvarez, D. A. Tennant. Witnessing entanglement in quantum magnets using neutron scattering. Phys. Rev. B 103, 224434 (2021).

[2] L. S. Wu, S. E. Nikitin, Z. Wang, W. Zhu, C. D. Batista, A. M. Tsvelik, A. M. Samarakoon, D. A. Tennant, M. Brando, L. Vasylechko, M. Frontzek, A. T. Savici, G. Sala, G. Ehlers, A. D. Christianson, M. D. Lumsden, A. Podlesnyak, Tomonaga–Luttinger liquid behavior and spinon confinement in YbAlO3, Nature Comm., 10, 698 (2019).

    

Critical Low-Energy Spin Dynamics in the BEC-Type Antiferromagnets

The NMR nuclear spin-lattice relaxation rate (1/T₁) data in quantum spin systems provide privileged access to low-energy spin fluctuations and are directly comparable to theoretical predictions for the corresponding spin-spin correlation functions. In particular, gapless quasi-1D systems are addressed by the Tomonaga-Luttinger Liquid (TLL) theory, a purely 1D, effective, low-energy description, providing a 1D-critical, power-law prediction for the temperature (T) dependence of 1/T₁. We showed that in real compounds an RPA-based correction factor has to be applied to this power-law, in order to account for the enhancement of the 1/T₁ rate induced by the 3D-critical fluctuations related to the low-T BEC ordering. Using this TLL+RPA description, we successfully fitted the 1/T₁(T) data in a spin-ladder compound (C₇H₁₀N)₂CuBr₄ (DIMPY) and in an Ising spin chain BaCo₂V₂O₈, providing thereby the first direct determination of the TLL interaction parameter K that confirms the theoretical predictions [1].

We now focus on describing spin fluctuations in quasi-2D systems, where our results in Ba₂CuSi₂O₆Cl₂ suggest that the 1/T₁ data could provide a clear signature for the system’s effective dimensionality. However, we find only a partial agreement with the Quantum Monte Carlo (QMC) simulations, leaving the subject open to further investigation.

Finally, from the 1/T₁ data recorded precisely at the saturation field in the SrZnVO(PO₄)₂ compound we learn that the theoretically predicted quantum critical T^3/4 dependence cannot be experimentally accessed in any compound, because the convergence into this low-T limit is too slow and the theoretical prediction is no longer valid when the BEC transition is too close. Nevertheless, the complete description provides correct semi-quantitative account of the data [2].   

First-principles investigation of the electronic and magnetic properties of quasi-one-dimensional MoBr3

We investigate the electronic and magnetic properties of molybdenum tribromide, MoBr₃ using first-principles density functional theory. MoBr₃ consists of weakly coupled one-dimensional chains in which each Mo³⁺ ion is surrounded by a Br octahedron, face-sharing with neighboring octahedra. The ground state structure exhibits dimerization of Mo-Mo pairs with alternating short and long bonds, consistent with the experimental report. We find an insulating ground state with antiferromagnetic ordering having a magnetic moment of 1.8 µ_B on each Mo atom, smaller than the fully polarized value of 3 µ_B from the d³ filling of Mo, indicating orbital-dependent hybridization, which reduces the magnetic moment of Mo- d_z² orbitals extending along the dimer direction. Comparison of the electronic structures of dimerized and non-dimerized antiferromagnetic phases shows that the dimerized phase is preferred. Energy lowering by a bonding-antibonding splitting of the Mo-d_z² bands from dimerization is larger than increasing the magnetic moment without dimerization, indicating the dominant inter-orbital hopping exceeding the Hund coupling for the d_z² orbitals. We identify the interplay between on-site and inter-site interaction in the system with nominal Mo-d³ filling leads to orbital-dependent suppression of the magnetic moments, manifested from the quasi one-dimensional geometry.   

Neutron diffraction studies on the Pr3HfBi5 magnetic structure

Members of the Ln3MBi5 family (Ln=Pr, Nd, Sm; M=Zr, Hf) crystallize in the P6₃/mcm space group, hosting the anti-Hf5Sn3Cu structure type. [1] Hypervalent Bi²⁻ chains and face-sharing MBi₆ octahedra form one-dimensional chains along the c-axis, and a framework of Ln³⁺ cations charge balances and separates the two motifs. The local symmetry of the Ln ion is orthorhombic, which for Pr³⁺ splits the J = 4 multiplet into 9 singlets and would typically result in a non-magnetic Pr³⁺ ion. However, Pr₃HfBi₅ orders antiferromagnetically at 4 K with a wavevector k = (1/2, 1/2, 1/10). Bulk magnetization measurements further show strong magnetic anisotropy, with a broad ordering temperature in susceptibility along the c-axis, and a sharp transition within the ab-plane. Here, we present neutron diffraction results on the magnetic structure of Pr₃HfBi₅ and compare to the magnetic structures of isostructural materials. For example, Pr₃TiSb₅ is non-magnetic [2] despite the Pr-Pr bonds being closer together than in Pr₃HfBi₅, where an increase in the exchange coupling strength would be expected, suggesting that subleties in the CEF splitting lead to the long range magnetic order here.

[1] J. F. Khoury et al. Z. Anorg. Allg. Chem., 648, e202200123 (2022).

[2] C. Ritter et al. J. Phys.: Condens. Matter, 33, 245801 (2021).   

Magnetic Field Induced Transitions in Spin-1 Antiferromagnet NiNb2O6

Recent observations of quantum critical excitations (QCE) in columbite systems such as NiNb₂O₆ and CoNb₂O₆ have brought great attention to the field of Quantum Materials so that QCE can be realized for T > 0 K. [1,2]. Here we present detailed studies of magnetic field induced transitions in NiNb₂O₆ mapped on the field-temperature (H-T) phase diagram. The crystal structure analysis of the prepared sample of NiNb₂O₆ using X-ray diffraction and Rietveld refinement reveals orthorhombic crystal structure of space group is Pbcn (D_2h¹⁴) with lattice parameters a = 14.038(3) Å, b = 5.684(3) Å and c = 5.025(3) Å. The unit cell essentially consists of layers of Ni–Nb–Nb–Ni–Nb–Nb–Ni with slightly distorted hexagonal-closed-packed oxygen octahedra perpendicular to the a-axis. Low-temperature magnetic susceptibility (χ-T) measurements reveal antiferromagnetic (AFM) behavior below the Néel temperature T_N ~ 5.8 K along with two field induced transitions at H_C1 ~ 9.7 kOe and H_C2 ~ 27.8 kOe. The best fits of χ vs. T data for T > 40 K to modified Curie-Weiss law χ = χ₀ + C/(T-θ) with χ₀ = -2.3 × 10^-4 emu mol^-1 Oe^-1 yield θ = +11 K, and C = 1.36 emu K mol^-1 Oe^-1, the latter yielding the effective magnetic moment µ = 3.3 µ_B /Ni²⁺ ion confirming the effective spin S = 1 and g = 2.3, and the principal exchange interaction J₀ being ferromagnetic as in CoNb₂O₆ [3]. The H-T phase diagram mapped using the M-H isotherms and χ -T data at different fields will be discussed along with the intra-chain (J₀) and inter-chain (J₁ and J₂) exchange interactions determined from H_C1 and H_C2.

References:

[1] Y. Xu, et al. Phys. Rev. X 12, 021020 (2022)

[2] T. Liang et al.  Nat. Commun. 6, 7611 (2015)

[3] S. Thota et al., Phys. Rev. B 103, 064415 (2021)   

Quasiballistic transport and long-living fermionic excitations in long-range anisotropic Heisenberg model

Purely ballistic transport is a rare feature even for integrable models. By numerically studying the Heisenberg chain with the power-law exchange, J∼1/r^α, where r is a distance, we show that for spin anisotropy Δ≈exp(-α+2) the system exhibits a quasiballistic spin transport and the presence of fermionic exictations which do not decay up to extremely long times ∼10³/J. This conclusion is reached on the base of the dynamics of spin domains, the dynamical spin conductivity, inspecting the matrix elements of the spin-current operator, and by the analysis of most conserved operators. Our results smoothly connects two models where fully ballistic transport is present: free particles with nearest-neighbor hopping and the isotropic Haldane-Shastry model.   

Phase Transitions in the Ferromagnetic Region of the spin-S Bilinear-Biquadratic Spin Chain

We study ferromagnetic region of the spin-S bilinear-biquadratic spin chain. While the spin S=1 case has been massively studied, higher-S case has been less studied. In this study, we focus on the ferromagnetic region in the higher-S case and find an exact phase-transition point between fully polarized ferromagnetic-phase and partially polarized ferromagnetic-phase by using numerical exact-diagonalization method up to S=3. The partially polarized ferromagnetic-phase has fractional magnetization M=1-1/(2S) under zero magnetic-field; for example, M=2/3 for S=3/2, and M=3/4 for S=2. In addition, at a high symmetric point in the partially polarized ferromagnetic-phase, we find rigorous eigen-state correspondence between spin-S model and spin-1/2 antiferromagnetic model, which can be generalized to any dimensional lattices. This is nothing but ``spin-1/2 liquefaction'' of ferromagnet. Even after spontaneous magnetization, the ground state has quantum entanglement due to a spin-1/2 antiferromagnetic quantum state in ferromagnetic classical background. External magnetic field generated by this ``fractional ferromagnet'' has the potential to become a manipulation handle of an entangled quantum state in the context of quantum computer science.