8 Magnetism,Structure and Interactions at the Atomic Scale 165 The trimers have two non-equivalent sites(C-center,E,E'-edge positions). Ferromagnetic states of the trimers,either low spin(LSF)or high spin(HSF) states,have parallel moments at the sites C and E,E,but the moments have different sign at C and E,E'in the antiferromagnetic state(AF).The atoms at the edge positions (E,E')have the same moment (MEME)for LSF, HSF and AF states.Another possible magnetic state,which is compatible with the chemical symmetry of the system is an antisymmetric (AS)one. The magnetic moment at the central atom of the trimer is zero and the moments at the edge positions have different sign (ME=-ME). We concentrate our discussion on the multiplicity of magnetic states to V and Mn.For the single V adatom only a high spin state with a moment of 3.0 uB is obtained.For the V2 dimer we find both a ferromagnetic and an antiferromagnetic state with moments of 2.85 and 2.58 uB respectively.The antiferromagnetic state has the lowest energy being about 0.2 eV/atom lower than the ferromagnetic one. The magnetic moments for all the different magnetic states of the V and Mn trimers are summarized in Table 8.2.All the magnetic states have a lower total energy than the paramagnetic state.The AF state is the ground state of the V trimer.The energy difference between the AF and LSF state in V is about 8 meV/atom.The LSF state is more stable than the HSF state.The ground state of the Mn trimer is also the antiferromagnetic state. The energy difference between the ground state and the HSF state is only 2 meV/atom.This energy difference corresponds to a temperature difference of 25 K.A transition between the two states caused by temperature changes or an external field leads to a change of the total moment of the Mn trimer of 7.8 uB.Such a strong change of the total moment,controlled by an external parameter opens a new field for an experimental proof of the theoretical results. Table 8.2.Magnetic moments (in uB)for the atoms of the trimers V3 and Mng onCu(001). V3 Mns state Me Mc ME ME Mc ME' HSF2.852.582.854.033.834.03 LSF 2.631.412.634.040.014.04 AF 2.63-2.022.633.99-3.883.99 AS 2.620.00-2.623.980.00-3.98 We have shown,that metamagnetic behaviour exists in supported clus- ters.It is shown,that the energy differences between different magnetic states can be small,which can lead to a change of the magnetic state of the cluster by an external parameter.The energy differences between different magnetic8 Magnetism, Structure and Interactions at the Atomic Scale 165 The trimers have two non-equivalent sites (C - center, E, E - edge positions). Ferromagnetic states of the trimers, either low spin (LSF) or high spin (HSF) states, have parallel moments at the sites C and E, E , but the moments have different sign at C and E, E in the antiferromagnetic state (AF). The atoms at the edge positions (E, E ) have the same moment (ME = ME
) for LSF, HSF and AF states. Another possible magnetic state, which is compatible with the chemical symmetry of the system is an antisymmetric (AS) one. The magnetic moment at the central atom of the trimer is zero and the moments at the edge positions have different sign (ME = −ME
). We concentrate our discussion on the multiplicity of magnetic states to V and Mn. For the single V adatom only a high spin state with a moment of 3.0 µB is obtained. For the V2 dimer we find both a ferromagnetic and an antiferromagnetic state with moments of 2.85 and 2.58 µB respectively. The antiferromagnetic state has the lowest energy being about 0.2 eV/atom lower than the ferromagnetic one. The magnetic moments for all the different magnetic states of the V and Mn trimers are summarized in Table 8.2. All the magnetic states have a lower total energy than the paramagnetic state. The AF state is the ground state of the V trimer. The energy difference between the AF and LSF state in V is about 8 meV/atom. The LSF state is more stable than the HSF state. The ground state of the Mn trimer is also the antiferromagnetic state. The energy difference between the ground state and the HSF state is only 2 meV/atom. This energy difference corresponds to a temperature difference of 25 K. A transition between the two states caused by temperature changes or an external field leads to a change of the total moment of the Mn trimer of 7.8 µB. Such a strong change of the total moment, controlled by an external parameter opens a new field for an experimental proof of the theoretical results. Table 8.2. Magnetic moments (in µB) for the atoms of the trimers V3 and Mn3 on Cu(001). V3 Mn3 state ME MC ME
ME MC ME
HSF 2.85 2.58 2.85 4.03 3.83 4.03 LSF 2.63 1.41 2.63 4.04 0.01 4.04 AF 2.63 -2.02 2.63 3.99 -3.88 3.99 AS 2.62 0.00 -2.62 3.98 0.00 -3.98 We have shown, that metamagnetic behaviour exists in supported clus￾ters. It is shown, that the energy differences between different magnetic states can be small, which can lead to a change of the magnetic state of the cluster by an external parameter. The energy differences between different magnetic