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Quantum antiferromagnets realizing the square-kagome lattice are proving to be a promising platform for nontrivial phenomena in frustrated magnetism. We carry out a theoretical analysis of the recently synthesized compound nabokoite {\nab} based on a density functional theory energy mapping which establishes an unusual Heisenberg Hamiltonian with a hierarchy of couplings which suggests a description in terms of effective spin liquid models. Owing to the decoration of the square-kagome lattice with a seventh Cu site, nabokoite is characterized by highly frustrated square pyramids that are antiferromagnetically coupled in a chiral arrangement. Employing classical Monte Carlo simulations, we are able to explain the two transitions observed in the low-temperature magnetization curve from the experimental measurements. Remarkably, we show that the low-field phase is only realized when the inter-layer coupling is included. On the other hand, the intermediate-field phase is also found in a purely two-dimensional model and is described by a spin liquid featuring a subextensive degeneracy with a ferrimagnetic component. We show that this phase can be approximated by a checkerboard lattice in a magnetic field. We finally assess the effects of quantum fluctuations in zero fields using the pseudo-Majorana functional renormalization group method and predict the spin structure factor for comparison with future neutron scattering measurements.

The unexpected discovery of intrinsic ferromagnetism in layered van der Waals materials has sparked interest in both their fundamental properties and their potential for novel applications. Recent studies suggest near room-temperature ferromagnetism in the pressurized van der Waals crystal CrGeTe$_3$. We perform a comprehensive experimental and theoretical investigation of magnetism and electronic correlations in CrGeTe$_3$, combining broad-frequency reflectivity measurements with density functional theory and dynamical mean-field theory calculations. Our experimental optical conductivity spectra trace the signatures of developing ferromagnetic order and of the insulator-to-metal transition (IMT) as a function of temperature and hydrostatic pressure. With increasing pressure, we observe the emergence of a mid-infrared feature in the optical conductivity, indicating the development of strong orbital-selective correlations in the high-pressure ferromagnetic phase. We find a peculiar relationship between the plasma frequency and Curie temperature of CrGeTe$_3$, which strongly suggests that a double-exchange mechanism is responsible for the observed near room-temperature ferromagnetism. In contrast to previous studies, our results clearly demonstrate the existence of an optical gap in the metallic phase, ruling out the collapse of the charge transfer gap under pressure., Comment: 8+15 pages, 4+20 figures

We herein report on a fast and convenient soft-chemical synthesis approach towards large 1T-CrTe2 van-der-Waals crystals. This compound is formed X-ray diffraction pure, with a complete conversion within just over 2 h from flux-grown LiCrTe2 crystals using diluted acids. Due to the availability of high-quality single crystals, we have confirmed the crystal structure for the first time by single-crystal X-ray diffraction experiments. For the acid deintercalated 1T-CrTe2 crystals, we find long-range ferromagnetic order with a Curie temperature of $T_{\rm C}$ = 318 K. We further revealed the magnetic structure of 1T-CrTe2 using low-temperature neutron powder diffraction experiments and determine the magnetic Hamiltonian using density functional theory. X-ray diffraction experiments of post-annealed crystals suggest a thermal stability of 1T-CrTe2 up to at least 100 {\deg}C. Our findings expand the synthesis methods for 1T-CrTe2 crystals, which hold promise for integrated room-temperature spintronics applications.

The chromium spinels MgCr2O4 and ZnCr2O4 are prime examples of the highly frustrated pyrochlore lattice antiferromagnet. Experiment has carefully established that both materials, upon cooling, distort to lower symmetry and order magnetically. We study the nature of this process by a combination of density-functional-theory based energy mapping and classical Monte Carlo simulations. We first computationally establish precise Heisenberg Hamiltonian parameters for the high temperature cubic and the low temperature tetragonal and orthorhombic structures of both spinels. We then investigate the respective ordering temperatures of high symmetry and low symmetry structures. We carefully compare our results with experimental facts and find that our simulations are remarkably consistent with a type of spin-Peierls mechanism, adapted to three dimensions, where the structural distortion is mediated by a magnetic energy gain due to a lower degree of frustration.

Spangolite (Cu$_6$Al(SO$_4$)(OH)$_{12}$Cl$\cdot$3H$_2$O) is a hydrated layered copper sulfate mineral whose crystal structure is well described by a depleted triangular lattice of Cu$^{2+}$ ions in each layer. Experimental measurements reveal a non-magnetic ground state at $T \sim 8\, \text{K}$ with magnetization properties dominated by dimerisation. We propose a concrete model of Cu$^{2+}$ spin-$1/2$ degrees of freedom on this geometrically frustrated and effectively two-dimensional maple-leaf lattice. The distorted geometry of the depleted triangular lattice layers results in a spatially anisotropic Heisenberg model featuring five symmetry inequivalent couplings with ferromagnetic bonds on hexagons and antiferromagnetic triangular bonds. The validity of the proposed Hamiltonian is demonstrated by state-of-the-art tensor network calculations which can assess both the nature of the ground state as well as low-temperature thermodynamics, including effects of a magnetic field. We provide theoretical support for a dimerized ground state by calculating the static spin structure factor as well as the magnetic susceptibility, the latter is shown to be in good agreement with experiment. We further predict the emergence of magnetisation plateaus at high values of an external magnetic field and study their melting with increasing temperature., Comment: 8 pages, 5 figures

Akali superoxides AO2 (A=Na, K, Rb, Cs), due to an open p shell of the oxygen ion O2^- with degenerate pi orbitals, have spin and orbital degrees of freedom. The complex magnetic, orbital, and structural phase transitions observed experimentally in this family of materials are only partially understood. Based on density functional theory, we derive a strong-coupling effective model for the isostructural compounds AO2 (A=K, Rb, Cs) from a two-orbital Hubbard model. We find that CsO2 has highly frustrated exchange interactions in the a-b plane, while the frustration is weaker for RbO2 and KO2. We solve the resulting Kugel-Khomskii model in the mean-field approximation. We show that CsO2 exhibits an antiferro-orbital (AFO) order with the ordering vector q=(1,0,0) and a stripe antiferromagnetic order with q=(1/2,0,0), which is consistent with recent neutron scattering experiments. We discuss the role of the pi-orbital degrees of freedom for the experimentally observed magnetic transitions and interpret the as-yet-unidentified T_s2=70K transition in CsO2 as an orbital ordering transition., Comment: 17 pages, 22 figures, 2 tables

Discovery of high-temperature superconductivity (HTSC) in strongly correlated cuprates opened a new chapter in condensed matter physics, breaking existing stereotypes of what is a material base for a good superconductor ("Matthias rules"), at the same time emphasizing richness and challenge of strongly correlated physics, personified by the most strongly correlated 3d ion, Cu2+. A recently reported new compound, CuAg(SO4)2, combines in a fascinating way the same ion with the most strongly correlated 4d one, Ag2+. In this Letter, we present a detailed analysis of electronic and magnetic properties of this material, and show that it is very different from the HTSC cuprates in several different ways, and opens a door into further research of superconductivity and magnetism, in particular altermagnetism, in strongly correlated materials., Comment: 6 pages, 5 figures, supplement

The integrated Berry curvature is a geometric property that has dramatic implications for material properties. This study investigates the integrated Berry curvature and other contributions to the anomalous Hall effect in CrGeTe$_3$ as a function of pressure. The anomalous Hall effect is absent in the insulating phase of CrGeTe$_3$ and evolves with pressure in a dome-like fashion as pressure is applied. The dome's edges are characterized by Fermi surface deformations, manifested as mixed electron and hole transport. We corroborate the presence of bipolar transport by ab-initio calculations which also predict a nonmonotonic behavior of the Berry curvature as a function of pressure. Quantitative discrepancies between our calculations and experimental results indicate that additional scattering mechanisms, which are also strongly tuned by pressure, contribute to the anomalous Hall effect in CrGeTe$_3$.

Let $p$ and $q$ be two distinct odd primes, $p

The spin-dependent band structure of CoS$_2$ which is a candidate for a half-metallic ferromagnet was investigated by both spin- and angle-resolved photoemission spectroscopy and theoretical calculations, in order to reappraise the half-metallicity and electronic correlations. We determined the three-dimensional Fermi surface and the spin-dependent band structure. As a result, we found that a part of the minority spin bands is on the occupied side in the vicinity of the Fermi level, providing spectroscopic evidence that CoS$_2$ is not but very close to a half-metal. Band calculations using density functional theory with generalized gradient approximation showed a good agreement with the observed majority spin $e_g$ bands, while it could not explain the observed band width of the minority-spin eg bands. On the other hand, theoretical calculations using dynamical mean field theory could better reproduce the strong mass renormalization in the minority-spin $e_g$ bands. All those results strongly suggest the presence of anomalously enhanced spin-dependent electron correlation effects on the electronic structure in the vicinity of the half-metallic state. We also report the temperature dependence of the electronic structure across the Curie temperature and discuss the mechanism of the thermal demagnetization. Our discovery of the anomalously large spin-dependent electronic correlations not only demonstrates a key factor in understanding the electronic structure of half-metals but also provides a motivation to improve theoretical calculations on spin-polarized strongly correlated systems., Comment: 53 pages, 25 figures, 1 table

$\require{mhchem}$The square-kagome lattice Heisenberg antiferromagnet is a highly frustrated Hamiltonian whose material realizations have been scarce. We theoretically investigate the recently synthesized $\ce{Na6Cu7BiO4(PO4)4Cl3}$ where a Cu$^{2+}$ spin-$1/2$ square-kagome lattice (with six site unit cell) is decorated by a seventh magnetic site alternatingly above and below the layers. The material does not show any sign of long-range magnetic order down to 50 mK despite a Curie-Weiss temperature of $-212$ K indicating a quantum paramagnetic phase. Our DFT energy mapping elicits a purely antiferromagnetic Hamiltonian that features longer range exchange interactions beyond the pure square-kagome model and, importantly, we find the seventh site to be strongly coupled to the plane. We combine two variational Monte Carlo approaches, pseudo-fermion/Majorana functional renormalization group and Schwinger-Boson mean field calculations to show that the complex Hamiltonian of $\ce{Na6Cu7BiO4(PO4)4Cl3}$ still features a nonmagnetic ground state. We explain how the seventh Cu$^{2+}$ site actually aids the stabilization of the disordered state. We predict static and dynamic spin structure factors to guide future neutron scattering experiments., Comment: 5 pages, 4 figures. Supplement: 7 pages, 11 figures v2: minor revisions in text and figure labels

While the surface-bulk correspondence has been ubiquitously shown in topological phases, the relationship between surface and bulk in Landau-like phases is much less explored. Theoretical investigations since 1970s for semi-infinite systems have predicted the possibility of the surface order emerging at a higher temperature than the bulk, clearly illustrating a counterintuitive situation and greatly enriching phase transitions. But experimental realizations of this prediction remain missing. Here, we demonstrate the higher-temperature surface and lower-temperature bulk phase transitions in CrSBr, a van der Waals (vdW) layered antiferromagnet. We leverage the surface sensitivity of electric dipole second harmonic generation (SHG) to resolve surface magnetism, the bulk nature of electric quadrupole SHG to probe bulk spin correlations, and their interference to capture the two magnetic domain states. Our density functional theory calculations show the suppression of ferromagnetic-antiferromagnetic competition at the surface responsible for this enhanced surface magnetism. Our results not only show unexpected, richer phase transitions in vdW magnets, but also provide viable ways to enhance magnetism in their 2D form.

The hope that copper doped lead apatite Pb$_9$Cu(PO$_4$)$_6$O is a room-temperature superconductor has largely been dashed by global research efforts. Nevertheless, according to the current state of knowledge, the material has interesting magnetic properties, and research groups around the world have prepared high quality samples. We use a fluctuation exchange approximation (FLEX) approach to study the magnetic tendencies in Pb$_9$Cu(PO$_4$)$_6$O. We find ferromagnetic fluctuations very close to the filling of the stoichiometric compound which can be understood from Fermi surface nesting at the M point. This is similar to the one-band triangular lattice Hamiltonian at three-quarter filling. Interestingly, the special kz dependence of the Pb$_9$Cu(PO$_4$)$_6$O band structure makes it very sensitive to doping. Only slight charge doping switches between antiferromagnetic and ferromagnetic fluctuations. If the material could become superconducting, it might be easily switchable between singlet and triplet superconductivity., Comment: 6 pages, 6 figures

Quantum spin liquids (QSLs) have become a key area of research in magnetism due to their remarkable properties, such as long-range entanglement, fractional excitations, pinch-point singularities, and topologically protected phenomena. In recent years, the search for QSLs has expanded into the three-dimensional world, where promising features have been found in materials that form pyrochlore and hyper-kagome lattices, despite the suppression of quantum fluctuations due to high dimensionality. One such material is the $S = 1$ K$_2$Ni$_2$(SO$_4$)$_3$ compound, which belongs to the langbeinite family consisting of two interconnected trillium lattices. Although magnetically ordered, K$_2$Ni$_2$(SO$_4$)$_3$ has been found to exhibit a highly dynamical and correlated state which can be driven into a pure quantum spin liquid under magnetic fields of only $B \simeq 4$~T. In this article, we combine inelastic neutron scattering measurements with pseudo-fermion functional renormalization group (PFFRG) and classical Monte Carlo (cMC) calculations to study the magnetic properties of K$_2$Ni$_2$(SO$_4$)$_3$, revealing a high level of agreement between the experiment and theory. We further reveal the origin of the dynamical state in K$_2$Ni$_2$(SO$_4$)$_3$ by studying a larger set of exchange parameters, uncovering an `island of liquidity' around a focal point given by a magnetic network composed of tetrahedra on a trillium lattice.

For the first time, we enable the execution of hybrid machine learning methods on real quantum computers with 100 data samples and real-device-based simulations with 5,000 data samples, thereby outperforming the current state of research of Suryotrisongko and Musashi from 2022 who were dealing with 1,000 data samples and quantum simulators (pure software-based emulators) only. Additionally, we beat their reported accuracy of $76.8\%$ by an average accuracy of $91.2\%$, all within a total execution time of 1,687 seconds. We achieve this significant progress through two-step strategy: Firstly, we establish a stable quantum architecture that enables us to execute HQML algorithms on real quantum devices. Secondly, we introduce new hybrid quantum binary classification algorithms based on Hoeffding decision tree algorithms. These algorithms speed up the process via batch-wise execution, reducing the number of shots required on real quantum devices compared to conventional loop-based optimizers. Their incremental nature serves the purpose of online large-scale data streaming for DGA botnet detection, and allows us to apply hybrid quantum machine learning to the field of cybersecurity analytics. We conduct our experiments using the Qiskit library with the Aer quantum simulator, and on three different real quantum devices from Azure Quantum: IonQ, Rigetti, and Quantinuum. This is the first time these tools are combined in this manner., Comment: 32 pages, 4 figures, 5 tables

Layered van der Waals ferromagnets, which preserve their magnetic properties down to exfoliated monolayers, are fueling an abundance of fundamental research and nanoscale device demonstration. CrGeTe$_3$ is a prime example for this class of materials. Its temperature-pressure phase diagram features an insulator-to-metal transition and a significant increase of ferromagnetic Curie-Weiss temperatures upon entering the metallic state. We use density functional theory to understand the magnetic exchange interactions in CrGeTe$_3$ at ambient and elevated pressure. We calculate Heisenberg exchange couplings, which provide the correct ferromagnetic ground state and explain the experimentally observed pressure dependence of magnetism in CrGeTe$_3$. Furthermore, we combine density functional theory with dynamical mean field theory to investigate the effects of electronic correlations and the nature of the high pressure metallic state in CrGeTe$_3$., Comment: 15 pages, 12 figures

The magnetic excitation spectrum and Hamiltonian of the quantum magnet BaCuTe2O6 is studied by inelastic neutron scattering (INS) and density functional theory (DFT). INS on powder and single crystal samples reveals overlapping spinon continuua - the spectrum of an antiferromagnetic spin-1/2 spin chain - due to equivalent chains running along the a, b, and c directions. Long-range magnetic order onsets below TN = 6.3 K due to interchain interactions, and is accompanied by the emergence of sharp spin-wave excitations which replace the continuua at low energies. The spin-wave spectrum is highly complex and was successfully modelled achieving excellent agreement with the data. The extracted interactions reveal an intrachain interaction, J3 = 2.9 meV, while the antiferromagnetic hyperkagome interaction J2, is the sub-leading interaction responsible for coupling the chains together in a frustrated way. DFT calculations reveal a similar picture for BaCuTe2O6 of dominant J3 and sub-leading J2 antiferromagnetic interactions and also indicate a high sensitivity of the interactions to small changes of structure which could explain the very different Hamiltonians observed in the sister compounds SrCuTe2O6 and PbCuTe2O6., Comment: 12 pages, 8 figures

We report on the synthesis of LiCrTe$_2$ single crystals and on their anisotropic magnetic properties. We have obtained these single crystals by employing a Te/Li-flux synthesis method. We find LiCrTe$_2$ to crystallize in a TlCdS$_2$ -type structure with cell parameters of $a$ = 3.9512(5) \r{A} and $c$ = 6.6196(7) \r{A} at $T$ = 175 K. The content of lithium in these crystals was determined to be near stoichiometric by means of neutron diffraction. We find a pronounced magnetic transition at $T^{\rm ab}_{\rm N}$ = 144 K and $T^{\rm c}_{\rm N}$ = 148 K, respectively. These transition temperatures are substantially higher than earlier reports on polycrystalline samples. We have performed neutron powder diffraction measurements that reveal that the long-range low-temperature magnetic structure of single crystalline LiCrTe$_2$ is an A-type antiferromagnetic (AFM) structure. Our DFT calculations are in good agreement with these experimental observations. We find the system to be easy axis with moments oriented along the $c$-direction experimentally as well as in our calculations. Thereby, the magnetic Hamiltonian can be written as $H = H_{\rm Heisenberg} + \sum_i K_c (S_i^z)^2$ with $K_c=-0.34K$ (where $|S^z|=\frac{3}{2}$). We find LiCrTe$_2$ to be highly anisotropic, with a pronounced metamagnetic transition for $H \perp ab$ with a critical field of $\mu H_{MM}$(5 K) $\approx$ 2.5 T. Using detailed orientation-dependent magnetization measurements, we have determined the magnetic phase diagram of this material. Our findings suggest that LiCrTe$_2$ is a promising material for exploring the interplay between crystal structure and magnetism, and could have potential applications in spin-based 2D devices.

We investigate the crystallographic and magnetic properties of a chromium-based thiospinel CuGaCr$_{4}$S$_{8}$. From a synchrotron x-ray diffraction experiment and structural refinement, Cu and Ga atoms are found to occupy the tetrahedral $A$-sites in an alternate way, yielding breathing pyrochlore Cr network. CuGaCr$_{4}$S$_{8}$ undergoes a magnetic transition associated with a structural distortion at 31 K in zero magnetic field, indicating that the spin-lattice coupling is responsible for relieving the geometrical frustration. When applying a pulsed high magnetic field, a sharp metamagnetic transition takes place at 40 T, followed by a 1/2-magnetization plateau up to 103 T. These phase transitions accompany dielectric anomalies, suggesting the presence of helical spin correlations in low-field phases. The density-functional-theory calculation reveals that CuGaCr$_{4}$S$_{8}$ is dominated by antiferromagnetic and ferromagnetic exchange couplings within small and large tetrahedra, respectively, in analogy with CuInCr$_{4}$S$_{8}$. We argue that $A$-site-ordered Cr thiospinels serve as an excellent platform to explore diverse magnetic phases along with pronounced magnetoelastic and magnetodielectric responses., Comment: 12 pages, 13 figures

The mutual coupling of spin and lattice degrees of freedom is ubiquitous in magnetic materials and potentially creates exotic magnetic states in response to the external magnetic field. Particularly, geometrically frustrated magnets serve as a fertile playground for realizing magnetic superstructure phases. Here, we observe an unconventional two-step magnetostructural transition prior to a half-magnetization plateau in a breathing pyrochlore chromium spinel by means of state-of-the-art magnetization and magnetostriction measurements in ultrahigh magnetic fields available up to 600 T. Considering a microscopic magnetoelastic theory, the intermediate-field phase can be assigned to a magnetic superstructure with a three-dimensional periodic array of 3-up-1-down and canted 2-up-2-down spin molecules. We attribute the emergence of the magnetic superstructure to a unique combination of the strong spin-lattice coupling and large breathing anisotropy., Comment: 10 pages, 5 figures, SI: 15 pages, 14 figures

As a highly frustrated model Hamiltonian with an exact dimer ground state, the Heisenberg antiferromagnet on the maple leaf lattice is of high theoretical interest, and a material realization is intensely sought after. We determine the magnetic Hamiltonian of the copper mineral bluebellite using density functional theory based energy mapping. As a consequence of the significant distortion of the spin $S=1/2$ maple leaf lattice, we find two of the five distinct nearest neighbor couplings to be ferromagnetic. Solution of this Hamiltonian with density matrix renormalization group calculations points us to the surprising insight that this particular imperfect maple leaf lattice, due to the strongly ferromagnetic Cu$^{2+}$ dimer, realizes an effective $S=1$ breathing kagome Hamiltonian. In fact, this is another highly interesting Hamiltonian which has rarely been realized in materials. Analysis of the effective model within a bond-operator formalism allows us to identify a valence bond solid ground state and to extract thermodynamic quantities using a low-energy bosonic mean-field theory. We resolve the puzzle of the apparent one-dimensional character of bluebellite as our calculated specific heat has a Bonner-Fisher-like shape, in good agreement with experiment., Comment: 7 pages, 4 figures