2.3 Spin Generation and Injection
31
2.3.5 Discussion of Spin Injection Process in Two Cases
In this direction, we will discuss spin injection process in two distinctively different
cases of electron transfer through interface: (i) from a ferromagnetic (FM) material
to a non-magnetic (NM) one, and (ii) from one ferromagnetic material (FM1) to
another ferromagnetic FM (FM2) material.
(i) Spin injection from a ferromagnetic (FM) to a non-magnetic (NM) material
In order to assess the spin injection process from a ferromagnetic to a nonmagnetic/paramagnetic material through an interfacial barrier, the associated spin
injection efficiency (η) can be calculated using the following equation:
η =
r F P σ F + r i P σ i + r N P σ N
r F + r N + r i
(2.7)
where P σ F , P σ N and P σ i are the conductivity polarizations of the bulk ferromagnet,
bulk paramagnet and that of their interface, respectively (Zutic et al. 2004). η is
calculated as a weighted average of P σ F , P σ i and P σ N and the weights are proportional
to the corresponding resistances. Effective resistance of the bulk ferromagnet, bulk
paramagnet and the interface between them are denoted by r F, r N and r i , respectively.
It should be noted that it is the characteristics of charge injection from the ferromagnet
that decide P σ i . Obviously, P σ N = 0 as per definition. Thus, Eq. (2.7) reduces to
η =
r F P σ F + r i P σ i
r F + r N + r i
(2.8)
The quantity η gives us a measure how efficiently, as the name suggests, spins are
getting injected into the non-magnetic/paramagnetic material from the ferromagnetic one. Now, we will discuss the diversified cases based on the above-mentioned
expression of η.
Case (i): Ohmic contact between metallic ferromagnetic and paramagnetic
material
It can be understood that in this case, r i = 0 and r F ≈ r N , thus yielding η ≈ P σ F . As
generally P σ F is recognized to be high, it thus implies significant spin injection in
this case. In fact, experimental observation of spin injection has indeed been obtained
almost in all-metal structures (Jedema et al. 2001).
Case (ii): Ohmic contact between metallic ferromagnetic and paramagnetic
semiconductor: conductivity mismatch problem
It can be understood that in this case, r i = 0 and r F r N , thus yielding η
P σ F , i.e., poor injection of spin. This in turn implies that spin injection process
does not take place efficiently from a metallic ferromagnetic to a semiconducting
paramagnetic material through an Ohmic contact. This phenomenon is known as
31
2.3.5 Discussion of Spin Injection Process in Two Cases
In this direction, we will discuss spin injection process in two distinctively different
cases of electron transfer through interface: (i) from a ferromagnetic (FM) material
to a non-magnetic (NM) one, and (ii) from one ferromagnetic material (FM1) to
another ferromagnetic FM (FM2) material.
(i) Spin injection from a ferromagnetic (FM) to a non-magnetic (NM) material
In order to assess the spin injection process from a ferromagnetic to a nonmagnetic/paramagnetic material through an interfacial barrier, the associated spin
injection efficiency (η) can be calculated using the following equation:
η =
r F P σ F + r i P σ i + r N P σ N
r F + r N + r i
(2.7)
where P σ F , P σ N and P σ i are the conductivity polarizations of the bulk ferromagnet,
bulk paramagnet and that of their interface, respectively (Zutic et al. 2004). η is
calculated as a weighted average of P σ F , P σ i and P σ N and the weights are proportional
to the corresponding resistances. Effective resistance of the bulk ferromagnet, bulk
paramagnet and the interface between them are denoted by r F, r N and r i , respectively.
It should be noted that it is the characteristics of charge injection from the ferromagnet
that decide P σ i . Obviously, P σ N = 0 as per definition. Thus, Eq. (2.7) reduces to
η =
r F P σ F + r i P σ i
r F + r N + r i
(2.8)
The quantity η gives us a measure how efficiently, as the name suggests, spins are
getting injected into the non-magnetic/paramagnetic material from the ferromagnetic one. Now, we will discuss the diversified cases based on the above-mentioned
expression of η.
Case (i): Ohmic contact between metallic ferromagnetic and paramagnetic
material
It can be understood that in this case, r i = 0 and r F ≈ r N , thus yielding η ≈ P σ F . As
generally P σ F is recognized to be high, it thus implies significant spin injection in
this case. In fact, experimental observation of spin injection has indeed been obtained
almost in all-metal structures (Jedema et al. 2001).
Case (ii): Ohmic contact between metallic ferromagnetic and paramagnetic
semiconductor: conductivity mismatch problem
It can be understood that in this case, r i = 0 and r F r N , thus yielding η
P σ F , i.e., poor injection of spin. This in turn implies that spin injection process
does not take place efficiently from a metallic ferromagnetic to a semiconducting
paramagnetic material through an Ohmic contact. This phenomenon is known as