ICTS

Motivated by the recent findings in the Ba₃CuSb₂O₉ system, we have investigated Sr₃CuM₂O₉ [M= Sb, Nb] for possible spin liquid behaviour. Due to the different ionic size of Sr compared to Ba, the Sr-based systems crystallize in a different structure that the Ba-system. The bulk susceptibility of the Sr-based compounds shows a Curie-Weiss behaviour with a large, AF Θ_CW but no sign of ordering down to 1.8 K. Our specific heat data show no anomalies down to 0.3 K and a power law behaviour of the magnetic heat capacity is seen. ¹²¹Sb and ⁹³Nb NMR data also do not show any evidence of LRO. These data point towards quantum spin liquid (QSL) behaviour.

The system Y₂CuTiO₆ contains edge-shared triangular planes where the vertices are occupied by magnetic Cu and nonmagnetic Ti atoms in equal proportion. In spite of the large dilution of the triangular magnetic lattice, the magnetic susceptibility shows a large, AF Θ_CW (about 240 K) without any sign of ordering down to 1.8 K. The magnetisation in a low field (50 Oe) shows no bifurcation in ZFC/FC curves down to 0.5 K. Likewise, the heat capacity shows no anomalies and the magnetic contribution has a power law behaviour at low-temperatures. Our muSR measurements down to 50 mK also do not show any signs of ordering. Our ⁸⁹Y NMR results also do not show any signs ordering. These observations are typical of potential quantum spin liquid systems. In the present case, however, the magnetic heat capacity C_m depends on the magnetic field H. We observed that the data could be scaled such that H^γC_m/T vs T/H follow a universal curve with γ = 0.6. Such a scaling behaviour has been suggested in systems with random singlet formation. While the randomness of the exchange coupling has been suggested in YbMgGaO₄ due to Mg/Ga site disorder (with no depletion of the magnetic lattice), in the present case it is surprising that in spite of the large (50%) depletion of the lattice, no spin freezing is observed.

I will present the results of our bulk and local probe measurements on the above systems.

Spin liquids, despite their apparently featureless ground states, are exotic magnetic states which host fractionalised excitations and emergent gauge fields. Interestingly, quenched disorder can nucleate defects with unusual properties and thus reveal the hidden collective excitations of such states. In this talk, I will explain how disorder affects the physics of a prototypical frustrated magnet, dipolar spin ice, both at high and low temperatures and in fact leads to a new phase at low temperature, a "topological spin glass”, which shows signatures of both spin liquidity and glassiness. I will also describe a new cluster Monte Carlo algorithm that allows us to study the continuous phase transition to the topological spin glass and reliably extract the critical temperature and exponents.

The honeycomb lattice iridates A₂IrO₃ (A = Na, Li) were proposed as candidates for the realization of the Kitaev Heisenberg model with hopes of stabilizing Kitaev’s quantum Spin-Liquid (QSL). However, both materials were experimentally found to have magnetically ordered ground states. We report single crystal growth of a new layered honeycomb lattice iridate K₂IrO₃ with a different inter-layer stacking sequence compared to Na₂IrO₃ and $\alpha$-Li₂IrO₃. From magnetic susceptibility χ versus temperature T data we find $S_{eff} = 1/2$ moments interacting strongly with a Weiss temperature $\theta ≈ -200$~K and no sign of magnetic order or spin freezing down to $T = 1.8$~K. Heat capacity data show a broad maximum around 30 K which is insensitive to magnetic fields. These behaviours are consistent with expectations for a Quantum Spin Liquid.

Several novel quantum spin states will be presented for highly frustrated quantum spin systems such as triangular and honycome lattices. The spin-orbital interaction is also considered. In particular，possible spin liquid states will be also discussed for those systems.

Geometrical frustration in the kagome lattice leads to localization of magnetic excitations into resonating hexagons. Recent numerical studies [1,2] of the spin-1/2 kagome-lattice antiferromagnet in an applied field demonstrated that these easily localized magnons can induce various magnon crystal phases, which result in the appearance of many plateau structures in the magnetization process. We studied how these plateau states melt into non-plateau phases in the kagome antiferromagnet with varying a magnetic field [3]. We examined instabilities of the plateau phases by means of degenerate perturbation theory, and found some emergent supersolid phases below the m=5/9 plateau. In the supersolid states the pattern of resonating hexagons are preserved from the plateau crystal state and the originally polarized spins outside the hexagons dominantly join the superfluid component, or equivalently, participate in the magnetization process.

[1] S. Nishimoto, N. Shibata, and C. Hotta, Nat. Commun. 4, 2287 (2013). [2] S. Capponi, O. Derzhko, A. Honecker, A. M. Läuchli, and J. Richter, Phys. Rev. B 88, 144416 (2013). [3] X. Plat, T. Momoi, and C. Hotta, Phys. Rev. B 98, 014415 (2018).

Chao-Hung Du^1,2, K. C Rule³, C.-W. Wang⁴, S. Yano⁴, F.-C. Chou⁵

¹Department of Physics, Tamkang University, Taiwan
²Research Center for X-ray Science, Tamkang University, Taiwan
³Australian Center for Neutron Scattering, ANSTO, Australia
⁴Neutron Group, National Synchrotron Radiation Research Center, Taiwan
⁵Center for Condensed Matter Sciences, National Taiwan University, Taiwan

The double-perovskites exhibit many fundamentally interesting chemical and physical properties; they can have electronic structures raging from insulator, metallic, halfmetallic to superconductor; they can also have different magnetic order parameters; or even simultaneously containing the multiple order parameters, such as multiferroicity. The double-perovskite ferrite YBaCuFeO₅ (YBCFO) is such a material to show a rich phase diagram. Using a modified floating zone growth method, we are able to grow the high-quality single crystal of YBCFO for the detailed studies using neutron scattering. Using neutron powder and single crystal diffraction, YBCFO was observed to show a commensurate-incommensurate magnetic transition at T_N~ 175 K. This incommensurate phase develops into a spiral spin ordering with a propagating vector along c-axis. Further using neutron TOF and triple-axis spectrometers, we observed that the spiral spin ordering shows a very unusual dispersion behavior as a function of temperature, which could be the consequence of a strong coupling between the spin moments of Fe³⁺ and Cu²⁺ and their d_z orbitals. This finding also calls for the analytically modeling for the further understanding the mechanism behind.

References:

1. Y.-C. Lai, et. al., J. of Physics: Condes. Matt. 29, 145801 (2017)
2. W.-C. Liu, et. al., J Appl. Cryst. 49, 1721 (2016)
3. M. Morin, et. al., Nature Comm. 7, 13758 (2016)
4. D. Dey, et. al., Scientific Report 8, 2404 (2018)

We propose many-body invariants for multipolar higher-order topological insulators by generalizing Resta's pioneering work on polarizations. The many-body invariants are designed to measure the distribution of electron charge in unit cells and thus can detect quantized multipole moments purely from the bulk ground state wavefunctions. Using the invariants, we prove the bulk-boundary correspondence of the higher-order topological insulators. Further, we show that our invariants can diagnose the corner charge of rotational- symmetric crystalline insulators. Application of our invariants to spin systems as well as various other aspects of the many-body invariants will be discussed.

A fundamental motif in frustrated magnetism is the tetrahedral cluster -- four spins with each pair separated by the same distance. If the spins are coupled by Heisenberg couplings, they must add to zero to minimize energy. This leads to a simple mathematical criterion for classical ground states -- we have four vectors which are constrained to add to zero. We show that this leads to a five-dimensional space of allowed states. Remarkably, this space has 'non-manifold' structure. It contains 'singular' points about which it appears to be six dimensional. We use this construction to build a semi-classical theory for the tetrahedral cluster. In the low-energy limit, it takes a very simple form. It decomposes into two independent objects -- a rigid rotor (a spinning top) and a free spin. This free spin is perhaps the simplest example of an 'emergent' quantity, arising from angular variables in the spin configuration. This provides an elegant way to understand the energy spectrum and physical properties of tetrahedral molecular magnets.

Magnetic systems are characterised by microscopic interaction strengths that couple magnetic moments of different atomic sites. Depending on the magnitudes, signs and ranges of these interactions, various magnetic ground states can be realised, the simplest examples being various collinear magnetic arrangements. In simple systems exhibiting transitions from paramagnetic to ordered (ferro- or antiferro-) magnetic states with the lowering of temperature, one may obtain an estimate of the net interaction strength from the temperature-intercept (Ɵ_CW) of the inverse-susceptibility plot as a function of the temperature via the Curie-Weiss Law. This magnitude of Ɵ_CW is often a good indication of the transition temperature. However, there are many systems where the magnetic ordering temperature is significantly suppressed compared to Ɵ_CW due to frustrations in the magnetic interactions. In extreme cases, no magnetic ordering is found down to the lowest temperature probed despite a sizable value of Ɵ_CW, prompting one to believe that such systems have an exotic ground state, known as quantum spin liquid, characterised, among other things, by an absence of ordering despite sizable interactions between various magnetic sites. We have been probing several new systems that are likely candidates of this class of compounds. I shall discuss some of these systems in my presentation.

The search for quantum spin (-orbital) liquids (QSL) -materials where local moments are well formed but continue to fluctuate quantum mechanically down to zero temperature still remains a fundamental challenge in condensed matter physics. In this talk, we shall show that the electronic structure of 6H perovskite type quaternary iridates Ba₃MIr₂O₉, have all the necessary ingredients to host QSL state. In Ba₃MIr₂O₉, Ir ions form structural dimers and non-magnetic M provides a knob to tailor the valence of Ir leading to emergent quantum phases. As a first example [1], we shall consider the pentavalent (d⁴) 6H perovskite iridate Ba₃ZnIr₂O₉ and argue that the ground state of this system is a realization of novel spin-orbital liquid state. Our results reveal that such a system provides a very close realization of the elusive J=0 state where Ir local moments are spontaneously generated due to the comparable energy scales of the singlet-triplet splitting driven by spin-orbit coupling (SOC) and the super-exchange interaction mediated by strong intra-dimer hopping. While the Ir ions within the structural Ir2O9 dimer prefers to form a spin-orbit singlet states(SOS) with no resultant moment, however substantial frustrated inter-dimer exchange interactions induce quantum fluctuations in the SOS states favoring spin-orbital liquid phase at low enough temperature. As a second example [2] we shall consider the d^4.5 insulator Ba₃YIr₂O₉ and explain the origin of the pressure induced magnetic transition to a spin-orbital liquid state in this system. We shall also discuss the importance of Kitaev interactions in the realization QSL phases for the d⁵ members of the same family[3]. Finally we shall compare our results with d³ [4] and d⁴ [5] Ir based double perovskites, particularly explain the origin of moments and presence of spin-orbital singlets in Ba₂YIrO_{6 .}

References

[1] A. Nag et. al. Phys. Rev. Lett. 116, 375501 2016

[2] S.K. Panda et. al. Phys. Rev. B 92, 180403 (Rapid Comm.), 2015

[3] S. Bhowal, S. Ganguly and I. Dasgupta, 2018 (Submitted for publication)

[4] S. Bhowal and I. Dasgupta, Phys Rev B 97 , 024406 (2018)

[5] A. Nag et. al., Phys Rev B 98, 014431 (2018)

Recently, Kitaev’s model is drawing considerable attention as a platform to study quantum spin liquid, and several compounds, such as RuCl₃ and H₃LiIr₂O₆, are proposed as candidates to support this spin liquid phase. Among many non-trivial properties, the Kitaev’s spin liquid phases host unusual excitations: spins are fractionalized into itinerant Majorana fermions and Visons, and the latter behave as abelian/non-abelian anyons. To diagnose the formation of Kitaev’s spin liquid in actual materials, and to understand the nature of its exotic response, the understanding of these elementary excitations is essential.

In this contribution, we present an exact analytical solution of dynamical correlation function for Kitaev’s spin liquid. With this solution, we will address how local disturbance of the system, such as impurity, manifests itself in the thermodynamic and dynamical properties, in association with the nature of fractionalized excitations. In particular, we will focus on the Vison zero-energy state appearing around the site vacancy, and discuss how to observe it experimentally.

The recent discovery of topological semimetals, which possess distinct electron-band crossing with non-trivial topological characteristics, has stimulated intense research interest. By extending the notion of symmetry-protected band crossing into one of the simplest magnetic groups, namely by including the symmetry of time-reversal followed by space-inversion, we predict the existence of topological magnon-band crossing in three-dimensional (3D) antiferromagnets. The crossing takes the forms of Dirac points and nodal lines, in the presence and absence, respectively, of the conservation of the total spin along the ordered moments. In a concrete example of a Heisenberg spin model for a “spin-web” compound, Cu₃TeO₆, we demonstrate the presence of Dirac magnons over a wide parameter range using linear spin-wave approximation [1]. Inelastic neutron scattering experiments have been carried out to detect the bulk magnon-band crossing in a single-crystal sample. The highly interconnected nature of the spin lattice suppresses quantum fluctuations and facilitates our experimental observation, leading to remarkably clean experimental data and very good agreement with the linear spin-wave calculations. The predicted topological Dirac points are confirmed [2].

[1] K. Li et al., PRL 119, 247202 (2017).
[2] W. Yao et al., Nature Physics 14, 1011 (2018).

Topological spin texture consisting of multiple-q spin spiral is of great interest for novel quantum transport phenomena and spintronic functions. A recent interesting example is a magnetic skyrmion, which is a topologically stable, vortex-like spin object discovered in noncentrosymmetric systems allowing the Dzyaloshinskii-Moriya (DM) interaction [1,2]. The title compound SrFeO₃ is a promising candidate of the centrosymmetric compound hosting a novel skyrmion lattice in the absence of the DM interaction. SrFeO₃ has been known as a rare oxide showing both helimagnetism and metallic conduction while preserving the centrosymmetric cubic lattice. While the magnetic ground state has been believed to be a simple proper-screw-type spin order for long time, we have found that the magnetic phase diagram of SrFeO₃ hosts a rich variety of helimagnetic phases, two of which show novel topological helimagnetic orders [3].

In this presentation, I will show the topologically nontrivial helimagnetic phases in the simple cubic perovskite SrFeO₃, which were discovered by the polarized and unpolarized small angle neutron scattering (SANS) measurements on the single crystalline samples. We found that SrFeO₃ shows two kinds of multiple-q helimagnetic structures: an anisotropic double-q spin spiral and an isotropic quadruple-q spiral hosting a three-dimensional lattice of topological singularities [4]. As a related topic, our recent discovery of a novel helimagnetic phase in the isostructural cubic perovskite Sr_1-xBa_xCoO₃ by Sakai et al. will be also presented [5]. These perovskite-type oxides not only diversify the family of SkX host materials, but furthermore provides an experimental missing link between centrosymmetric lattices and topological helimagnetic order.

This work was done in collaboration with T. Nakajima, J. -H. Kim, D. S. Inosov, Y. Tokunaga, S. Seki, N. Kanazawa, Y. W. Long, Y. Kaneko, R. George, K. Seemann, J. S. White, J. L. Gavilano, Y. Taguchi, T. Arima, B. Keimer, and Y. Tokura. This work is supported by JST PRESTO Hyper-nano-space design toward Innovative Functionality (Grant No. JPMJPR1412) and the JSPS Grant-in-Aid for Scientific Research (A) Grant No. 17H01195.

[1] S. Mühlbauer et al., Science 323, 915 (2009).

[2] S. Seki, X. Z. Yu, S. Ishiwata, and Y. Tokura, Science 336, 198 (2012).

[3] S. Ishiwata et al., Phys. Rev. B 84, 054427 (2011).

[4] S. Ishiwata et al., arXiv:1806.02309.

[5] H. Sakai et al., Phys. Rev. Mater. 2, 104412 (2018).

The magnetic field response of the Mott-insulating honeycomb iridate Na₂IrO₃ is investigated using torque magnetometry measurements in magnetic fields up to 60 tesla. A peak-dip structure is observed in the torque response at magnetic fields corresponding to an energy scale close to the zigzag ordering (≈ 15K) temperature. Using exact diagonalization calculations, we show that such a distinctive signature in the torque response constrains the effective spin models for these classes of Kitaev materials to ones with dominant ferromagnetic Kitaev interactions, while alternative models with dominant antiferromagnetic Kitaev interactions are excluded. We further show that at high magnetic fields, long range spin correlation functions decay rapidly, signaling a transition to a long-sought-after field-induced quantum spin liquid beyond the peak-dip structure. Kitaev systems are thus revealed to be excellent candidates for field-induced quantum spin liquids, similar physics having been suggested in another Kitaev material α−RuCl3.

A simple Néel order can be destroyed by geometrical cancellation of magnetic interactions between nearest-neighbor spins on triangle-based networks or by competitions among two or more kinds of interactions. Stabilized alternatively are quantum disordered states called the spin liquid or unusual long-range orders having emergent degrees of freedom such as chirality or topological excitations. Extensive theoretical studies have proposed fascinating states of matter in various classes of models with frustration, and experimental studies have been undertaken to search for related exotic phenomena in real candidate compounds. However, there are numerous obstacles to clarify the frustration physics: the selection of a ground state from macroscopically large number of states existing next to it within a small energy range is subtle and is rather difficult to predict even by the state-of-the-art calculation techniques. Moreover, the ground state is often severely influenced by perturbations like anisotropy or additional interactions to the simplest Heisenberg model. Furthermore to experiments, the presence of crystallographic disorder, which does exist more or less in actual compounds, tends to disturb and mask the intrinsic properties of frustrated systems. Therefore, one has to be careful to enjoy the interesting frustration physics.

In my presentation, I will focus on some frustrated spin systems from materials point of view. A particular emphasis will be on two kagome-type copper minerals: volborthite [1] and Cd-kapellasite (CdK) [2]. The others are so-called J₁–J₂ magnets with first and second-neighbor interactions in 1D chains [NaCuMoO₄(OH), 3] and 2D square lattices [AMoOPO₄Cl (A = K, Rb), 4]. In addition, I would like to address our recent trials searching for novel magnets in 5d transition metal compounds.

References

[1] H. Ishikawa, M. Yoshida, K. Nawa, M. Jeong, S. Krämer, M. Horvatić, C. Berthier, M. Takigawa, M. Akaki, A. Miyake, M. Tokunaga, K. Kindo, J. Yamaura, Y. Okamoto and Z. Hiroi, Phys. Rev. Lett. 114, 227202 (2015).

[2] R. Okuma, T. Yajima, D. Nishio-Hamane, T. Okubo and Z. Hiroi, Phys. Rev. B 95, 094427 (2017).

The Hida model, defined on honeycomb lattice, is a spin-1/2 Heisenberg model of antiferromagnetic hexagons (with nearest-neighbour interaction, J_A) coupled via ferromagnetic bonds (with exchange interaction, J_F). It applies to the spin-gapped organic materials, m-MPYNN · X (for X = I, BF4, ClO4). For |J_F | ≫ JA, it reduces to the spin-1 kagome Heisenberg antiferromagnet (KHA). Motivated by the recent findings of spontaneously trimerized singlet (TS) ground state for the spin-1 KHA, we investigate the evolution of the ground state of Hida model from weak to strong J_F /J_A using triplon analysis and Schwinger boson mean-field theory. Our study of the Hida model shows that its uniform hexagonal singlet (HS) phase for weak J_F /J_A soon gives way to the dimerized hexagonal singlet (D-HS) ground state, which for strong J_F /J_A approaches the TS state. We further find that the evolution from the uniform HS phase for spin-1/2 Hida model to the TS phase for spin-1 KHA happens through two quantum phase transitions: (1) the spontaneous dimerization transition at small J_F /J_A (~ −0.28) from the uniform HS to D-HS phase, and (2) the moment formation transition at moderate J_F /J_A (~ −1.46) across which the pair of spin-1/2’s on every FM bond begins to behave as bound moment that tends to spin-1 for large negative J_F’s. The TS ground state of the spin-1 KHA is thus adiabatically connected to the D-HS ground state of the Hida model. Our calculations imply that the m-MPYNN · X salts realize the D-HS phase at low temperatures, which can be ascertained through a distinguishing feature in neutron diffraction.

We study transport across junctions of a Weyl and a multi-Weyl semimetal separated by a region of thickness d which has a barrier potential U_0. We show that the tunneling conductance G of such a junction becomes independent of the barrier strength in the thin barrier limit. We show that this independence is a consequence of the change in the topological winding number of the Weyl nodes across the junction and point out that it has no analogue in tunneling conductance of either junctions of two-dimensional topological materials (such as graphene or topological insulators) or those made out of Weyl or multi-Weyl semimetals with same topological winding numbers. We study this phenomenon both for normal-barrier-normal (NBN) and normal-barrier-superconducting (NBS) junctions involving Weyl and multi-Weyl semimetals and discuss experiments which can test our theory.

Weak Mott insulators emerge from 5d electron systems with strong spin-orbit interactions. Coulomb repulsion (U) between electrons in 5d orbitals is not strong enough to suppress charge degrees of freedom completely. For example, the charge gap is comparable to the magnon-band width for strontium iridates. Such electron systems can be described by the Hubbard model with an intermediate U, which would be in the crossover regime between Slater and Mott insulators. Reliable calculation for the intermediate-U region is theoretically challenging because of the lack of a small parameter in the model. We have developed a new numerical approach that enables efficient calculation of dynamical quantities at finite temperatures in the broad-U region. The sampling of auxiliary vector fields from the Boltzmann distribution and the real time dynamics of the density matrix are successfully combined in our method.

In the presentation, I will explain our semi-classical approach that fully captures spatial fluctuations of the systems. As an application of the newly developed method, the dynamical spin structure factor and the dielectric constant for the kagome lattice will be demonstrated, where the ground state has an octahedral spin configuration with a chiral symmetry breaking. Importantly, our approach is applicable to various systems without any restrictions on the type of hopping, the type of lattice, and electron filling. The broad U region is accessible up to the temperature comparable to the charge gap.

The competition between Ruderman, Kittel, Kasuya and Yosida (RKKY) interaction and the Kondo effect in Ce and Yb based intermetallic compounds have been studied quite extensively. These studies on the Ce and Yb-based intermetallic compounds have resulted in a plethora of interesting phenomena like heavy fermion, valence fluctuation, unconventional superconductivity, quantum phase transition etc. All these interesting properties occurs due to the hybridization of the localized 4f electron with the conduction electrons. A weak hybridization usually results in a magnetic ground state, while a stronger hybridization results in a weaker localization of the 4f electron pushing the system eventually to a non-magnetic ground state. The hybridization strength and the effects due to the crystal electric field (CEF) depend on the atomic environment around the Ce-atom in the unit cell, which includes the interatomic distances between the Ce and other atoms on different crystallographic sites. Most of the Ce-compounds possess a single unique atomic position for the Ce atom in the unit cell. However, there are cerium compounds which host multiple sites for Ce atoms in the unit cell. In this talk, I will present some of our recent results on the crystal growth and anisotropic physical properties of some Ce-based intermetallic compounds.