One-dimensional Quantum Antiferromagnet Research Articles

Quantum-Critical Spin Dynamics in Quasi-One-Dimensional Antiferromagnets

By means of nuclear spin-lattice relaxation rate T(1)(-1), we follow the spin dynamics as a function of the applied magnetic field in two gapped quasi-one-dimensional quantum antiferromagnets: the anisotropic spin-chain system NiCl(2)-4SC(NH(2))(2) and the spin-ladder system (C(5)H(12)N)(2)CuBr(4). In both systems, spin excitations are confirmed to evolve from magnons in the gapped state to spinons in the gapless Tomonaga-Luttinger-liquid state. In between, T(1)(-1) exhibits a pronounced, continuous variation, which is shown to scale in accordance with quantum criticality. We extract the critical exponent for T(1)(-1), compare it to the theory, and show that this behavior is identical in both studied systems, thus demonstrating the universality of quantum-critical behavior.

Topological effects in nanomagnetism: from superparamagnetism to chiral quantum solitons

Micromagnetics has been the method of choice to interpret experimental data in the area of microscopic magnetism for several decades. In this article, we show how progress has been made to extend this formalism to include thermal and quantum fluctuations in order to describe recent experimental developments in nanoscale magnetism. For experimental systems with constrained dimensions such as nanodots, atomic chains, nanowires, and thin films, topological defects such as solitons, vortices, skyrmions, and monopoles start to play an increasingly important role, all forming novel types of quasiparticles in patterned low-dimensional magnetic systems. We discuss in detail how soliton–antisoliton pairs of opposite chirality form non-uniform energy barriers against thermal fluctuations in nanowires or pillars. As a consequence of their low barrier energy compared to uniform reversal, they limit the thermal stability of perpendicular recording media. For sufficiently short samples, the non-uniform energy barrier continuously merges into the conventional uniform Néel–Brown barrier. Partial formation of chiral domain walls also determines the magnetic properties of granular nanostructured magnets and exchange spring systems. For a long time, the reconciliation between micromagnetics and quantum mechanics has remained an unresolved challenge. Here it is demonstrated how inclusion of Berry's phase in a micromagnetic action allows for a semiclassical quantization of spin systems, a method that is demonstrated by the simple example of an easy-plane spin. This powerful method allows for a description of quantum dynamics of solitons and breathers which in the latter case agrees with the anisotropic spin-½ XYZ-model. The domain wall or soliton chirality plays an important role as it is coupled to the wavevector of the quasiparticle dispersion. We show how this quantum soliton chirality is detected by polarized neutron scattering in one-dimensional quantum antiferromagnets.

Synthesis and structural characterization of uranium-doped Ca2CuO3, a one-dimensional quantum antiferromagnet

The technological settings of a modified sol-gel method for the preparation of highly fine homogeneous powder of Ca2CuO3 doped with uranium 238 (x= 0.0–0.05) is presented. The analysis of structure, purity of phases and the justification for the role of uranium in the given compounds are provided, together with an almost complete classification of the observed optical phonons by means of Raman, IR measurements and ab initio calculations. A significant reduction in particle size was achieved by doping, and a strong correlation between resistivity and doping concentration was observed and explained using the phonon-assisted electron hopping conduction model. The persistence of a covalent insulation state in all compounds is an interesting feature of this doping.

Quantum dynamics and entanglement of spins on a square lattice

Bulk magnetism in solids is fundamentally quantum mechanical in nature. Yet in many situations, including our everyday encounters with magnetic materials, quantum effects are masked, and it often suffices to think of magnetism in terms of the interaction between classical dipole moments. Whereas this intuition generally holds for ferromagnets, even as the size of the magnetic moment is reduced to that of a single electron spin (the quantum limit), it breaks down spectacularly for antiferromagnets, particularly in low dimensions. Considerable theoretical and experimental progress has been made in understanding quantum effects in one-dimensional quantum antiferromagnets, but a complete experimental description of even simple two-dimensional antiferromagnets is lacking. Here we describe a comprehensive set of neutron scattering measurements that reveal a non-spin-wave continuum and strong quantum effects, suggesting entanglement of spins at short distances in the simplest of all two-dimensional quantum antiferromagnets, the square lattice Heisenberg system.

Dynamical properties of a gas of solitons in one-dimensional quantum antiferromagnets

The influence of the soliton-magnon coupling on the dynamical properties of quantum antiferromagnets is studied as a function of the external magnetic field and the temperature. The specific case of tetramethyl ammonium manganese chloride is analyzed above and below the transition temperature. The existence of a dissipative regime for the soliton motion is conjectured and its influence on the dynamical structure factor---which might be experimentally detected---is reported.

Dynamics of the one-dimensional quantum antiferromagnet with Dzyaloshinski–Moriya interactions

The in-plane dynamical correlation function for the quantum one-dimensional antiferromagnet with a Dzyaloshinski–Moriya antisymmetric exchange term is calculated asymptotically exactly at low temperatures using a projection operator technique proposed by G. Reiter. The static correlation functions needed for the dynamics are evaluated using the harmonic approximation. Apart from a broadening of the spin-wave peak, the two-magnon processes give rise to additional resonances in the spectrum when the anisotropy parameter associated to the Dzyaloshinski–Moriya exchange is greater than the exchange constant.

Middle-field cusp singularities in the magnetization process of one-dimensional quantum antiferromagnets

We study the zero-temperature magnetization process $(M\ensuremath{-}H$ curve) of one-dimensional quantum antiferromagnets using a variant of the density-matrix renormalization group method. For both the $S=1/2$ zig-zag spin ladder and the $S=1$ bilinear-biquadratic chain, we find clear cusp-type singularities in the middle-field region of the $M\ensuremath{-}H$ curve. These singularities are successfully explained in terms of the double-minimum shape of the energy dispersion of the low-lying excitations. For the $S=1/2$ zig-zag spin ladder, we find that the cusp formation accompanies the Fermi-liquid to non-Fermi-liquid transition.

δ-function Bose-gas picture ofS=1antiferromagnetic quantum spin chains near critical fields

We study the zero-temperature magnetization curve $(M\ensuremath{-}H$ curve) of the one-dimensional quantum antiferromagnet of spin one. The Hamiltonian H we consider is of the bilinear-biquadratic form: $H={\ensuremath{\sum}}_{i}f({s}_{i}\ensuremath{\cdot}{s}_{i+1})$ (+Zeeman term) where ${s}_{i}$ is the spin operator at site i and $f(X)=X+\ensuremath{\beta}{X}^{2}$ with $0<~\ensuremath{\beta}<1.$ We focus on validity of the $\ensuremath{\delta}$-function Bose-gas picture near the two critical fields: upper-critical field ${H}_{s}$ above which the magnetization saturates and the lower-critical field ${H}_{c}$ associated with the Haldane gap. As for the behavior near ${H}_{s},$ we take ``low-energy effective S matrix'' approach, where the correct effective Bose-gas coupling constant c is extracted from the two down-spin S matrix in its low-energy limit. We find that the resulting value of c differs from the spin-wave value. We draw the $M\ensuremath{-}H$ curve by using the resultant Bose gas, and compare it with numerical calculation where the product-wave-function renormalization-group (PWFRG) method, a variant of White's density-matrix renormalization group method, is employed. Excellent agreement is seen between the PWFRG calculation and the correctly mapped Bose-gas calculation. We also test the validity of the Bose-gas picture near the lower-critical field ${H}_{c}.$ Comparing the PWFRG-calculated $M\ensuremath{-}H$ curves with the Bose-gas prediction, we find that there are two distinct regions, I and II, of $\ensuremath{\beta}$ separated by a critical value ${\ensuremath{\beta}}_{c}(\ensuremath{\approx}0.41).$ In region I, $0<\ensuremath{\beta}<{\ensuremath{\beta}}_{c},$ the effective Bose coupling c is positive but rather small. The small value of c makes the ``critical region'' of the square-root behavior $M\ensuremath{\sim}\sqrt{H\ensuremath{-}{H}_{c}}$ very narrow. Further, we find that in the $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\beta}}{\ensuremath{\beta}}_{c}\ensuremath{-}0,$ the square-root behavior transmutes to a different one, $M\ensuremath{\sim}(H\ensuremath{-}{H}_{c}{)}^{\ensuremath{\theta}}$ with $\ensuremath{\theta}\ensuremath{\approx}1/4.$ In region II, ${\ensuremath{\beta}}_{c}<\ensuremath{\beta}<1,$ the square-root behavior is more pronounced as compared with region I, but the effective coupling c becomes negative.

Static vacancies in a one-dimensional Heisenberg model

The effect of static vacancies created in a one-dimensional quantum antiferromagnet has been studied. The impurity Hamiltonian is solved where one obtains a bound state giving rise to δ-function density of states. The longitudinal part of the impurity–host spin interaction makes this peak into an asymmetric algebraic singularity. It is argued that the bound state corresponds to a local moment in the system giving rise to Curie-like contribution to the susceptibility. The implications of the present model in the recently discovered one-dimensional antiferromagnets such as Sr 2 CuO 3 and Ca 2 CuO 3 are discussed.

Instability of a one-dimensional quantum antiferromagnet under magnetic anisotropy

It is shown by using the exact quantum-mechanical solution that a one-dimensional antiferromagnetic Heisenberg spin chain is unstable to the emergence of an easy-plane magnetic anisotropy in a real three-dimensional crystal. It is shown that the magnetic anisotropy is due to a Jahn–Teller type effect, i.e., a strong spin–lattice coupling. A change in the equilibrium position of ligands induces magnetic anisotropy in the spin chain.

Magnetization process of a one-dimensional quantum antiferromagnet: The product-wave-function renormalization group approach

The product-wave-function renormalization group method, a new numerical renormalization group scheme proposed recently, is applied to one-dimensional quantum spin chains in a magnetic field. We find the zero-temperature magnetization curve of the spin chains, which excellently agrees with the exact solution in the whole range of the field.

Spin stiffness of mesoscopic quantum antiferromagnets.

We study the spin stiffness of a one-dimensional quantum antiferromagnet in the whole range of system sizes $L$ and temperatures $T$. We show that for integer and half-odd integer spin cases the stiffness differs fundamentally in its $L$ and $T$ dependences, and that in the latter case the stiffness exhibits a striking dependence on the parity of the number of sites. Integer spin chains are treated in terms of the nonlinear sigma model, while half-odd integer spin chains are discussed in a renormalization group approach leading to a Luttinger liquid with Aharonov-Bohm-type boundary conditions.

Mechanism of spin and charge separation in one-dimensional quantum antiferromagnets.

We reconsider the problem of separation of spin and charge in one-dimensional quantum antiferromagnets. We show that spin and charge separation in one-dimensional strongly correlated systems cannot be described by the slave-boson or fermion representation within any perturbative treatment of the interactions between the slave holons and slave spinons. The constraint of single occupancy must be implemented exactly. As a result the slave fermions and bosons are not part of the physical spectrum. Instead, the excitations that carry the separate spin and charge quantum numbers are solitons. To prove this result, it is sufficient to study the pure spinon sector in the slave-boson representation. We start with a short-range resonating-valence-bond state spin liquid mean-field theory for the frustrated antiferromagnetic spin-1/2 chain. We derive an effective theory for the fluctuations of the Affleck-Marston and Anderson order parameters. We show how to recover the phase diagram as a function of the frustration by treating the fluctuations nonperturbatively.

Interplay of holon and spinon dynamics in doped anisotropic Heisenberg chains

The role played by doping in one-dimensional quantum antiferromagnets is investigated using a decoupling of the charge and spin degrees of freedom that allows for magnetic phase changes when the concentration of holes increases. Our approach predicts quasi-continuous as well as discontinuous metal-insulator transitions, depending on the nature of the corresponding magnetic transformation. We also provide a clue for the observed behavior of the Hall coefficient, with a sign change caused by doping, suggesting that the change in the character of carriers is related to different magnetic correlations.

On the spectral function of a hole in a one-dimensional quantum antiferromagnet

We discuss the spectral function of a single hole moving in a one-dimensional quantum antiferromagnet. The latter is described by an anisotropic version of thet-J model, wheret is the hopping matrix element. We introduce two independent coupling parametersJ‖ andJ⊥ for the Ising and the transverse part of the Heisenberg exchange. Strong electronic correlations which are incorporated in the model prevent the use of usual diagrammatic techniques for dynamic Green functions based on Wick's theorem. For that reason a new projection technique for general correlation functions in terms of cumulants is used. We consider the case of max . For the case of small transverse coupling relative to the Ising part, we give exact expressions for the one hole correlation function. In the limit of vanishing spin fluctuations our result reduces to earlier calculations of the motion of a hole in a one-dimensional Neel state. However, the inclusion of the spin fluctuations leads to drastic modifications of the spectral function.