research

Quantum magnetism

Intercalant-mediated Kitaev exchange in Ag3LiIr2O6


The recently synthesized Ag3LiIr2O6 has been proposed as a Kitaev magnet in proximity to the quantum spin liquid phase. We explore its microscopic Hamiltonian and magnetic ground state using many-body quantum chemistry methods and exact diagonalization techniques. Our calculations establish a dominant bond dependent ferromagnetic Kitaev exchange between Ir sites and find that the inclusion of Ag 4d orbitals in the configuration interaction calculations strikingly enhances the Kitaev exchange. Furthermore, using exact diagonalization of the nearest-neighbor fully anisotropic JKΓ Hamiltonian, we obtain the magnetic phase diagram as a function of further neighbor couplings. We find that the antiferromagnetic off-diagonal coupling stabilizes long range order, but the structure factor calculations suggest that the material is very close to the quantum spin liquid phase and the ordered state can easily collapse into a liquid by small perturbations such as structural distortion or bond disorder.


Physical Review Research 4, 033025 (2022)

Magnetic phase diagram in the Γxy − Γyz plane for J = −0.3 meV, K= −11.2 meV,  J2=J3=0 meV. Possible magnetic phases are shown along with schematic drawings of spin configurations.
Phase diagram obtained by ED for the effective spin model in H3LiIr2O6 as a function of the second- and third-neighbor isotropic couplings, respectively, J2 and J3. Schematic spin configurations are also shown.
NN Kitaev and Heisenberg couplings for variable Ir–O–Ir angles in model C2/m-type structures, spin–orbit MRCI results. The NN Ir–Ir distance is set to 3.08 Å and the Ir–O bond lengths are for a given Ir–O–Ir angle all the same. The variation of the Ir–O–Ir angle is the result of gradual trigonal compression.

Strong effect of hydrogen order on magnetic Kitaev interactions in H3LiIr2O6

Very recently a quantum liquid was reported to form in H3LiIr2O6, an iridate proposed to be a close realization of the Kitaev honeycomb model. To test this assertion we perform detailed quantum chemistry calculations to determine the magnetic interactions between Ir moments. We find that weakly bond dependent ferromagnetic Kitaev exchange dominates over other couplings, but still is substantially lower than in Na2IrO3. This reduction is caused by the peculiar position of the interlayer species: removing hydrogen cations next to a Ir2O2 plaquette increases the Kitaev exchange by more than a factor of 3 on the corresponding Ir Ir link. Consequently, any lack of hydrogen order will have a drastic effect on the magnetic interactions and strongly promote spin disordering.


Phys. Rev. Lett. 121, 197203 (2018).

Chemical Science, 10, 8166 (2019).

Large off-diagonal exchange couplings and spin liquid states in C3-symmetric iridates

Iridate oxides on a honeycomb lattice are considered promising candidates for realization of quantum spin liquid states. We investigate the magnetic couplings in a structural model for a honeycomb iridate K2IrO3, with C3 point-group symmetry at the Ir sites, which is an end member of the recently synthesized iridate family KxIryO2. Using ab initio quantum chemical methods, we elucidate the subtle relationship between the real space symmetry and magnetic anisotropy and show that the higher point-group symmetry leads to high frustration with strong magnetic anisotropy driven by the unusually large off-diagonal exchange couplings (Γ's) as opposed to other spin-liquid candidates considered so far. Consequently, large quantum fluctuations imply lack of magnetic ordering consistent with the experiments. Exact diagonalization calculations for the fully anisotropic K J Γ Hamiltonian reveal the importance of the off-diagonal anisotropic exchange couplings in stabilizing a spin liquid state and highlight an alternative route to stabilize spin liquid states for ferromagnetic K.


Phys. Rev. B 100, 144422 (2019).

Figure: Ground-state phase diagram by ED with a 24-site cluster: (a) in the Γxy Γyz plane using the MRCI values of J and K; (b) in the J2−J3 plane using the MRCI values of J, K, Γxy, and Γyz. Schematic spin configurations are also shown. The star symbol in (a) indicates the position of MRCI parameter set and it corresponds to the origin in (b). A realistic range for K2IrO3 is located with shaded area in (b). Specific heat for the (c) threefold SDW and (d) zigzag phases, obtained by the ED calculations with a 12-site cluster. (e) Inverse magnetic susceptibility for the most likely realistic values of the extended range Heisenberg couplings J2 and J3. The dotted line is χ=2.1/(T−θ)with θ = −135K.

Pressure-induced dimerization and valence bond crystal formation in the Kitaev-Heisenberg magnet α−RuCl3

Magnetization and high-resolution x-ray diffraction measurements of the Kitaev-Heisenberg material α−RuCl3 reveal a pressure-induced crystallographic and magnetic phase transition at a hydrostatic pressure of p ∼0.2 GPa. This structural transition into a triclinic phase is characterized by a very strong dimerization of the Ru-Ru bonds, accompanied by a collapse of the magnetic susceptibility. Ab initio quantum-chemistry calculations disclose a pressure-induced enhancement of the direct 4d−4d bonding on particular Ru-Ru links, causing a sharp increase of the antiferromagnetic exchange interactions. These combined experimental and computational data show that the Kitaev spin-liquid phase in α−RuCl3 strongly competes with the crystallization of spin singlets into a valence bond solid.


Phys. Rev. B 97, 241108(R) (2018).

Temperature-pressure phase diagram of α−RuCl3. The solid and open black circles represent the transition TS2 in magnetization by cooling and by warming, respectively. The red squares represent the transition TS2 from x-ray diffraction. The striped area represents the region where phase separation occurs. The error bars on pressure for the magnetization measurements come from the thermal expansion of the pressure cell. The lines are guides to the eye.
Spectral function calculated for various strain values: a LSAT, −0.52% (compressive strain), b GSO, +1.53% (tensile strain) corresponding to ARPES (negative energies) and inversed photoemission spectra (positive energy). The horizontal axis is the 2D crystal momentum. The vertical axis is the energy (eV), where zero energy represents the Fermi level.

Evolution of electronic and magnetic properties of Sr2IrO4 under strain


Motivated by properties-controlling potential of the strain, we investigate strain dependence of structure, electronic, and magnetic properties of Sr2IrO4 using complementary theoretical tools: ab-initio calculations, analytical approaches (rigid octahedra picture, Slater-Koster integrals), and extended 𝑡−J model. We find that strain affects both Ir-Ir distance and Ir-O-Ir angle, and the rigid octahedra picture is not relevant. Second, we find fundamentally different behavior for compressive and tensile strain. One remarkable feature is the formation of two subsets of bond- and orbital-dependent carriers, a compass-like model, under compression. This originates from the strain-induced renormalization of the Ir-O-Ir superexchange and O on-site energy. We also show that under compressive (tensile) strain, Fermi surface becomes highly dispersive (relatively flat). Already at a tensile strain of 1.5%, we observe spectral weight redistribution, with the low-energy band acquiring almost purely singlet character. These results can be directly compared with future experiments.

npj Quantum Materials 7 (1), 90 (2022).

Influence of multiplet structure on Sr2IrO4 photoemission spectra

Most of the low-energy effective descriptions of spin-orbit driven Mott insulators consider spin-orbit coupling (SOC) as a second-order perturbation to electron-electron interactions. However, when SOC is comparable to anisotropic Hund's coupling, such as in Ir, the validity of this formally weak SOC approach is not a priori known. Depending on the relative strength of SOC and anisotropic Hund's coupling, different descriptions of the multiplet structure should be employed in the weak and strong SOC limits, viz. LS and jj coupling schemes, respectively. We investigate the implications of both the coupling schemes on the low-energy effective t−J model and calculate the angle-resolved photoemission (ARPES) spectra using self-consistent Born approximation. In particular, we obtain the ARPES spectra of quasi-two-dimensional square-lattice iridate Sr2IrO4 in both weak and strong SOC limits. The differences in the limiting cases are understood in terms of the composition and relative energy splittings of the multiplet structure. Our results indicate that the LS coupling scheme yields better agreement with the experiment, thus providing an indirect evidence for the validity of LS coupling scheme for iridates. We also discuss the implications for other metal ions with strong SOC.


Phys. Rev. B 98, 064422 (2018).

PES spectral function of the low-energy (polaronic) model developed for the quasi-two-dimensional iridates within the jj coupling scheme and solved using the self-consistent Born approximation. The value of Coulomb splitting Δ varies so that singlet-triplet splitting: λ− 5/8Δ is (a) λ/2, (b) λ/3, (c) λ/4. ARPES experimental data (reproduced from Ref. [40]) and spectral function calculated within the LS coupling scheme (reproduced from Ref. [18]) are shown for comparison in (d) and (e) respectively. Here spin-orbit coupling λ = ξ/2 where one-particle SOC ξ = 0.382 eV following Ref. [41]; hopping integrals calculated as the best fit to the density-functional theory (DFT) band structure: t1 = −0.2239 eV, t2 = −0.373 eV, t′ = −0.1154 eV, t3 = −0.0592 eV, t'' = −0.0595 eV; spectra offset by (a)–(c) E = −0.97 eV, (e) E = −0.77 eV; broadening δ=0.01 eV.

Spin–orbit coupling, orbitally entangled antiferromagnetic order, and collective spin–orbital excitations in Sr2VO4



With electron filling n= 1 in the Sr2VO4 compound, the octahedrally coordinated  orbitals are strongly active when the tetragonal distortion induced crystal field is tuned by external agent such as pressure. Considering the full range of crystal field induced tetragonal splitting in a realistic three-orbital model, collective spin–orbital excitations are investigated using the generalized self-consistent plus fluctuation approach. At ambient pressure, an entangled orbital + antiferromagnetic order is found to be stabilized beyond a critical value (∼ 30 meV) of spin–orbit coupling which is in the realistic range for 3d ions. The behavior of the calculated energy scales of collective excitations with crystal field is consistent with that of the transition temperatures with pressure as obtained from susceptibility and resistivity anomalies in high-pressure studies.


Journal of Physics: Condensed Matter 35 (4), 045801 (2022)


Coupled spin-charge order in frustrated itinerant triangular magnets. 

We uncover four spin-charge ordered ground states in the strong coupling limit of the Kondo lattice model on triangular geometry. The results are obtained using Monte Carlo simulations, with a classical treatment of localized moments. Two of the states at one-third electronic filling (n = 1/3) consist of decorated ferromagnetic chains coupled antiferromagnetically with the neighboring chains. The third magnetic ground state is noncollinear, consisting of antiferromagnetic chains separated by a pair of canted ferromagnetic chains. An even more unusual magnetic ground state, a variant of the 120∘ Yafet-Kittel phase, is discovered at n = 2/3. These magnetic orders are stabilized by opening a gap in the electronic spectrum: a “band effect.” All the phases support modulations in the electronic charge density due to the presence of magnetically inequivalent sites. In particular, the charge ordering pattern found at n= 2/3 is observed in various triangular lattice systems, such as 2H−AgNiO2, 3R−AgNiO2, and NaxCoO2.


Phys. Rev. B 91, 140403(R) (2015).

(a) Energy per site at T/t0= 0.002 as a function of JAF obtained via MC simulations (circles) for a filling fraction of n = 1/3. Various straight lines are the energies of different phases as indicated by legends. (b) The electronic density of states for three ground states, DS1, DS2, and C-AF. (c)–(e) Snapshots of the MC configurations for the three ground states. The arrows indicate the spin directions, and the circle sizes indicate the local charge density. The smaller circles have been filled to highlight the pattern of charge ordering.

Doped frustrated molecular magnets

MMs with triangular and tetrahedral motifs are particularly appealing due to frustration, leading to degeneracy in the ground state. Here, using Kondo description of a doped molecular magnet, we show that introducing electrons in magnetic clusters can lead to multiple spin states due to a subtle interplay of geometrical frustration effects, electron itinerancy and Kondo coupling. The various low- and high-spin states are stable over a wide range of parameters, leading to a rich phase diagram. We are now studying the role of asymmetry and Dzyaloshinskii-Moriya interactions in stabilizing multiple spin states in frustrated magnetic clusters.


Scientific Reports 7, 42255 (2017).

(a,b) Spin-spin correlations as a function of (a) the ferromagnetic Kondo coupling KF and (b) the ferromagnetic Kondo coupling KAF for different values of the external magnetic field B. (c,d) The phase diagram showing different spin-states of the doped triangular cluster in the B − KAF plane for different values of the exchange coupling (c) JAF = 0.2 and (d) JAF = 1.0. HS and LS, respectively, correspond to High-Spin and Low-Spin state while IS1 and IS2 are Intermediate Spin states.
Magnetic properties of {Ln2} molecules. (Top) A schematic representation of the effective interactions and the corresponding magnetic Hamiltonian. (Bottom) A schematic representation of alignment of Ln magnetic moments in {Ln2} according to ab initio calculations: collinear in {Tb2} and {Dy2}, tilted in {Ho2} (the arrows indicate directions of the single-ion quantization axis for each Ho), easy-plane in {Er2}, in the latter the Ln spins are visualized as ellipsoids; In the bottom right is shown the magnetic relaxation processes as a function of temperature.

Endohedral metallofullerenes Ln2@C2n (2n >= 74):

A combined experimental and theoretical effort into a systematic investigation of the series of endohedral metallofullerenes (EMFs) Ln2@Cn2 with Ln2 = Gd2, Tb2, Dy2, Ho2, Er2, TbGd and TbY reveals not only that Tb2@C80 is an excellent single molecule magnet (SMM), but also highlights the role of structural symmetry in forming a  was carried out experimentally and theoretically (using DFT, quantum chemistry and effective Hamiltonian). Our work highlights the importance of composition and anisotropy in obtaining good SMMs.


Nature Communications 10, 571 (2019). 

(a) Spin Hamiltonian coupled to a bath (b) Spin Hamiltonian with an explicitly defined phonon coupled to bath. (c) Linear energy dispersion of a ground state doublet diabatic states ∣∣↑⏐⟩ and ∣∣⏐↓⟩ as a function of a magnetic field (H), and visual representation of two-state Hamiltonian elements, with state energy difference ∆ = 𝜀u−𝜀d and coupling 𝛺 between them. The system dissipates through system-bath (ℬ) interaction with a coupling/rate 𝛾e. (d) Probability to find system in ∣∣↑⏐⟩ (grey) or ∣∣⏐↓⟩ (red) state over time, while system wavefunction (s(t)=u(t)∣∣↑⏐⟩+d(t)∣∣⏐↓⟩ evolve in time accordingly to a dissipative Liouvile dynamics with 𝛾e = 0 (solid lines) and 𝛾e >> 𝛺 (dash line). 
Comparison of (a) theoretical and (b) experimental temperature dependences of relaxation times, computations are performed with two different values of 𝛀𝒆 and the empirical mean-field γe parameter defined as 𝛄𝒆 ∼ T6. (c) Magnetic hysteresis curves computed with at 1.8 and 8 K for a constant parameter 𝛀𝒆(𝟎.𝟐) = 0.01 Hz, and computed at 1.8 K for the field dependent parameter 𝛀𝒆=𝟏/(𝟏.+𝟏𝟐𝟐𝟓 𝑯ˆ𝟐). (d) Experimentally observed hysteresis for DySc2N@C80 at T=1.8 and 8 K for a single crystal and for a diluted system.

Modelling magnetodynamics

With single-molecule magnets research on the rise as a result of recent advantages in the field, like remarkable high blocking temperatures up to 60 Kelvin [Nature, 548, 439, 2017], gigantic coercivity up to 80 Tesla [Nat Commun., 10, 571, 2019], magnetization stability in the thin films, further applications are seriously in the scope. The possible venue here is to develop a theory of magnetic moment manipulation and control at the microscopic level. Theory of optimal control in quantum dynamics in complex systems is well-developed. For example, the uses of density matrix techniques have been well summarized already in the early ‘60s by Fano, Haar, and many others. Thus, in many respects, the task is to reframe that research into the language of the problem at hand, and into familiar terms for the community. Recently, it was already proven the Redfield reduced density matrix techniques are applicable for slow-relaxing single-molecule magnets [Nat Commun., 8, 14620, 2017]. In our recent contribution [PCCP,20, 11656, 2018], we have outlined the use of Lindblad dynamics in combination with a few axioms in the rationalization of the relaxation behavior of single-molecule magnets. In this report we put this approach in the context of the magentodynamics theory, showing the close connection to the Landau-Lifshitz-Gilbert model and presenting further elaboration for the proposed method.


Chemrxiv pre-print

Discovery, crystal growth, and characterization of garnet Eu2PbSb2Zn3O12

Single crystal specimens of previously unknown garnet Eu2PbSb2Zn3O12 were grown in a reactive PbO:PbF2 flux medium. The crystals were characterized by a combination of X‐ray crystallography, magnetization measurements, and the optical techniques of Raman, photoluminescence, and UV/Vis spectroscopy. The material exhibits Van Vleck paramagnetism associated with the J = 0 state of Eu3+, which was possible to accurately fit to a theoretical model. Band structure calculations were performed and compared to the experimental band gap of 1.98 eV. The crystals demonstrate photoluminescence associated with the 4f 6 configuration of the Eu3+ ions sitting at the distorted 8‐coordinate garnet A site. The title compound represents a unique quinary contribution to a relatively unexplored area of rare earth bearing garnet crystal chemistry.


Eur. J. Inorg. Chem. 2020, 2512 (2020).

(a) Temperature dependence of the magnetic susceptibility of Eu2PbSb2Zn3O12 measured under an applied field of 1 kOe and zero field cooled (blue) and field cooled conditions (red). The curves approximately overlap. (b) Field dependence of the magnetization of Eu2PbSb2Zn3O12 measured at 1.8 K. (c) The Van Vleck paramagnetic susceptibility for Eu3+ ions as a function of temperature for different values of on‐site spin orbit coupling λ [K]. The inset shows the relative splitting of the multiplets 7FJ which depend only on λ. (d) The fit of the zero field cooled (ZFC) data considering only Van Vleck paramagnetism (χVV) and the full model considering also additional contribution from the Eu2+ impurity ions (χimp).
Exact diagrammatic representation of coupled equations for components of χ−+ (shaded box) in terms of the irreducible particle-hole propagator ϕ(q , ω) (open box).

The first-order quantum corrections to the irreducible particle-hole propagator ϕ(q, ω).

Fermionic representation for the ferromagnetic Kondo lattice model: Diagrammatic study of spin-charge coupling effects on magnon excitations. 

A purely fermionic representation is introduced for the ferromagnetic Kondo lattice model that allows conventional diagrammatic tools to be employed to study correlation effects. Quantum 1/S corrections to magnon excitations are investigated by using a systematic inverse-degeneracy expansion scheme that incorporates correlation effects in the form of self-energy and vertex corrections, while explicitly preserving the continuous spin-rotation symmetry. Magnon self-energy is studied in the full range of interaction strength and is shown to result in strong magnon damping and anomalous softening for zone-boundary modes, which accounts for several zone-boundary anomalies observed in recent spin-wave measurements of ferromagnetic manganites.


Phys. Rev. B 77, 134447 (2008).

Magnetic excitations in iron pnictides


Spin wave dispersion and damping are investigated in the metallic SDW state of different itinerant electron models including a small interlayer hopping. Magnetic excitations in iron pnictides are shown to be well understood in terms of physical mechanisms characteristic of metallic magnets, such as carrier-induced ferromagnetic spin couplings, intra-band particle-hole excitations, and the spin-charge coupling mechanism, which is also important in ferromagnetic manganites


arXiv pre-print