J Richter

Otto-von-Guericke-Universität Magdeburg, Magdeburg, Saxony-Anhalt, Germany

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Publications (239)553.23 Total impact

  • O. Götze, J. Richter
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    ABSTRACT: We use the coupled cluster method to high orders of approximation in order to calculate the ground-state phase diagram of the XXZ spin-$s$ kagome antiferromagnet with easy-plane anisotropy, i.e. the anisotropy parameter $\Delta$ varies between $\Delta=1$ (isotropic Heisenberg model) and $\Delta=0$ ($XY$ model). We find that for the extreme quantum case $s=1/2$ the ground state is magnetically disordered in the entire region $0 \le \Delta \le 1$. For $s=1$ the ground state is disordered for $0.818 < \Delta \le 1$, it exhibits $\sqrt{3}\times\sqrt{3}$ magnetic long-range order for $0.281 < \Delta <0.818$, and $q=0$ magnetic long-range order for $0 \le \Delta < 0.281$. We confirm the recent result of Chernyshev and Zhitomirsky (Phys. Rev. Lett. 113, 237202 (2014)) that the selection of the ground state by quantum fluctuations is different for small $\Delta$ ($XY$ limit) and for $\Delta$ close to one (Heisenberg limit), i.e., $q=0$ magnetic order is favored over $\sqrt{3}\times\sqrt{3}$ for $0\le \Delta <\Delta_c$ and vice versa for $\Delta_c < \Delta \le 1$. We calculate $\Delta_c$ as a function of the spin quantum number $s$.
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    ABSTRACT: We consider the antiferromagnetic spin-1/2 $XXZ$ Heisenberg model on a frustrated diamond-chain lattice in a $z$- or $x$-aligned external magnetic field. We use the strong-coupling approach to elaborate an effective description in the low-temperature strong-field regime. The obtained effective models are spin-1/2 $XY$ chains which are exactly solvable through the Jordan-Wigner fermionization. We perform exact-diagonalization studies of the magnetization curves to test the quality of the effective description. The results may have relevance for the description of the azurite spin-chain compound.
    Journal of Magnetism and Magnetic Materials 11/2014; 379. · 2.00 Impact Factor
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    ABSTRACT: We investigate the antiferromagnetic canting instability of the spin-1/2 kagome ferromagnet, as realized in the layered cuprates Cu$_3$Bi(SeO$_3)_2$O$_2$X (X=Br, Cl, and I). While the local canting can be explained in terms of competing exchange interactions, the direction of the ferrimagnetic order parameter fluctuates strongly even at short distances on account of frustration which gives rise to an infinite ground state degeneracy at the classical level. In analogy with the kagome antiferromagnet, the accidental degeneracy is fully lifted only by non-linear 1/S corrections, rendering the selected uniform canted phase very fragile even for spins-1/2, as shown explicitly by coupled-cluster calculations. To account for the observed ordering, we show that the minimal description of these systems must include the microscopic Dzyaloshinsky-Moriya interactions, which we obtain from density-functional band-structure calculations. The model explains all qualitative properties of the kagome francisites, including the detailed nature of the ground state and the anisotropic response under a magnetic field. The predicted magnon excitation spectrum and quantitative features of the magnetization process call for further experimental investigations of these compounds.
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    Johannes Richter, Ronald Zinke, Damian J. J. Farnell
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    ABSTRACT: We use the coupled cluster method to high orders of approximation in order to calculate the ground-state energy, the ground-state magnetic order parameter, and the spin gap of the spin-1/2 J_1-J_2 model on the square lattice. We obtain values for the transition points to the magnetically disordered quantum paramagnetic phase of J_2^{c1}=0.454J_1 and J_2^{c2}= 0.588 J_1. The spin gap is zero in the entire parameter region accessible by our approach, i.e. for J_2 \le 0.49J_1 and J_2 > 0.58J_1. This finding is in favor of a gapless spin-liquid or a near-critical quantum paramagnetic ground state in this parameter regime.
    Physics of Condensed Matter 08/2014; 88(1). · 1.46 Impact Factor
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    ABSTRACT: We investigate ground states of $s$=1/2 Heisenberg antiferromagnets on the eleven two-dimensional (2D) Archimedian lattices by using the coupled cluster method. Magnetic interactions and quantum fluctuations play against each other subtly in 2D quantum magnets and the magnetic ordering is thus sensitive to the features of lattice topology. Archimedean lattices are those lattices that have 2D arrangements of regular polygons and they often build the underlying magnetic lattices of insulating quasi-two-dimensional quantum magnetic materials. Hence they allow a systematic study of the relationship between lattice topology and magnetic ordering. We find that the Archimedian lattices fall into three groups: those with semiclassical magnetic ground-state long-range order, those with a magnetically disordered (cooperative quantum paramagnetic) ground state, and those with a fragile magnetic order. The most relevant parameters affecting the magnetic ordering are the coordination number and the degree of frustration present.
    Physical Review B 05/2014; 89:184407. · 3.66 Impact Factor
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    Oleg Derzhko, Johannes Richter
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    ABSTRACT: We investigate a mechanism to establish ground-state ferromagnetism in flat-band Hubbard systems based on a kind of {\it order-from-disorder} effect driven by dispersion. As a paradigm we consider a frustrated diamond chain, where for ideal diamond geometry the lowest one-electron band is flat, but the ground state remains paramagnetic for arbitrary on-site repulsion $U$. We focus on half filling of the flat band. By using numerical and analytical arguments we present the ground-state phase diagram for a distorted diamond chain, i.e., the former flat band becomes dispersive. Driven by the interplay of dispersion and interaction the ground state is ferromagnetic if the interaction exceeds a critical value $U_c$.
    Physical Review B 04/2014; 90(4). · 3.66 Impact Factor
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    ABSTRACT: We investigate the spin-1/2 Heisenberg model on the delta chain (sawtooth chain) with ferromagnetic nearest-neighbor and antiferromagnetic next-neighbor interactions. For a special ratio between these interactions there is a class of exact ground states formed by localized magnons and the ground state is macroscopically degenerate with a large residual entropy per spin $s_0=\frac{1}{2}\ln 2$. An important feature of this model is a sharp decrease of the gaps for excited states with an increase of the number of magnons. These excitations give an essential contribution to the low-temperature thermodynamics. The behavior of the considered model is compared with that of the delta chain with both antiferromagnetic interactions.
    Physical Review B 02/2014; 90(1). · 3.66 Impact Factor
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    ABSTRACT: The spin-1/2 alternating Heisenberg chain system Na$_3$Cu$_2$SbO$_6$ features two relevant exchange couplings: $J_{1a}$ within the structural Cu$_2$O$_6$ dimers and $J_{1b}$ between the dimers. Motivated by the controversially discussed nature of $J_{1a}$, we perform extensive density-functional-theory (DFT) calculations, including DFT+$U$ and hybrid functionals. Fits to the experimental magnetic susceptibility using high-temperature series expansions and quantum Monte Carlo simulations yield the optimal parameters $J_{1a}\!=\!-217$ K and $J_{1b}\!=\!174$ K with the alternation ratio $\alpha=J_{1a}/J_{1b}\simeq-1.25$. For the closely related system Na$_2$Cu$_2$TeO$_6$, DFT yields substantially enhanced $J_{1b}$, but weaker $J_{1a}$. The comparative analysis renders the buckling of the chains as the key parameter altering the magnetic coupling regime. By simulating the dispersion relations of the alternating chain model and comparing them to the inelastic neutron scattering data $[$Y. Miura et al., J. Phys. Soc. Jpn. 77, 104709 (2008)$]$, we obtain an unequivocal evidence for a ferromagnetic $J_{1a}$ in Na$_3$Cu$_2$SbO$_6$.
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    ABSTRACT: Motivated by recent experiments on low-dimensional frustrated quantum magnets with competing nearest-neighbor exchange coupling J1 and next nearest-neighbor exchange coupling J2 we investigate the magnetic susceptibility of two-dimensional J1-J2 Heisenberg models with arbitrary spin quantum number s. We use exact diagonalization and high-temperature expansion up to order 10 to analyze the influence of the frustration strength J2/J1 and the spin quantum number s on the position and the height of the maximum of the susceptibility. The derived theoretical data can be used to get information on the ratio J2/J1 by comparing with susceptibility measurements on corresponding magnetic compounds.
    Journal of Physics Conference Series 01/2014; 529(1).
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    ABSTRACT: We present the high-temperature expansion (HTE) up to 10th order of the specific heat C and the uniform susceptibility χ for Heisenberg models with arbitrary exchange patterns and arbitrary spin quantum number s. We encode the algorithm in a C++ program which allows to get explicitly the HTE series for concrete Heisenberg models. We apply our algorithm to pyrochlore ferromagnets and kagome antiferromagnets using several Padé approximants for the HTE series. For the pyrochlore ferromagnet we use the HTE data for χ to estimate the Curie temperature Tc as a function of the spin quantum number s. We find that Tc is smaller than that for the simple cubic lattice, although both lattices have the same coordination number. For the kagome antiferromagnet the influence of the spin quantum number s on the susceptibility as a function of renormalized temperature T /s(s + 1) is rather weak for temperatures down to T /s(s + 1) ∼ 0.3. On the other hand, the specific heat as a function of T /s(s + 1) noticeably depends on s. The characteristic maximum in C(T) is monotonously shifted to lower values of T /s(s + 1) when increasing s.
    Physical Review B 01/2014; 89:014415. · 3.66 Impact Factor
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    ABSTRACT: We consider the spin-1/2 antiferromagnetic Heisenberg model on the two-dimensional square-kagome lattice with almost dispersionless lowest magnon band. For a general exchange coupling geometry we elaborate low-energy effective Hamiltonians which emerge at high magnetic fields. The effective model to describe the low-energy degrees of freedom of the initial frustrated quantum spin model is the (unfrustrated) square-lattice spin-1/2 $XXZ$ model in a $z$-aligned magnetic field. For the effective model we perform quantum Monte Carlo simulations to discuss the low-temperature properties of the square-kagome quantum Heisenberg antiferromagnet at high magnetic fields. We pay special attention to a magnetic-field driven Berezinskii-Kosterlitz-Thouless phase transition which occurs at low temperatures.
    Low Temperature Physics 12/2013; 40(6). · 0.88 Impact Factor
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    R. O. Kuzian, V. V. Laguta, J. Richter
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    ABSTRACT: We consider a lattice of antiferromagnetically interacting equal spins that have a ferrimagnetic ground state. We show that a special arrangement of S=5/2 Fe$^{3+}$ ions in double perovskites AFe$_{1/2}$M$_{1/2}$O$_{3}$ exhibits the ferrimagnetic ordering below T_{fe} ~ 5.6J_1 (J_1/k_B ~ 50 K), which is close to room temperature. Small clusters of the same structure exhibit a superparamagnetic behavior at T < T_{fe}. The possibility of formation of such clusters explains the room-temperature (superpara)magnetism in 3d-metal based oxides.
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    ABSTRACT: We clarify the existence of several magnetization plateaux for the kagome $S=1/2$ antiferromagnetic Heisenberg model in a magnetic field. Using approximate or exact localized magnon eigenstates, we are able to describe in a similar manner the plateau states that occur for magnetization per site $m=1/3$, 5/9, and 7/9 of the saturation value. These results are confirmed using large-scale Exact Diagonalization on lattices up to 63 sites.
    Physical Review B 10/2013; 88(14):144416. · 3.66 Impact Factor
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    ABSTRACT: We present a comprehensive macroscopic thermodynamic study of the quasi-one-dimensional (1D) $s = \tfrac{1}{2}$ frustrated spin-chain system linarite. Susceptibility, magnetization, specific heat, magnetocaloric effect, magnetostriction, and thermal-expansion measurements were performed to characterize the magnetic phase diagram. In particular, for magnetic fields along the b axis five different magnetic regions have been detected, some of them exhibiting short-range-order effects. The experimental magnetic entropy and magnetization are compared to a theoretical modelling of these quantities using DMRG and TMRG approaches. Within the framework of a purely 1D isotropic model Hamiltonian, only a qualitative agreement between theory and the experimental data can be achieved. Instead, it is demonstrated that a significant symmetric anisotropic exchange of about 10% is necessary to account for the basic experimental observations, including the 3D saturation field, and which in turn might stabilize a triatic (three-magnon) multipolar phase.
    Physical Review B 05/2013; 88(18). · 3.66 Impact Factor
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    ABSTRACT: We consider the spin-1/2 antiferromagnetic Heisenberg model on three frustrated lattices (the diamond chain, the dimer-plaquette chain and the two-dimensional square-kagome lattice) with almost dispersionless lowest magnon band. Eliminating high-energy degrees of freedom at high magnetic fields, we construct low-energy effective Hamiltonians which are much simpler than the initial ones. These effective Hamiltonians allow a more extended analytical and numerical analysis. In addition to the standard strong-coupling perturbation theory we also use a localized-magnon based approach leading to a substantial improvement of the strong-coupling approximation. We perform extensive exact diagonalization calculations to check the quality of different effective Hamiltonians by comparison with the initial models. Based on the effective-model description we examine the low-temperature properties of the considered frustrated quantum Heisenberg antiferromagnets in the high-field regime. We also apply our approach to explore thermodynamic properties for a generalized diamond spin chain model suitable to describe azurite at high magnetic fields. Interesting features of these highly frustrated spin models consist in a steep increase of the entropy at very small temperatures and a characteristic extra low-temperature peak in the specific heat. The most prominent effect is the existence of a magnetic-field driven Berezinskii-Kosterlitz-Thouless phase transition occurring in the two-dimensional model.
    Physical review. B, Condensed matter 04/2013; 88(9). · 3.66 Impact Factor
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    ABSTRACT: We quantify the instability towards the formation of multipolar states in coupled spin-1/2 chain systems with a frustrating J1-J2 exchange, in parameter regimes that are of directly relevance to edge-shared cuprate spin-chain compounds. Three representative types of inter-chain coupling and the presence of uniaxial exchange anisotropy are considered. The magnetic phase diagrams are determined by Density Matrix Renormalization Group calculations and completed by exact analytic results for the nematic and dipolar phases. We establish that the residual couplings strongly affect the pitch of spiral states and their instability to multipolar phases. Our theoretical results bring to the fore novel candidate materials close to quantum nematic/triatic ordering.
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    ABSTRACT: Coupled s = 1/2 frustrated Heisenberg chains with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor exchange interactions in high magnetic field are studied by density-matrix renormalization group (DMRG) and hard-core boson (HCB) approaches at T = 0. First, we propose an appropriate one-dimensional array for the construction of a 3D system to be studied with the DMRG method and demonstrate the performance by comparing the ground-state energy to the exact solution. Next, the binding energy of multimagnon bound state is calculated as a function of interchain coupling. We find that the multimagnon bound state is easily destroyed by weak interchain coupling. In the 2-magnon phase the DMRG results are supported by the HCB approach.
    Journal of Physics Conference Series 12/2012; 400(3):2069-.
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    ABSTRACT: We apply the coupled cluster method and exact diagonalzation to study the uniform susceptibility and the ground-state magnetization curve of the triangular-lattice spin-1 Heisenberg antiferromagnet. Comparing our theoretical data for the magnetization curve with recent measurements on the s=1 triangular lattice antiferromagnet Ba3NiSb2O9 we find a very good agreement.
    Journal of the Physical Society of Japan 10/2012; 82:015002. · 1.48 Impact Factor
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    ABSTRACT: We calculate the temperature dependence of the correlation length xi and the uniform susceptibility chi_0 of the frustrated J1-J2 square-lattice Heisenberg ferromagnet in the collinear stripe phase using Green-function technique. The height chi_{max} and the position T(chi_{max}) of the maximum in the chi_0(T) curve exhibit a characteristic dependence on the frustration parameter J2/|J1|, which is well described by power laws, chi_{max}=a(J2-J2^c)^{-nu} and T(chi_{max})=b(J_2-J_2^c), where J2^c = 0.4 and nu is of the order of unity.The correlation length diverges at low temperatures as xi \propto e^{A/T}, where A increases with growing J2/|J1|. We also compare our results with recent measurements on layered vanadium phosphates and find reasonable agreement.
    Physical review. B, Condensed matter 10/2012; 87(5). · 3.66 Impact Factor
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    ABSTRACT: We investigate the location and nature of the para-ferro transition of interacting electrons in dispersionless bands using the example of the Hubbard model on the Tasaki lattice. This case can be analyzed as a geometric site-percolation problem where different configurations appear with nontrivial weights. We provide a complete exact solution for the 1D case and develop a numerical algorithm for the 2D case. In two dimensions the paramagnetic phase persists beyond the uncorrelated percolation point, and the grand-canonical transition is via a first-order jump to an unsaturated ferromagnetic phase.
    Physical Review Letters 08/2012; 109(9):096404. · 7.73 Impact Factor

Publication Stats

3k Citations
553.23 Total Impact Points


  • 1992–2014
    • Otto-von-Guericke-Universität Magdeburg
      • Institute of Theoretical Physics (ITP)
      Magdeburg, Saxony-Anhalt, Germany
  • 2011
    • Georg-August-Universität Göttingen
      • Institute for Theoretical Physics
      Göttingen, Lower Saxony, Germany
    • Donostia International Physics Center
      San Sebastián, Basque Country, Spain
  • 2010
    • Technische Universität Braunschweig
      • Institut für Theoretische Physik
      Braunschweig, Lower Saxony, Germany
  • 2009
    • The University of Manchester
      • School of Physics and Astronomy
      Manchester, ENG, United Kingdom
  • 2008
    • Max Planck Institute for Chemical Physics of Solids
      Dresden, Saxony, Germany
  • 1999–2007
    • Technische Universität Dresden
      • Institut für theoretische Physik
      Dresden, Saxony, Germany
  • 2006
    • Max Planck Institute of Physics
      München, Bavaria, Germany
  • 2004–2006
    • National Academy of Sciences of Ukraine
      • Institute for Condensed Matter Physics
      Kievo, Kyiv City, Ukraine
    • Universität Augsburg
      Augsberg, Bavaria, Germany
  • 2001
    • Universität Osnabrück
      Osnabrück, Lower Saxony, Germany
  • 1991–1992
    • Technische Universität Dortmund
      Dortmund, North Rhine-Westphalia, Germany