A surprising relation between double exchange and Heisenberg model spectra: Application to half-doped manganites

The Zener polarons recently found in half-doped manganites are usually seen as mixed valence entities ruled by a double exchange Hamiltonian involving only correlated electrons of the metals. They can however be considered as ferrimagnetic local units if the holes are localized on the bridging oxygen atoms as implicitely suggested by recent mean-field it ab initio calculations. In the latter case, the physics is ruled by a Heisenberg Hamiltonian involving magnetic oxygen bridges. This paper shows that the spectra resulting from the resolution of both models are analytically identical. This single resulting model spectrum accurately reproduces the spectrum of Zener polarons in Pr0.6Ca0.4MnO3 manganite studied by means of explicitely correlated ab initio calculations. Since the physics supported by each model are different, the analysis of the exact Hamiltonian ground state wave function should a priori enables one to determine the most appropriate model. It will be shown that neither the spectrum nor the wavefunction analysis bring any decisive arguments to settle the question. Such undecidability would probably be encountered in experimental information.Comment: 4 pages, 2 figure

Ab initio study of the CE magnetic phase in half-doped manganites: Purely magnetic versus double exchange description

The leading electronic interactions governing the local physics of the CE phase of half-doped manganites are extracted from correlated ab initio calculations performed on an embedded cluster. The electronic structure of the low-energy states is dominated by double exchange configurations and O-2$p_{\sigma}$ to Mn-3d charge transfer configurations. The model spectra of both a purely magnetic non-symmetric Heisenberg Hamiltonian involving a magnetic oxygen and two non-symmetric double exchange models are compared to the \textit{ab initio} one. While a satisfactory agreement between the Heisenberg spectrum and the calculated one is obtained, the best description is provided by a double exchange model involving excited non-Hund atomic states. This refined model not only perfectly reproduces the spectrum of the embedded cluster in the crystal geometry, but also gives a full description of the local double-well potential energy curve of the ground state (resulting from the interaction of the charge localized electronic configurations) and the local potential energy curves of all excited states ruled by the double exchange mechanism

A renormalized excitonic method in terms of block excitations. Application to spin lattices

Dividing the lattice into blocks with singlet ground state and knowing the exact low energy spectrum of the blocks and of dimers (or trimers) of blocks, it is possible to approach the lowest part of the lattice spectrum through an excitonic type effective model. The potentialities of the method are illustrated on the 1-D frustrated chain and the 1/5-depleted square and the plaquette 2-D lattices. The method correctly locates the phase transitions between gapped and non-gapped phases.Comment: Submitted for publication in Phys. Rev.

Interplay between Local Anisotropies in Binuclear Complexes

A systematic study has been undertaken to determine how local distortions affect the overall (molecular) magnetic anisotropies in binuclear complexes. For this purpose we have applied a series of distortions to two binuclear Ni(II) model complexes and extracted the magnetic anisotropy parameters of multispin and giant-spin model Hamiltonians. Furthermore, local and molecular magnetic axes frames have been determined. It is shown that certain combinations of local distortions can lead to constructive interference of the local anisotropies and that the largest contribution to the anisotropic exchange does not arise from the second-rank tensor normally included in the multispin Hamiltonian, but rather from a fourth-rank tensor. From the comparison of the extracted parameters, simple rules are obtained to maximize the molecular anisotropy by controlling the local magnetic anisotropy, which opens the way to tune the anisotropy in binuclear or polynuclear complexes

Theoretical studies of the phase transition in the anisotropic 2-D square spin lattice

The phase transition occurring in a square 2-D spin lattice governed by an anisotropic Heisenberg Hamiltonian has been studied according to two recently proposed methods. The first one, the Dressed Cluster Method, provides excellent evaluations of the cohesive energy, the discontinuity of its derivative around the critical (isotropic) value of the anisotropy parameter confirms the first-order character of the phase transition. Nevertheless the method introduces two distinct reference functions (either N\'eel or XY) which may in principle force the discontinuity. The Real Space Renormalization Group with Effective Interactions does not reach the same numerical accuracy but it does not introduce a reference function and the phase transition appears qualitatively as due to the existence of two domains, with specific fixed points. The method confirms the dependence of the spin gap on the anisotropy parameter occurring in the Heisenberg-Ising domain

Direct generation of local orbitals for multireference treatment and subsequent uses for the calculation of the correlation energy

We present a method that uses the one-particle density matrix to generate directly localized orbitals dedicated to multireference wave functions. On one hand, it is shown that the definition of local orbitals making possible physically justified truncations of the CAS ~complete active space! is particularly adequate for the treatment of multireference problems. On the other hand, as it will be shown in the case of bond breaking, the control of the spatial location of the active orbitals may permit description of the desired physics with a smaller number of active orbitals than when starting from canonical molecular orbitals. The subsequent calculation of the dynamical correlation energy can be achieved with a lower computational effort either due to this reduction of the active space, or by truncation of the CAS to a shorter set of references. The ground- and excited-state energies are very close to the current complete active space self-consistent field ones and several examples of multireference singles and doubles calculations illustrate the interest of the procedur

Decoherence-free molecular spin qubits with chemically designed frequencies

Resumen del trabajo presentado a la XII Reunión del grupo de física de la materia condensada de la RSEF (GEFES), celebrada en Salamanca del 1 al 3 de febrero de 2023.We report a sizeable quantum tunnelling splitting for the mononuclear Ni(II) molecular complexes [Ni(Me6tren)Cl](ClO4) (1) and [Ni(2-Imdipa)(NCS)](NCS) (2). With their S = 1 ground state and strong anisotropy, these molecules provide a realization of the simplest non-Kramers system (integer spin). The “clock transition” between levels associated with superpositions of mS = ±1 spin states, with its characteristic non-linear magnetic field dependence, has been directly monitored by heat capacity experiments. The comparison of complex 1 with a Co derivative (S = 3/2), for which tunnelling is forbidden, shows that the clock transition leads to an effective suppression of intermolecular spin–spin interactions. We also show that the splitting admits a chemical tuning via the modification of the ligand shell that determines the magnetic anisotropy. In particular, the weaker magnetic anisotropy of complex 2 makes its qubit frequency compatible with superconducting microwave circuits, and has allowed its direct detection by on-chip broadband transmission experiments.Peer reviewe

Analytical Derivations for the Description of Magnetic Anisotropy in Transition Metal Complexes

International audienceThis chapter is dedicated to the rationalization of magnetic anisotropy in metal complexes. Analytical derivations allow one to predict the nature and magnitude of both the zero-field-splitting and the anisotropies of magnetic exchange. The first section is devoted to mononuclear complexes. It addresses the effect of spin–orbit coupling (SOC) in two different cases: (i) when the ground state is non-degenerate and a second-order SOC applies. The effect of the SOC can then be modeled by an energy splitting of the MS components of the ground spin state. Illustrations of the power of these analytical derivations for the rationalization of the ZFS of various complexes are presented; (ii) when the ground state is (almost) degenerate, a first-order SOC applies. A more sophisticated model is here derived which rationalizes the obtaining of a giant value of the ZFS in a Ni(II) complex. The second section is devoted to the derivation of multi-spin models for binuclear complexes. We will determine the physical content of both the symmetric and the antisymmetric exchange tensors in the case of two centers with spin S = 1/2. A peculiar derivation concerns the Dzyaloshinskii–Moriya (antisymmetric exchange) interaction in case of a local degeneracy of the orbitals and shows how the first-order SOC can generate giant values of this anisotropy of exchange. In the last subsection, we will show that the usual multi-spin model for spin S = 1 centers is not valid and derive an appropriate model involving a four-rank exchange tensor. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG

Magnetism in Binuclear Compounds: Theoretical Insights

International audienceThis chapter is devoted to theoretical calculations aimed at determining the electronic structure of binuclear complexes, including isotropic and anisotropic interactions in both the strong and in the weak-exchange coupling limits. The theory of effective Hamiltonians is used to extract magnetic anisotropy terms in various regimes and in particular those for which the giant-spin approximation holds. While only a second-rank symmetric tensor is necessary to describe the zero-field splitting in centrosymmetric compounds with a single electron on each metal ion, a 4-rank tensor must also be introduced to describe the anisotropic exchange in the case of two unpaired electrons per metal ion. The magnitude of these additional interactions was found to be larger than those of the well admitted 2-rank tensor. Even though, the magnetic anisotropy of binuclear complexes can often be predicted from the knowledge of the local anisotropy of its mononuclear constituents, the large magnitude of the 4-rank tensor makes theoretical calculations important if not mandatory to rationalize experimental results on firm grounds in systems where anisotropic binuclear interactions are important