Tarifas actuales de los acueductos estudiados

This forms M3+_-F-Cu2+_-F-M3+_{chains, which run in all three dimensions. Superexchange}

interactions have been well documented to occur in fluorides55 and it is reasonable to

expect that magnetic coupling via the superexchange mechanism can occur in this

system. The Goodenough-Kanamori-Anderson (GKA) Rules55 provide a set of semi-

quantitative guidelines for determining the type of magnetic interactions present in a system with magnetic coupling via superexchange. According to the GKA rules, strong antiferromagnetic coupling is to be expected when magnetic ions are bonded at 180° apart. This antiferromagnetic interaction is weakened as the bond angles deviate from

180°, opening up the potential for other interactions to prevail. Compound 2.1 contains

V3+ and Cu2+, possessing 2 and 1 unpaired electrons, respectively. No magnetic ordering

is observed in this compound, although there is very slight deviation from Curie-Weiss behavior below 10 K, which accounts for the slightly negative Weiss temperature.

Compound 2.2 also does not display magnetic ordering; in fact it is a model paramagnet.

The Weiss temperature of 2.2 is nearly exactly 0 K, exemplifying its Curie-Weiss

behavior through 2 K. The calculated spin-only magnetic moments agree well with the observed magnetic moment, attained from the Curie-Weiss fit of the inverse magnetic susceptibility data.

Figure 2.8: UV-Visible Spectra for Compounds 2.1-2.6. The normalized UV/Visible

spectra for compounds 2.1-2.6. All compounds show an absorption edge at low

wavelength, a M3+ specific d-d absorption, and an absorption corresponding to Cu2+. Table 1.4 details these absorbances.

Table 2.4: UV-Vis Band Assignments for Compounds 2.1-2.6 Compound Band Gap UV/vis Peak and Assignment

1 3.48 eV λmax = 426, 264 nm 3T1g3T2g, 3T1g3T1g (3P)

2 3.51 eV λmax = 439 nm 4A2g4T2g

3 3.49 eV λmax = 496 nm 5Eg5T2g

4 3.41 eV None No Spin-Allowed Transitions

5 3.43 eV λmax = 426 nm 3T1g3T2g

Figure 2.9: Magnetic Susceptibility Data for Compounds 2.1-2.6. The magnetic

susceptibility and inverse magnetic susceptibility of materials 2.1-2.6. Both the field

cooled and zero-field cooled data is shown, and overlay perfectly for all materials except

2.3, which shows slight field dependence at 2 K.

Table 2.5: Curie-Weiss Constants for Compounds 2.1-2.6 Compound 1 2 3 4 5 6

μeff (μB/F.U.) 4.88 6.39 7.78 8.95 7.43 8.17

μcalc* (μB/F.U.) 5.00 6.24 7.55 8.89 7.21 7.80

θ -6.7 K -0.6 K -2.2 K 2.3 K -2.7 -0.9 K

Figure 2.10: Magnetization Data for Compounds 2.1-2.6. The magnetization plots for

materials 2.1-2.6. Five quadrant measurements were performed at 2 K for all reported

Compound 2.3, which contains Mn3+, exhibits more complicated magnetic behavior. It has been observed that magnetically coupled ions can undergo a cooperative

Jahn-Teller effect56. This cooperative effect may be ferrodistortive, which results in

antiferromagnetic coupling, or antiferrodistortive, which in turn leads to ferromagnetic coupling. Ferrodistortive ordering occurs between two Jahn-Teller ions where the elongated (axial) axis of one ion is bonded to the non-elongated (equatorial) axis of the other ion. Since the Mn3+ _{ions are bonded to Cu}2+ _{ions through a fluoride bridge (both of}

which exhibit a strong Jahn-Teller effect), this cooperative distortive effect is expected.

In fact, 2.3 exhibits ferrodistortive ordering, consisting of the elongated Cu-F bonds

being connected to the short Mn-F bonds, shown in Figure 2.11. Compound 3 displays

Curie-Weiss behavior above ~10 K, and deviates significantly from Curie-Weiss behavior at temperatures below 10 K. At ~5.8 K there is a ferromagnetic deviation, followed by a sharper antiferromagnetic deviation at 3.8 K. The magnetic susceptibility

and inverse susceptibility are shown in Figure 2.12. The paper by Nunez et al46 provides

an in depth analysis of the magnetism of this sample, however in our sample, consisting of ground crystals, we do not observe the spontaneous magnetization they report below 4 K. Instead, the FC and ZFC data agree perfectly down to 2 K, and no hysteresis is observed, even at 2 K. Figure 2.13 shows the magnetization plot. It is likely that the magnetic ordering is due to antiferromagnetic interactions. This notion is strengthened by the fact that the Mn3+ and Cu2+ Jahn-Teller ions are arranged in a ferrodistortive manner, which is expected to lead to antiferromagnetic ordering, suggesting that the observed magnetization is due to a canted antiferromagnetic spin alignment. Despite the ferrodistortive ordering of the crystal structure, there is a clear ferromagnetic-like

Figure 2.11: Ferrodistortive Ordering in 2.3. A view down the b crystallographic axis showing ferrodistortive ordering. Ferrodistortive ordering occurs between two Jahn- Teller ions where elongated (axial) axis of one is bonded to the non-elongated (equatorial) axis of the other. Manganese is shown as purple octahedra, copper is shown as blue octahedra, oxygen is shown in red, fluorine in bright green, and hydrogens have been omitted for clarity.

Figure 2.12: Low Temperature Susceptibility of 2.3. The magnetic susceptibility and

inverse susceptibility data for 2.3. Data was collected in a ZFC measurement with a 0.1 T

applied field. The temperature range is 2 K to 50 K to highlight the low temperature magnetic transitions at ~8 K and 3.8 K. Magnetic transitions can be clearly seen in the inverse susceptibility (red).

Figure 2.13: Magnetization of 2.3. The magnetization plot for compound 3. The applied field swept from -5 T – 5 T, and the measurements were taken at 2 K. The magnetization plot shows ordering corresponding to a sharp jump in magnetization at low fields. There is no hysteresis, indicating an antiferromagnetic ordering. Above the ordering, there is a linear dependence with field that does not saturate, even at 5 T.

Figure 2.14: Low Temperature Susceptibility of 2.4 The magnetic susceptibility and

inverse susceptibility plot of 2.4. Data was collected in a ZFC measurement with a 0.1 T

applied magnetic field. Data is shown in the range of 2 K – 50 K to highlight the antiferromagnetic transition at ~3.8 K.

transition ~9 K, which can be seen in Figure 2.12. As canted spins are likely for Mn3+ and

Cu2+ _{based on the Mn-F-Cu bond angles of ~124°, we suppose that this is due to a canted}

antiferromagnetic ordering of the spins. The magnetic susceptibility plot for compound

2.4 is shown in Figure 2.14. Fe3+ is not a Jahn-Teller ion and so the cooperative effect is