A first-principles linear response theory for open quantum systems and its application to Orbach and direct magnetic relaxation in Ln-based coordination polymers
Mikolaj Żychowicz, Jakub J. Zakrzewski, Szymon Chorazy, Alessandro Lunghi
cond-mat.mtrl-sciquant-phSubmitted Mar 19, 2026• Announced Mar 20, 2026
Single-Molecule Magnets (SMMs) exhibit slow magnetic relaxation as a result of axial magnetic anisotropy inhibiting spin-phonon transitions. In order to establish a direct link between physical observables and the microscopic theory of magnetic relaxation, we here develop and numerically implement a first-principles linear-response theory for open quantum systems that provides access to the complex a.c. magnetic susceptibility in the presence of an oscillating a.c. magnetic field. Once combined with density functional theory and multiconfigurational electronic structure simulations, this formalism is applied in a fully first-principles fashion to three cyanido-bridged Ln/Y-based coordination polymers with general formula {Ln$^{III}_x$ Y$^{III}_{1-x}$ [Co(CN)$_6$]}, where Ln = Yb (1), Tb (2), and Dy (3). The method is able to reproduce the low-temperature direct relaxation process and its field dependence, as well as the high-temperature Orbach relaxation regime for all the investigated compounds. These results demonstrate the feasibility of ab initio simulations of magnetic a.c.susceptibility in lanthanide-based SMMs and support the potential of further development of ab initio open quantum systems methods towards the completion of a magnetization dynamics theory.
Single-Molecule Magnets (SMMs) exhibit slow magnetic relaxation as a result of axial magnetic anisotropy inhibiting spin-phonon transitions. In order to establish a direct link between physical observables and the microscopic theory of magnetic relaxation, we here develop and numerically implement a first-principles linear-response theory for open quantum systems that provides access to the complex a.c. magnetic susceptibility in the presence of an oscillating a.c. magnetic field. Once combined with density functional theory and multiconfigurational electronic structure simulations, this formalism is applied in a fully first-principles fashion to three cyanido-bridged Ln/Y-based coordination polymers with general formula {LnxIII Y1−xIII [Co(CN)6]}, where Ln = Yb (1), Tb (2), and Dy (3). The method is able to reproduce the low-temperature direct relaxation process and its field dependence, as well as the high-temperature Orbach relaxation regime for all the investigated compounds. These results demonstrate the feasibility of ab initio simulations of magnetic a.c.susceptibility in lanthanide-based SMMs and support the potential of further development of ab initio open quantum systems methods towards the completion of a magnetization dynamics theory.
Spin-phonon interactions are known to drive magnetic relaxation in solid-state systems but are generally overlooked as a contribution to spin decoherence through dephasing. Here, we extend quantum master equations to account for coherence terms and describe the full effect of up to two-phonon processes on spin dynamics. We implement this method fully ab initio for a molecule with large magnetization blocking temperature and show that, although strong axial magnetic anisotropy ensures slow magnetic relaxation approaching seconds at 77 kelvins, the superposition of Kramers doublets is coherent for less than 10 nanoseconds due to a two-phonon pure dephasing mechanism. This process, in principle, applies to any quantum system interacting with a thermal bath of phonons, advancing our understanding of quantum decoherence in solid-state systems.
The coordination complexes of Yb(III) exhibit some of the longest spin coherence times among 4f compounds, making them a promising platform for molecular quantum technologies. While spin-phonon relaxation remains a limiting factor for coherence times even at low temperature, its control through chemical design has the potential to push these spin qubits prototypes beyond current limits. With the aim of providing insights on how to chemically control spin-phonon relaxation, we here present a full ab initio study of spin-phonon dynamics for three Yb(III) molecules exhibiting minimal chemical differences, yet quantitatively different spin relaxation times. Results show that low-temperature relaxation is governed by Raman processes triggered by a small group of largely delocalized low-energy phonons. The analysis of these contributions highlights that the modulation of spin-phonon coupling by molecular structure modifications beyond the first coordination shell are highly non-trivial in nature and hard to rationalize in simple chemical terms. These findings call for a conceptual step change from the attempt to use simple magneto-structural correlations to interpret the effect of molecular structural modifications on spin-phonon relaxation, and present predictive first-principles frameworks as a potential driving force of future chemical design strategies
Molecular magnets are ideal systems to probe the realm that borders quantum and classical physics, as well as to study decoherence phenomena in nanoscale systems. The control of the quantum behavior of these materials and their structural characteristics requires synthesis of new complexes with desirable properties which will allow probing of the fundamental aspects of nanoscale physics and quantum information processing. Of particular interest among the magnetic molecular materials are single-molecule magnets (SMMs) and antiferromagnetic (AFM) molecular wheels in which the spin state of the molecule is known to behave quantum mechanically at low temperatures. In previous experiments the dynamics of the magnetic moment of the molecules is governed by incoherent quantum tunneling. Short decoherence times are mainly due to interactions between molecular magnets within the crystal and interactions of the electronic spin with the nuclear spin of neighboring ions within the molecule. This decoherence problem has imposed a limit to the understanding of the molecular spin dynamics and the sources of decoherence in condensed matter systems. Particularly, intermolecular dipolar interactions within the crystal, which shorten the coherence times in concentrated samples, have stymied progress in this direction. Several recent works have reported a direct measurement of the decoherence time in molecular magnets. This has been done by eliminating the dephasing created by dipolar interactions between neighboring molecules. This has been achieved by a) a dilution of the molecules in a liquid solution to decrease the dipolar interaction by separating the molecules, and b) by polarizing the spin bath by applying a high magnetic field at low temperatures. Unfortunately, both approaches restrict the experimental studies of quantum dynamics. For example, the dilution of molecular magnets in liquid solution causes a dispersion of the molecular spin orientation and anisotropy axes, while the large fields required to polarize the spin bath overcome the anisotropy of the molecular spin. In this thesis I have explored two methods to overcome dipolar interactions in molecular magnets: a) studying the dynamics of molecular magnets in single crystals where the separation between magnetic molecules is obtained by chemical doping or where the high crystalline quality allows observations intrinsic to the quantum mechanical nature of the tunneling of the spin, and b) studying the electronic transport through an individual magnetic molecule which has been carefully placed in a single-electron transistor device. I have used EPR microstrip resonators to measure Fe17Ga molecular wheels within single crystals of Fe18 AFM wheels, as well as demonstrating, for the first time in a Single Molecule Magnet, the complete suppression of a Quantum Tunneling of the Magnetization transition forbidden by molecular symmetry.
We use ab initio electronic-structure methods to investigate random-matrix theory (RMT) universality in molecular electronic structure. Using single-reference electronic structure methods, including Hartree-Fock, configuration-interaction singles (CIS), density functional theory, and linear-response time-dependent density-functional theory, we compute single-particle orbital energies and many-electron excitations of several representative molecules (benzene, alanine, 1-phenylethylamine, methyloxirane, and helicene chains). For generic low-symmetry geometries, the unfolded spectra of these ab initio Hamiltonians exhibit Wigner-Dyson level statistics of the Gaussian orthogonal ensemble (GOE). For extended helicene chains we explicitly restrict to bound valence excitations below the ionization threshold and still observe GOE statistics, indicating that the RMT universality is present for physical states of direct relevance to real molecules. We further explore the electric and magnetic field dependence of the molecular electronic spectra. The variance of electric polarizability (level curvature K) is predicted to be non-analytic in the magnetic field which serves as an infrared cutoff, <K^2> proportional to log(1/|B|). We observe a transition to the Gaussian unitary ensemble (GUE) by increasing the magnetic fields, although it occurs only at magnetic fields far beyond experimentally accessible scales. Our results indicate that random matrix universality provides a general framework for organizing ab initio predictions of interacting electron spectra in complex systems.
With single-molecule magnets research on the rise as a result of recent advantages in the field, like remarkable high blocking temperatures up to 60 Kelvin [Nature, 548, 439, 2017], gigantic coercivity up to 80 Tesla [Nat Commun., 10, 571, 2019], magnetization stability in the thin films, further applications are seriously in the scope. The possible venue here is to develop a theory of magnetic moment manipulation and control at the microscopic level. Theory of optimal control in quantum dynamics in complex systems is well-developed. For example, the uses of density matrix techniques have been well summarized already in the early ‘60s by Fano, Haar, and many others. Thus, in many respects, the task is to reframe that research into the language of the problem at hand, and into familiar terms for the community. Recently, it was already proven the Redfield reduced density matrix techniques are applicable for slow-relaxing single-molecule magnets [Nat Commun., 8, 14620, 2017]. In our recent contribution[PCCP,20, 11656, 2018], we have outlined the use of Lindblad dynamics in combination with a few axioms in the rationalization of the relaxation behavior of single-molecule magnets. In this report we put this approach in the context of the magentodynamics theory, showing the close connection to the Landau-Lifshitz-Gilbert model and presenting further elaboration for the proposed method.
With single-molecule magnets research on the rise as a result of recent advantages in the field, like remarkable high blocking temperatures up to 60 Kelvin [Nature, 548, 439, 2017], gigantic coercivity up to 80 Tesla [Nat Commun., 10, 571, 2019], magnetization stability in the thin films, further applications are seriously in the scope. The possible venue here is to develop a theory of magnetic moment manipulation and control at the microscopic level. Theory of optimal control in quantum dynamics in complex systems is well-developed. For example, the uses of density matrix techniques have been well summarized already in the early ‘60s by Fano, Haar, and many others. Thus, in many respects, the task is to reframe that research into the language of the problem at hand, and into familiar terms for the community. Recently, it was already proven the Redfield reduced density matrix techniques are applicable for slow-relaxing single-molecule magnets [Nat Commun., 8, 14620, 2017]. In our recent contribution[PCCP,20, 11656, 2018], we have outlined the use of Lindblad dynamics in combination with a few axioms in the rationalization of the relaxation behavior of single-molecule magnets. In this report we put this approach in the context of the magentodynamics theory, showing the close connection to the Landau-Lifshitz-Gilbert model and presenting further elaboration for the proposed method.