We present a minimal model that provides a description of the magnetic and thermodynamic properties of Eu. The model contains two exchange coupling parameters, which are calculated using Density Functional Theory, and a local easy axis magnetic anisotropy term. The classical ground state of the system is a generalization of the well known 120$^circ$ structure observed in triangular antiferromagnets. Monte Carlo simulations show two phase transitions as a function of the temperature. With increasing temperature, the system transitions from the ground state into a high-entropy collinear antiferromagnet, which in turn at higher temperatures presents a second order transition to a paramagnetic state. A high enough external magnetic field parallel to the anisotropy axis produces a spin-flop transition at low temperatures. The field also reduces the temperature range of stability of the collinear antiferromagnet phase and leads to a single phase transition as a function of the temperature. The reported behavior of the specific heat, the magnetization, and the magnetic susceptibility is in agreement with the available experimental data. Finally, we present the magnetic phase diagrams for magnetic fields parallel and perpendicular to the easy axis.
We compute the magnetocaloric effect (MCE) in the GdTX (T=Sc, Ti, Co, Fe; X=Si, Ge) compounds as a function of the temperature and the external magnetic field. To this end we use a density functional theory approach to calculate the exchange-coupling interactions between Gd$^{3+}$ ions on each compound. We consider a simplified magnetic Hamiltonian and analyze the dependence of the exchange couplings on the transition metal T, the p-block element X, and the crystal structure (CeFeSi-type or CeScSi-type). The most significant effects are observed for the replacements Ti $to$ Sc or Fe $to$ Co which have an associated change in the parity of the electron number in the 3d level. These replacements lead to an antiferromagnetic contribution to the magnetic couplings that reduces the Curie temperature and can even lead to an antiferromagnetic ground state. We solve the magnetic models through mean field and Monte Carlo calculations and find large variations among compounds in the magnetic transition temperature and in the magnetocaloric effect, in agreement with the available experimental data. The magnetocaloric effect shows a universal behavior as a function of temperature and magnetic field in the ferromagnetic compounds after a scaling of the relevant energy scales by the Curie temperature $T_C$.
We present a theoretical analysis of the magnetic phase diagram of CeTi$_{1-x}$Sc$_{x}$Ge and GdFe$_{1-x}$Co$_{x}$Si as a function of the temperature and the Sc and Co concentration $x$, respectively. CeScGe and GdCoSi, as many other RTX (R=rare earth, T=transition metal, X=p-block element) compounds, present a tetragonal crystal structure where bilayers of R are separated by layers of T and X. While GdFeSi and CeTi$_{0.75}$Sc$_{0.25}$Ge are ferromagnetic, CeScGe and GdCoSi order antiferromagnetically with the R 4f magnetic moments on the same bilayer aligned ferromagnetically and magnetic moments in nearest neighbouring bilayers aligned antiferromagnetically. The antiferromagnetic transition temperature $T_N$ decreases with decreasing concentration $x$ in both compounds and for low enough values of $x$ the compounds show a ferromagnetic behavior. Based on these observations we construct a simplified model Hamiltonian that we solve numerically for the specific heat and the magnetization. We find a good qualitative agreement between the model and the experimental data. Our results show that the main magnetic effect of the Sc $to$ Ti and Co $to$ Fe substitution in these compounds is consistent with a change in the sign of the exchange coupling between magnetic moments in neighbouring bilayers. We expect a similar phenomenology for other magnetic RTX compounds with the same type of crystal structure.
We analyze the quantum entanglement between opposite spin projection electrons in the ground state of the Anderson impurity model. In this model, a single level impurity with intralevel repulsion U is tunnel coupled to a free electron gas. The Anderson model presents a strongly correlated many body ground state with mass enhanced quasiparticle excitations. We find, using both analytical and numerical tools, that the quantum entanglement between opposite spin projection electrons is a monotonic universal function of the quasiparticle mass enhancement Z. The mass enhancement, which is used to quantify the correlations in quantum many body systems, could therefore be used to quantify spin entanglement.
We analyze the electronic properties of interacting crystal field split three band systems. Using a rotationally invariant slave boson approach we analyze the behavior of the electronic mass renormalization as a function of the intralevel repulsion $U$, the Hunds coupling $J$, the crystal field splitting, and the number of electrons per site $n$. We first focus on the case in which two of the bands are identical and the levels of the third one are shifted by $Delta>0$ with respect to the former. We find an increasing quasiparticle mass differentiation between the bands, for system away from half-filling ($n=3$), as the Hubbard interaction $U$ is increased. This leads to orbital selective Mott transitions where either the higher energy band (for $4>n>3$) or the lower energy degenerate bands ($2<n<3$) become insulating for $U$ larger than a critical interaction $U_{c}(n)$. Away from the half-filled case $|n-3|gtrsim 0.3$ there is a wide range of parameters for $U<U_c(n)$ where the system presents a Hunds metal phase with the physics dominated by the local high spin multiplets. Finally, we study the fate of the $n=2$ Hunds metal as the energy splitting between orbitals is increased for different possible crystal distortions. We find a strong sensitivity of the Hunds metal regime to crystal fields due to the opposing effects of $J$ and the crystal field splittings on the charge distribution between the bands.
We analyze, from a quantum information theory perspective, the possibility of realizing a SU(4) entangled Kondo regime in semiconductor double quantum dot devices. We focus our analysis on the ground state properties and consider the general experimental situation where the coupling parameters of the two quantum dots differ. We model each quantum dot with an Anderson type Hamiltonian including an interdot Coulomb repulsion and tunnel couplings for each quantum dot to independent fermionic baths. We find that the spin and pseudospin entanglements can be made equal, and the SU(4) symmetry recovered, if the gate voltages are chosen in such a way that the average charge occupancies of the two quantum dots are equal, and the double occupancy on the double quantum dot is suppressed. We present density matrix renormalization group numerical results for the spin and pseudospin entanglement entropies, and analytical results for a simplified model that captures the main physics of the problem.
The dynamical mean field theory (DMFT) has become a standard technique for the study of strongly correlated models and materials overcoming some of the limitations of density functional approaches based on local approximations. An important step in this method involves the calculation of response functions of a multiorbital impurity problem which is related to the original model. Recently there has been considerable progress in the development of techniques based on the density matrix renormalization group (DMRG) and related matrix product states (MPS) implying a substantial improvement to previous methods. In this article we review some of the standard algorithms and compare them to the newly developed techniques, showing examples for the particular case of the half-filled two-band Hubbard model.
We analyze the low energy properties of a device with $N+1$ quantum dots in a star configuration. A central quantum dot is tunnel coupled to source and drain electrodes and to $N$ quantum dots. Extending previous results for the $N=2$ case we show that, in the appropriate parameter regime, the low energy Hamiltonian of the system is a ferromagnetic Kondo model for a $S=(N-1)/2$ impurity spin. For small enough interdot tunnel coupling, however, a two-stage Kondo effect takes place as the temperature is decreased. The spin $1/2$ in the central quantum dot is Kondo screened first and at lower temperatures the antiferromagnetic coupling to the side coupled quantum dots leads to an underscreened $S=N/2$ Kondo effect. We present numerical results for the thermodynamic and spectral properties of the system which show a singular behavior at low temperatures and allow to characterize the different strongly correlated regimes of the device.
The discovery in 2001 of superconductivity in some heavy fermion compounds of the RMIn$_5$ (R=4f or 5f elements, M=Co, Rh, Ir) family, has triggered enormous amount of research pointing to understand the physical origin of superconductivity and its relation with magnetism. Although many properties have been clarified, there are still crutial questions that remain unanswered. One of these questions is the particular role of the transition metal in determining the value of critical superconducting temperature (Tc). In this work, we analyse an interesting regularity that is experimentally observed in this family of compounds, where the lowest Neel temperatures are obtained in the Co-based materials. We focus our analysis on the GdMIn$_5$ compounds and perform density-functional-theory based total-energy calculations to obtain the parameters for the exchange coupling interactions between the magnetic moments located at the Gd$^{3+}$ ions. Our calculations indicate that the ground state of the three compounds is a $C$-type antiferromagnet determined by the competition between the first- and second-neighbor exchange couplings inside GdIn$_3$ planes and stabilized by the couplings across MIn$_2$ planes. We then solve a model with these magnetic interactions using a mean-field approximation and Quantum Monte Carlo simulations. The results obtained for the calculated Neel and Curie-Weiss temperatures, the specific heat and the magnetic susceptibility are in very good agreement with the existent experimental data. Remarkably, we show that the first neighbor interplane exchange coupling in the Co-based material is much smaller than in the Rh and Ir analogues due to a more two dimensional behaviour in the former. This result explains the observed lower Neel temperature in Co-115 systems and may shed light on the fact that the Co-based 115 superconductors present the highest Tc.
We analyze the transport properties of a double quantum dot device in the side-coupled configuration. A small quantum dot (QD), having a single relevant electronic level, is coupled to source and drain electrodes. A larger QD, whose multilevel nature is considered, is tunnel-coupled to the small QD. A Fermi liquid analysis shows that the low temperature conductance of the device is determined by the total electronic occupation of the double QD. When the small dot is in the Kondo regime, an even number of electrons in the large dot leads to a conductance that reaches the unitary limit, while for an odd number of electrons a two stage Kondo effect is observed and the conductance is strongly suppressed. The Kondo temperature of the second stage Kondo effect is strongly affected by the multilevel structure of the large QD. For increasing level spacing, a crossover from a large Kondo temperature regime to a small Kondo temperature regime is obtained when the level spacing becomes of the order of the large Kondo temperature.
