We present a detailed study on the microscopic origin of magnetism in suspended and dielectrically embedded CrI$_3$ monolayer. To this end, we down-fold two distinct minimal generalized Hubbard models with different orbital basis sets from \emph{ab initio} calculations using the constrained random phase approximation. Within mean-field approximation, we show that these models are capable of describing the formation of localized magnetic moments in CrI$_3$ and of reproducing electronic properties of full \emph{ab initio} calculations. We utilize the magnetic force theorem to study microscopic magnetic exchange channels between the different orbital manifolds. We find a multi-orbital super-exchange mechanism as the origin of magnetism in CrI$_3$ resulting from a detailed interplay between effective ferro- and anti-ferromagnetic Cr-Cr $d$ coupling channels, which is decisively affected by the ligand (I) $p$ orbitals. We show how environmental screening such as resulting from encapsulation with hexagonal boron nitride (hBN) of the CrI$_3$ monolayer affects the Coulomb interaction in the film and how this successively controls its magnetic properties. Driven by a non-monotonic interplay between nearest and next-nearest neighbour exchange interactions we find the magnon dispersion and the Curie temperature to be non-trivially affected by the environmental dielectric screening.
Motivated by the recent wealth of exotic magnetic phases emerging in two-dimensional frustrated lattices, we investigate the origin of possible magnetism in the monolayer family of triangular lattice materials $MX_2$ ($M$={V, Mn, Ni}, $X$={Cl, Br, I}). We first show that consideration of general properties such as filling and hybridization enables to formulate trends for the most relevant magnetic interaction parameters. In particular, we observe that the effects of spin-orbit coupling (SOC) can be effectively tuned through the ligand elements as the considered 3$d$ transition metal ions do no…
We investigate the magnetic properties of archetypal transition-metal oxides MnO, FeO, CoO and NiO under very high pressure by x-ray emission spectroscopy at the Kβline. We observe a strong modification of the magnetism in the megabar range in all the samples except NiO. The results are analyzed within a multiplet approach including charge-transfer effects. The pressure dependence of the emission line is well accounted for by changes of the ligand field acting on the d electrons and allows us to extract parameters like local d-hybridization strength, O-2p bandwidth and ionic crystal field acro…
Linearly polarized spectra of far-infrared (IR) transmission in HoMn2O5 multiferroic single crystals have been studied in the frequency range between 8.5 and 105 cm-1 and for temperatures between 5 K and 300 K. Polarization of IR-active excitations depends on the crystallographic directions in HoMn2O5 and is sensitive to the magnetic phase transitions. We attribute some of the infrared-active excitations to electric-dipole transitions between ligand-field split states of Ho3+ ions. For light polarization along crystalline b-axis, the oscillator strength of electric dipoles at low frequencies (…
Ferromagnetism in the two-dimensional CrI$_3$ has generated a lot of excitement, and it was recently proposed that the spin-orbit coupling (SOC) in Iodine may generate bond-dependent spin interactions leading to magnetic anisotropy. Here we derive a microscopic spin model of S=3/2 on transition metals surrounded by heavy ligands in honeycomb Mott insulators using a strong-coupling perturbation theory. For ideal octahedra we find Heisenberg and Kitaev interactions, which favor the magnetic moment along the cubic axis via quantum fluctuations. When a slight trigonal distortion of the octahedra i…
Van der Waals (VdW) materials have opened new directions in the study of low dimensional magnetism. A largely unexplored arena is the intrinsic tuning of VdW magnets toward new ground-states. The chromium trihalides provided the first such example with a change of inter-layer magnetic coupling emerging upon exfoliation. Here, we take a different approach to engineer new ground-states, not by exfoliation, but by tuning the spin-orbit coupling (SOC) of the non-magnetic ligand atoms (Cl,Br,I). We synthesize a three-halide series, CrCl$_{3-x-y}$Br$_{x}$I$_{y}$, and map their magnetic properties as…
The crystal structures of Ni$X_2$(pyz)$_2$ ($X$ = Cl (\textbf{1}), Br (\textbf{2}), I (\textbf{3}) and NCS (\textbf{4})) were determined at 298~K by synchrotron X-ray powder diffraction. All four compounds consist of two-dimensional (2D) square arrays self-assembled from octahedral NiN$_4$$X_2$ units that are bridged by pyz ligands. The 2D layered motifs displayed by \textbf{1}-\textbf{4} are relevant to bifluoride-bridged [Ni(HF$_2$)(pyz)$_2$]$Z$F$_6$ ($Z$ = P, Sb) which also possess the same 2D layers. In contrast, terminal $X$ ligands occupy axial positions in \textbf{1}-\textbf{4} and caus…
Fifteen parameters characterizing the crystal field of rare-earth ions in the RMO$_3$ perovskites (R = Pr, Nd, M = Ga, Co) are calculated by expanding the local Hamiltonian expressed in the basis of Wannier functions into a series of spherical tensor operators. The method contains a single adjustable parameter that characterizes the hybridization of R($4f$) states with the states of oxygen ligands. Subsequently the energy levels and magnetic moments of trivalent R ion are determined by diagonalization of an effective Hamiltonian which, besides the crystal field, contains the $4f$ electron-elec…
The importance of covalent bonding for the magnetism of 3d metal complexes was first noted by Pauling in 1931. His point became moot, however, with the success of the ionic picture of Van Vleck, where ligands influence magnetic electrons of 3d ions mainly through electrostatic fields. Anderson's theory of spin superexchange later established that covalency is at the heart of cooperative magnetism in insulators, but its energy scale was believed to be small compared to other inter-ionic interactions and therefore it was considered a small perturbation of the ionic picture. This assertion fails …
The detailed analysis of the problem of possible magnetic behavior of the carbon-based structures was fulfilled to elucidate and resolve (at least partially) some unclear issues. It was the purpose of the present paper to look somewhat more critically into some conjectures which have been made and to the peculiar and contradictory experimental results in this rather indistinct and disputable field. Firstly the basic physics of magnetism was briefly addressed. Then a few basic questions were thoroughly analyzed and critically reconsidered to elucidate the possible relevant mechanism (if any) wh…
Less common ligand coordination of transition-metal centers is often associated with peculiar valence-shell electron configurations and outstanding physical properties. One example is the Fe$^+$ ion with linear coordination, actively investigated in the research area of single-molecule magnetism. Here we address the nature of 3$d^9$ states for Cu$^{2+}$ ions sitting in the center of trigonal bipyramidal ligand cages in the quasi-two-dimensional honeycomb compound InCu$_{2/3}$V$_{1/3}$O$_3$, whose unusual magnetic properties were intensively studied in the recent past. In particular, we discuss…
We study the interplay of strong electron correlations and intra-triangle spin exchange at two-thirds filling of the single-orbital Hubbard model on the decorated honeycomb lattice using rotationally invariant slave bosons. We find that the spin exchange tunes between a spin-$1$ Mott insulator, a metal, and a spin-$0$ Mott insulator when the exchange is antiferromagnetic. The Mott insulators occur from effective intra-triangle multi-orbital interactions and are adiabatically connected to the ground state of an isolated triangle. An antiferromagnetic spin exchange, as determined by the Goodenou…
Properties in magnetic ordered states of graphene nanoribbons with zigzag shaped edges are investigated by applying mean-field approximation to the Hubbard model with on-site repulsion $U$. We observe that magnetic moments and critical temperature show anomalous power-law dependences as a function of $U$; the actual values of the power are determined by only the width of ribbons. Such singular behaviours are found to be due to localized nature of the electronic states close to Fermi energy.
Oxygen vacancies play a crucial role in the control of the electronic, magnetic, ionic, and transport properties of functional oxide perovskites. Rare earth nickelates (RENiO$_{3-x}$) have emerged over the years as a rich platform to study the interplay between the lattice, the electronic structure, and ordered magnetism. In this study, we investigate the evolution of the electronic and magnetic structure in thin films of RENiO$_{3-x}$, using a combination of X-ray absorption spectroscopy and imaging, resonant X-ray scattering, and extended multiplet ligand field theory modeling. We find that …
Microscopic origin of the ferromagnetic (FM) exchange coupling in CrCl$_3$ and CrI$_3$, their common aspects and differences, are investigated on the basis of density functional theory combined with realistic modeling approach for the analysis of interatomic exchange interactions. We perform a comparative study based on the pseudopotential and linear muffin-tin orbital methods by treating the effects of electron exchange and correlation in GGA and LSDA, respectively. The results of ordinary band structure calculations are used in order to construct the minimal tight-binding type models describ…
The discovery of multiferroic behavior in monolayer NiI$_2$ provides a new symmetry-broken state in van der Waals monolayers, featuring the simultaneous emergence of helimagnetic order and ferroelectric order at a critical temperature of $T=21$ K. However, the microscopic origin of multiferroic order in NiI$_2$ monolayer has not been established, and in particular, the role of non-colinear magnetism and spin-orbit coupling in this compound remains an open problem. Here we reveal the origin of the two-dimensional multiferroicity in NiI$_2$ using first-principles electronic structure methods. We…
Magnetic insulators are a key resource for next-generation spintronic and topological devices. The family of layered metal halides promises ultrathin insulating multiferroics, spin liquids, and ferromagnets, but new characterization methods are required to unlock their potential. Here, we report tunneling through the layered magnetic insulator CrI3 as a function of temperature and applied magnetic field. We electrically detect the magnetic ground state and inter-layer coupling and observe a field-induced metamagnetic transition. The metamagnetic transition results in magnetoresistances of 95%,…
The properties of the novel heavy fermion superconductor Ce$_3$PtIn$_{11}$ are investigated by thermodynamic and transport measurements at ambient and under hydrostatic pressure. At ambient pressure the compound exhibits two successive magnetic transitions at $T_1$ $\approx$ 2.2 K and $T_{\rm N}$ $\approx$ 2 K into antiferromagnetically ordered states and enters into a heavy fermion superconducting phase below $T_{\rm c}$ $\approx$ 0.32 K. The coexistence of long-range magnetic order and superconductivity is discussed in the context of the existence of the two crystallographically inequivalent…
CrI3 is a two-dimensional ferromagnetic van der Waals material with a charge gap of 1.1-1.2 eV. In this study, the electronic structure and magnetism of CrI3 are investigated by using density functional theory and dynamical mean-field theory. Our calculations successfully reproduce a charge gap of 1.1 eV in the paramagnetic state when a Hund coupling JH = 0.7 eV is included with an on-site Hubbard U = 5 eV. In contrast, with a large U value of 8 eV and negligible Hund coupling JH, CrI3 is predicted to be a moderately correlated metal in the paramagnetic state. We conclude that CrI3 is a Mott-H…
We report extensive studies on the CeCo$_{1-x}$Fe$_{x}$Ge$_3$ alloys, which show quantum critical point (QCP) due to damping the antiferromagnetic order in CeCoGe$_3$ down to 0 K by doping with the paramagnetic CeFeGe$_3$ compound. The presence of QCP is confirmed by detecting the non-Fermi liquid behavior (NFL) using a wide range of the experimental methods: magnetic susceptibility, specific heat, electrical resistivity, magnetoresistance, and thermoelectric power. In the case of the thermoelectric power we find a clear enhancement of the Seebeck coefficient for $x$ around 0.6, i.e. in the ne…
Magnetic susceptibility, M-H plot, magnetoresistance and thermoelectric power of the RuSr2Eu1.5Ce0.5Cu2O10 superconductor are measured. Values of the magnetic transition temperature Tmag, superconductivity transition temperature Tc, upper critical field Hc2, chemical potential mu, and energy width for electric conduction W(sigma) are obtained from these measurements. It has been found that Tmag = 140 K, Tc = 25 K (33 K) from susceptibility (magnetoresistance) measurements, Hc2 (0) > 32 T, mu = 8 meV, and W(sigma) = 58.5 meV. These values are compared with other ruthenate superconductors, and r…
With understood exceptions, conventional superconductivity does not coexist with long-range magnetic order[1]. In contrast, unconventional superconductivity develops near a boundary separating magnetically ordered and magnetically disordered phases[2,3]. A maximum in the superconducting transition temperature Tc develops where this boundary extrapolates to T=0 K, suggesting that fluctuations associated with this magnetic quantum-critical point are essential for unconventional superconductivity[4,5]. Invariably though, unconventional superconductivity hides the magnetic boundary when T < Tc, pr…
We give a review of recent results on the heavy fermion superconductor CeRhIn$_5$ which presents ideal conditions to study the interplay of antiferromagnetism and superconductivity. The main results are the appearance of domains of microscopic coexistence of antiferromagnetism and superconductivity under both, pressure and magnetic field scans. At zero magnetic field, under pressure coexistence appears from the onset of pressure induced superconductivity up to the critical pressure $p_c^\star$ where antiferrmognetism disappears abruptly. Under magnetic field, re-entrance of magnetic order insi…
We investigate the behavior of a $d$-$d$ transition in NiO using a new x-ray spectrometer with 0.025 eV resolution at 15816 eV, and via ab-initio ligand field theory calculations. The transition at ~1.7 eV energy transfer is measured at temperatures between 20 and 800 K, at a momentum transfer |$\bf{Q}$| = 6.52 Å$^{-1}$. Fine structure is clearly observed at 20 K. As temperature is increased, the excitation shifts to lower energy and broadens. We explain the energy shift as being related to thermal expansion and to magnetism. The broadening is well fit considering thermal fluctuations of the N…
Magnetic insulators have proved to be fertile ground for studying new types of quantum many body states, and I survey recent experimental and theoretical examples. The insights and methods transfer also to novel superconducting and metallic states. Of particular interest are critical quantum states, sometimes found at quantum phase transitions, which have gapless excitations with no particle- or wave-like interpretation, and control a significant portion of the finite temperature phase diagram. Remarkably, their theory is connected to holographic descriptions of Hawking radiation from black ho…
The quantum critical point (QCP) in the archetypical heavy-fermion compound CeCu$_6$ doped by Au is described, accounting for the localized $4f$-electron of Ce, using realistic electronic structure calculations combined with dynamical mean-field theory (DMFT). Magnetism trends in Ce(Cu$_{1-ε}$Au$_ε$)$_6$ are compared with those in Co-doped CeCu$_{5}$, which resides on the non-ferromagnetic side of the composition space of one of the earliest rare-earth permanent magnet compounds, Ce(Co,Cu)$_5$. The construction of a realistic Doniach phase diagram shows that the system crosses over a magnetic …
We study the spin-1 honeycomb lattice magnets with frustrated exchange interactions. The proposed microscopic spin model contains first and second neighbor Heisenberg interactions as well as the single-ion anisotropy. We establish a rich phase diagram that includes a featureless quantum paramagnet and various spin spiral states induced by the mechanism of order by quantum disorder. Although the quantum paramagnet is dubbed featureless, it is shown that, the magnetic excitations develop a contour degeneracy in the reciprocal space at the band minima. These contour degenerate excitations are res…
Some physical implications involved in a new concept, termed the "quantum protectorate" (QP), are developed and discussed. This is done by considering the idea of quantum protectorate in the context of quantum theory of magnetism. It is suggested that the difficulties in the formulation of quantum theory of magnetism at the microscopic level, that are related to the choice of relevant models, can be understood better in the light of the QP concept . We argue that the difficulties in the formulation of adequate microscopic models of electron and magnetic properties of materials are intimately r…
The magnetic properties of iron-based superconductors $A$Fe$_2$As$_2$ ($A=$K, Cs, and Rb), which are characterized by the V-shaped dependence of the critical temperature ($T_{\rm c}$) on pressure ($P$) were studied by means of the muon spin rotation/relaxation technique. In all three systems studied the magnetism was found to appear for pressures slightly below the critical one ($P_{\rm c}$), i.e. at pressure where $T_{\rm c}(P)$ changes the slope. Rather than competing, magnetism and superconductivity in $A$Fe$_2$As$_2$ are coexisting at $P\gtrsim P_{\rm c}$ pressure region. Our results suppo…
We report the effect of hydrostatic pressure on the electronic state of the antiferromagnet UIrGe, which is isostructural and isoelectronic with the ferromagnetic superconductors UCoGe and URhGe. The Neel temperature decreases with increasing pressure. We constructed a p-T phase diagram and estimated the critical pressure pc, where the antiferromagnetism vanishes, as 12 GPa. The antiferromagnetic/paramagnetic transition appears to be first order.
In the heavy fermion superconductor CeCoIn5 (Tc=2.3K) the critical field is large, anisotropic and displays hysteresis. The magnitude of the critical-field anisotropy in the a-c plane can be as large as 70 kOe and depends on orientation. Critical field measurements in the (110) plane suggest 2D superconductivity, whereas conventional effective mass anisotropy is observed in the (100) plane. Two distinct field-induced magnetic phases are observed: Ha appears deep in the superconducting phase, while Hb intersects Hc2 at T=1.4 K and extends well above Tc. These observations suggest the possible r…
We report the discovery of pressure-induced superconductivity, with T_c=2 K, in the heavy-fermion antiferromagnet Ce_2RhIn_8, where superconductivity and magnetic order coexist over an extended pressure interval. A T-linear resistivity in the normal state, accessed by an applied magnetic field, does not appear to derive from the existence of a 2D quantum-critical spin-density wave.
In this work we study the Double Exchange-Holstein (DE-H) model with an electron-phonon interaction $γ$ coupled to magnetism. The analysis is performed combining a mean-field approximation for the double exchange interaction and the Lang-Firsov transformation for the electron-phonon interaction. Discontinuous magnetic transitions appear when the dependence of $g$ with $m$ is sufficiently large, resembling those experimentally observed in manganites. We observe that the characteristic resistivity peak that arises near the critical temperature appears for broad ranges of the system parameter val…
The existence of the V3+ ion orbital moment is the open issue of the nature of magnetism in the van der Waals ferromagnet VI3. The huge magnetocrystalline anisotropy in conjunction with the significantly reduced ordered magnetic moment compared to the spin-only value provides strong but indirect evidence of a significant V orbital moment. We used the unique capability of X-ray magnetic circular dichroism to determine the orbital component of the total magnetic moment and provide for the first time a direct proof of an exceptionally sizable orbital moment of the V3+ ion in VI3. Our ligand field…
In the low doping region an incommensurate magnetic phase is observed in LSCO. By means of the composite operator method we show that the single-band 2D Hubbard model describes the experimental situation. In the higher doping region, where experiments are not available, the incommensurability is depressed owing to the van Hove singularity near the Fermi level. A proportionality between the incommensurability amplitude and the critical temperature is predicted, suggesting a close relation between superconductivity and incommensurate magnetism.
We report a new peculiar effect of the interaction between a sublattice of frustrated quantum spin-1/2 chains and a sublattice of pseudospin-1/2 centers (quantum electric dipoles) uniquely co-existing in the complex oxide Li2ZrCuO4. 7Li nuclear magnetic-, Cu2+ electron spin resonance and a complex dielectric constant data reveal that the sublattice of Li+-derived electric dipoles orders glass like at Tg ~ 70 K yielding a spin site nonequivalency in the CuO2 chains. We suggest that such a remarkable interplay between electrical and spin degrees of freedom might strongly influence the properties…
The mysterious pseudogap phase of cuprate superconductors ends at a critical hole doping level p* but the nature of the ground state below p* is still debated. Here, we show that the genuine nature of the magnetic ground state in La2-xSrxCuO4 is hidden by competing effects from superconductivity: applying intense magnetic fields to quench superconductivity, we uncover the presence of glassy antiferromagnetic order up to the pseudogap boundary p* ~ 0.19, and not above. There is thus a quantum phase transition at p*, which is likely to underlie highfield observations of a fundamental change in e…
A Kondo-lattice theory is applied to the crossover between local-moment magnetism for almost half fillings of electrons and itinerant-electron magnetism away from the half filling. In clean systems with no disorder, the bandwidth W^* of quasiparticles is non-zero and of the order of |J| at T=0K even in the limit of the half filling, with J the superexchange interaction constant between nearest neighbors. The so called Gutzwiller's term also contributes to W^* away from the half filling; it is approximately proportional to doping concentrations measured from the half filling. Magnetism is enhan…
