No Arabic abstract
The ground state of frustrated (antiferromagnetic) triangular molecular magnets is characterized by two total-spin $S =1/2$ doublets with opposite chirality. According to a group theory analysis [M. Trif textit{et al.}, Phys. Rev. Lett. textbf{101}, 217201 (2008)] an external electric field can efficiently couple these two chiral spin states, even when the spin-orbit interaction (SOI) is absent. The strength of this coupling, $d$, is determined by an off-diagonal matrix element of the dipole operator, which can be calculated by textit{ab-initio} methods [M. F. Islam textit{et al.}, Phys. Rev. B textbf{82}, 155446 (2010)]. In this work we propose that Coulomb-blockade transport experiments in the cotunneling regime can provide a direct way to determine the spin-electric coupling strength. Indeed, an electric field generates a $d$-dependent splitting of the ground state manifold, which can be detected in the inelastic cotunneling conductance. Our theoretical analysis is supported by master-equation calculations of quantum transport in the cotunneling regime. We employ a Hubbard-model approach to elucidate the relationship between the Hubbard parameters $t$ and $U$, and the spin-electric coupling constant $d$. This allows us to predict the regime in which the coupling constant $d$ can be extracted from experiment.
A fundamental requirement in the circuit model of quantum information processing is the realization of fault-tolerant multi-qubit quantum gates with entangling capabilities. A key step towards this end is to achieve control of qubit states through geometric phases at very small spatial scales in an effective and feasible way. A spin-electric coupling present in antiferromagnetic triangular single-molecule magnets (SMMs) allows for manipulation of the spin (qubit) states with a great flexibility. Here, we establish an all-electrical two-qubit geometric phase shift gate acting on the four-fold ground state manifold of a triangular SMM, which represents an effective two-qubit state space. We show that a two-qubit quantum gate with arbitrary entangling power can be achieved through the Berry phase effect, induced by adiabatically varying an external electric field in the plane of the molecule.
Motivated by recent experiments on $alpha$-RuCl$_3$, we investigate a possible quantum spin liquid ground state of the honeycomb-lattice spin model with bond-dependent interactions. We consider the $K-Gamma$ model, where $K$ and $Gamma$ represent the Kitaev and symmetric-anisotropic interactions between spin-1/2 moments on the honeycomb lattice. Using the infinite density matrix renormalization group (iDMRG), we provide compelling evidence for the existence of quantum spin liquid phases in an extended region of the phase diagram. In particular, we use transfer matrix spectra to show the evolution of two-particle excitations with well-defined two-dimensional dispersion, which is a strong signature of quantum spin liquid. These results are compared with predictions from Majorana mean-field theory and used to infer the quasiparticle excitation spectra. Further, we compute the dynamical structure factor using finite size cluster computations and show that the results resemble the scattering continuum seen in neutron scattering experiments on $alpha$-RuCl$_3$. We discuss these results in light of recent and future experiments.
Frustrated magnets are known to support two-dimensional topological solitons, called skyrmions. A continuum model for frustrated magnets has recently been shown to support both two-dimensional skyrmions and three-dimensional knotted solitons (hopfions). In this note we derive lower bounds for the energies of these solitons expressed in terms of their topological invariants. The bounds are linear in the degree in the case of skyrmions and scale as the Hopf degree to the power 3/4 in the case of hopfions.
Coherent control of individual molecular spins in nano-devices is a pivotal prerequisite for fulfilling the potential promised by molecular spintronics. By applying electric field pulses during time-resolved electron spin resonance measurements, we measure the sensitivity of the spin in several antiferromagnetic molecular nanomagnets to external electric fields. We find a linear electric field dependence of the spin states in Cr$_7$Mn, an antiferromagnetic ring with a ground-state spin of $S=1$, and in a frustrated Cu$_3$ triangle, both with coefficients of about $2~mathrm{rad}, mathrm{s}^{-1} / mathrm{V} mathrm{m}^{-1}$. Conversely, the antiferromagnetic ring Cr$_7$Ni, isomorphic with Cr$_7$Mn but with $S=1/2$, does not exhibit a detectable effect. We propose that the spin-electric field coupling may be used for selectively controlling individual molecules embedded in nanodevices.
The reversal of the magnetization of crystals of molecular magnets that have a large spin and high anisotropy barrier generally proceeds below the blocking temperature by quantum tunneling. This is manifested as a series of controlled steps in the hysteresis loops at resonant values of the magnetic field where energy levels on opposite sides of the barrier cross. An abrupt reversal of the magnetic moment of the entire crystal can occur instead by a process commonly referred to as a magnetic avalanche, where the molecular spins reverse along a deflagration front that travels through the sample at subsonic speed. In this chapter, we review experimental results obtained to date for magnetic deflagration in molecular nanomagnets.