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We investigate the phonon spectrum of pure and rare-earth substituted langasites. For electric fields oriented along the $c$ axis, a strong low-frequency phonon is observed, softening at lower temperature in all samples studied. The dielectric contribution and temperature dependence of this mode is the primary source of the large $[\ensuremath{\varepsilon}(0)\ensuremath{\sim}100]$ static dielectric permittivity observed in these systems. Softening of this mode with increasing mass of the rare-earth substitutes further suggests that langasites are close to a structural instability at low temperatures. The application of a magnetic field to a diluted Ho-langasite sample reveals a shift in the strong absorption band at THz frequencies associated with this soft lattice mode, suggesting spin-lattice effects may also be at play in these systems.

We theoretically study the quench dynamics of the local magnetization in a hybrid Majorana-wire--quantum-dot system coupled to external leads. In order to thoroughly understand the origin of the dot magnetization dynamics, we consider either normal metal or ferromagnetic electrodes. In the first case, the magnetization arises exclusively from the proximity to the topological superconductor hosting Majorana zero-energy modes and the associated development of an induced exchange field. We predict a nonmonotonic dependence of the dot's magnetization in the odd-occupation regime and show that the dynamics is governed by the magnitude of the coupling to Majorana wire. However, when the system is coupled to ferromagnetic leads, the ferromagnet and Majorana contributions to the effective exchange field are competing with each other and reveal a nontrivial dynamical behavior. As a result, the time-dependent magnetization can undergo multiple sign changes preceding the relaxation to a new thermal value. We also identify the transport regime, where fine tuning of the coupling to Majorana wire within a narrow range allows one to manipulate the magnetic state of the system. The effect of spin polarization of the leads and influence of the finite overlap between the Majorana edge modes are also examined. Moreover, we analyze the quench in the energy of the quantum dot orbital level and demonstrate that the rather straightforward charge dynamics can disguise nontrivial time evolution of the magnetization. Finally, we compare predicted dynamics with results obtained for quantum dot coupled to spin-polarized fermionic bound state instead of Majorana zero-energy mode.

Magnetization, magnetic torque, and terahertz absorption spectroscopy measurements reveal various magnetic phases in the polar ferrimagnet Mn${}_{2}$Mo${}_{3}$O${}_{8}$. The metamagnetic transitions as well as the spin-wave resonances in the center and at the boundary of the Brillouin zone are quantitatively described by a mean-field spin model. Supplemented by $a\phantom{\rule{0}{0ex}}b\phantom{\rule{0.333em}{0ex}}i\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}o$ calculations, the authors identify the competition between easy-plane and easy-axis single-ion anisotropies, acting respectively on tetrahedral and octahedral Mn sites, as the key feature leading to the rich phase diagram in this compound family.

Based on reliable ab initio computations and the numerical renormalization group method, systematic studies on a two-dimensional GaSe monolayer with Co adatoms have been carried out. It is shown that the stable lowest-energy configuration of the system involves the Co adatom located over a Ga atom. For such a configuration, it is demonstrated that the electronic and magnetic properties of the system can be effectively controlled by means of external factors, such as magnetic field, gate voltage, or temperature. Moreover, if properly tuned, the GaSe-Co system can also exhibit the Kondo effect. The development of the Kondo phenomenon is revealed in the local density of states of the Co adatom, its magnetic field dependence, which presents the splitting of the Kondo peak, as well as in the temperature dependence of the conductance, which exhibits scaling typical of the spin-$\frac{1}{2}$ Kondo effect.

We theoretically study the quench dynamics of induced anisotropy of a large-spin magnetic molecule coupled to spin-polarized ferromagnetic leads. The real-time evolution is calculated by means of the time-dependent density-matrix numerical renormalization group method implemented within the matrix product states framework, which takes into account all correlations in a very accurate manner. We determine the system response to a quench in the spin-dependent coupling to ferromagnetic leads. In particular, we focus on the transient dynamics associated with crossing from the weak- to the strong-coupling regime, where the Kondo correlations become important. The dynamics is examined by calculating the time-dependent expectation values of the spin-quadrupole moment and the associated spin operators. We identify the relevant timescales describing the quench dynamics and determine the influence of the effective exchange coupling of molecules and spin polarization of the leads on the dynamical behavior of the system. Furthermore, the generalization of our predictions for large spin values of molecules is considered. Finally, we analyze the effect of finite temperature and show that it gives rise to a reduction of magnetic anisotropy by strong suppression of the time-dependent spin-quadrupole moment due to thermal fluctuations.

The transport behavior of a double quantum dot side-attached to a topological superconducting wire hosting Majorana zero-energy modes is studied theoretically in the strong correlation regime. It is shown that Majorana modes can leak to the whole nanostructure, giving rise to a subtle interplay between the two-stage Kondo screening and the half-fermionic nature of Majorana quasiparticles. In particular, the coupling to the topological wire is found to reduce the effective exchange interaction between the two quantum dots in the absence of normal leads. Interestingly, it also results in an enhancement of the second-stage Kondo temperature when the normal leads are attached. Moreover, it is shown that the second stage of the Kondo effect can become significantly modified in one of the spin channels due to the interference with the Majorana zero-energy mode, yielding the low-temperature conductance equal to $G=G_0/4$, where $G_0 = 2e^2/h$, instead of $G=0$ in the absence of the topological superconducting wire. We also identify a nontrivial spin-charge ${\rm SU}(2)$ symmetry present in the system at a particular point in parameter space, despite lack of the spin nor charge conservation. Finally, we discuss the consequences of a finite overlap between two Majorana modes, as relevant for short Majorana wires., Comment: 16 pages, 15 figures, accepted in Phys. Rev. B

We study the spin-resolved subgap transport in a triple quantum-dot system coupled to one superconducting and two ferromagnetic leads. We examine the Andreev processes in the parallel and antiparallel alignments of ferromagnets magnetic moments in both the linear and nonlinear response regimes. The emphasis is put on the analysis of the current cross-correlations between the currents flowing through the left and right arms of the device and relevant electron waiting time distributions. We show that both quantities can give an important insight into the subgap transport processes and their analysis can help optimizing the system parameters for achieving the considerable Andreev current and efficient Cooper pair splitting. Strong positive values of cross-correlations are associated with the presence of tunneling processes enhancing the Cooper pair splitting efficiency, while short waiting times for electrons tunneling through distinct ferromagnetic contacts indicate fast splitting of emitted Cooper pairs. In particular, we study two detuning schemes and show that antisymmetric shift of side quantum dots energy levels is favorable for efficient Cooper pair splitting. The analysis of spin-resolved waiting time distributions supports the performance enhancement due to the presence of ferromagnetic contacts, which is in particular revealed for short times. Finally, we consider the effect of changing the inter-dot hopping amplitude and predict that strong inter-dot correlations lead to a reduction of Andreev transport properties in low-bias limit.

We investigate the quench dynamics of a quantum dot strongly coupled to spin-polarized ferromagnetic leads. The real-time evolution is calculated by means of the time-dependent density-matrix numerical renormalization group method implemented within the matrix product states framework. We examine the system's response to a quench in the spin-dependent coupling strength to ferromagnetic leads as well as in the position of the dot's orbital level. The spin dynamics is analyzed by calculating the time-dependent expectation values of the quantum dot's magnetization and occupation. Based on these, we determine the time-dependence of a ferromagnetic-contact-induced exchange field and predict its nonmonotonic build-up. In particular, two time scales are identified, describing the development of the exchange field and the dot's magnetization sign change. Finally, we study the effects of finite temperature on the dynamical behavior of the system.

We investigate theoretically the interplay of proximity effects due to the presence of a superconductor and normal ferromagnetic leads on the formation of the spintronic quadrupolar exchange field in a large-spin molecule. We show that the spintronic anisotropy can be enhanced by a few orders of magnitude, and tuned by changing the strength of coupling to the superconductor. Especially large anisotropy is generated in the vicinity of the charge parity changing transition of the molecule. We also provide predictions of measurable spectral properties being the hallmarks of these phenomena., Comment: Published version, 16 pages, 13 figures (including appendices)

We show that the Kondo screening in a correlated double-quantum-dot structure may be caused solely by the proximity of a superconductor which induces nonlocal pairing by Andreev reflection processes. This leads to an effective exchange interaction, which we estimate perturbatively, and we corroborate the analytical predictions by the numerical renormalization group calculations, using an effective model for the superconductor-proximized nanostructure. We determine the dependence of the relevant Kondo temperature on the coupling to the superconductor and predict a characteristic modification of conventional low-temperature transport behavior, which can be used to experimentally distinguish this phenomenon from other Kondo effects. The occurrence of nonlocal pairing exchange does not depend on the details of the proposed setup; therefore, it can also be relevant for the bulk materials, such as heavy-fermion compounds.

The Andreev transport through a large-spin magnetic molecule, such as a single molecular magnet, attached to superconducting and ferromagnetic leads is studied theoretically by means of the real-time diagrammatic technique. It is shown that due to the proximity effect, molecular Andreev bound states form in the system, with energies depending on the intrinsic parameters of the molecule. We study the spin-resolved Andreev current, conductance, and tunnel magnetoresistance in both the linear and nonlinear response regimes and find regions of negative differential conductance, as well as either enhanced or negative tunnel magnetoresistance. The mechanisms leading to those effects are thoroughly discussed. It is also shown that the tunnel magnetoresistance can provide information about particular spin multiplets responsible for the Andreev reflection processes.

We study the spin-polarized transport through a triple-quantum-dot molecule weakly coupled to ferromagnetic leads. The analysis is performed by means of the real-time diagrammatic technique, including up to the second order of perturbation expansion with respect to the tunnel coupling. The emphasis is put on the impact of dark states on spin-resolved transport characteristics. It is shown that the interplay of coherent population trapping and cotunneling processes results in a highly nontrivial behavior of the tunnel magnetoresistance, which can take negative values. Moreover, a super-Poissonian shot noise is found in transport regimes where the current is blocked by the formation of dark states, which can be additionally enhanced by spin dependence of tunneling processes, depending on the magnetic configuration of the device. The mechanisms leading to those effects are thoroughly discussed.

The Andreev transport properties of double quantum dot based Cooper pair splitters with one superconducting and two normal leads are studied theoretically in the Kondo regime. The influence of the superconducting pairing correlations on the local density of states, Andreev transmission coefficient, and Cooper pair splitting efficiency is thoroughly analyzed. It is shown that finite superconducting pairing potential quickly suppresses the $\text{SU}(2)$ Kondo effect, which can however reemerge for relatively large values of coupling to superconductor. In the $\text{SU}(4)$ Kondo regime, a crossover from the $\text{SU}(4)$ to the $\text{SU}(2)$ Kondo state is found as the coupling to superconductor is enhanced. The analysis is performed by means of the density-matrix numerical renormalization group method.

The finite-frequency transport properties of a large-spin molecule attached to ferromagnetic contacts are studied theoretically in the Kondo regime. The focus is on the behavior of the dynamical conductance in the linear response regime, which is determined by using the numerical renormalization group method. It is shown that the dynamical conductance depends greatly on the magnetic configuration of the device and intrinsic parameters of the molecule. In particular, conductance exhibits characteristic features for frequencies corresponding to the dipolar and quadrupolar exchange fields resulting from the presence of spin-dependent tunneling. Moreover, a dynamical spin accumulation in the molecule, associated with the off-diagonal-in-spin component of the conductance, is predicted. This spin accumulation becomes enhanced with increasing the spin polarization of the leads, and it results in a nonmonotonic dependence of the conductance on frequency, with local maxima occurring for characteristic energy scales.

The spin-resolved transport properties of a single-wall carbon nanotube quantum dot, with an attached single molecular magnet, are studied theoretically. With the aid of the real-time diagrammatic technique in the lowest-order perturbation expansion with respect to the tunnel coupling, the current, differential conductance, and the tunnel magnetoresistance (TMR) are determined in both the linear and nonlinear response regimes. It is shown that transport properties depend greatly on both the shell filling sequence of the carbon nanotube and the type of exchange interaction between the molecular magnet and nanotube. This results in highly nontrivial behavior of the TMR, which is especially visible in the low bias voltage regime. Depending on the gate voltage and parameters of the system, we find transport regimes where either a greatly enhanced or negative TMR develops. The mechanism leading to such behavior is associated with nonequilibrium spin accumulation, which builds up in the antiparallel magnetic configuration of the device. We show that it is crucial whether the spin accumulation occurs in the highest-weight spin states or in states with lower spin values. While in the former case it leads to enhanced TMR, in the latter case it may result in negative tunnel magnetoresistance. In addition, we analyze how the above effects depend on the magnitude of the molecular magnet's spin, and show that this dependence is generally nonmonotonic.