Transition metal ions with long-lived spin states represent the minimum size magnetic bit. Here, the authors study the spin–lattice relaxation of a cobalt(II) complex and demonstrate the role of time-reversal symmetry that hinders direct spin–phonon processes regardless of the sign of the magnetic anisotropy.

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Origin of slow magnetic relaxation in Kramers ions with non-uniaxial anisotropy

Lanthanide-based single-molecule magnets are leading materials for achieving magnetization blocking at the level of one molecule. In this paper, we examine the physical requirements for efficient magnetization blocking in single-ion complexes and identify the design principles for achieving very high magnetization blocking barriers in lanthanide-based compounds. The key condition is the preponderant covalent binding of the Ln ion to one of the ligand atoms, tremendously enhancing the axial crystal field. We also make an overview of practical schemes for the implementation of this principle. These are (1) the effective lowering of the coordination number via displacement of the Ln ion to one of the atoms in the coordination polyhedron, (2) the design of two-coordinated complexes, and (3) the stabilization of diatomic compounds in cages and on surfaces. The last proposal is appealing in connection to spintronics applications, especially via the exploration of robust and highly anisotropic [LnX] units displaying multilevel blocking barriers of thousands of Kelvin and prospects for room-temperature magnetization blocking.

Strategies toward High-Temperature Lanthanide-Based Single-Molecule Magnets.

The key characteristic of single-molecule magnets (SMMs) is the anisotropy-induced blocking barrier, which should be as efficient as possible, i.e., to be able to provide long magnetic relaxation times at elevated temperatures. The strategy for the design of efficient SMMs on the basis of transition-metal complexes such as Mn12Ac is well established, which is not the case of complexes involving strongly anisotropic metal ions such as cobalt(II) and lanthanides (Ln). While strong intraionic anisotropy in the latter allows them to block the magnetization already in mononuclear complexes, the presence of several such ions in a complex does not result automatically in more efficient SMMs. Here, the magnetic blocking in the series of isostructural 3d–4f complexes CoII–LnIII–CoII, Ln = Gd, Tb, and Dy, is analyzed using an originally developed ab initio based approach for the investigation of blocking barriers. The theoretical analysis allows one to explain the counterintuitive result that the Co–Gd–Co complex i...

Interplay of strongly anisotropic metal ions in magnetic blocking of complexes.

We report a detailed analysis of the Drude weights for both thermal and spin transport in one-dimensional spin-$\frac{1}{2}$ systems by means of exact diagonalization and analytic approaches at finite temperatures. Transport properties are studied first for the integrable $\mathrm{XXZ}$ model and second for various nonintegrable systems such as the dimerized chain, the frustrated chain, and the spin ladder. We compare our results obtained by exact diagonalization and mean-field theory with those of the Bethe ansatz, bosonization, and other numerical studies in the case of the anisotropic Heisenberg model both in the gapless and gapped regime. In particular, we find indications that the Drude weight for spin transport is finite in the thermodynamic limit for the isotropic chain. For the nonintegrable models, a finite-size analysis of the numerical data for the Drude weights is presented, covering the entire parameter space of the dimerized and frustrated chain. We also discuss which conclusions can be drawn from bosonization regarding the question of whether the Drude weights are finite or not. One of our main results is that the Drude weights vanish in the thermodynamic limit for nonintegrable models.

https://arxiv.org/pdf/cond-mat/0304595.pdf

Zero-frequency transport properties of one-dimensional spin- 1 2 systems

Magnetic light scattering in low-dimensional quantum spin systems

Bound states made from two triplet excitations on the Shastry-Sutherland lattice are investigated. Based on the perturbative unitary transformation by flow equations quantitative properties like dispersions and qualitative properties like symmetries are determined. The high order results [up to (J2/J1)(14)] permit one to fix the parameters of SrCu2(BO3)(2) precisely: J1 = 6.16(10) meV, x J2/J1 = 0.603(3), J( perpendicular) = 1.3(2) meV. At the border of the magnetic Brillouin zone a general double degeneracy is derived. An unexpected instability in the triplet channel at x = 0.63 indicates a transition towards another phase. The possible nature of this phase is discussed.

Dispersion and symmetry of bound states in the shastry-sutherland model

We investigate the anti-adiabatic limit of an anti-ferromagnetic S = 1/2 Heisenberg chain coupled to Einstein phonons. The flow equation method is used to decouple the spin and the phonon part of the Hamiltonian. In the effective spin model long range spin-spin interactions are generated. We determine the phase transition from a gapless state to a gapped (dimerized) phase, which occurs at a non-zero value of the spin-phonon coupling. In the effective phonon sector a phonon hardening is observed.

Effective spin models for spin-phonon chains by flow equations

A computer aided high temperature expansion of the magnetic susceptibility and the magnetic specific heat is presented and demonstrated for frustrated and unfrustrated spin chains. The results are analytic in nature since the calculations are performed in the integer domain. They are provided in the form of polynomials allowing quick and easy fits. Various representations of the results are discussed. Combining high temperature expansion coefficients and dispersion data yields very good agreement already in low order of the expansion which makes this approach very promising for the application to other problems, for instance in higher dimensions.

High temperature expansion for frustrated and unfrustrated S=1/2 spin chains

By high-temperature series expansion, exact diagonalization, and temperature density-matrix renormalization the magnetic susceptibility $\ensuremath{\chi}(T)$ and the specific heat $C(T)$ of dimerized and frustrated $S=1/2$ chains are computed. All three methods yield reliable results, in particular, for not too small temperatures or not too small gaps. The series-expansion results are provided in the form of polynomials allowing very fast and convenient fits in data analysis using algebraic programs. We discuss the difficulty to extract more than two coupling constants from the temperature dependence of $\ensuremath{\chi}(T).$

Thermodynamic properties of the dimerized and frustrated S = 1 / 2 chain

By high-temperature series expansion and exact complete diagonalization the magnetic susceptibility $\ensuremath{\chi}(T)$ and the specific heat $C(T)$ of a two-leg $S=1/2$ ladder with cyclic (four-spin) exchange are computed. Both methods yield convincing results for not too small temperatures. We find that a small amount of cyclic exchange influences the thermodynamic properties significantly. Our results can serve as reliable basis for an efficient analysis of experimental data.

Alexander Bühler

Papers

Dispersion and symmetry of bound states in the shastry-sutherland model

Effective spin models for spin-phonon chains by flow equations

High temperature expansion for frustrated and unfrustrated S=1/2 spin chains

Thermodynamic properties of the dimerized and frustrated S = 1 / 2 chain

Thermodynamic Properties of Spin Ladders with Cyclic Exchange