[Show abstract][Hide abstract] ABSTRACT: Motivated by recent experiments on volborthite single crystals showing a wide 1/3-magnetization plateau, we perform microscopic modeling by means of density functional theory (DFT) with the single-crystal structural data as a starting point. Using DFT+U, we find four leading magnetic exchanges: antiferromagnetic J and J2, as well as ferromagnetic J' and J1. Simulations of the derived spin Hamiltonian show good agreement with the experiment. The 1/3-plateau phase pertains to polarized magnetic trimers formed by strong J bonds. An effective J$\rightarrow\infty$ model shows a tendency towards condensation of magnon bound states preceding the plateau phase.
[Show abstract][Hide abstract] ABSTRACT: We apply the coupled cluster method to high orders of approximation and exact
diagonalizations to study the ground-state properties of the triangular-lattice
spin-$s$ Heisenberg antiferromagnet. We calculate the fundamental ground-state
quantities, namely, the energy $e_0$, the sublattice magnetization $M_{\rm
sub}$, the in-plane spin stiffness $\rho_s$ and the in-plane magnetic
susceptibility $\chi$ for spin quantum numbers $s=1/2, 1, \ldots, s_{\rm max}$,
where $s_{\rm max}=9/2$ for $e_0$ and $M_{\rm sub}$, $s_{\rm max}=4$ for
$\rho_s$ and $s_{\rm max}=3$ for $\chi$. We use the data for $s \ge 3/2$ to
estimate the leading quantum corrections to the classical values of $e_0$,
$M_{\rm sub}$, $\rho_s$, and $\chi$. In addition, we study the magnetization
process, the width of the 1/3 plateau as well as the sublattice magnetizations
in the plateau state as a function of the spin quantum number $s$.
Journal of Magnetism and Magnetic Materials 08/2015; DOI:10.1016/j.jmmm.2015.08.113 · 1.97 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: In this review we recapitulate the basic features of the flat-band spin
systems and briefly summarize earlier studies in the field. Main emphasis is
made on recent developments which include results for both spin and electron
flat-band models. In particular, for flat-band spin systems we highlight
field-driven phase transitions for frustrated quantum Heisenberg
antiferromagnets at low temperatures, chiral flat-band states, as well as the
effect of a slight dispersion of a previously strictly flat band due to
nonideal lattice geometry. For electronic systems, we discuss the universal
low-temperature behavior of several flat-band Hubbard models, the emergence of
ground-state ferromagnetism in the square-lattice Tasaki-Hubbard model and the
related Pauli-correlated percolation problem, as well as the dispersion-driven
ground-state ferromagnetism in flat-band Hubbard systems. Closely related
studies and possible experimental realizations of the flat-band physics are
also described briefly.
International Journal of Modern Physics B 05/2015; 29(12):1530007. DOI:10.1142/S0217979215300078 · 0.94 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We use the coupled cluster method implemented to high orders of approximation
to investigate the frustrated spin-$\frac{1}{2}$ $J_{1}$--$J_{2}$--$J_{3}$
antiferromagnet on the honeycomb lattice with isotropic Heisenberg interactions
of strength $J_{1} > 0$ between nearest-neighbor pairs, $J_{2}>0$ between
next-nearest-neighbor pairs, and $J_{3}>0$ between next-next-neareast-neighbor
pairs of spins. In particular, we study both the ground-state (GS) and
lowest-lying triplet excited-state properties in the case $J_{3}=J_{2} \equiv
\kappa J_{1}$, in the window $0 \leq \kappa \leq 1$ of the frustration
parameter, which includes the (tricritical) point of maximum classical
frustration at $\kappa_{{\rm cl}} = \frac{1}{2}$. We present GS results for the
spin stiffness, $\rho_{s}$, and the zero-field uniform magnetic susceptibility,
$\chi$, which complement our earlier results for the GS energy per spin, $E/N$,
and staggered magnetization, $M$, to yield a complete set of accurate
low-energy parameters for the model. Our results all point towards a phase
diagram containing two quasiclassical antiferromagnetic phases, one with
N\'{e}el order for $\kappa < \kappa_{c_{1}}$, and the other with collinear
striped order for $\kappa > \kappa_{c_{2}}$. The results for both $\chi$ and
the spin gap $\Delta$ provide compelling evidence for a quantum paramagnetic
phase that is gapped over a considerable portion of the intermediate region
$\kappa_{c_{1}} < \kappa < \kappa_{c_{2}}$, especially close to the two quantum
critical points at $\kappa_{c_{1}}$ and $\kappa_{c_{2}}$. Each of our fully
independent sets of results for the low-energy parameters is consistent with
the values $\kappa_{c_{1}} = 0.45 \pm 0.02$ and $\kappa_{c_{2}} = 0.60 \pm
0.02$, and with the transition at $\kappa_{c_{1}}$ being of continuous (and
probably of the deconfined) type and that at $\kappa_{c_{2}}$ being of
first-order type.
[Show abstract][Hide abstract] 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 $s$.
Physical Review B 01/2015; 91(10). DOI:10.1103/PhysRevB.91.104402 · 3.74 Impact Factor
[Show abstract][Hide abstract] 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. DOI:10.1016/j.jmmm.2014.11.082 · 1.97 Impact Factor
[Show abstract][Hide abstract] 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.
Physical Review B 09/2014; 91(2). DOI:10.1103/PhysRevB.91.024416 · 3.74 Impact Factor
[Show abstract][Hide abstract] 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.
[Show abstract][Hide abstract] 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. DOI:10.1103/PhysRevB.89.184407 · 3.74 Impact Factor
[Show abstract][Hide abstract] 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). DOI:10.1103/PhysRevB.90.045152 · 3.74 Impact Factor
[Show abstract][Hide abstract] 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). DOI:10.1103/PhysRevB.90.014441 · 3.74 Impact Factor
[Show abstract][Hide abstract] 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$_6$.
[Show abstract][Hide abstract] 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). DOI:10.1088/1742-6596/529/1/012023
[Show abstract][Hide abstract] 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. DOI:10.1103/PhysRevB.89.014415 · 3.74 Impact Factor
[Show abstract][Hide abstract] 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). DOI:10.1063/1.4881184 · 0.79 Impact Factor
[Show abstract][Hide abstract] 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.
Physical Review B 10/2013; 90(13). DOI:10.1103/PhysRevB.90.134415 · 3.74 Impact Factor
[Show abstract][Hide abstract] 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. DOI:10.1103/PhysRevB.88.144416 · 3.74 Impact Factor
[Show abstract][Hide abstract] 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). DOI:10.1103/PhysRevB.88.184410 · 3.74 Impact Factor
[Show abstract][Hide abstract] 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.
[Show abstract][Hide abstract] 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.