Effect of a flat band on a multiband two-dimensional Lieb lattice with intra- and interband interactions.

In this study, we explore the effect of a single flat band in the electronic properties of a ferromagnetic two-dimensional Lieb lattice using the multiband Hubbard model with polarized carriers, spin-up and spin-down. We employ the self-consistent dynamical mean field theory and a Green functions cumulant expansion around the atomic limit to obtain the correlated densities of states while varying the intra- and interband interactions. Our findings demonstrate a renormalization of the correlated density of states in both the spin-up and spin-down carriers as we varied the intra- and interband interactions. We conclude that the presence of a flat band enables the system to maintain a metal state with itinerant ferromagnetism in the spin-up carrier.

Enhancement of the magnetocaloric effect in geometrically frustrated cluster spin glass systems.

In this work, we theoretically demonstrate that a strong enhancement of the magnetocaloric effect is achieved in geometrically frustrated cluster spin-glass systems just above the freezing temperature. We consider a network of clusters interacting randomly which have triangular structure composed of Ising spins interacting antiferromagnetically. The intercluster disorder problem is treated using a cluster spin glass mean-field theory, which allows exact solution of the disordered problem. The intracluster part can be solved using exact enumeration. The coupling between the inter and intracluster problem incorporates the interplay between effects coming from geometric frustration and disorder. As a result, it is shown that there is the onset of cluster spin glass phase even with very weak disorder. Remarkably, it is exactly within a range of very weak disorder and small magnetic field that is observed the strongest isothermal release of entropy.

Geometrical frustration and cluster spin glass with random graphs.

We develop a based on a sparse random graph to account for the interplay between geometric frustration and disorder in cluster magnetism. Our theory allows introduction of the cluster network connectivity as a controllable parameter. Two types of inner cluster geometry are considered: triangular and tetrahedral. The theory was developed for general, nonuniform intracluster interactions, but in the present paper the results presented correspond to uniform, antiferromagnetic (AF) intraclusters interaction J_{0}/J. The clusters are represented by nodes on a finite connectivity random graph, and the intercluster interactions are randomly Gaussian distributed. The graph realizations are treated in replica theory using the formalism of order parameter functions, which allows one to calculate the distribution of local fields and, as a consequence, the relevant observable. In the case of triangular cluster geometry, there is the onset of a classical spin liquid state at a temperature T^{*}/J and then, a cluster spin glass (CSG) phase at a temperature T_{/}J. The CSG ground state is robust even for very weak disorder or large negative J_{0}/J. These results does not depend on the network connectivity. Nevertheless, variations in the connectivity strongly affect the level of frustration f_{p}=-Θ_{CW}/T_{f} for large J_{0}/J. In contrast, for the nonfrustrated tetrahedral cluster geometry, the CSG ground state is suppressed for weak disorder or large negative J_{0}/J. The CSG boundary phase presents a reentrance which is dependent on the network connectivity.

Ising spin glass in a random network with a Gaussian random field.

We investigate thermodynamic phase transitions of the joint presence of spin glass (SG) and random field (RF) using a random graph model that allows us to deal with the quenched disorder. Therefore, the connectivity becomes a controllable parameter in our theory, allowing us to answer what the differences are between this description and the mean-field theory i.e., the fully connected theory. We have considered the random network random field Ising model where the spin exchange interaction as well as the RF are random variables following a Gaussian distribution. The results were found within the replica symmetric (RS) approximation, whose stability is obtained using the two-replica method. This also puts our work in the context of a broader discussion, which is the RS stability as a function of the connectivity. In particular, our results show that for small connectivity there is a region at zero temperature where the RS solution remains stable above a given value of the magnetic field no matter the strength of RF. Consequently, our results show important differences with the crossover between the RF and SG regimes predicted by the fully connected theory.

Multicritical points in a model for 5f-electron systems under pressure and magnetic field.

We investigate the evolution of multicritical points under pressure and magnetic field in a model described by two 5fbands (calledαandß) that hybridize with a single itinerant conduction band. The interaction is given by the direct Coulomb and the Hund's rule exchange terms. Three types of orderings are considered: two conventional spin density waves (SDWs) and an exotic SDW, i.e., with no magnetic moment formation. The conventional SDWs phases, are characterized bymfß>mfαandmfα>mfß, respectively, wheremfαandmfßare the intraband staggered magnetizations. The exotic SDW, which has time reversal symmetry, is described by a purely imaginary order parameter. This phase is related to a band mixing given by the spin-flip part of the Hund's rule exchange interaction. As result, without magnetic field, the phase diagrams of temperature (T) versus pressure (given by the variation of the bandwidth (W)) shows a sequence of phase transitions involving the three phases which gives rise to multicritical points. The presence of the magnetic field (hz) has drastic effects on part of the phase diagram and the location of the multicritical points.

Enhancement of the spin-orbit coupling by strong electronic correlations in transition metal and light actinide compounds.

A simple variational argument is presented which indicates that the spin-orbit coupling in itinerant systems can be enhanced by strong electronic correlations. The importance of the enhancement in the formation of the giant magnetic anisotropy found in the metallic paramagnetic and magnetically ordered states of compounds containing transition metal and light actinide elements (such as tetragonal Sr2RhO4, Sr2IrO4, the cubic uranium monochalcogenides and tetragonal URu2Si2) is discussed.

Field-induced glassy state in disordered cluster antiferromagnets.

We investigate the role of antiferromagnetic spin clusters on the glassiness induced by uniform and random fields. We consider an antiferromagnetic disordered model that is treated within the replica method, resulting in an effective single-cluster problem. Our results show that regimes of weak and intermediate disorder are suitable for highly unusual phenomena. For the case of a uniform field, cluster polarization can favor a cluster spin-glass state, i.e. the magnetic field increases the freezing temperature at intermediate disorders. In addition, random fields introduce local perturbations that allow uncompensated cluster states, supporting cluster freezing even at very weak disorders. The theoretical framework presented here can be useful for the understanding of phenomena observed in magnetic glassy systems that have spin clusters as building blocks instead of individual spins. In particular, we suggest that our results can help to explain the magnetic behaviour of the rare earth TbIn0.99Mn0.01O3, which has been recently proposed to be composed of antiferromagnetic clusters, presenting a field-induced increase of the freezing temperature.

Breakdown of the coherence effects and Fermi liquid behavior in YbAl3 nanoparticles.

A change in the Kondo lattice behavior of bulk YbAl3 has been observed when the alloy is shaped into nanoparticles (≈12 nm). Measurements of the electrical resistivity show inhibited coherence effects and deviation from the standard Fermi liquid behavior (T 2-dependence). These results are interpreted as being due to the effect of the disruption of the periodicity of the array of Kondo ions provoked by the size reduction process. Additionally, the ensemble of randomly placed nanoparticles also triggers an extra source of electronic scattering at very low temperatures (≈15 K) due to quantum interference effects.

Multicritical points and topology-induced inverse transition in the random-field Blume-Capel model in a random network.

The interplay between quenched disorder provided by a random field (RF) and network connectivity in the Blume-Capel (BC) model is the subject of this paper. The replica method is used to average over the network randomness. It offers an alternative analytic route to both numerical simulations and standard mean field approaches. The results reveal a rich thermodynamic scenario with multicritical points that are strongly dependent on network connectivity. In addition, we also demonstrate that the RF has a deep effect on the inverse melting transition. This highly nontrivial type of phase transition has been proposed to exist in the BC model as a function of network topology. Our results confirm that the topological mechanism can lead to an inverse melting transition. Nevertheless, our results also show that as the RF becomes stronger, the paramagnetic phase is affected in such way that the topological mechanism for inverse melting is disabled.

Spin liquid and infinitesimal-disorder-driven cluster spin glass in the kagome lattice.

The interplay between geometric frustration (GF) and bond disorder is studied in the Ising kagome lattice within a cluster approach. The model considers antiferromagnetic short-range couplings and long-range intercluster disordered interactions. The replica formalism is used to obtain an effective single cluster model from where the thermodynamics is analyzed by exact diagonalization. We found that the presence of GF can introduce cluster freezing at very low levels of disorder. The system exhibits an entropy plateau followed by a large entropy drop close to the freezing temperature. In this scenario, a spin-liquid (SL) behavior prevents conventional long-range order, but an infinitesimal disorder picks out uncompensated cluster states from the multi-degenerate SL regime, potentializing the intercluster-disordered coupling and bringing the cluster spin-glass state. To summarize, our results suggest that the SL state combined with low levels of disorder can activate small clusters, providing hypersensitivity to the freezing process in geometrically frustrated materials and playing a key role in the glassy stabilization. We propose that this physical mechanism could be present in several geometrically frustrated materials. In particular, we discuss our results in connection with the recent experimental investigations of the Ising kagome compound Co3Mg(OH)6Cl2.

Interplay between spin-glass clusters and geometrical frustration.

The presence of spin-glass (SG) order in highly geometrically frustrated systems is analyzed in a cluster SG model. The model considers infinite-range disordered interactions among cluster magnetic moments and the J(1)-J(2) model couplings between Ising spins of the same cluster. This model can introduce two sources of frustration: one coming from the disordered interactions and another coming from the J(1)-J(2) intracluster interactions (intrinsic frustration). The framework of one-step replica symmetry breaking is adopted to obtain a one-cluster problem that is exactly solved. As a main result we create phase diagrams of the temperature T versus intensity of the disorder J, where the paramagnetic-SG phase transition occurs at T(f) when T decreases for high-J values. For low-J values, the SG order is absent for antiferromagnetic clusters without intrinsic frustration. However, the SG order can be observed within the intracluster intrinsic frustration regime even for lower intensity of disorder. In particular, the results indicate that the presence of small clusters in geometrically frustrated antiferromagnetic systems can help stabilize the SG order within a weak disorder.

Correlated cluster mean-field theory for spin-glass systems.

The competition between cluster spin glass (CSG) and ferromagnetism or antiferromagnetism is studied in this work. The model considers clusters of spins with short-range ferromagnetic or antiferromagnetic (FE-AF) interactions (J_{0}) and long-range disordered couplings (J) between clusters. The problem is treated by adapting the correlated cluster mean-field theory of D. Yamamoto [Phys. Rev. B 79, 144427 (2009)]. Phase diagrams T/J×J_{0}/J are obtained for different cluster sizes n_{s}. The results show that the CSG phase is found below the freezing temperature T_{f} for lower intensities of J_{0}/J. The increase of short-range FE interaction can favor the CSG phase, while the AF one reduces the CSG region by decreasing the T_{f}. However, there are always critical values of J_{0} where AF or FE orders become stable. The results also indicate a strong influence of the cluster size in the competition of magnetic phases. For AF cluster, the increase of n_{s} diminishes T_{f} reducing the CSG phase region, which indicates that the cluster surface spins can play an important role in the CSG arising.

Spin-1 Hopfield model under a random field.

The goal of the present work is to investigate the role of trivial disorder and nontrivial disorder in the three-state Hopfield model under a Gaussian random field. In order to control the nontrivial disorder, the Hebb interaction is used. This provides a way to control the system frustration by means of the parameter a=p/N, varying from trivial randomness to a highly frustrated regime, in the thermodynamic limit. We performed the thermodynamic analysis using the one-step replica-symmetry-breaking mean field theory to obtain the order parameters and phase diagrams for several strengths of a, the anisotropy constant, and the random field.

Inverse melting and inverse freezing in a three-state spin-glass model with finite connectivity.

The phase diagrams of the three-state Ghatak-Sherrington spin-glass (or random Blume-Capel) model are obtained in mean-field theory with replica symmetry in order to study the effects of a ferromagnetic bias and finite random connectivity in which each spin is connected to a finite number of other spins. It is shown that inverse melting from a ferromagnetic to a low-temperature paramagnetic phase may appear for small but finite disorder and that inverse freezing appears for large disorder. There can also be a continuous inverse ferromagnetic to spin-glass transition.

Inverse freezing in a cluster Ising spin-glass model with antiferromagnetic interactions.

Inverse freezing is analyzed in a cluster spin-glass (SG) model that considers infinite-range disordered interactions between magnetic moments of different clusters (intercluster interaction) and short-range antiferromagnetic coupling J(1) between Ising spins of the same cluster (intracluster interaction). The intercluster disorder J is treated within a mean-field theory by using a framework of one-step replica symmetry breaking. The effective model obtained by this treatment is computed by means of an exact diagonalization method. With the results we build phase diagrams of temperature T/J versus J(1)/J for several sizes of clusters n(s) (number of spins in the cluster). The phase diagrams show a second-order transition from the paramagnetic phase to the SG order at the freezing temperature T(f) when J(1)/J is small. The increase in J(1)/J can then destroy the SG phase. It decreases T(f)/J and introduces a first-order transition. In addition, inverse freezing can arise at a certain range of J(1)/J and large enough n(s). Therefore, the nontrivial frustration generated by disorder and short-range antiferromagnetic coupling can introduce inverse freezing spontaneously.

Inverse freezing in the Ghatak-Sherrington model with a random field.

The present work studies the Ghatak-Sherrington (GS) model in the presence of a magnetic random field (RF). Previous results obtained from the GS model without a RF suggest that disorder and frustration are the key ingredients to produce spontaneous inverse freezing (IF). However, in this model, the effects of disorder and frustration always appear combined. In that sense, the introduction of RF allows us to study the IF under the effects of a disorder which is not a source of frustration. The problem is solved within the one step replica symmetry approximation. The results show that the first order transition between the spin glass and the paramagnetic phases, which is related to the IF for a certain range of crystal field D, is gradually suppressed when the RF is increased.

The van Hemmen-Kondo model for disordered cerium systems.

The interplay between disorder and strong correlations has been observed experimentally in disordered cerium alloys such as Ce(Ni, Cu) or Ce(Pd, Rh). In the case of Ce(Ni, Cu) alloys with a Cu concentration x between 0.6 and 0.3, the first studies have shown a smooth transition with decreasing temperature from a spin glass phase to ferromagnetism; for x smaller than 0.2, a Kondo phase has been observed. The situation is more complicated now due to the recent observation of magnetic clusters. The competition between the Kondo effect, the spin glass (SG) and the ferromagnetic (FE) ordering has been extensively studied theoretically. The Kondo effect is described by the usual mean-field approximation; we have treated the SG behavior successively by the Sherrington-Kirkpatrick model, then by the Mattis model and finally by the van Hemmen model, which takes both a ferromagnetic part and a site-disorder random part for the intersite exchange interaction. We present here the results obtained by the van Hemmen-Kondo model: for a large Kondo exchange JK, a Kondo phase is obtained while, for smaller JK, the succession of an SG phase, a mixed SG-FE one and finally an FE one has been obtained with decreasing temperature. This model improves the theoretical description of disordered Kondo systems by providing a simpler approach for further calculations of magnetic clusters and can, therefore, account for recent experimental data on disordered cerium systems.