120
4 Tunnelling Magnetoresistance (TMR)
4.4.2 Effect of Magnetic Excitations on the MR
Up to this point of discussion, we have only considered the elastic tunnelling process
that does not lead to creation or absorption of excitations at the junction. This is an
oversimplified assumption, since in this case different kinds of interactions between
quasiparticles were not considered. However, in realistic scenario, there are a number
of inelastic processes feasible in a junction. Such inelastic processes can of course
influence MR.
An evident signature of inelastic process is their distinctive temperature dependences. Increase in temperature means more available thermal energy, k B T, i.e., an
increased number of excitations in the system. An alternative way to provide energy
to a junction is through the applied voltage to the system. In case of applied bias,
the associated energy scale is eV. Therefore, it comes out that the contribution to the
conductance of inelastic processes scales in the similar manner with temperature or
voltage.
4.4.3 Effect of Magnetic Properties of the Interface on MR
Recalling the very basic features of interfaces, it can be stated that atoms at the
interfaces of a given junction are surrounded by an environment that is significantly
different from that at the bulk of each electrode. Consequently, this may lead to
the change in the magnetic structure of the interface (Mattis 1988). Indeed, the
characterization of the interfacial magnetic properties is pretty difficult. Also, no
unique formulation can offer solution to the problem. A simple estimation of the
changes of the interfacial magnetic structure can be done by analysing a semi-infinite
chain of ferromagnetically coupled spins. For instance, reduction in the number of
nearest neighbours causes a shift of the density of magnetic excitations towards lower
energies. Thus, at low temperatures the spins at the surface undergo more fluctuations
compared to than in the bulk. Such fluctuations at the interface is detrimental to MR.
Additionally, the surface excitations can also mediate spin-flip processes and thereby
may cause decrease in MR of the junction.
4.4.4 Effect of Charging in Granular Systems on MR
In case of magnetic granular systems, metallic junctions mainly determine its transport properties. MR of such magnetic grains is usually determined by the tunnelling
of conduction electrons across the interfaces between neighbouring grains or grain
boundaries. Now, addition of one electron charge in a given grain increase its charge
and thereby causes change in its electrostatic energy, which is approximately equal
to [e
2 /(εR)], where R is the average radius of the grain and ε the dielectric constant
4 Tunnelling Magnetoresistance (TMR)
4.4.2 Effect of Magnetic Excitations on the MR
Up to this point of discussion, we have only considered the elastic tunnelling process
that does not lead to creation or absorption of excitations at the junction. This is an
oversimplified assumption, since in this case different kinds of interactions between
quasiparticles were not considered. However, in realistic scenario, there are a number
of inelastic processes feasible in a junction. Such inelastic processes can of course
influence MR.
An evident signature of inelastic process is their distinctive temperature dependences. Increase in temperature means more available thermal energy, k B T, i.e., an
increased number of excitations in the system. An alternative way to provide energy
to a junction is through the applied voltage to the system. In case of applied bias,
the associated energy scale is eV. Therefore, it comes out that the contribution to the
conductance of inelastic processes scales in the similar manner with temperature or
voltage.
4.4.3 Effect of Magnetic Properties of the Interface on MR
Recalling the very basic features of interfaces, it can be stated that atoms at the
interfaces of a given junction are surrounded by an environment that is significantly
different from that at the bulk of each electrode. Consequently, this may lead to
the change in the magnetic structure of the interface (Mattis 1988). Indeed, the
characterization of the interfacial magnetic properties is pretty difficult. Also, no
unique formulation can offer solution to the problem. A simple estimation of the
changes of the interfacial magnetic structure can be done by analysing a semi-infinite
chain of ferromagnetically coupled spins. For instance, reduction in the number of
nearest neighbours causes a shift of the density of magnetic excitations towards lower
energies. Thus, at low temperatures the spins at the surface undergo more fluctuations
compared to than in the bulk. Such fluctuations at the interface is detrimental to MR.
Additionally, the surface excitations can also mediate spin-flip processes and thereby
may cause decrease in MR of the junction.
4.4.4 Effect of Charging in Granular Systems on MR
In case of magnetic granular systems, metallic junctions mainly determine its transport properties. MR of such magnetic grains is usually determined by the tunnelling
of conduction electrons across the interfaces between neighbouring grains or grain
boundaries. Now, addition of one electron charge in a given grain increase its charge
and thereby causes change in its electrostatic energy, which is approximately equal
to [e
2 /(εR)], where R is the average radius of the grain and ε the dielectric constant