9.6 Complexes with K 5 L COO
11.1.2 SQUID Magnetometry
The magnetic susceptibility measurements in this work (temperature dependence as well as variable temperature variable field (VTVH) measurements) were recorded via SQUID (Superconducting Quantum Interference Device) magnetometry. The magnetic susceptibil-ity describes a dependency of the magnetizationM of a sample from an external magnetic field H. SQUID magnetometer are sensitive enough to measure extremely subtle electro-magnetic fields (5×10–15T) and are hence well suited to examine the magnetization of very low amounts of a magnetic material.[226]. A central component of a SQUID magne-tometer is a superconducting loop with a so-calledweak link. The closed superconducting loop is often made of a niobium alloy. Superconducting materials such as these alloys ex-hibit a complete lack of electrical resistance below a certain transition temperature. The superconducting loop however is interrupted at one position/junction and the supercon-ducting material is replaced by an insulator.[227] The size of this "gap" usually lies in the range of a few nanometers. This junction (superconductor-insulator-superconductor) is more commonly known asJosephson junction. The barrier (Josephson junction) for the electric current in the superconducting material can be overcome by the tunneling (Cooper electron pairs) of electrons. A small tunneling current can be detected. If a small external magnetic field is applied to a superconducting loop, a screening current starts circulating through the loop, compensating the external flux, also known as theMeissner effect.[227]
This is flux is quantized and can only be described by integer multiples of the magnetic flux quantum. The tunneling current within the Josephson junction is very sensitive to the applied external field. Small variations of the magnetic field can lead to a temporarily collapse of the superconducting current, which can be detected. The measurement of a sample in a SQUID magnetometer is realized only indirectly. The sample is moved through a system of superconducting detection coils, which are connected to the superconduction ring (SQUID) with superconducting wires. The detection coils couple inductively with the SQUID sensor. Hence the magnetic moment of the sample induces an electric cur-rent in the detection coils at a given temperature which is passed on to the SQUID and detected.[227] As the sample moves through the coils the magnetic dipole moment of the sample induces an electric current in the detection coils. The SQUID functions as a highly linear current-to-voltage converter, so that variations in the current of the detection coil circuit produce corresponding variations in the SQUID output voltage as a function of the direction of the sample movement and its position with respect to the coil.[228] A basic setup of a SQUID magnetometer and the respective output signal are depicted in Figure 11.1.
The output signal can be transformed to obtain a value for the magnetization M of the sample at an applied magnetic fieldH at a given temperature.[230]
M=χV·H (11.1)
The volume magnetic susceptibility of the sample resembles the proportionality factor betweenM and H and describes the response of the sample to the applied magnetic field.
The volume magnetic susceptibility is a dimensionless figure and can be converted to a molar magnetic susceptibility according to[231]:
−
Figure 11.1: Left: Setup of a SQUID magnetometer with one Josephson junction. The sample is moved along the z-axis, parallel to the applied magnetic field. Right: Output signal detected by the SQUID. Respective potential in dependency of the position of the sample within the detection coils.[229]
χm=χV·V
n[cm3/mol] (11.2)
The temperature dependence of the molar magnetic susceptibility in 3d metals can usually be described by the Curie law in its spin only form assuming that the orbital angular momentum for these metals is close to zero.[230–232]
χm= NA
The Curie constant C is can be derived from quantum mechanical considerations via the van Vleck equation[230], which includes the Eigenvalues and Eigenfunctions from pertur-bation theory and will not be discussed in detail in this respect.
Generally, for the evaluation of a SQUID experiment it should be noted that the measured susceptibility contains three main contributions which are
χ=χpara+χdia+χTIP (11.4)
In this respect χdia describes diamagnetic temperature independent contributions which result from the experimental setup whereasχTIPis a pure orbital momentum effect. Hence, measurements are usually corrected for these two contributions.
The molar magnetic susceptibility is moreover closely related to the effective magnetic moment µeff. Its relation with the magnetic susceptibility for spin only systems can be described by the following equation[230,232,233]:
µeff
To describe magnetism in polynuclear molecular compounds, which do not behave according to the idealized model of a paramagnet the magnetic coupling of paramagnetic centers has to be considered. In this respect the intramolecular exchange coupling via superexchange plays a most important role.
The intramolecular exchange coupling of paramagnetic centers for isotropic exchange can be described phenomenologically by the Heisenberg-Dirac-van-Vleck-Hamiltonian. For a system of two magnetic centers with a spin S the Hamiltonian could be described as[230,231]:
Hˆ = –2JSˆ1ˆS2 (11.6) In this context J describes the coupling constant of the two magnetic iron centers. The magnitude ofJis important for the evaluation whether the two iron sites are ferromagneti-cally or antiferromagnetiferromagneti-cally coupled. For ferromagnetiferromagneti-cally coupled centers the magnetic spins of both iron sites point in the same direction (J> 0), whereas for antiferromagnet-ically coupled centers the magnetic spins point in opposite directions (J < 0). For the evaluation of the measured data further effects were included in the Hamiltonian such as zerofield and Zeeman splitting so that the full Hamiltonian can be described as follows:
Hˆ =Hˆexc+HˆZFS+HˆZeem (11.7) Mechanistically, the intramolecular exchange coupling can occur direct via the spin orbitals of two metal sites in very close proximity or indirect via orbitals of a bridg-ing ligand, which is often referred to as superexchange.[234] Different concepts were developed to qualitatively explain the superexchange mediated by bridging ligand orbitals.[230,232] An important parameter that describes the exchange coupling in this respect is the overlap integral of two magnetic orbitals. If the overlap integral is zero, the magnetic orbitals of the two magnetic centers as well as the orbitals of the bridging ligand are orthogonal to each other and a ferromagnetic interaction can be expected.
For overlap integrals between zero and one, a partial or full overlap of the magnetic orbitals can be expected. Hence these magnetic centers interact antiferromagnetically.[235]
For the investigated pyrazolate bridged dinuclear iron complexes in this work typically weak antiferromagnetic coupling is experimentally observed. Individual overlap integrals were not calculated for the investigated complexes.