Session S53: 1D Spin Chains: New Path

Bespoke S = 1 quantum magnets based on planar, staggered or chiral architectures

We aim to control the spatial exchange and single-ion anisotropies (D) in bespoke S = 1 Ni(II) quantum magnets so that we may determine the Hamiltonian parameters to access novel regions of magnetic-field/temperature phase diagrams. Early work led to [Ni(HF₂)(pyz)₂]SbF₆ (pyz = pyrazine) which contains Ni-FHF-Ni chains (J_FHF) cross-linked by Ni-pyz-Ni segments (J_pyz) to form a tetragonal network [1]. The material undergoes long-range XY-AFM order below T_N = 12.2 K with collinear Ni(II) moments aligned in the [Ni(pyz)₂]²⁺ plane. High-field M(H) and inelastic neutron scattering (INS) revealed D ≈ J_FHF >> J_pyz. Exploiting differences in donor-atom hardness yields anisotropic lattice-strain by introducing isotropic Zn(II) ions in [Zn_0.8Ni_0.2(HF₂)(pyz)₂]SbF₆ [2]. Dimensional reduction of [Ni(HF₂)(pyz)₂]SbF₆ with monocoordinate 3,5-lutidine (lut) leads to neutral molecules of NiX₂(lut)₄ (X = HF₂, F‧H₂O, Cl, Br, I) that pack in X-Ni-X‧‧‧X-Ni-X columns [3]. The more diffuse electron density of iodide affords I‧‧‧I close contacts and Haldane physics with J_1D = 17.5 K and D = -1.2 K [4]. NiBr₂(lut)₄ displays weak intrachain coupling and D > 0 whilst X = HF₂, F‧H₂O and Cl demonstrate single-ion behavior [3]. Further chemical substitution of pyz for pyrimidine (pym) produces staggered or chiral topologies and enhanced magnetic interactions along Ni-pym-Ni relative to Ni-pyz-Ni. Along these lines, two new Q1D chains have been synthesized: staggered [Ni(pym)(H₂O)₂(NO₃)₂] [5], which is isostructural to the well-known S = 1/2 Cu(II) sine-Gordon system [6], and chiral Q1D [Ni(pym)(H₂O)₄]SO₄‧H₂O [5]. Both materials exhibit multiple field-induced phase transitions at low-temperatures. Lastly, we will describe a unique 3D chiral Ni(II) framework based on a diamond lattice with 90° alternately-rotated Ni(II) sites [5]. Time permitting, the structural and magnetic properties of these materials will be discussed.   

Magnetic interactions in the S=1/2 1D spin-chain metal-organic compound Cu(N2H5)2(SO4)2

Low dimensional 1D chains or 2D layers of magnetic ions with reduced spin offer promising routes to drive non-trivial topological and quantum behavior. Coordination polymers, or equivalently magnetic metal-organic frameworks (MOFs), with both organic and inorganic building blocks provide the ability to design these tailored structural motifs due to the versatility and predictability of organic chemistry. In this presentation we will focus on one such intriguing series of compounds M(N₂H₅)2(SO₄)₂, where M is a transition metal ion, which forms isolated 1D-spin chains. The behavior of the S=1/2 Cu compound is compared with the S=5/2 Mn material through detailed low temperature elastic and inelastic neutron measurements and analysis. These provide insights into the magnetic interactions and structure in these materials. In addition, polarized neutron diffraction measurements were utilized to determine the local susceptibility tensor in both compounds and these results will be discussed.    

Electronic and magnetic structure of 4f atomic chains on Au(111) substrate

The study of low-dimensional magnetic systems has been greatly enhanced by the unique ability to create one- (1D) and two-dimensional atomic arrangements of magnetic atoms on a variety of substrates.  These studies have focused on transition metal atoms and islands deposited on insulating and metallic surfaces, including superconductors.  Scanning probe techniques have unveiled rich magnetic phase diagrams and different excitation spectra.  We direct here our attention to the study of 1D atomic chains formed by rare-earth 4f systems on the Au(111) surface, and study their electronic and magnetic configurations by different theoretical techniques.  Ab initio calculations using VASP with GGA+U and HSE functional, with and without spin-orbit interactions, allow for full structural relaxation of the system. 1D chains of Eu atoms on Au(111) surface show minimal charge transfer, reflecting physisorption of neutral Eu on gold.  Different spatial and magnetic configurations and relative spin orientations are parameterized in terms of a spin-Hamiltonian with collinear and non-collinear exchange interactions, as spin-orbit coupling on the substrate is substantial.  Typical exchange parameters of ~0.5 meV promise readily observable characteristics in low-temperature experiments.  Luttinger-Tisza and exact diagonalization approaches of the spin system predict interesting phase diagrams for these structures.    

Decoupled Spin Dynamics in the Rare-Earth Orthoferrite YbFeO3

We present an inelastic neutron scattering study of magnetic dynamics in YbFeO₃ at temperatures below and above the spin-reorientation (SR) transition T_SR = 7.6K and in magnetic field. The spectrum of magnetic excitations consists of two types of collective modes that are well separated in energy: gapped magnons with a typical bandwidth of ~60 meV, associated with the antiferromagnetically (AFM) ordered 3d subsystem, and quasi-1D AFM fluctuations of ~1 meV within the rare-earth subsystem. The spin dynamics of the Fe subsystem could be well described in the frame of semiclassical linear spin-wave theory. The rotation of the net moment of the Fe subsystem at T_SR drastically changes the excitation spectrum of the Yb subsystem, inducing the transition between two regimes with magnon and spinon fluctuations. At T < T_SR, the Yb spin chains have a well-defined field-induced ferromagnetic ground state, and the spectrum consists of a sharp single-magnon mode, a two-magnon bound state, and a two-magnon continuum, whereas at T > T_SR only a gapped broad spinon continuum dominates the spectrum. The observation of a fractional spinon continuum in YbFeO₃ demonstrates that Kramers rare-earth based magnets can provide realizations of various aspects of quantum low-dimensional physics.   

Magnetic, Electronic, and Thermal Properties of the Quasi-one-dimensional Antiferromagnet CrCl2

 CrCl₂ is an orthorhombic, quasi-one dimensional antiferromagnet (AFM) with (100) chains of CrCl₂ weakly bonded to neighboring chains. Ab initio electronic structure calculations show that an AFM configuration along the chain direction is the magnetic ground state, the second lowest state is ferromagnetic (FM), and the third lowest state consists of FM chains with AFM coupling to neighboring chains. Calculated phonon dispersions show that the structure is dynamically stable. The magnetic anisotropy energy (MAE) of 1.35 meV/u.c. favors cross-chain (001) alignment of the Néel vector as opposed to parallel chain alignment. Within the cross-chain direction, a smaller MAE of 0.76 meV/u.c. favors the (001) alignment over (010). Applying strain and electric field, we are able to control the Néel vector in thin films and 1D atomic wire structures. To elucidate the underlying mechanism of magnetic anisotropy, we analyze the spin-orbit coupling energy and orbital momentum of the Cr atoms.   

Magnetic superexchange mechanism and pressure-induced orbital reordering by unconventional degrees of freedom in the homoleptic hybrid perovskite [(CH3)2NH2]Cu(HCOO)3.

We present the results of a combined experimental approach on the homoleptic perovskite-like coordination polymer [(CH₃)₂NH₂]Cu(HCOO)₃, where neutron diffraction and magnetisation measurements were used to solve the ground state magnetic structure, while electron charge density distribution and orbital occupancy were determined by high-resolution X-ray diffraction. The latter enabled a microscopic analysis of the chemical bonding in this quasi-1D antifferomagnet, from which we established the mechanism of magnetic exchange through formate anions and criteria for the applicability of Goodenough-Kanamori-Anderson (GKA) rules to superexchange mediated by polyatomic ligands. Moreover, through in-situ, high-pressure x-ray diffraction experiments we showed that [(CH₃)₂NH₂]Cu(HCOO)₃ undergoes a pressure-induced orbital reordering phase transition above 5.20 GPa. This transition is distinct from previously reported Jahn-Teller switching in coordination polymers, which required at least two different ligands that crystallize in a reverse spectrochemical series. We demonstrated that the orbital reordering phase transition in [(CH₃)₂NH₂]Cu(HCOO)₃ is instead primarily driven by unconventional octahedral tilts and shifts of the framework, and/or a reconfiguration of A-site cation ordering. These structural instabilities are unique to the coordination polymer perovskites, and may form the basis for undiscovered orbital reorientation phenomena in this broad family of materials. Moreover, based on the derived criteria for the applicability of GKA rules, we anticipate a change between two different A-type magnetic structures in which the antiferromagnetic stacking direction has switched.   

Magnetic Excitation of Cu2(MoO4)(SeO3)

One-dimensional spin chain systems have been attracting renewed interest in terms of a magnon or spinon-band splitting, which is found in ??-Cu₂V₂O₇ and Cs₂CuCl₄. A key parameter for the band splitting is an intrachain antisymmetric Dzyaloshinskii-Moriya interaction. To expand the variety of materials that can exhibit the band splitting, we have further searched for a possible quasi one-dimensional antiferromagnet and found Cu₂(MoO₄)(SeO₃) is a candidate. Single crystal magnetic susceptibility measurements show an anomaly at T_N ~ 23 K in all directions. A broad peak near 50 K suggested one dimensionality. The negative Curie-Weiss temperature Θ = -95.6(3) K confirms that the dominant exchange interaction between Cu²⁺ ions in Cu2(MoO4)(SeO3) is antiferromagnetic. By neutron powder diffraction experiment, we determined that Cu₂(MoO₄)(SeO₃) orders with antiferromagnetic structure, where the magnetic moments are mostly parallel (or antiparallel) to the one-dimensional direction. The inelastic neutron scattering experiment revealed the magnon dispersion along the (11L) direction. A continuum like excitation around (110) was observed. Additionally, the magnetic  excitation has a gap of ~ 1.0 meV suggesting the presence of an anisotropy in this compound.   

Pair spin dynamics in the spin 1/2 antiferromagnetic Heisenberg-Ising chain

We study pair spin dynamical structure factor of the spin-1/2 antiferromagnetic Heisenberg-Ising chain. Based on the Bethe ansatz formalism, various excitations at different energy scales are identified in the pair spin dynamics. With sum rules' guidance, we find that string excitations dominate the dynamical spectrum compared with low-energy fractional excitations. Our results establish a comprehensive picture for the pair spin dynamics, and will thus concretely facilitate measurements of relevant excitations in proper experimental setup.   

Electron spins interactions in the spin-Peierls phase of the organic spin chain compounds (o-DMTTF)2X (X=Cl,Br and I)

The gapped spin chains systems are usually non magnetic at low temperature however a break in translational symmetry can create a S = ½ ground state. The defect polarizes a large number of spins around it and pinnes a magnetic soliton [1]. By means of Electron Spin Resonance spectroscopy we report the experimental quantum coherence of a soliton of spin ½  [2,3] and a soliton-dimer with the quantum dynamics of a spin 1. We show the soliton can be either single or paired with a large exchange coupling and a probability of 50 % due to the one-dimensionnal nature of the system [4].   

Critical temperature of one-dimensional Ising model with long-range interaction revisited

We present a generalized expression for the transfer matrix of finite and infinite one-dimensional spin chains within a magnetic field with spin pair interaction J/r^p, where r = 1,2,...,n_v is the distance between two spins, n_v is the number of nearest neighbors reached by the interaction. With this generalized expression, we calculate the partition function, the Helmholtz free energy, and the specific heat for both finite and infinite ferromagnetic 1D Ising models within a zero external magnetic field. We focus on the temperature T_max where specific heat reaches its maximum. We calculate J/(k_B T_max) numerically for every values of n_v in {1,2,..., 25}, which we interpolate and then extrapolate up to the critical temperature as a function of p, using a novel functional approach. Two different procedures are used to reach the infinite spin chain with an infinite interaction range: increasing the chain size and the interaction range by the same amount, and increasing the interaction range for the infinite chain. Our critical temperatures as a function of p fall within the upper and lower bounds reported in the literature and show a better coincidence with many existing approximations for p close to 1 than for the p values near 2.