Session U15: Focus Session: 1D Quantum Magnetism

Dynamical Structure Factors of quasi-one-dimensional antiferromagnets

For a long time it has been impossible to accurately calculate the dynamical structure factors (spin-spin correlators as a function of momentum and energy) of quasi-one-dimensional antiferromagnets. For integrable Heisenberg chains, the recently developed ABACUS method (a first-principles computational approach based on the Bethe Ansatz) now yields highly accurate (over 99\% of the sum rule) results for the DSF for finite chains, allowing for a very precise description of neutron-scattering data over the full momentum and energy range. We show remarkable agreement between results obtained with ABACUS and experiment.   

Dynamical spin structure factor for the anisotropic spin-1/2 chain

The longitudinal spin structure factor for the XXZ-chain at small wave-vector $q$ is obtained using Bethe Ansatz, field theory methods and the Density Matrix Renormalization Group. It consists of a peak with peculiar, non-Lorentzian shape and a high-frequency tail. We show that the width of the peak is proportional to $q^2$ for finite magnetic field compared to $q^3$ for zero field. For the tail we derive an analytic formula without any adjustable parameters and demonstrate that the integrability of the model directly affects the lineshape.   

Bound magnon states in the frustrated ferromagnetic 1D chain

We studied a one-dimensional Heisenberg chain with ferromagnetic nearest-neighbour $J_1$ and antiferromagnetic next-nearest-neighbour interactions $J_2$ in a magnetic field. Starting from the fully polarized high-field state, we calculated the saturation field and the dispersions of the lowest lying n-magnon excitations, and examined the possibility of a multi-magnon ground state near the ferromagnetic limit.   

High Frequency Electron Paramagnetic Resonance studies of NiCl$_{2}$-4SC(NH$_{2})_{2}$

High-frequency (50 to 311~GHz) Electron Paramagnetic Resonance (HFEPR) measurements have been performed on a single-crystal sample of the easy-plane $S$~=~1 linear-chain Heisenberg antiferromagnet NiCl$_{2}${\-}4SC(NH$_{2})_{2}$ (DTN). DTN has received much interest due to the possibility that it undergoes a Bose-Einstein condensation of the $S^{z}$~=~1 excitations (magnons) in the vicinity of the field tuned crossing of the $S^{z}$~= 0 and 1 states. Low-temperature frequency-dependent studies provide a direct measure of the zero-field spin gap separating the $S^{z}$ = 0 and 1 states. Lower frequency (92~GHz), temperature dependent studies with $B$//$c$ reveal two resonances either side of the $S^{z}$ = 0 and 1 crossing. Strong shifts and changes in the lineshapes of these resonances as the temperature is raised from 2~to ~15~K can be understood in terms of the gradual population of multi-magnon states. The trends observed from HFEPR experiments can be reproduced via numerical simulations using accepted values for the intra-chain Heisenberg interaction $J$ and the local anisotropy parameter $D$.   

Magnetic Excitations in the Spin-1 Anisotropic Heisenberg Antiferromagnetic Chain System NiCl$_2$-4SC(NH$_2$)$_2$

Electron spin resonance studies of magnetic excitations in NiCl$_2$-4SC(NH$_2$)$_2$ (DTN, a quantum $S=1$ chain system with strong easy-pane anisotropy and a new candidate for the Bose-Einstein condensation of the spin degrees of freedom) in fields up to 25 T are presented. Based on analysis of the frequency-field dependence of single-magnon mode in the high- field spin-polarized phase and previous experimental results [Phys. Rev. Lett. 96, 07724 (2006)], a revised set of spin- Hamiltonian parameters is obtained. Our results yield $D=8.9$ K, $J_c=2.2$ K, and $J_{a,b}=0.18$ K for the anisotropy, intra- and inter-chain exchange interactions, respectively. These values are used to calculate the AFM-phase boundary, low- temperature magnetization and the frequency-field dependence of two-magnon bound-state excitations predicted by theory and observed in DTN for the first time. Excellent quantitative agreement with experimental data is obtained.   

Far-infrared study of gapped spin excitations in the chains of Sr$_{14}$Cu$_{24}$O$_{41}$

We studied using far-infrared spectroscopy, magnetic field and temperature dependence of the spin gap modes in the chains of Sr$_{14}$Cu$_{24}$O$_{41}$. Two triplet modes T$_{1}$ and T$_{2}$ were found in the center of the Brillouin zone at E$_{1}$=77.8 cm$^{-1 }$(9.65 meV) and E$_{2}$=87.7 cm$^{-1 }$(10.86 meV) in zero magnetic field. Both excitations are electric dipole active modes. T$_{1}$ mode is excited when the light E-vector is along the $b$ crystallographic axis and T$_{2}$ is excited when the light E-vector is along the $a$-axis, both perpendicular to the chain direction. The selection rules of the transitions are compatible with dynamic Dzyaloshinskii-Moria interaction mechanism. Up to the field of 18T the electron g-factors of two modes are similar, g$_{1c}$=2.049 and g$_{2c}$=2.055 with magnetic field applied along the chains. Linewidth of both modes is 1 cm$^{-1}$ (0.12 meV) at 4K and increases with T. The temperature dependence of the mode energies is in agreement with the inelastic neutron scattering (INS) results from other groups. However the T$_{1}$ mode has not been observed by INS. The zone structure model of magnetic excitations in the chains is not complete and must include a triplet mode at 9.65 meV in the center of the magnetic Brillouin zone.   

Quasi one-dimensional magnetism driven by unusual orbital ordering in CuSb$_2$O$_6$

Cuprate compounds, including the family of high-Tc-superconductors, exhibit a large variety of exotic physical properties. This variety is determined by the interplay of different interactions; mainly covalency, ligand-fields and strong correlation effects. A nearly universal component of cuprate systems is a strongly elongated CuO$_6$-octahedron wherein the exotic behaviour finds its origin in the deceivingly simple planar Cu-O orbital lying in its basal plane. In this well established standard scenario, the involvement of the apical out-of-plane orbitals is not settled completely. The surprisingly regular CuO$_6$-octahedra of CuSb$_2$O$_6$ offer a unique opportunity to elucidate this scenario due to the changed balance of interactions in this system. We present an electronic structure study resulting in an hitherto unobserved ground state originating from a competition of in- and out-of-plane orbitals. Our results show that strong Coulomb correlation drives a surprising and unique orbital ordering. This, gives rise to an unusual and strongly one-dimensional magnetic ordering that is unlike any ordering observed in conventional low-dimensional cuprates. Our results provide a unique and natural interpretation of recent neutron data.   

Interplay of Dzyaloshinskii-Moriya and magnetic field in a one dimensional spin-$\frac{1}{2}$ Heisenberg antiferromagnetic chain

We study a one dimensional spin-1/2 Heisenberg antiferromagnetic chain in the presence of a magnetic field and a Dzyaloshinskii-Moriya (DM) interaction term. The case of a staggered DM term and a magnetic field perpendicular to it has been considered previously in Ref.[1]. It was shown that in both weak and strong magnetic field, DM term is a strongly relevant operator leading to the opening of a gap. The spin ordering takes place along a direction perpendicular to both the DM vector and the magnetic field. We consider the case of a uniform DM term, perpendicular to the magnetic field. In the limit of a strong magnetic field, the uniform DM term generates a marginally relevant operator that opens up a gap which scales as a power law with the DM term. The spin ordering takes place along the DM vector. In the limit of weak magnetic field, in comparison with the DM term, no relevant terms are generated, and the spin chain remains gapless. \newline [1] I. Affleck and M. Oshikawa, Phys. Rev. B 60, 1038 (1999).   

Oxygen hole-doping effects on magnetic properties of the spin-chain system Ca$_{2+x}$Y$_{2-x}$Cu$_5$O$_{10-\delta}$

The magnetic properties of the low-dimensional spin-chain system Ca$_{2+x}$Y$_{2-x}$Cu$_5$O$_{10-\delta}$ were studied as a function of oxygen content. The temperature dependence of the magnetic moment and specific heat were measured for a series of samples with different oxygen contents, prepared by solid state reaction under various oxygen pressures up to 225 atm and characterized by x-ray diffraction and iodometric titration. At fixed oxygen pressure, oxygen deficiency increases with Ca doping. For example, when annealed at 1 atm O$_2$ pressure, the $x=0$ sample was multiphased due to excess oxygen, whereas the samples with $x>1.2$ were also multiphased due to oxygen deficiency. With decreasing oxygen deficiency, the antiferromagnetic transition temperature decreases for $x=0.50$, $x=0.75$, $x=0.90$, and $x=1.00$ doped samples. In particular, for the fully oxygenated $x=1.00$ sample the transition is completely suppressed, which is contrary to the single crystal result recently published by K. Kudo $et$ $al$.\footnote{K. Kudo, S. Kurogi, and Y.Koike, Physical Review B \textbf{71}, 104413 (2005)}, where long range order disappeared at $x\approx1.4$ for the apparently oxygen-deficient crystals. A new magnetic phase diagram is proposed to include both Ca doping and oxygen deficiency.   

Anomalous Curie response of an impurity in a quantum critical spin-$1/2$ Heisenberg antiferromagnet

There is a disagreement concerning the low-temperature ($T$) magnetic susceptibility $\chi ^z_{{\rm imp}}\sim {\mathcal C}/T$ of a spin-$S$ impurity in a nearly quantum critical antiferromagnetic host. Field-theoretical work~[1] predicted an anomalous Curie constant $S^2/3<{\mathcal C}0$ quantum Monte Carlo simulations in order to resolve the controversy. Our main result is for a vacancy in a quantum critical spin-$1/2$ Heisenberg antiferromagnet on a bilayer lattice. In our susceptibility data for the $S=1/2$ impurity we observe a Curie constant ${\mathcal C}=0.262(2)$. Although the value falls outside the predicted range, it should correspond to an anomalous impurity response, as proposed in Ref.~[1]. [1]~S.~Sachdev, C.~Buragohain, and M.~Vojta, Science \textbf{286}, 2479 (1999); M.~Vojta, C.~Buragohain, and S.~Sachdev, Phys. Rev. B \textbf{61}, 15152 (2000). [2]~O.~P.~Sushkov, Phys. Rev. B \textbf{62}, 12135 (2000). [3]~M.~Troyer, Prog. Theor. Phys. Supp. \textbf{145}, 326 (2002).   

Thermal response functions for 1D strongly correlated electron systems

Thermal response functions of strongly correlated electron systems are of appreciable interest to the physics community from both a theoretical and technological point of view. Here we focus on one-dimensional models, namely the Hubbard and infinitely correlated $t$-$J$ models. Using exact diagonalization on finite sized systems we calculate the dynamical thermal response functions as functions of temperature, i.e., the electrical conductivity, the Peltier coefficient, and the thermal conductivity via the Kubo formulas. This in turn allows us to calculate the thermopower (Seebeck coefficient), Lorentz number, and the dimensionless figure of merit. By considering a geometrically frustrated system (inclusion of second neighbor hops into the Hubbard model) the thermopower is shown to be enhanced at intermediate temperatures. We also benchmark the finite temperature Lancos method.   

Quantum Monte Carlo study of a spin-Peierls model in a magnetic field

We present results of a quantum Monte Carlo study of a quasi one-dimensional XY spin model coupled to quantum phonons. We compare different updating techniques for the Stochastic Series Expansion method and present autocorrelation time data. We are able to reduce autocorrelation times by using loop update techniques for both spin and phonon degrees of freedom. We determine the critical phonon coupling for the spin-Peierls state, and discuss the dependence on the phonon frequency, magnetic field, and inter-chain coupling.   

Magnetic field dependence of spin-forbidden electronic excitations reflects the Haldane or paramagnetic ground state

We compare the zero-field and magnetic field-dependent optical spectra of the Haldane chain compound NENB (Ni[en]$_2$NO$_2$BF$_4 $; en = C$_2$N$_2$H$_{8}$) and the paramagnetic compound, Ni(en) $_3$(ClO$_4$)$_2$,H$_2$O. Due to similar electronic coordination of Ni$^{2+}$, the two materials show similar zero-field $d-d$ electronic transitions, including a spin-forbidden (SF) transition at 1.58 eV, overlapping a broad spin-allowed band at 1.45 eV. The relatively greater intensity of the SF band in the Haldane compound suggests activation by a spin exchange mechanism, whereas a spin-orbit coupling origin is likely in the paramagnet. A second narrower SF spin flip transition appears in NENB at 1.66 eV. In both compounds, the SF excitations are sensitive to applied field $H$. In NENB, the SF intensity is suppressed by $H$, consistent with behavior of spin exchange-activated bands. In Ni(en)$_3$(ClO$_4$)$-2$,H$_2 $O, the SF field sensitivity appears to combine an energy shift and intensity decrease. Details of the $H$ dependence reflect the magnetic ground state of the material: the field sensitivity commences only above $H_C$ $\approx$ 10 T, in the Haldane compound, whereas the field-induced modifications begin immediately at $H$ = 0 T in the paramagnet.   

Spin waves in LiCu$_{2}$O$_{2}$ and NaCu$_{2}$O$_{2}$: far-infrared study in magnetic field.

Frustrated magnetic interactions influence the ground state properties of spin systems. They may drive spin chain systems into a helicoidally ordered phase. Excitations in the helicoidally ordered phase are gapless spin waves. Anisotropic interactions create a finite gap at zero wave vector, \textbf{\textit{q}} = 0. LiCu$_{2}$O$_{2}$ and NaCu$_{2}$O$_{2}$ are quasi-1D systems with a weak interaction between Cu$^{2+}$ spin chains. Both compounds enter spin spiral state at low temperature (LiCu$_{2}$O$_{2}$ at 24K and NaCu$_{2}$O$_{2}$ at 12K). Here we report results of far-infrared (FIR) study where the absorption of light from 3 to 100cm$^{-1}$ by spin waves in LiCu$_{2}$O$_{2}$ and NaCu$_{2}$O$_{2}$ is measured. Light is absorbed by magnetic excitations at \textbf{\textit{q}} = 0 and at wave vectors that are multiples of the spiral wave vector, $\pm n$\textbf{\textit{Q}}. In magnets with a noncollinear spin ordering, such as a spin spiral, both components of light, magnetic and electric, may induce optical transitions. Measurements were performed from 3K to 30K and in fields up to 12T. To elucidate the selection rules, polarized light and different sample geometries were used. The magnetic field dependence of line positions and intensities is analyzed within a continuum model of a spiral magnet.   

Magnetic anisotropy of doped (Fe, Mn, Cr) NbSe$_{2}$

We investigated the behavior of magnetic dopants (Mn, Fe, Cr) in NbSe$_{2}$ at relatively large concentrations of approximately 1{\%}. Magnetic measurements show a pronounced magnetic anisotropy of these interstitial alloys, as evidenced in qualitatively different magnetization reversal dynamics for the magnetic fields applied in-plane and out-of-plane of these quasi two-dimensional samples. Element-specific characterization indicates that magnetic dopants are distributed approximately evenly throughout samples, thus ruling out clustering as a primary mechanism behind the observed anisotropy. For an arbitrary orientation of the applied field with respect to the sample plane, an interesting reorientation-like behavior is observed at magnetic fields below the value needed for the magnetization saturation. The details of this reorientation depend on the angle between the applied field and the sample plane. This behavior is temperature dependant, and was observed below the Peierls transition (T$_{P}$ = 33 K), but above the superconducting transition T$_{C}$. We discuss the nature of these measurements in the light of the proposed models of doped NbSe$_{2}$. This research was supported by the NSF grant (DMR 04-05500). I acknowledge Prof. R. E. Thorne for making samples available, and CCMR staff for assistance.