455 research outputs found
DFT-based microscopic magnetic modeling for low-dimensional spin systems
In the vast realm of inorganic materials, the Cu2+-containing cuprates form one of the richest classes. Due to the combined effect of crystal-field, covalency and strong correlations, all undoped cuprates are magnetic insulators with well-localized spins S=1/2, whereas the charge and orbital degrees of freedom are frozen out. The combination of the spin-only nature of their magnetism with the unique structural diversity renders cuprates as excellent model systems. The experimental studies, boosted by the discovery of high-temperature superconductivity in doped La2CuO4, revealed a fascinating variety of magnetic behaviors observed in cuprates. A digest of prominent examples should include the spin-Peierls transition in CuGeO3, the Bose-Einstein condensation of magnons in BaCuSi2O6, and the quantum critical behavior of Li2ZrCuO4. The magnetism of cuprates originates from short-range (typically, well below 1 nm) exchange interactions between pairs of spins Si and Sj, localized on Cu atoms i and j. Especially in low-dimensional compounds, these interactions are strongly anisotropic: even for similar interatomic distances |Rij|, the respective magnetic couplings Jij can vary by several orders of magnitude. On the other hand, there is an empirical evidence for the isotropic nature of this interaction in the spin space: different components of Si are coupled equally strong. Thus, the magnetism of cuprates is mostly described by a Heisenberg model, comprised of Jij(Si*Sj) terms. Although the applicability of this approach to cuprates is settled, the model parameters Jij are specific to a certain material, or more precisely, to a particular arrangement of the constituent atoms, i.e. the crystal structure. Typically, among the infinite number of Jij terms, only several are physically relevant. These leading exchange couplings constitute the (minimal) microscopic magnetic model. Already at the early stages of real material studies, it became gradually evident that the assignment of model parameters is a highly nontrivial task. In general, the problem can be solved experimentally, using elaborate measurements, such as inelastic neutron scattering on large single crystals, yielding the magnetic excitation spectrum. The measured dispersion is fitted using theoretical models, and in this way, the model parameters are refined.
Despite excellent accuracy of this method, the measurements require high-quality samples and can be carried out only at special large-scale facilities. Therefore, less demanding (especially, regarding the sample requirements), yet reliable and accurate procedures are desirable. An alternative way to conjecture a magnetic model is the empirical approach, which typically relies on the Goodenough-Kanamori rules. This approach links the magnetic exchange couplings to the relevant structural parameters, such as bond angles. Despite the unbeatable performance of this approach, it is not universally applicable. Moreover, in certain cases the resulting tentative models are erroneous. The recent developments of computational facilities and techniques, especially for strongly correlated systems, turned density-functional theory (DFT) band structure calculations into an appealing alternative, complementary to the experiment. At present, the state-of-the-art computational methods yield accurate numerical estimates for the leading microscopic exchange couplings Jij (error bars typically do not exceed 10-15%).
Although this computational approach is often regarded as ab initio, the actual procedure is not parameter-free. Moreover, the numerical results are dependent on the parameterization of the exchange and correlation potential, the type of the double-counting correction, the Hubbard repulsion U etc., thus an accurate choice of these crucial parameters is a prerequisite. In this work, the optimal parameters for cuprates are carefully evaluated based on extensive band structure calculations and subsequent model simulations.
Considering the diversity of crystal structures, and consequently, magnetic behaviors, the evaluation of a microscopic model should be carried out in a systematic way. To this end, a multi-step computational approach is developed. The starting point of this procedure is a consideration of the experimental structural data, used as an input for DFT calculations. Next, a minimal DFT-based microscopic magnetic model is evaluated. This part of the study comprises band structure calculations, the analysis of the relevant bands, supercell calculations, and finally, the evaluation of a microscopic magnetic model. The ground state and the magnetic excitation spectrum of the evaluated model are analyzed using various simulation techniques, such as quantum Monte Carlo, exact diagonalization and density-matrix renormalization groups, while the choice of a particular technique is governed by the dimensionality of the model, and the presence or absence of magnetic frustration.
To illustrate the performance of the approach and tune the free parameters, the computational scheme is applied to cuprates featuring rather simple, yet diverse magnetic behaviors: spin chains in CuSe2O5, [NO]Cu(NO3)3, and CaCu2(SeO3)2Cl2; quasi-two-dimensional lattices with dimer-like couplings in alpha-Cu2P2O7 and CdCu2(BO3)2, as well as the 3D magnetic model with pronounced 1D correlations in Cu6Si6O18*6H2O. Finally, the approach is applied to spin liquid candidates --- intricate materials featuring kagome-lattice arrangement of the constituent spins. Based on the DFT calculations, microscopic magnetic models are evaluated for herbertsmithite Cu3(Zn0.85Cu0.15)(OH)6Cl2, kapellasite Cu3Zn(OH)6Cl2 and haydeeite Cu3Mg(OH)6Cl2, as well as for volborthite Cu3[V2O7](OH)2*2H2O. The results of the DFT calculations and model simulations are compared to and challenged with the available experimental data.
The advantages of the developed approach should be briefly discussed. First, it allows to distinguish between different microscopic models that yield similar macroscopic behavior. One of the most remarkable example is volborthite Cu3[V2O7](OH)2*2H2O, initially described as an anisotropic kagome lattice. The DFT calculations reveal that this compound features strongly coupled frustrated spin chains, thus a completely different type of magnetic frustration is realized.
Second, the developed approach is capable of providing accurate estimates for the leading magnetic couplings, and consequently, reliably parameterize the microscopic Hamiltonian. Dioptase Cu6Si6O18*6H2O is an instructive example showing that the microscopic theoretical approach eliminates possible ambiguity and reliably yields the correct parameterization.
Third, DFT calculations yield even better accuracy for the ratios of magnetic exchange couplings. This holds also for small interchain or interplane couplings that can be substantially smaller than the leading exchange. Hence, band structure calculations provide a unique possibility to address the interchain or interplane coupling regime, essential for the magnetic ground state, but hardly perceptible in the experiment due to the different energy scales.
Finally, an important advantage specific to magnetically frustrated systems should be mentioned. Numerous theoretical and numerical studies evidence that low-dimensionality and frustration effects are typically entwined, and their disentanglement in the experiment is at best challenging. In contrast, the computational procedure allows to distinguish between these two effects, as demonstrated by studying the long-range magnetic ordering transition in quasi-1D spin chain systems.
The computational approach presented in the thesis is a powerful tool that can be directly applied to numerous S=1/2 Heisenberg materials. Moreover, with minor modifications, it can be largely extended to other metallates with higher value of spin. Besides the excellent performance of the computational approach, its relevance should be underscored: for all the systems investigated in this work, the DFT-based studies not only reproduced the experimental data, but instead delivered new valuable information on the magnetic properties for each particular compound.
Beyond any doubt, further computational studies will yield new surprising results for known as well as for new, yet unexplored compounds. Such "surprising" outcomes can involve the ferromagnetic nature of the couplings that were previously considered antiferromagnetic, unexpected long-range couplings, or the subtle balance of antiferromagnetic and ferromagnetic contributions that "switches off" the respective magnetic exchange. In this way, dozens of potentially interesting systems can acquire quantitative microscopic magnetic models.
The results of this work evidence that elaborate experimental methods and the DFT-based modeling are of comparable reliability and complement each other. In this way, the advantageous combination of theory and experiment can largely advance the research in the field of low-dimensional quantum magnetism. For practical applications, the excellent predictive power of the computational approach can largely alleviate designing materials with specific properties.:List of Figures
List of Tables
List of Abbreviations
1. Introduction
2. Magnetism of cuprates
3. Experimental methods
4. DFT-based microscopic modeling
5. Simulations of a magnetic model
6. Model spin systems: challenging the computational approach
7. Kagome lattice compounds
8. Summary and outlook
Appendix
Bibliography
List of publications
Acknowledgment
Square-lattice magnetism of diaboleite Pb2Cu(OH)4Cl2
We report on the quasi-two-dimensional magnetism of the natural mineral
diaboleite Pb2Cu(OH)4Cl2 with a tetragonal crystal structure, which is closely
related to that of the frustrated spin-1/2 magnet PbVO3. Magnetic
susceptibility of diaboleite is well described by a Heisenberg spin model on a
diluted square lattice with the nearest-neighbor exchange of J~35 K and about
5% of non-magnetic impurities. The dilution of the spin lattice reflects the
formation of Cu vacancies that are tolerated by the crystal structure of
diaboleite. The weak coupling between the magnetic planes triggers the
long-range antiferromagnetic order below TN~11 K. No evidence of magnetic
frustration is found. We also analyze the signatures of the long-range order in
heat-capacity data, and discuss the capability of identifying magnetic
transitions with heat-capacity measurements.Comment: 10 pages, 10 figures + Supplementary Informatio
The spin gap in malachite Cu2(OH)2CO3 and its evolution under pressure
We report on the microscopic magnetic modeling of the spin-1/2 copper mineral
malachite at ambient and elevated pressures. Despite the layered crystal
structure of this mineral, the ambient-pressure susceptibility and
magnetization data can be well described by an unfrustrated
quasi-one-dimensional magnetic model. Weakly interacting antiferromagnetic
alternating spin chains are responsible for a large spin gap of 120K. Although
the intradimer Cu-O-Cu bridging angles are considerably smaller than the
interdimer angles, density functional theory (DFT) calculations revealed that
the largest exchange coupling of 190K operates within the structural dimers.
The lack of the inversion symmetry in the exchange pathways gives rise to
sizable Dzyaloshinskii-Moriya interactions which were estimated by
full-relativistic DFT+U calculations. Based on available high-pressure crystal
structures, we investigate the exchange couplings under pressure and make
predictions for the evolution of the spin gap. The calculations evidence that
intradimer couplings are strongly pressure-dependent and their evolution
underlies the decrease of the spin gap under pressure. Finally, we assess the
accuracy of hydrogen positions determined by structural relaxation within DFT
and put forward this computational method as a viable alternative to elaborate
experiments
Frustrated spin chain physics near the Majumdar-Ghosh point in szenicsite Cu(MoO)(OH)
In this joint experimental and theoretical work magnetic properties of the
Cu mineral szenicsite Cu(MoO)(OH) are investigated. This
compound features isolated triple chains in its crystal structure, where the
central chain involves an edge-sharing geometry of the CuO plaquettes,
while the two side chains feature a corner-sharing zig-zag geometry. The
magnetism of the side chains can be described in terms of antiferromagnetic
dimers with a coupling larger than 200 K. The central chain was found to be a
realization of the frustrated antiferromagnetic - chain model with
K and a sizable second-neighbor coupling . The central and
side chains are nearly decoupled owing to interchain frustration. Therefore,
the low-temperature behavior of szenicsite should be entirely determined by the
physics of the central frustrated - chain. Our heat-capacity
measurements reveal an accumulation of entropy at low temperatures and suggest
a proximity of the system to the Majumdar-Ghosh point of the antiferromagnetic
- spin chain,
Quantum Anomalous Hall State in Ferromagnetic SrRuO (111) Bilayers
SrRuO heterostructures grown in the (111) direction are a rare example of
thin film ferromagnets. By means of density functional theory plus dynamical
mean field theory we show that the half-metallic ferromagnetic state with an
ordered magnetic moment of 2/Ru survives the ultimate dimensional
confinement down to a bilayer, even at elevated temperatures of 500K. In
the minority channel, the spin-orbit coupling opens a gap at the linear band
crossing corresponding to filling of the shell. We
demonstrate that the respective state is Haldane's quantum anomalous Hall state
with Chern number =1, without an external magnetic field or magnetic
impurities.Comment: 5 pages, 3 figure
beta-Cu2V2O7: a spin-1/2 honeycomb lattice system
We report on band structure calculations and a microscopic model of the
low-dimensional magnet beta-Cu2V2O7. Magnetic properties of this compound can
be described by a spin-1/2 anisotropic honeycomb lattice model with the
averaged coupling \bar J1=60-66 K. The low symmetry of the crystal structure
leads to two inequivalent couplings J1 and J1', but this weak spatial
anisotropy does not affect the essential physics of the honeycomb spin lattice.
The structural realization of the honeycomb lattice is highly non-trivial: the
leading interactions J1 and J1' run via double bridges of VO4 tetrahedra
between spatially separated Cu atoms, while the interactions between structural
nearest neighbors are negligible. The non-negligible inter-plane coupling
Jperp~15 K gives rise to the long-range magnetic ordering at TN~26 K. Our model
simulations improve the fit of the magnetic susceptibility data, compared to
the previously assumed spin-chain models. Additionally, the simulated ordering
temperature of 27 K is in remarkable agreement with the experiment. Our study
evaluates beta-Cu2V2O7 as the best available experimental realization of the
spin-1/2 Heisenberg model on the honeycomb lattice. We also provide an
instructive comparison of different band structure codes and computational
approaches to the evaluation of exchange couplings in magnetic insulators.Comment: 11 pages, 10 figures, 2 tables: revised version, extended description
of simulation result
Two energy scales of spin dimers in clinoclase Cu3(AsO4)(OH)3
Magnetic susceptibility and microscopic magnetic model of the mineral
clinoclase Cu3(AsO4)(OH)3 are reported. This material can be well described as
a combination of two nonequivalent spin dimers with the sizable magnetic
couplings of J about 700 K and J(D2) about 300 K. Based on density functional
theory calculations, we pinpoint the location of dimers in the crystal
structure. Surprisingly, the largest coupling operates between the structural
Cu2O6 dimers. We investigate magnetostructural correlations in Cu2O6 structural
dimers, by considering the influence of the hydrogen position on the magnetic
coupling. Additionally, we establish the hydrogen positions that were not known
so far and analyze the pattern of hydrogen bonding
CaCu2(SeO3)2Cl2: spin-1/2 Heisenberg chain compound with complex frustrated interchain couplings
We report the crystal structure, magnetization measurements, and
band-structure calculations for the spin-1/2 quantum magnet CaCu2(SeO3)2Cl2.
The magnetic behavior of this compound is well reproduced by a uniform spin-1/2
chain model with the nearest-neighbor exchange of about 133 K. Due to the
peculiar crystal structure, spin chains run in the direction almost
perpendicular to the structural chains. We find an exotic regime of frustrated
interchain couplings owing to two inequivalent exchanges of 10 K each. Peculiar
superexchange paths grant an opportunity to investigate bond-randomness effects
under partial Cl-Br substitution.Comment: Extended version: 9 pages, 7 figures, 4 table
- …