Modeling Magnetic Anisotropy of Single Chain Magnets in ∣d/J∣≥1|d/J| \geq 1 Regime

Single molecule magnets (SMMs) with single-ion anisotropies $\mathbf d$, comparable to exchange interactions J, between spins have recently been synthesized. In this paper, we provide theoretical insights into the magnetism of such systems. We study spin chains with site spins, s=1, 3/2 and 2 and on-site anisotropy $\mathbf d$ comparable to the exchange constants between the spins. We find that large $\mathbf d$ leads to crossing of the states with different $M_S$ values in the same spin manifold of the $\mathbf d = 0$ limit. For very large $\mathbf d$'s we also find that the $M_S$ states of the higher energy spin states descend below the $M_S$ states of the ground state spin manifold. Total spin in this limit is no longer conserved and describing the molecular anisotropy by the constants $D_M$ and $E_M$ is not possible. However, the total spin of the low-lying large $M_S$ states is very nearly an integer and using this spin value it is possible to construct an effective spin Hamiltonian and compute the molecular magnetic anisotropy constants $D_M$ and $E_M$. We report effect of finite sizes, rotations of site anisotropies and chain dimerization on the effective anisotropy of the spin chains

Modeling Molecular Magnets with Large Exchange and On-Site Anisotropies

Spins in molecular magnets can experience both anisotropic exchange interactions and on-site magnetic anisotropy. In this paper we study the effect of exchange anisotropy on the molecular magnetic anisotropy both with and without on-site anisotropy. When both the anisotropies are small, we find that the axial anisotropy parameter $D_M$ in the effective spin Hamiltonian is the sum of the individual contributions due to exchange and on-site anisotropies. We find that even for axial anisotropy of about $15\%$, the low energy spectrum does not correspond to a single parent spin manifold but has intruders states arising from other parent spin. In this case, the low energy spectrum can not be described by an effective Hamiltonian spanning the parent spin space. We study the magnetic susceptibility, specific heat as a function of temperature and magnetization as a function of applied field to characterize the system in this limit. We find that there is synergy between the two anisotropies, particularly for large systems with higher site spins.Comment: 30 pages, 11 figures and 3 tables. Supporting information included after the main articl

Computing magnetic anisotropy constants of single molecule magnets

We present here a theoretical approach to compute the molecular magnetic anisotropy parameters, DM and EM for single molecule magnets in any given spin eigenstate of exchange spin Hamiltonian. We first describe a hybrid constant MS-valence bond (VB) technique of solving spin Hamiltonians employing full spatial and spin symmetry adaptation and we illustrate this technique by solving the exchange Hamiltonian of the Cu6Fe8 system. Treating the anisotropy Hamiltonian as perturbation, we compute the DM and EM values for various eigenstates of the exchange Hamiltonian. Since, the dipolar contribution to the magnetic anisotropy is negligibly small, we calculate the molecular anisotropy from the single-ion anisotropies of the metal centers. We have studied the variation of DM and EM by rotating the single-ion anisotropies in the case of Mn12Ac and Fe8 SMMs in ground and few low-lying excited states of the exchange Hamiltonian. In both the systems, we find that the molecular anisotropy changes drastically when the single-ion anisotropies are rotated. While in Mn12Ac SMM DM values depend strongly on the spin of the eigenstate, it is almost independent of the spin of the eigenstate in Fe8 SMM. We also find that the DM value is almost insensitive to the orientation of the anisotropy of the core Mn(IV) ions. The dependence of DM on the energy gap between the ground and the excited states in both the systems has also been studied by using different sets of exchange constants

A Kinetic Model for Photoswitching of magnetism in the High Spin Molecule [Mo(IV)(CN)2(CN-Cu(II)(tren))6](ClO4)8

The heptanuclear complex [Mo(IV)(CN)2(CN-CuL)6]8+ exhibits photomagnetism. An earlier microscopic model showed that the transition dipole moments for excitation in different spin manifolds are similar in magnitude. In this paper, we attribute photomagnetism to the long lived S=3 charge transfer excited state for which there appears to be sufficient experimental evidence. We model the photomagnetism by employing a kinetic model which includes internal conversions and intersystem crossings. The key feature of the model is assumption of the existence of two kinds of S=3 states: one which has no direct pathway for internal conversion and the other characterized by slow kinetics for internal conversion to the low-energy states. The trapped S=3 state can decay via a thermally activated barrier to the other S=3 state. The experimental temperature dependence of magnetization plot is fitted using rate constants with Arrhenius dependence. The two different experimental cMT vs. T curves obtained with different irradiation times are fitted with our model. Our studies show that the photomagnetism in these systems is governed by kinetics and not due to differences in oscillator strengths for excitation of the different spin states.Comment: 17 pages including 5 figures. Submitted to Phys. Rev.

Microscopic Model for Photoinduced Magnetism in the Molecular Complex [Mo(IV)(CN)2(CN−CuL)6]8+[Mo(IV)(CN)_2(CN-CuL)_6]^{8+} Perchlorate

A theoretical model for understanding photomagnetism in the heptanuclear complex $[Mo(IV)(CN)_2(CN-CuL)_6]^{8+}$ perchlorate is developed. It is a many-body model involving the active orbitals on the transition metal ions. The model is exactly solved using a valence bond approach. The ground state solution of the model is highly degenerate and is spanned by five S=0 states, nine S=1 states, five S=2 states and one S=3 state. The orbital occupancies in all these states correspond to six $Cu(II)$ ions and one diamagnetic $Mo(IV)$ ion. The optically excited charge-transfer (CT) state in each spin sector occur at nearly the same excitation energy of 2.993 eV for the physically reasonable parameter values. The degeneracy of the CT states is largest in the S=3 sector and so is the transition dipole moment from the ground state to these excited states. Thus laser irradiation with light of this energy results in most intense absorption in the S=3 sector. The life-time of the S=3 excited states is also expected to be the largest as the number of states below that energy is very sparse in this spin sector when compared to other spin sectors. These twin features of our model explain the observed photomagnetism in the $[Mo(IV)(CN)_2(CN-CuL)_6]^{8+}$ complex.Comment: 8 pages, 6 figures and 1 tabl

Microscopic Model for High-spin vs. Low-spin ground state in [Ni2M(CN)8][Ni_2{M(CN)_8]} (M=MoV,WV,NbIVM=Mo^V, W^V, Nb^{IV}) magnetic clusters

Conventional superexchange rules predict ferromagnetic exchange interaction between Ni(II) and M (M=Mo(V), W(V), Nb(IV)). Recent experiments show that in some systems this superexchange is antiferromagnetic. To understand this feature, in this paper we develop a microscopic model for Ni(II)-M systems and solve it exactly using a valence bond approach. We identify the direct exchange coupling, the splitting of the magnetic orbitals and the inter-orbital electron repulsions, on the M site as the parameters which control the ground state spin of various clusters of the Ni(II)-M system. We present quantum phase diagrams which delineate the high-spin and low-spin ground states in the parameter space. We fit the spin gap to a spin Hamiltonian and extract the effective exchange constant within the experimentally observed range, for reasonable parameter values. We also find a region in the parameter space where an intermediate spin state is the ground state. These results indicate that the spin spectrum of the microscopic model cannot be reproduced by a simple Heisenberg exchange Hamiltonian.Comment: 8 pages including 7 figure

A Theoretical Approach for Computing Magnetic Anisotropy in Single Molecule Magnets

We present a theoretical approach to calculate the molecular magnetic anisotropy parameters, $D_M$ and $E_M$ for single molecule magnets in any eigenstate of the exchange Hamiltonian, treating the anisotropy Hamiltonian as a perturbation. Neglecting inter-site dipolar interactions, we calculate molecular magnetic anisotropy in a given total spin state from the known single-ion anisotropies of the transition metal centers. The method is applied to $Mn_{12}Ac$ and $Fe_8$ in their ground and first few excited eigenstates, as an illustration. We have also studied the effect of orientation of local anisotropies on the molecular anisotropy in various eigenstates of the exchange Hamiltonian. We find that, in case of $Mn_{12}Ac$, the molecular anisotropy depends strongly on the orientation of the local anisotropies and the spin of the state. The $D_M$ value of $Mn_{12}Ac$ is almost independent of the orientation of the local anisotropy of the core $Mn(IV)$ ions. In the case of $Fe_8$, the dependence of molecular anisotropy on the spin of the state in question is weaker.Comment: 8 pages, 12 figures, 2 table

Novel structural parameters of Ig -Ag complexes yield a quantitative description of interaction specificity and binding affinity

Antibody-antigen complexes challenge our understanding, as analyses to datefailed to unveil the key determinants of binding affinity and interaction specificity. We par-tially fill this gap based on novel quantitative analyses using two standardized databases, theIMGT/3Dstructure-DB and the structure affinity benchmark.First, we introduce a statistical analysis of interfaces which enables the classification of ligand types(protein, peptide, chemical; cross-validated classification error of 9.6%), and yield binding affinitypredictions of unprecedented accuracy (median absolute error of 0.878 kcal/mol). Second, weexploit the contributions made by CDRs in terms of position at the interface and atomic packingproperties to show that in general, VH CDR3 and VL CDR3 make dominant contributions tothe binding affinity, a fact also shown to be consistent with the enthalpy - entropy compensationassociated with pre-configuration of CDR3.Our work suggests that the affinity prediction problem could be solved from databases of highresolution crystal structures of complexes with known affinity

Theoretical approach for computing magnetic anisotropy in single molecule magnets

We present a theoretical approach to calculate the molecular magnetic anisotropy parameters, $D_{M}$ and $E_M$ for single molecule magnets in any eigenstate of the exchange Hamiltonian, treating the anisotropy Hamiltonian as a perturbation. Neglecting intersite dipolar interactions, we calculate molecular magnetic anisotropy in a given total spin state from the known single-ion anisotropies of the transition metal centers. The method is applied to $Mn_{12}Ac$ and $Fe_8$ in their ground and first few excited eigenstates, as an illustration. We have also studied the effect of orientation of local anisotropies on the molecular anisotropy in various eigenstates of the exchange Hamiltonian. We find that, in case of $Mn_{12}Ac$, the molecular anisotropy depends strongly on the orientation of the local anisotropies and the spin of the state. The $D_M$ value of $Mn_{12}Ac$ is almost independent of the orientation of the local anisotropy of the core Mn(IV) ions. In the case of $Fe_8$, the dependence of molecular anisotropy on the spin of the state in question is weaker. We have also calculated the anisotropy constants for several sets of exchange parameters and found that in $Mn_{12}Ac$ the anisotropy increases with spin excitation gap, while in $Fe_{8}$, the anisotropy is almost independent of the gap