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Spin-orbit coupling (SOC) offers a large variety of novel and extraordinary magnetic and electronic properties in otherwise `ordinary pool' of heavy ion oxides. Here we present a detailed study on an apparently isolated hexagonal 2$H$ spin-chain $d^4$ iridate Sr$_3$LiIrO$_6$ (SLIO) with geometric frustration. Our structural studies clearly reveal perfect Li-Ir chemical order in this compound. Our combined experimental and {\it ab-initio} electronic structure investigations establish a magnetic ground state with finite Ir$^{5+}$ magnetic moments in this compound, contrary to the anticipated nonmagnetic $J$=0 state. Furthermore, the dc magnetic susceptibility ($\chi$), heat capacity ($C_p$) and spin-polarized density functional theory (DFT) studies unravel that despite having noticeable antiferromagnetic correlation among the Ir$^{5+}$ local moments, this SLIO system evades any kind of magnetic ordering down to at least 2 K due to geometrical frustration, arising from the comparable interchain Ir-O-O-Ir superexchange interaction strengths, hence promoting SLIO as a potential quantum spin liquid candidate., Comment: 13 pages, 5 figures. arXiv admin note: text overlap with arXiv:2107.04431

We report bulk Rashba spin splitting (RSS) and associated Dirac surface state in (Bi$_{0.9}$Sb$_{0.1})_2$Se$_3$, exhibiting dominant $p$-type conductivity. We argue from the synchrotron diffraction studies that origin of the bulk RSS is due to a structural transition to a non-centrosymmetric $R3m$ phase below $\sim$ 30 K. The Shubnikov-de Haas Van (SdH) oscillations observed in the magnetoresistance curves at low temperature and the Landau level fan diagram, as obtained from these oscillations, confirm the presence of nontrivial Dirac surface state. The magnetization data at low temperature exhibit substantial orbital magnetization consistent with the bulk RSS. The existance of both the bulk RSS and Dirac surface states are confirmed by first principles density functional theory calculations. Coexistence of orbital magnetism, bulk RSS, and Dirac surface state is unique for $p$-type (Bi$_{0.9}$Sb$_{0.1})_2$Se$_3$, making it an ideal candidate for spintronic applications.

Spin-orbit coupling (SOC) often gives rise to interesting electronic and magnetic phases in an otherwise ordinary pool of paramagnetic heavy metal oxides. In presence of strong SOC, assumed to be working in $j$-$j$ coupling regime, 5$d^4$ iridates are generally speculated to possess a nonmagnetic $J_{eff}$~=~0 singlet ground state, which invariably gets masked due to different solid-state effects (e.g. hopping). Here, we try to probe the trueness of the atomic SOC-based proposal in an apparently 1-dimensional system, Sr$_3$NaIrO$_6$, possessing a 2$H$ hexagonal structure with well separated Ir$^{5+}$ (5$d^4$) ions. But all the detailed experimental as well as theoretical characterizations reveal that the ground state of Sr$_3$NaIrO$_6$ is not nonmagnetic, rather accommodating a significantly high effective magnetic moment on Ir$^{5+}$ ion. However our combined dc susceptibility ($\chi$), ${}^{23}$Na nuclear magnetic resonance (NMR), muon-spin-relaxation/rotation ($\mu$SR) and heat capacity ($C_p$) measurements clearly refute any sign of spin-freezing or ordered magnetism among the Ir$^{5+}$ moments due to geometrical exchange frustration, while in-depth zero-field (ZF) and longitudinal field (LF) $\mu$SR investigations strongly point towards inhomogeneous quantum spin-orbital liquid (QSOL)-like ground state. In addition, the linear temperature dependence of both the NMR spin-lattice relaxation rate and the magnetic heat capacity at low temperatures suggest low-lying gapless spin excitations in the QSOL phase of this material. Finally, we conclude that the effective SOC realised in $d^4$ iridates are unlikely to offer a ground state which will be consistent with a purely atomic $j$-$j$ coupling description., Comment: 13 pages, 12 figures

Recently, there have been contrary claims of Kitaev spin-liquid behaviour and ordered behavior in the honeycomb compound Ag$_3$LiIr$_2$O$_6$ based on various experimental signatures. Our investigations on this system reveal a low-temperature ordered state with persistent dynamics down to the lowest temperatures. Magnetic order is confirmed by clear oscillations in the muon spin relaxation ($\mu$SR) time spectrum below 9 K till 52 mK. Coincidentally in $^7$Li nuclear magnetic resonance, a wipe-out of the signal is observed below $\sim$ 10 K which again strongly indicates magnetic order in the low temperature regime. This is supported by our density functional theory calculations which show an appreciable Heisenberg exchange term in the spin Hamiltonian that favors magnetic ordering. The $^7$Li shift and spin-lattice relaxation rate also show anomalies at $\sim$ 50 K. They are likely related to the onset of dynamic magnetic correlations, but their origin is not completely clear. Detailed analysis of our $\mu$SR data is consistent with a co-existence of incommensurate N\'eel and striped environments. A significant and undiminished dynamical relaxation rate ($\sim 5$ MHz) as seen in $\mu$SR deep into the ordered phase indicates enhanced quantum fluctuations in the ordered state., Comment: 11 pages, 10 figures

We report gapless quantum spin liquid behavior in the layered triangular Sr$_{3}$CuSb$_{2}$O$_{9}$ (SCSO) system. X-ray diffraction shows superlattice reflections associated with atomic site ordering into triangular Cu planes well-separated by Sb planes. Muon spin relaxation ($\mu$SR) measurements show that the $S = \frac{1}{2}$ moments at the magnetically active Cu sites remain dynamic down to 65 mK in spite of a large antiferromagnetic exchange scale evidenced by a large Curie-Weiss temperature $\theta_{\mathrm{cw}} \simeq $ -143 K as extracted from the bulk susceptibility. Specific heat measurements also show no sign of long-range order down to 0.35 K. The magnetic specific heat ($\mathit{C}$$_{\mathrm{m}}$) below 5 K reveals a $\mathit{C}$$_{\mathrm{m}}$ $=$ $\gamma T$ + $\alpha T$$^{2}$ behavior. The significant $T$$^{2}$ contribution to the magnetic specific heat invites a phenomenology in terms of the so-called Dirac spinon excitations with a linear dispersion. From the low-$T$ specific heat data, we estimate the dominant exchange scale to be $\sim $ 36 K using a Dirac spin liquid ansatz which is not far from the values inferred from microscopic density functional theory calculations ($\sim $ 45 K) as well as high-temperature susceptibility analysis ($\sim$ 70 K). The linear specific heat coefficient is about 18 mJ/mol-K$^2$ which is somewhat larger than for typical Fermi liquids., Comment: 16 pages, 21 figures, including supplementary material. A $S = \frac{1}{2}$ Dirac spin liquid scenario has been put forward to explain the field-dependent specific heat data. Comments are welcome

The abstract of Phys. Rev. Lett. 121, 157001 (2018) claims to "demonstrate, using ab initio computations, a new trend suggesting that the cuprates with stronger out-of-CuO$_{2}$-plane chemical bonding between the apical anion (O, Cl) and apical cation (e.g., La, Hg, Bi, Tl) are generally correlated with higher $T_{c\,\max}$ in experiments". We point out that this trend is included in the long-known [Phys. Rev. Lett. 87, 047003 (2001)] correlation of $T_{c\,\max}$ with the hopping range of the electrons at (the most interlayer-bonding sheet of) the Fermi-surface. Contrary to the impression given in Phys. Rev. Lett. 121, 157001 (2018), the correlation mentioned in Phys. Rev. Lett. 87, 047003 (2001) is not simply with the distance, $d_{A},$ of apical oxygen from the nearest CuO$_{2}$ plane; but rather, as stated in the abstract of Phys. Rev. Lett. 87, 047003 (2001), "It is controlled by the energy of the axial orbital, a hybrid between Cu 4$s$, apical-oxygen 2$p_{z},$ and farther orbitals.", Comment: 1 page. Comment to Phys. Rev. Lett. 121, 157001 (2018)

Investigation of elementary excitations has advanced our understanding of many-body physics governing most physical properties of matter. Recently spin-orbit excitons have drawn much attention, whose condensates near phase transitions exhibit Higgs mode oscillations, a long-sought physical phenomenon [Nat. Phys. {\bf 13}, 633 (2017)]. These critical transition points resulting from competing spin-orbit coupling (SOC), local crystalline symmetry and exchange interactions, are not obvious in Iridium based materials, where SOC prevails in general. Here, we present results of resonant inelastic x-ray scattering on a spin-orbital liquid Ba$_3$ZnIr$_2$O$_9$ and three other 6H-hexagonal perovskite iridates which show magnetism, contrary to non-magnetic singlet ground state expected due to strong SOC. Our results show that substantial hopping between closely placed Ir$^{5+}$ ions within Ir$_2$O$_9$ dimers in these 6H-iridates, modifies spin-orbit coupled states and reduces spin-orbit excitation energies. Here, we are forced to use at least a two-site model, to match the excitation spectrum going in line with the strong intra-dimer hopping. Apart from SOC, low energy physics of iridates is thus critically dependent on hopping, and may not be ignored even for systems having moderate hopping, where the excitation spectra can be explained using an atomic model. SOC which is generally found to be 0.4-0.5~eV in iridates, is scaled in effect down to $\sim$0.26~eV for the 6H-systems, sustaining the hope to achieve quantum criticality by tuning Ir-Ir separation., Comment: 12 Pages, Main text has 4 figures, SI which is added at the end of the main text has 5 figures and two tables

The system Ag[Li$_{1/3}$Mn$_{2/3}$]O$_{2}$ belongs to a quaternary 3R-delafossite family and crystallizes in a monoclinic symmetry with space group $C\,2/m$ and the magnetic Mn$^{4+}$($S=3/2$) ions form a honeycomb network in the $ab$-plane. An anomaly around 50 K and the presence of antiferromagnetic (AFM) coupling (Curie-Weiss temperature $\theta_{CW}\sim-51$ K) were inferred from our magnetic susceptibility data. The magnetic specific heat clearly manifests the onset of magnetic ordering in the vicinity of 48\,K and the recovered magnetic entropy, above the ordering temperature, falls short of the expected value, implying the presence of short-range magnetic correlations. The (ESR) line broadening on approaching the ordering temperature $T_{{\rm N}}$ could be described in terms of a Berezinski-Kosterlitz-Thouless (BKT) scenario with $T_{{\rm KT}}=40(1)$ K. $^{7}$Li NMR line-shift probed as a function of temperature tracks the static susceptibility (K$_{iso}$) of magnetically coupled Mn$^{4+}$ ions. The $^{7}$Li spin-lattice relaxation rate (1/$T$$_{1}$) exhibits a sharp decrease below about 50 K. Combining our bulk and local probe measurements, we establish the presence of an ordered ground state for the honeycomb system Ag$_{3}$LiMn$_{2}$O$_{6}$.Our ab-initio electronic structure calculations suggest that in the $ab$-plane, the nearest neighbor (NN) exchange interaction is strong and AFM, while the next NN and the third NN exchange interactions are FM and AFM respectively. In the absence of any frustration the system is expected to exhibit long-range, AFM order, in agreement with experiment., Comment: 11 pages, 13 figures, accepted in Phys Rev B

We have investigated the thermodynamic and local magnetic properties of the Mott insulating system Ag$_{3}$LiRu$_{2}$O$_{6}$ containing Ru$^{4+}$ (4$d$$^{4}$) for novel magnetism. The material crystallizes in a monoclinic $C2/m$ structure with RuO$_{6}$ octahedra forming an edge-shared two-dimensional honeycomb lattice with limited stacking order along the $c$-direction. The large negative Curie-Weiss temperature ($\theta_{CW}$ = -57 K) suggests antiferromagnetic interactions among Ru$^{4+}$ ions though magnetic susceptibility and heat capacity show no indication of magnetic long-range order down to 1.8 K and 0.4 K, respectively. $^{7}$Li nuclear magnetic resonance (NMR) shift follows the bulk susceptibility between 120-300 K and levels off below 120 K. Together with a power-law behavior in the temperature dependent spin-lattice relaxation rate between 0.2 and 2 K, it suggest dynamic spin correlations with gapless excitations. Electronic structure calculations suggest an $S = 1$ description of the Ru-moments and the possible importance of further neighbour interactions as also bi-quadratic and ring-exchange terms in determining the magnetic properties. Analysis of our $\mu$SR data indicates spin freezing below 5 K but the spins remain on the borderline between static and dynamic magnetism even at 20 mK., Comment: 10 pages, 11 figures. accepted in Phys. Rev. B

The magnetic correlations in the austenite phase and the consequent martensitic transition in inverse magnetocaloric alloys, Ni$_{2}$Mn$_{1+x}$Sn$_{1-x}$, have been a matter of debate for decades. We conclusively establish using {\it ab initio} phonon calculations that the spin alignment of excess Mn at the Sn site (Mn$_{Sn}$) with the existing Mn in the unit cell in the high temperature cubic phase of Ni-Mn-Sn alloy is ferromagnetic (FM), and not ferrimagnetic (FI), resolving a long lasting controversy. Using first principles density functional perturbation theory (DFPT), we observe an instability of the TA$_{2}$ mode along the $\Gamma$-M direction in the FM phase, very similar to that observed in the prototypical ferromagnetic shape memory alloy (FSMA) Ni$_{2}$MnGa. This specific instability is not observed in the FI phase. Further finite temperature first principles lattice dynamics calculations reveal that at 300 K the FM phase becomes mechanically stable, while the FI phase continue to remain unstable providing credence to the fact that the high-temperature phase has FM order. These results will be primordial to understand the magneto-structural properties of this class of compounds., Comment: Supplemental materials are uploaded as a separate .pdf file

While it was speculated that 5$d^4$ systems would possess non-magnetic $J$~=~0 ground state due to strong Spin-Orbit Coupling (SOC), all such systems have invariably shown presence of magnetic moments so far. A puzzling case is that of Ba$_2$YIrO$_6$, which in spite of having a perfectly cubic structure with largely separated Ir$^{5+}$ ($d^4$) ions, has consistently shown presence of weak magnetic moments. Moreover, we clearly show from Muon Spin Relaxation ($\mu$SR) measurements that a change in the magnetic environment of the implanted muons in Ba$_2$YIrO$_6$ occurs as temperature is lowered below 10~K. This observation becomes counterintuitive, as the estimated value of SOC obtained by fitting the RIXS spectrum of Ba$_2$YIrO$_6$ with an atomic $j-j$ model is found to be as high as 0.39~eV, meaning that the system within this model is neither expected to possess moments nor exhibit temperature dependent magnetic response. Therefore we argue that the atomic $j-j$ coupling description is not sufficient to explain the ground state of such systems, where despite having strong SOC, presence of hopping triggers delocalisation of holes, resulting in spontaneous generation of magnetic moments. Our theoretical calculations further indicate that these moments favour formation of spin-orbital singlets in the case of Ba$_2$YIrO$_6$, which is manifested in $\mu$SR experiments measured down to 60~mK., Comment: 20 Pages, 7 Figures

The pyrovanadate alpha-Cu2V2O7 belongs to the orthorhombic (Fdd2) class of crystals with noncentrosymmetric crystal structure. Recently, the compound has been identified to be a magnetic multiferroic with a substantial electric polarization below the magnetic transition temperature TC = 35 K. Here we report the results of our inelastic neutron scattering (INS) studies on a polycrystalline sample of alpha-Cu2V2O7. Our INS data clearly show the existence of dispersive spin wave excitations below TC with a zone-boundary energy of 11 meV at 5 K.We have analyzed the data using linear spin wave theory, which shows good agreement between the experiment and calculation. The analysis is consistent with the third nearest neighbor exchange interaction playing a dominant role in the magnetism of the material., Comment: 5 pages, 5 figures

We have carried out a detailed first-principles study of a d$^{4.5}$ quaternary iridate Ba$_3$YIr$_2$O$_9$ both in its 6H-perovskite-type ambient pressure (AP) phase and also for the high pressure (HP) cubic phase. Our analysis reveals that the AP phase belongs to the intermediate spin-orbit coupling (SOC) regime. This is further supported by the identification of the spin moment as the primary order parameter (POP) obtained from a magnetic multipolar analysis. The large $t_{2g}$ band width renormalizes the strength of SOC and the Ir intersite exchange interaction dominates resulting in long range magnetic order in the AP phase. In addition to SOC and Hubbard $U$, strong intradimer coupling is found to be crucial for the realization of the insulating state. At high pressure (HP) the system undergoes a structural transformation to the disordered cubic phase. In sharp contrast to the AP phase, the calculated exchange interactions in the HP phase are found to be much weaker and SOC dominates leading to a quantum spin orbital liquid (SOL) state.

We investigate magnetic, thermal, and dielectric properties of SrCuTe2O6, which is isostructural to PbCuTe2O6, a recently found, Cu-based 3D frustrated magnet with a corner sharing triangular spin network having dominant first and second nearest neighbor (nn) couplings [B. Koteswararao, et al. Phys. Rev. B 90, 035141 (2014)]. Although SrCuTe2O6 has a structurally similar spin network, but the magnetic data exhibit the characteristic features of a typical quasi -one-dimensional magnet, which mainly resulted from the magnetically dominant third nn coupling, uniform chains. The magnetic properties of this system are studied via magnetization (M), heat capacity (Cp), dielectric constant, measurements along with ab-initio band structure calculations. Magnetic susceptibility chi(T) data show a broad maximum at 32 K and the system orders at low temperatures TN1=5.5 K and TN2=4.5 K, respectively. The analysis of chi(T) data gives an intra-chain coupling, J3/kB, to be about - 42 K with non-negligible frustrated inter-chain couplings (J1/kB and J2/kB). The hopping parameters obtained from LDA band structure calculations also suggest the presence of coupled uniform chains. The observation of simultaneous anomalies in dielectric constant at TN1 and TN2 suggests the presence of magneto-dielectric effect in SrCuTe2O6. A magnetic phase diagram is also built based on M, C p, and dielectric constant results., Comment: 16 pages, 9 figures

We report $\alpha$-Cu$_2$V$_2$O$_7$ to be an improper multiferroic with the simultaneous development of electric polarization and magnetization below $T_C$ = 35 K. The observed spontaneous polarization of magnitude 0.55 $\mu$Ccm$^{-2}$ is highest among the copper based improper multiferroic materials. Our study demonstrates sizable amount of magneto-electric coupling below $T_C$ even with a low magnetic field. The theoretical calculations based on density functional theory (DFT) indicate magnetism in $\alpha$-Cu$_2$V$_2$O$_7$ is a consequence of {\em ferro-orbital} ordering driven by polar lattice distortion due to the unique pyramidal (CuO$_{5}$) environment of Cu. The spin orbit coupling (SOC) further stabilize orbital ordering and is crucial for magnetism. The calculations indicate that the origin of the giant ferroelectric polarization is primarily due to the symmetric exchange-striction mechanism and is corroborated by temperature dependent X-ray studies.