Session Y55: Correlated Electron Materials III

The Beauty of Broken Spatial Inversion Symmetry

Noncentrosymmetric (NCS) magnets, lacking spatial inversion symmetry in the structure, play an instrumental role in the potential realization of multifunctional properties, topological magnetic spin textures, and spin liquids. These spin-based properties are at the forefront of recent technological advances in spintronics and quantum information science. Despite impressive progress in investigating NCS magnets, scientists still seek to understand the appropriate coupled spin, orbital, and phonon degrees of freedom necessary for creating and tuning targeted physical phenomena and capabilities for materials. To address this, my research team applies design logic and unmatched tunability innate to extended solids to produce materials favoring desired functionalities and to relate the adjustment of electronic frontier states to underlying magnetic interactions. For example, based on design considerations, we created a new NCS magnet, CaMnTeO₆, that features a 2-D triangular layered structure and incommensurate magnetic ground state. The static magnetic moment extracted from neutron diffraction at T = 1.6 K is consistent with that from heat capacity measurements down to T = 100 mK, but only ~ 46% the expected value for S = 3/2, suggesting some low-lying magnetic excitations and potential entanglement between spins. In this talk, I will share our current update on how and why precisely placing spin carriers in appropriate NCS frameworks provides a worthwhile pathway for realizing new physical phenomena.   

Fluctuations and going beyond mean field theory in the triangular lattice Hubbard model

Mean field theory techniques have been and continue to be widely applied

in the study of strongly correlated many-body systems. For these systems, the advantage

of mean field theory comes from fact that it provides qualitative, and sometimes quantitative,

information on the tendency of the many-body system to develop ordered phases when

other theoretical methods might not apply. However, the strength of its wide use

comes at the cost of ignoring fluctuations in the relevant degrees of freedom of

the model. Hence, ordered phases found from a mean field study of a model Hamiltonian

may not be stable when fluctuations are included. In recent Hartree-Fock mean field

calculations for the Hubbard model on the triangular lattice at electron density n = 2/3,

we found a charge-ordered collinear antiferromagnetic phase on the honeycomb

sublattice above a critical interaction, U_c/t. The geometric frustration inherent to  

the triangular lattice enhances fluctuations in the Hubbard model. Therefore, we discuss

different numerical methods that incorporate fluctuations and how they can

be applied to the n = 2/3 triangular lattice Hubbard model. We present preliminary results

from numerical calculations.   

Excitation spectra of intertwined spin and orbital degrees of freedom

Even without the spin-orbit coupling, spin and orbital still couple in insulating transition-metal oxides due to the superexchange. The low-energy spectrum is therefore made up not only of spin, but also orbital, and simultaneous spin-orbital excitations. All of these can now be measured owing to the advances in resonant inelastic x-ray scattering. This calls for an accurate theoretical modeling. Here, we study the excitation spectra of the spin-orbital chain (the Kugel-Khomskii model), which forms a low-energy theory of the insulating two-orbital Hubbard chain at quarter filling. We use the density-matrix renormalization group method to properly incorporate the spin-orbital fluctuations and obtain accurate spectra with high resolution. In this way, we go beyond the usual mean-field decoupling where the spin and orbital dynamics are treated as independent. We discuss the spin and orbital dynamical structure factors and comment upon the unique combined spin-orbital excitations.   

Elementary Building Blocks for Cluster Mott Insulators

The Hubbard model provides a rich playground for investigating the physics of a wide range of strongly correlated systems. An important limit in the model is the Mott insulating regime, where, at half-filling, electrons are localized on single atomic sites. In this work, we investigate extensions of this idea to cluster Mott insulators-- where electrons are now localized on clusters of sites. To that end, we study a plethora of different clusters, at different integer fillings, by constructing a general Hamiltonian for each cluster. This allows us to explore different regimes of the interplay of strong correlations and hopping within these clusters, and their respective emergent effective degrees of freedom. We then go beyond the single-orbital "cluster" Hubbard model and include multiple orbitals and interactions between them, including spin-orbit coupling. With these building blocks established, it will be possible to introduce inter-cluster hopping terms into the picture; depending on the nature of the resulting effective interactions, they can give rise to novel Hamiltonians, which might possibly host highly correlated and/or frustrated phases.   

Entanglement-enabled symmetry-breaking orders

A spontaneous symmetry-breaking order is conventionally described by a tensor-product wave-function of some few-body clusters. We discuss a type of symmetry-breaking orders, dubbed entanglement-enabled symmetry-breaking orders, which cannot be realized by any tensor-product state. Given a symmetry breaking pattern, we propose a criterion to diagnose if the symmetry-breaking order is entanglement-enabled, by examining the compatibility between the symmetries and the tensor-product description. For concreteness, we present an infinite family of exactly solvable gapped models on one-dimensional lattices with nearest-neighbor interactions, whose ground states exhibit entanglement-enabled symmetry-breaking orders from a discrete symmetry breaking. In addition, these ground states have gapless edge modes protected by the unbroken symmetries. We also propose a construction to realize entanglement-enabled symmetry-breaking orders with spontaneously broken continuous symmetries. Under the unbroken symmetries, some of our examples can be viewed as symmetry-protected topological states that are beyond the conventional classifications.   

Itinerant quasiparticle theory of the Mott insulator

     Linear spin wave theory of the Heisenberg model is foundational to the understanding of insulating antiferromagnetism, yet the canonical Holstein-Primakoff boson remains heretofore disconnected from itinerant electron dynamics.  By subtracting correlated hopping from the Hubbard-Heisenberg model, this work shows an itinerant, charged dynamic that precisely encompasses the chargeless Heisenberg model.  Specifically, time-dependent Hartree-Fock theory exactly reconciles with the H-P boson, yielding a spin wave dispersing with J_ij, but strictly independent of t_ij and U.  The equivalence holds when the Mott insulator is stable when Hubbard U dominates intra-sublattice bandwidth, U > W[t'_ij].

     At finite doping, the spin wave is Landau damped by the lower Hubbard band, and a zero sound mode disperses, both contingent on the presence and strength of inter-sublattice hopping. Beyond the usual spin and spacetime symmetries, the dynamic is doublon conserving and has SU(2) charge symmetry. Detuning correlated hopping renders potent p-h asymmetry distinct from flipping the sign of t' in the t'-t'-J model.

     Severe instabilities present when U is small while retaining strongly correlated hopping, pointing to limitations of the quasiparticle picture and expectations of quantum order. This work aims to motivate study of the symmetric and detuned dynamics with general (non-quasiparticle) analytical and numerical methods, in the context of cuprate phenomenology.   

Spin excitations in ferromagnetic metallic La2/3Ca1/3MnO3

We employ Mn L₃-edge Resonant Inelastic X-ray Scattering (RIXS) to investigate the collective spin excitations in ferromagnetic metallic La_2/3Ca_1/3MnO₃ (LCMO) thin film. With the benefit of high-resolution RIXS, we find a bulk-like ferromagnon dispersion along [h,h,h] which at low Q is consistent with prior neutron scattering results on single crystals. Importantly, extending Q above 0.3 r.l.u., where no neutron data are available, reveals a zone-boundary magnon flattening along [h,h,h]. We describe the magnon dispersion using the Heisenberg model with next-nearest-neighbor exchange coupling. The combination of our data and theory enables settling the inconsistency between neutron data and multiple theoretical approaches. In addition, above 70 meV, we identify a Mn-O stretching phonon, a higher order multi-phonon, and a bi-magnon modes. The visualization of all these excitations leads us to evaluate the spin-phonon coupling. Indeed, spin-phonon coupling is evidenced near the zone center along [h,h,h], with the mutual renormalization of the Jahn-Teller active phonon and the single spin-flip magnon, as well as damping of the magnon. Our results extend the knowledge of the elementary excitations of LCMO shedding light on the long-standing problem of its magnetic interactions.

    

Evolution of dual ferromagnetic behavior near coherent-incoherent crossover in perovskite ruthenate

The dual contribution of localized and itinerant electrons to magnetism in correlated ferromagnetic SrRuO₃ has been observed experimentally very recently [1]. What we want to know in the next step is how the magnetic behavior of localized and itinerant can be tailored. Here, we performed spin-resolved ARPES experiments on SrRuO₃ thin film with strain engineering. It shows that the tensilely strained SrRuO₃ displays an overall incoherent electronic structure whilst the compressively strained film has coherent band structure, which means that the ratio of localized and itinerant electrons in the system can be controlled. We could measure the strain-dependent spin-polarization of electrons near Fermi level, and at lower Hubbard band. We will show the evolution of spin and electronic sturcture of tunable dual ferromagnetic system in detail. Possible application of tunable correlated ferromagnetic system will be also discussed.

[1] S. Hahn et al., Phys. Rev. Lett. 127, 256401 (2021).   

Spin-resolved Electronic Structure of the Ferromagnetic Triple-layered Ruthenate Sr4Ru3O10

 We report spin-resolved electronic band structure studies of the triple-layered ruthenate Sr₄Ru₃O₁₀. Although the band structure of Sr₄Ru₃O₁₀ has been the subject of recent experimental and theoretical investigations [1,2]; there have been no reported spin-resolved experimental studies that explore in more details the complex magnetism of Sr₄Ru₃O₁₀. In this talk, we will present the first combined spin- and angle-resolved photoemission (SARPES) study of Sr₄Ru₃O₁₀ [3]. Our SARPES data reveal major effects of spin polarization in different parts of the Brillouin zone. We resolve two separate strong intensity narrow bands with opposite spin-polarization at 30 meV below the Fermi-level, which exhibit surprisingly dramatic temperature-dependent amplitude changes upon warming to the Curie temperature of the Sr₄Ru₃O₁₀ system. We will briefly discuss a tentative comparison between the SARPES data to spin-resolved density functional theory (DFT) calculations.

 

References

[1]. P. Ngabonziza, et al. , Sci. Rep. 10, 21062 (2020).

[2] G. Gebreyesus, et al., Phys. Rev. B 105, 165119 (2022).

[3] P. Ngabonziza, J. D. Denlinger, A. Fedorov, G. Cao, J. W. Allen, G. Gebreyesus, and R. M. Martin, in preparation (2022).

    

Slave-spin method for broken symmetry states: Néel antiferromagnetism and its phase separation in multi-orbital Hubbard models

We introduce the generalization of the Slave-Spin Mean-Field method to broken symmetry phases. Through a variational approach we derive the single-particle energy shift in the mean-field equations which generates the appropriate self-consistent field responsible for the stabilization of the broken symmetry. With this correction the different flavours of the slave-spin mean-field are actually the same method, and they give identical results to Kotliar-Ruckenstein slave-bosons and to the Gutzwiller approximation. We apply our formalism to the Néel antiferromagnetic state and study it in multi-orbital models as a function of the number of orbitals and Hund's coupling strength, providing phase-diagrams in the interaction-doping plane. We show that the doped antiferromagnet in proximity of half-filling is typically unstable towards phase separation into antiferromagnetic insulating and metallic zones or between antiferromagnetic and paramagnetic zones. Hund's coupling favors this instability.   

Poisson-Dirichlet distributions and weakly first-order spin-nematic phase transitions

Weakly first-order transitions, i.e. discontinuous phase transitions with very large correlation lengths, have become a vivid subject in condensed matter research and beyond in recent years. Therefore, establishing quantum systems in which weakly first-order phase transitions can be robustly demonstrated is of great interest. We present a quantitative characterization of generic weakly first-order thermal phase transitions out of planar spin-nematic states in three-dimensional spin-one quantum magnets, based on calculations using Poisson-Dirichlet distributions within a universal loop model formulation, combined with large-scale quantum Monte Carlo calculations. In contrast to earlier claims, the thermal melting of the nematic state is not continuous, instead we identify a weakly first-order transition. Furthermore, we obtain exact results for the order parameter distribution and cumulant ratios at the melting transition. Our findings establish the thermal melting of planar spin-nematic states as a generic platform for quantitative approaches to weakly first-order phase transitions in quantum systems with a continuous SU(2) internal symmetry.   

Compass-like manipulation of electronic structure in Sr3Ru2O7

Electronic nematicity has been found in a range of correlated electron materials, exhibiting strong symmetry-breaking reconstruction of electronic states without a significant lattice distortion. An enigmatic example of an electronic nematic state is found in Sr₃Ru₂O₇, where a large resistivity anisotropy is stabilized by external magnetic field [1]. The direction of the anisotropy can be controlled by the in-plane component of the magnetic field, which was explained by field-induced spin density waves [2].

Recently, STM measurements have revealed symmetry breaking of the electronic structure at the surface of Sr₃Ru₂O₇ even in zero magnetic field, providing new insights into the mechanism stabilizing the nematicity [3].

Here, we use low-temperature scanning tunnelling microscopy to study the electronic structure in Sr₃Ru₂O₇ in vector magnetic fields. We find that the electronic structure is strongly affected even by relatively small external field, and is evolving continuously as a function of field direction. Quasiparticle interference measurements allow us to relate the observed angle dependence to the electronic structure of the material. We observe the electronic anisotropy at temperatures much higher than in the bulk, demonstrating its robustness.

This result establishes compass-like control over the electronic structure in the surface layer of Sr₃Ru₂O₇. The continuous evolution of the electronic structure with field direction cannot be easily explained by reorientation of a spin-density wave order but suggests that the field-controlled nematic state at the surface is driven by spin-orbit coupling [4].

 

[1] R. A. Borzi et al., Science 315, 214 (2007).

[2] C. Lester et al., Nature Materials 14 (2015)

[3] C. A. Marques et al., Sci. Adv. 8, eabo7757 (2022).

[4] S. Raghu et al., Phys. Rev. B 79, 214402 (2009)

    

Investigation of the disruption of magnon gap and Weyl Fermion in SrRuO3 single crystal films by inelastic neutron scattering

SrRuO3 in powder [1] and single crystal [2] forms were found to exhibit a magnon gap due to the Weyl fermion node nearby its Fermi surface.  To understand the defect effect on the magnon gap and Weyl fermion, we follow the fact that the massive Ru defects and some oxygen vacancies can be easily created when SrRuO3 is grown in a thin film format.  In this study, two single crystalline ferromagnetic SrRuO3 films were prepared by the PLD method and examined by Inelastic neutron scattering experiments at SIKA, ANSTO. We found that both films show clear magnon dispersion curves following quadratic  relation along [002] direction. The film with fewer defects was found to have a dispersion curve with a small magnon gap of around 0.32meV [3], which is much smaller than Itoh’s and Jenni’s observations. We proposed a model, the impurity level near Fermi level, due to Ru and O vacancies, could weaken the spin-orbit coupling and the anticrossings, and eventually destroy the Weyl Fermion node. In addition, the electrons captured by defects and vacancies induce on-site Coulomb interactions that open a small magnon gap. Meanwhile, the magnon gap for the defect-rich film shows a zero magnon gap, strongly indicating the existence of Weyl fermion node is very sensitive to the presence of defects.

1.  S. Itoh, Y. Endoh, T. Yokoo S. Ibuka, J. -G. Park, Y. Kaneko, K. S. Takahashi, Y. Tokura, and N. Nagaosa, Nat. Commun. 7, 11788 (2016).

2.  K. Jenni, S. Kunkemo¨ller, D. Bru¨ning, T. Lorenz, Y. Sidis, A. Schneidewind, A. A. Nugroho, A. Rosch, D. I. Khomskii, and M. Braden, Phys. Rev. Lett. 123, 017202 (2019).

3.  G. D. Dwivedi, C.-M. Wu, Bo-Yu Chen, S. T. Lin, W.-Z. Qiu, S. J. Sun, Guangyong Xu, J. W. Lynn, J. W. Chiou, C.-H Lee, W.-H. Li, S. Yano, and H. Chou, Phys. Rev. B 101, 054403 (2021).   

Magnetic field dependence of the low-energy spinon states in strongly correlated chain cuprate Sr2CuO3

Sr₂CuO₃ is a model strongly correlated cuprate chain antiferromagnet with nearly ideal one-dimensional (1D) Heisenberg Luttinger-spin-liquid behavior [1]. While fractional spinon excitations in this material have bandwidth of up to 0.7 eV [2], it only orders three-dimensionally (3D) below T_N ≈ 5.5K, indicating extremely weak interchain coupling, J'/J < 5·10^-4. In the weakly 3D ordered antiferromagnetic phase, at T N, recent ESR experiments [3] have found an unusual spin excitation mode, which was conjectured to be a hybrid Higgs-Goldstone mode because it develops together with the field-dependent gapped transverse pseudo-Goldstone magnons, intrinsic to a collinear antiferromagnet with weak two-axial anisotropy. Additionally, ultrasound measurements indicated field-induced phase transitions to novel phases whose origin is unclear and which are unexpected in a system of coupled Luttinger liquids [4]. Here, we report neutron scattering measurements of the low-energy magnetic excitations in Sr₂CuO₃ covering the extent of the intra-chain dispersion in magnetic field up to 14T aiming to verify the ESR results. While magnetic field dependence of spin gaps observed in our measurements is consistent with the behavior expected for pseudo Goldstone magnons, the excitation spectrum seems to have substantial energy width which appears to depend on magnetic field. The observed behavior suggests that freely propagating unbound spinons might be present at low energies in the ordered phase, which would disagree with a standard chain mean field theory. 

References:

1. I. A. Zaliznyak, Nat. Mater. 4, 273 (2005).

2. A. C. Walters, T. G. Perring, J.-S. Caux, A. T. Savici, G. D. Gu, C.-C. Lee, W. Ku, and I. A. Zaliznyak, Nat. Phys. 5, 867 (2009).

3. E. G. Sergeicheva, S. S. Sosin, L. A. Prozorova, G. D. Gu, and I. A. Zaliznyak. Phys. Rev. B 95, 020411(R) (2017)

4. E. G. Sergeicheva, S. S. Sosin, D. I. Gorbunov, S. Zherlitsyn, G. D. Gu, and I. A. Zaliznyak. Phys. Rev. B 101, 201107(R) (2020)