Zero-temperature Magnetization Research Articles

Exact eigenstates and macroscopic magnetization jumps in strongly frustrated spinlattices

For a class of frustrated spin lattices including for example the 1D sawtooth chain, the 2DKagomé and checkerboard, as well as the 3D pyrochlore lattices, we construct exact producteigenstates consisting of several independent, localized one-magnon states in aferromagnetic background. Important geometrical elements of the relevant lattices aretriangles being attached to polygons or lines. Then the magnons can be trapped on thesepolygons/lines. If the concentration of localized magnons is small, they can be distributedrandomly over the lattice. On increasing the number of localized magnons, theirdistribution over the lattice becomes more and more regular, and finally the magnonscondense in a crystal-like state.The physical relevance of these eigenstates emerges in high magnetic fields where theybecome groundstates of the system. As a result a macroscopic magnetization jumpappears in the zero-temperature magnetization curve just below the saturationfield. The height of the jump decreases with increasing spin quantum numberand vanishes in the classical limit. Thus it is a true macroscopic quantum effect.

Magnetization plateaus in frustrated antiferromagnetic quantum spin models

Plateaus can be observed in the zero-temperature magnetization curve of quantum spinsystems at rational values of the magnetization. In one dimension, the appearance of aplateau is controlled by a quantization condition for the magnetization which involves thelength of the local spin and the volume of a translational unit cell of the ground state. Wediscuss examples of geometrically frustrated quantum spin systems with large (in generalunbounded) periodicities of spontaneous breaking of translational symmetry in the groundstate.In two dimensions, we discuss the square, triangular and Kagomé lattices using exact diagonalization (ED) forup to N = 40 sites.For the spin-1/2 XXZ model on the triangular lattice we study the nature and stability region of a plateau at onethird of the saturation magnetization. The Kagomé lattice gives rise to particularly richbehaviour with several plateaus in the magnetization curve and a jump due to localmagnon excitations just below saturation.

Structure and magnetization of two-dimensional vortex arrays in the presence of periodic pinning

Ground-state properties of a two-dimensional system of superconducting vortices in the presence of a periodic array of strong pinning centers are studied analytically and numerically. The ground states of the vortex system at different filling ratios are obtained using a simple geometric argument under the assumption that the penetration depth is much smaller than the spacing of the pin lattice. The results of this calculation are confirmed by numerical studies in which simulated annealing is used to locate the ground states of the vortex system. The zero-temperature equilibrium magnetization as a function of the applied field is obtained by numerically calculating the energy of the ground state for a large number of closely spaced filling ratios. The results show interesting commensurability effects such as plateaus in the $B\ensuremath{-}H$ diagram at simple fractional filling ratios.

Square-lattice [formula omitted] model and the Jordan–Wigner fermions: the ground-state and thermodynamic properties

Using the 2D Jordan–Wigner transformation we reformulate the square-lattice s= 1 2 XY(XZ) model in terms of noninteracting spinless fermions and examine the ground-state and thermodynamic properties of this spin system. We consider the model with two types of anisotropy: the spatial anisotropy interpolating between 2D and 1D lattices and the anisotropy of the exchange interaction interpolating between isotropic XY and Ising interactions. We compare the obtained (approximate) results with exact ones (1D limit, square-lattice Ising model) and other approximate ones (linear spin-wave theory and exact diagonalization data for finite lattices of up to N=36 sites supplemented by finite-size scaling). We discuss the ground-state and thermodynamic properties in dependence on the spatial and exchange interaction anisotropies. We pay special attention to the quantum phase transition driven by the exchange interaction anisotropy as well as to the appearance/disappearance of the zero-temperature magnetization in the quasi-1D limit.

Macroscopic magnetization jumps due to independent magnons in frustrated quantum spin lattices.

For a class of frustrated spin lattices including the Kagomé lattice we construct exact eigenstates consisting of several independent, localized one-magnon states and argue that they are ground states for high magnetic fields. If the maximal number of local magnons scales with the number of spins in the system, which is the case for the Kagomé lattice, the effect persists in the thermodynamic limit and gives rise to a macroscopic jump in the zero-temperature magnetization curve just below the saturation field. The effect decreases with increasing spin quantum number and vanishes in the classical limit. Thus it is a true macroscopic quantum effect.

Quantum toclassical transition for small magnetic clusters in a field

We study the zero-temperature magnetization of small clusters inwhich the atoms are coupled by an isotropic Heisenbergantiferromagnetic interaction. We obtain either a full orpartial energy spectrum. From this we obtain the magnetizationcurves as a series of steps for finite S. Each step ischaracterized by the space group symmetry of the cluster andmany different representations may be present. We theninvestigate the classical limit, S→∞, in which themagnetization curves are typically piecewise smooth curves orstraight lines. We find two basic types of behaviour, depending onwhether or not the steps are characterized by a single or manydifferent representations. This latter case is associated withextra hidden symmetry.

Dimensional crossover behaviour of the zero-temperature magnetization for the selective magnetic dilution

By a new type of effective field theory we have studied a selective magnetic dilution for the Ising ferromagnet having various sublattice structures. In the concentration dependence of the zero-temperature magnetization, we found an interesting dimensional crossover behaviour characteristic of the case of extreme site selectivity.

A spin- model for CsCuCl in an external magnetic field

CsCuCl_3 is a ferromagnetically stacked triangular spin-1/2 antiferromagnet. We discuss models for its zero-temperature magnetization process. The models range from three antiferromagnetically coupled ferromagnetic chains to the full three-dimensional situation. The situation with spin-1/2 is treated by expansions around the Ising limit and exact diagonalization. Further, weak-coupling perturbation theory is used mainly for three coupled chains which are also investigated numerically using the density-matrix renormalization group technique. We find that already the three-chain model gives rise to the plateau-like feature at one third of the saturation magnetization which is observed in magnetization experiments on CsCuCl_3 for a magnetic field perpendicular to the crystal axis. For a magnetic field parallel to the crystal axis, a jump is observed in the experimental magnetization curve in the region of again about one third of the saturation magnetization. In contrast to earlier spinwave computations, we do not find any evidence for such a jump with the model in the appropriate parameter region.

A spin-

CsCuCl 3 is a ferromagnetically stacked triangular spin-1/2 antiferromagnet. We discuss models for its zero-temperature magnetization process. The models range from three antiferromagnetically coupled ferromagnetic chains to the full three-dimensional situation. The situation with spin-1/2 is treated by expansions around the Ising limit and exact diagonalization. Further, weak-coupling perturbation theory is used mainly for three coupled chains which are also investigated numerically using the density-matrix renormalization group technique. We find that already the three-chain model gives rise to the plateau-like feature at one third of the saturation magnetization which is observed in magnetization experiments on CsCuCl 3 for a magnetic field perpendicular to the crystal axis. For a magnetic field parallel to the crystal axis, a jump is observed in the experimental magnetization curve in the region of again about one third of the saturation magnetization. In contrast to earlier spinwave computations, we do not find any evidence for such a jump with the model in the appropriate parameter region.

Doping-Induced Magnetization Plateaus

The low temperature magnetization process of antiferromagnetic spin-S chains doped with mobile spin-(S-1/2) carriers is studied in an exactly solvable model. For sufficiently high magnetic fields the system is in a metallic phase with a finite gap for magnetic excitations. In this phase which exists for a large range of carrier concentrations x the zero temperature magnetization is determined by x alone. This leads to plateaus in the magnetization curve at a tunable fraction of the saturation magnetization. The critical behaviour at the edges of these plateaus is studied in detail.

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.

A sharp decrease of resistivity in La0.7Ca0.3Mn0.96Cu0.04O3: Evidence for Cu-assisted coherent tunneling of spin Polarons

Nearly a 50% decrease of resistivity \rho (T,x) due to just 4% Cu doping on the Mn site of La(2/3)Ca(1/3)Mn(1-x)Cu(x)O(3) is observed. Attributing the observed phenomenon to the substitution induced decrease of the spin polaron energy E_s(x) below the Curie point T_C(x)=T_C(0)(1-x), all data are found to be well fitted by the nonthermal coherent tunneling expression \rho (T,x) = \rho_0*exp(-\gamma M^2(T,x)) assuming M(T,x)=M_R(x)+M_0(x)*tanh{\sqrt{[T_C(x)/T]^2-1}} for the magnetization in the ferromagnetic state. The best fits through all the data points yield M_0(x)= \sqrt(1-x)M_0(0), M_R(x)=\sqrt(x)M_0(0), and E_s(x)=E_s(0)(1-x)^4 for the Cu induced modifications of the Mn spins dominated zero-temperature spontaneous magnetization, the residual paramagnetic contribution, and spin-polaron energy, respectively, with E_s(0)=0.12 eV.

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.

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.

The two dimensional antiferromagnetic Heisenberg model in the presence of an external field

We present numerical results on the zero temperature magnetization curve and the static structure factors of the two dimensional antiferromagnetic Heisenberg model in the presence of an external field. The impact of frustration is also studied.

First-Order Phase Transition in theS=1Quantum Spin Chain with Partial Integrability

The zero-temperature magnetization curve of the S =1 antiferromagnetic XXZ chain with partial integrability is studied by the Bethe ansatz, combined with a numerical renormalization-group method. We find a magnetic first-order phase transition; the magnetization curve shows a discontinuity at a critical field h c . Due to the partial integrability, the low-field curve and the high-field curve each correspond to a part of the magnetization curve of the \(S=\frac12\)XXZ chain. We conclude that the obtained magnetization curve is exact in the whole range of the magnetic field.

An effective field theory for dilute anisotropic Heisenberg ferromagnets

Dilute anisotropic Heisenberg ferromagnets have been studied by an effective field theory based on a two-site cluster approximation with an Ising character assumed for the surrounding spins. The results for the Curie temperature, T C , and the critical concentration for magnetic ordering, are improvements on those of a single-site approximation where the exchange anisotropy cannot be accounted for. The initial reduction in T C with dilution is confirmed to decrease with increases in both the lattice coordination number and exchange anisotropy. Finally, by utilising its connection with the zero-temperature magnetization for the Ising system, the percolation probability is examined.

Molecular-field theory of moment reduction in Kondo systems with crystal-field effects

Several dense Kondo compounds have a low-temperature ordered phase in which the magnetic moments are reduced with respect to the values expected for the crystal-field (CEF) ground state. In the present work the phenomenon of moment reduction is studied within a molecular-field theory combined with a variational solution of the one-impurity Anderson model with CEF effects. The calculated zero-temperature magnetization and susceptibility agree well with available exact results; the present method is easily applied to systems of any symmetry. We first study the f1 configuration in cubic symmetry, for small values of the ratio TK/Δ between Kondo temperature and CEF splitting. With a Γ∞ ground state and a field along a 〈100〉 direction, an inflection point occurs in the magnetization curve, which gives rise to a first order transition in the zero-temperature phase diagram. This feature is not found for a field along 〈110〉 or 〈111〉, for which the transition is second order. For a Γ7 ground state and small values of TK/Δ, the magnetic-nonmagnetic transition is second order for all field directions. On increasing TK/Δ an inflection point in the magnetization curve appears first for a field along 〈111〉. The theory is applied to a study of cubic CeAg, CeAl2, CePb3, CeIn3, CeTe, and hexagonal CePd2Ga3. The bare value of the moment is found to be strongly increased by exchange coupling to excited CEF states, and the amount of Kondo reduction is found to be substantial, confirming the importance of the Kondo effect in these compounds.

Magnetization of High-Tc Molecule-Based Magnet V/TCNE/CH2Cl2

Abstract Room-temperature molecular magnets based on V/TCNE may be prepared via two routes, identified as V(C6H6)2/TCNE/CH2Cl2 and V(CO)6/TCNE/CH2Cl2. Both compounds have critical temperatures exceeding 350 K. The magnetization M(T,H) of samples prepared via both routes have been compared. The saturation magnetization of the V(CO)6-derived material (M0 ∼10 4 emu·Oe·mol−1) is larger than that observed for V(C6H6)6-derived materials (M0 ∼ 0.6 × 104emu·Oe·mol−1), and the behavior of M(T) at H = 100 Oe is more like that exhibited by crystalline magnets. Whereas V(C6H6)2/TCNE/CH2Cl2 has a linear M(T) for 5 ≈ T ≈ 300 K, the magnetization of V(CO)6/TCNE/CH2Cl2 follows the Bloch spin-wave form M(T) = M(0)(1 - BT3/2), where the zero-temperature magnetization M(0) is suppressed from M0 by the effect of random magnetic anisotropy (RMA). The values of M(0) and the spin-wave dispersion constant B, as well as the range of validity of the T3/2 law, vary among different preparations of the magnet, reflecting a correlatio...

On the magnetic three-sublattice model with two equivalent sublattices

The magnetic 3-sublattice model is analysed for the case that the 3 sublattices are coupled by a Heisenberg type of exchange interaction, and 2 of the 3 sublattices are equivalent and coupled by equal exchange parameters with the third sublattice. The possible magnetic configurations of the 3-sublattice system in a magnetic field are derived, and a classification is given of the combinations of sublattice magnetizations and exchange parameters according to the type of zero-temperature magnetization curve to which the combination corresponds. Finally it is proved that all phase transitions are of second-order type.