arXiv subjects

J. Richter

Publications and source records attributed to J. Richter.

At least 91 records · Page 5Linked to original sources

arXiv2008

Thermodynamics of the frustrated ferromagnetic spin-1/2 Heisenberg chain

We studied the thermodynamics of the one-dimensional J1-J2 spin-1/2 Heisenberg chain for ferromagnetic nearest-neighbor bonds J1 < 0 and frustrating antiferromagnetic next-nearest-neighbor bonds J1 > 0 using full diagonalization of finite rings and a second-order Green-function formalism. Thereby we focus on J2 < |J1|/4 where the ground state is still ferromagnetic, but the frustration influences the thermodynamic properties. We found that their critical indices are not changed by J2. The analysis of the low-temperature behavior of the susceptibility chi leads to the conclusion that this behavior changes from chi \propto T^{-2} at J2 < |J1|/4 to chi \propto T^{-3/2} at the quantum-critical point J2=|J1|/4. Another effect of the frustration is the appearance of an extra low-T maximum in the specific heat C_v(T) for J2 \gtrsim |J1|/8, indicating its strong influence on the low-energy spectrum.

cond-mat.str-el↗

arXiv2008

Thermodynamics of a one-dimensional frustrated spin-1/2 Heisenberg ferromagnet

We calculate the thermodynamic quantities (correlation functions , correlation length xi, spin susceptibility chi, and specific heat C_V) of the frustrated one-dimensional spin-half J2-J2 Heisenberg ferromagnet, i.e. for J2< 0.25|J1|, using a rotation-invariant Green's-function formalism and full diagonalization of finite lattices. We find that the critical indices are not changed by J2, i.e., chi = y_0 T^{-2} and xi = x_0 T^{-1} at T \to 0. However, the coefficients y_0 and x_0 linearly decrease with increasing J2 according to the relations y_0=(1-4J_2/|J_1|)/24 and x_0 =(1-4J_2/|J_1|)/4, i.e., both coefficients vanish at J2=0.25|J1| indicating the zero-temperature phase transition that is accompanied by a change of the low-temperature behavior of chi (xi) from chi \propto T^{-2} (xi \propto T^{-1}) at J2 < 0.25|J1| to chi \propto T^{-3/2} (xi \propto T^{-1/2}) at J2 = 0.25|J1|. In addition, we detect the existence of an additional low-temperature maximum in the specific heat when approaching the critical point at J2=0.25|J1|.

cond-mat.str-el↗

arXiv2008

The sawtooth chain: From Heisenberg spins to Hubbard electrons

We report on recent studies of the spin-half Heisenberg and the Hubbard model on the sawtooth chain. For both models we construct a class of exact eigenstates which are localized due to the frustrating geometry of the lattice for a certain relation of the exchange (hopping) integrals. Although these eigenstates differ in details for the two models because of the different statistics, they share some characteristic features. The localized eigenstates are highly degenerate and become ground states in high magnetic fields (Heisenberg model) or at certain electron fillings (Hubbard model), respectively. They may dominate the low-temperature thermodynamics and lead to an extra low-temperature maximum in the specific heat. The ground-state degeneracy can be calculated exactly by a mapping of the manifold of localized ground states onto a classical hard-dimer problem, and explicit expressions for thermodynamic quantities can be derived which are valid at low temperatures near the saturation field for the Heisenberg model or around a certain value of the chemical potential for the Hubbard model, respectively.

cond-mat.str-el↗

arXiv2008

The ground-state magnetic ordering of the spin-1/2 frustrated J1-J2 XXZ model on the square lattice

Using the coupled-cluster method for infinite lattices and the exact diagonalization method for finite lattices, we study the influence of an exchange anisotropy Delta on the ground-state phase diagram of the spin-1/2 frustrated J1-J2 XXZ antiferromagnet on the square lattice. We find that increasing Delta>1 (i.e. an Ising type easy-axis anisotropy) as well as decreasing Delta<1 (i.e. an XY type easy-plane anisotropy) both lead to a monotonic shrinking of the parameter region of the magnetically disordered quantum phase. Finally, at Delta~1.9 this quantum phase disappears, whereas in pure XY limit (Delta=0) there is still a narrow region around J2 =0.5J1 where the quantum paramagnetic ground-state phase exists.

cond-mat.str-el↗

arXiv2008

Modified kagome physics in the natural spin-1/2 kagome lattice systems - kapellasite Cu3Zn(OH)6Cl2 and haydeeite Cu3Mg(OH)6Cl2

The recently discovered natural minerals Cu3Zn(OH)6Cl2 and Cu3Mg(OH)6Cl2 are spin 1/2 systems with an ideal kagome geometry. Based on electronic structure calculations, we develop a realistic model which includes couplings across the kagome hexagons beyond the original kagome model that are intrinsic in real kagome materials. Exact diagonalization studies for the derived model reveal a strong impact of these couplings on the magnetic ground state. Our predictions could be compared to and supplied with neutron scattering, thermodynamic and NMR data.

cond-mat.str-el↗

arXiv2008

Intrinsic peculiarities of real material realizations of a spin-1/2 kagome lattice

Spin-1/2 magnets with kagome geometry, being for years a generic object of theoretical investigations, have few real material realizations. Recently, a DFT-based microscopic model for two such materials, kapellasite Cu3Zn(OH)6Cl2 and haydeeite Cu3Mg(OH)6Cl2, was presented [O. Janson, J. Richter and H. Rosner, arXiv:0806.1592]. Here, we focus on the intrinsic properties of real spin-1/2 kagome materials having influence on the magnetic ground state and the low-temperature excitations. We find that the values of exchange integrals are strongly dependent on O--H distance inside the hydroxyl groups, present in most spin-1/2 kagome compounds up to date. Besides the original kagome model, considering only the nearest neighbour exchange, we emphasize the crucial role of the exchange along the diagonals of the kagome lattice.

cond-mat.str-el↗

arXiv2008

The quantum $J_{1}$--$J_{1}'$--$J_{2}$ spin-1 Heisenberg model: Influence of the interchain coupling on the ground-state magnetic ordering in 2D

We study the phase diagram of the isotropic $J_{1}$--$J_{1}'$--$J_{2}$ Heisenberg model for spin-1 particles on an anisotropic square lattice, using the coupled cluster method. We find no evidence for an intermediate phase between the Néel and stripe states, as compared with all previous results for the corresponding spin-1/2 case. However, we find a quantum tricritical point at $J_{1}'/J_{1} \approx0.66 \pm 0.03$, $J_{2}/J_{1} \approx0.35\pm0.02$, where a line of second-order phase transitions between the quasi-classical Néel and stripe-ordered phases (for $J_{1}'/J_{1} \lesssim 0.66$) meets a line of first-order phase transitions between the same two states (for $J_{1}'/J_{1} \gtrsim 0.66$)

cond-mat.str-el↗

arXiv2008

Effect of anisotropy on the ground-state magnetic ordering of the spin-half quantum $J_1^{XXZ}$--$J_2^{XXZ}$ model on the square lattice

We study the zero-temperature phase diagram of the 2D quantum $J_{1}^{XXZ}$--$J_{2}^{XXZ}$ spin-1/2 anisotropic Heisenberg model on the square lattice. In particular, the effects of the anisotropy $Δ$ on the $z$-aligned Néel and (collinear) stripe states, as well as on the $xy$-planar-aligned Néel and collinear stripe states, are examined. All four of these quasiclassical states are chosen in turn as model states on top of which we systematically include the quantum correlations using a coupled cluster method analysis carried out to very high orders. We find strong evidence for two {\it quantum triple points} (QTP's) at ($Δ^{c} = -0.10 \pm 0.15, J_{2}^{c}/J_{1} = 0.505 \pm 0.015$) and ($Δ^{c} = 2.05 \pm 0.15, J_{2}^{c}/J_{1} = 0.530 \pm 0.015$), between which an intermediate magnetically-disordered phase emerges to separate the quasiclassical Néel and stripe collinear phases. Above the upper QTP ($Δ\gtrsim 2.0$) we find a direct first-order phase transition between the Néel and stripe phases, exactly as for the classical case. The $z$-aligned and $xy$-planar-aligned phases meet precisely at $Δ= 1$, also as for the classical case. For all values of the anisotropy parameter between those of the two QTP's there exists a narrow range of values of $J_{2}/J_{1}$, $α^{c_1}(Δ)<J_{2}/J_{1} <α^{c_2}(Δ)$, centered near the point of maximum classical frustration, $J_{2}/J_{1} = {1/2}$, for which the intermediate phase exists. This range is widest precisely at the isotropic point, $Δ= 1$, where $α^{c_1}(1) = 0.44 \pm 0.01$ and $α^{c_2}(1) = 0.59 \pm 0.01$. The two QTP's are characterized by values $Δ= Δ^{c}$ at which $α^{c_1}(Δ^{c})=α^{c_2}(Δ^{c})$.

cond-mat.str-el↗

arXiv2008

Enhanced low-temperature entropy and flat-band ferromagnetism in the t-J model on the sawtooth lattice

Using the example of the sawtooth chain, we argue that the t-J model shares important features with the Hubbard model on highly frustrated lattices. The lowest single-fermion band is completely flat (for a specific choice of the hopping parameters $t_{i,j}$ in the case of the sawtooth chain), giving rise to single-particle excitations which can be localized in real space. These localized excitations do not interact for sufficient spatial separations such that exact many-electron states can also be constructed. Furthermore, all these excitations acquire zero energy for a suitable choice of the chemical potential $μ$. This leads to: (i) a jump in the particle density at zero temperature, (ii) a finite zero-temperature entropy, (iii) a ferromagnetic ground state with a charge gap when the flat band is fully occupied and (iv) unusually large temperature variations when $μ$ is varied adiabatically at finite temperature.

cond-mat.str-el↗

arXiv2008

The quantum $J_1$-$J_1'$-$J_2$ spin-1/2 Heisenberg model: Influence of the interchain coupling on the ground-state magnetic ordering in 2D

We study the phase diagram of the 2D $J_1$-$J_1'$-$J_2$ spin-1/2 Heisenberg model by means of the coupled cluster method. The effect of the coupling $J_1'$ on the Neel and stripe states is investigated. We find that the quantum critical points for the Neel and stripe phases increase as the coupling strength $J_1'$ is increased, and an intermediate phase emerges above the region at $J_1' \approx 0.6$ when $J_1=1$. We find indications for a quantum triple point at $J_1' \approx 0.60 \pm 0.03$, $J_2 \approx 0.33 \pm 0.02$ for $J_1=1$.

cond-mat.str-el↗

arXiv2007

Enhanced magnetocaloric effect in frustrated magnetic molecules with icosahedral symmetry

We investigate the magnetocaloric properties of certain antiferromagnetic spin systems that have already been or very likely can be synthesized as magnetic molecules. It turns out that the special geometric frustration which is present in antiferromagnets that consist of corner-sharing triangles leads to an enhanced magnetocaloric effect with high cooling rates in the vicinity of the saturation field. These findings are compared with the behavior of a simple unfrustrated spin ring as well as with the properties of the icosahedron. To our surprise, also for the icosahedron large cooling rates can be achieved but due to a different kind of geometric frustration.

cond-mat.str-el↗

arXiv2007

The route of frustrated cuprates from antiferromagnetic to ferromagnetic spin-1/2 Heisenberg chains: Li2ZrCuO4 as a missing link near the quantum critical point

From thermodynamics, LSDA+U calculations and exact diagonalization studies of a five-band Hubbard (Cu 3d, O 2p) model on CuO2 stripes we found that Li2ZrCuO4 (Li2CuZrO4 in traditional notation) is close to a ferromagnetic critical point. Analyzing its measured susceptibility chi(T) and specific heat cp(T,H) within a Heisenberg model, we show that the ratio of the 2nd to the 1st neighbor exchange integrals alpha=-J2/J1 of the order of 0.3, i.e. it is close to the critical value alpha_c=1/4. Comparing with related chain cuprates we explain the rather strong field dependence of cp, the monotonous down shift of the peak of chi(T), and its increase for alpha approaching 1/4 + 0.

cond-mat.str-el↗

arXiv2006

Frustrated Quantum Antiferromagnets: Application of High-Order Coupled Cluster Method

We report on recent results for strongly frustrated quantum $J_1$-$J_2$ antiferromagnets in dimensionality d=1,2,3 obtained by the coupled cluster method (CCM). We demonstrate that the CCM in high orders of approximation allows us to investigate quantum phase transitions driven by frustration and to discuss novel quantum ground states. In detail we consider the ground-state properties of (i) the Heisenberg spin-1/2 antiferromagnet on the cubic lattice in d=1,2,3, and use the results for the energy, the sublattice magnetization and the spin stiffness as a benchmark test for the precision of the method; (ii) coupled frustrated spin chains (the quasi-one-dimensional $J_1$--$J_2$ model) and discuss the influence of the quantum fluctuations and the interchain coupling on the incommensurate spiral state present in the classical model; (iii) the Shastry-Sutherland antiferromagnet on the square lattice; and (iv) a stacked frustrated square-lattice Heisenberg antiferromagnet (the quasi-two-dimensional $J_1$--$J_2$ model), and discuss the influence of the interlayer coupling on the quantum paramagnetic ground-state phase that is present for the strictly two-dimensional model.

cond-mat.str-el↗

arXiv2006

Quantum $J_1$--$J_2$ antiferromagnet on the stacked square lattice: Influence of the interlayer coupling on the ground-state magnetic ordering

Using the coupled-cluster method (CCM) and the rotation-invariant Green's function method (RGM), we study the influence of the interlayer coupling $J_\perp$ on the magnetic ordering in the ground state of the spin-1/2 $J_1$-$J_2$ frustrated Heisenberg antiferromagnet ($J_1$-$J_2$ model) on the stacked square lattice. In agreement with known results for the $J_1$-$J_2$ model on the strictly two-dimensional square lattice ($J_\perp=0$) we find that the phases with magnetic long-range order at small $J_2< J_{c_1}$ and large $J_2> J_{c_2}$ are separated by a magnetically disordered (quantum paramagnetic) ground-state phase. Increasing the interlayer coupling $J_\perp>0$ the parameter region of this phase decreases, and, finally, the quantum paramagnetic phase disappears for quite small $J_\perp \sim 0.2 ... 0.3 J_1$.

cond-mat.str-el↗

arXiv2006

Zigzag spin-S chain near ferromagnet-antiferromagnet transition point

The properties of the ferromagnetic frustrated spin-S one-dimensional Heisenberg model in the vicinity of the transition point from the ferromagnetic to the singlet ground state is studied using the perturbation theory (PT) in small parameter characterizing the deviation from the transition point. The critical exponents defining the behavior of the ground state energy and spin correlation functions are determined using scaling estimates of infrared divergencies of the PT. It is shown that the quantum fluctuations for $s=1/2$ are sufficiently strong to change the classical critical exponents, while for spin systems with $s\geq 1$ the critical exponents remain classical. The dimerization in the singlet phase near the transition point is discussed.

cond-mat.str-el↗

arXiv2006

Green's function theory of quasi-two-dimensional spin-half Heisenberg ferromagnets: stacked square versus stacked kagomé lattice

We consider the thermodynamic properties of the quasi-two-dimensional spin-half Heisenberg ferromagnet on the stacked square and the stacked kagomé lattices by using the spin-rotation-invariant Green's function method. We calculate the critical temperature $T_C$, the uniform static susceptibility $χ$, the correlation lengths $ξ_ν$ and the magnetization $M$ and investigate the short-range order above $T_C$. We find that $T_C$ and $M$ at $T>0$ are smaller for the stacked kagomé lattice which we attribute to frustration effects becoming relevant at finite temperatures.

cond-mat.str-el↗

arXiv2006

Sr$_2$Cu(PO$_4$)$_2$: A real material realization of the 1D nearest neighbor Heisenberg chain

We present evidence that crystalline Sr_2Cu(PO_4)_2 is a nearly perfect one-dimensional (1D) spin-1/2 anti-ferromagnetic Heisenberg model (AHM) chain compound with nearest neighbor only exchange. We undertake a broad theoretical study of the magnetic properties of this compound using first principles (LDA, LDA+U calculations), exact diagonalization and Bethe-ansatz methodologies to decompose the individual magnetic contributions, quantify their effect, and fit to experimental data. We calculate that the conditions of one-dimensionality and short-ranged magnetic interactions are sufficiently fulfilled that Bethe's analytical solution should be applicable, opening up the possibility to explore effects beyond the infinite chain limit of the AHM Hamiltonian. We begin such an exploration by examining some extrinsic effects such as impurities and defects.

cond-mat.mtrl-sci↗

arXiv2006

Exact eigenstates of highly frustrated spin lattices probed in high fields

Strongly frustrated antiferromagnets such as the magnetic molecule {Mo72Fe30}, the kagome, or the pyrochlore lattice exhibit a variety of fascinating properties like low-lying singlets, magnetization plateaus as well as magnetization jumps. During recent years exact many-body eigenstates could be constructed for several of these spin systems. These states become ground states in high magnetic fields, and they also lead to exotic behavior. A key concept to an understanding of these properties is provided by independent localized magnons. The energy eigenvalue of these n-magnon states scales linearly with the number n of independent magnons and thus with the total magnetic quantum number M=Ns-n. In an applied field this results in a giant magnetization jump which constitutes a new macroscopic quantum effect. It will be demonstrated that this behavior is accompanied by a massive degeneracy, an extensive (T=0)-entropy, and thus a large magnetocaloric effect at the saturation field. The connection to flat band ferromagnetism will be outlined.

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