Spin Transfer Torque Magnetoresistive Random Access Memory
73
Another novel development is the abandonment of interfacial efforts entirely and
instead focused on shape anisotropy effect to induce magnetization in the out-of-plane
direction. High TMR and high thermal stability is achieved even with diameters less
than 7 nm, which could provide further scaling down to the 1× node and beyond [175,
176]. This would however, lead to very high aspect ratio of the free layer section and
subsequently the pMTJ stack, which may lead to additional integration challenges.
6 Experimental Techniques
6.1 Ferromagnetic Resonance Spectroscopy
The concept of ferromagnetic resonance (FMR) was first experimentally observed
in the 1946 by Griffiths [177] and subsequently theorized by Kittel [178], similar
to other nuclear resonance phenomena such as electron paramagnetic resonance and
nuclear magnetic resonance [179]. Under an external applied magnetic field, the
magnetic moment that arises from the orbital and spin angular momentum precess
at a particular frequency proportional to its gyromagnetic ratio. For the case of
ferromagnetic materials, additional intrinsic contributions, such as magneocrystalline
anisotropy or demagnetization energy, are to be considered in addition to the Zeeman
effect due to the external magnetic field, summing up to form an effective field H eff .
A resonance effect occurs when the precessing moment is subjected to an alternating
field of the same frequency, typically in the microwave range for ferromagnetic
materials as the gyromagnetic ratio is in the order of GHz per Tesla. An absorption
spectrum of the Lorentzian form is observed as the microwave is absorbed during
the process.
In spin wave resonance, FMR is a unique phenomenon where the spins precess
uniformly at the same phase, i.e. the wave vector k = 0 [180]. The collection of spins
is considered to be a single entity (i.e. macrospin approximation), and therefore can
be derived from the Landau-Lifshitz-Gilbert (LLG) equation. The following example
draws its solution laid out by Bilzer [181], but examines the case of a thin film with
PMA. The conditions set for the material of interest has an OOP easy axis along the
z-axis. Assuming that a strong external magnetic field H ext is applied in the z-axis that
aligns all magnetic moments to achieve saturation magnetization M s , the addition
of a small alternating field h ac in the x-axis (through an AC microwave source) will
perturb the magnetization M, which can be expressed as:
M = M s m ≈ m x ˆ
x + m y ˆ
y + M s ˆ
z,
(40)
where ˆ
x, ˆ
y and ˆ
z are unit vectors in Cartesian form. H eff is further defined as
H e f f = h ac ˆ
x + (H ext − M e f f )ˆ z
(41)
73
Another novel development is the abandonment of interfacial efforts entirely and
instead focused on shape anisotropy effect to induce magnetization in the out-of-plane
direction. High TMR and high thermal stability is achieved even with diameters less
than 7 nm, which could provide further scaling down to the 1× node and beyond [175,
176]. This would however, lead to very high aspect ratio of the free layer section and
subsequently the pMTJ stack, which may lead to additional integration challenges.
6 Experimental Techniques
6.1 Ferromagnetic Resonance Spectroscopy
The concept of ferromagnetic resonance (FMR) was first experimentally observed
in the 1946 by Griffiths [177] and subsequently theorized by Kittel [178], similar
to other nuclear resonance phenomena such as electron paramagnetic resonance and
nuclear magnetic resonance [179]. Under an external applied magnetic field, the
magnetic moment that arises from the orbital and spin angular momentum precess
at a particular frequency proportional to its gyromagnetic ratio. For the case of
ferromagnetic materials, additional intrinsic contributions, such as magneocrystalline
anisotropy or demagnetization energy, are to be considered in addition to the Zeeman
effect due to the external magnetic field, summing up to form an effective field H eff .
A resonance effect occurs when the precessing moment is subjected to an alternating
field of the same frequency, typically in the microwave range for ferromagnetic
materials as the gyromagnetic ratio is in the order of GHz per Tesla. An absorption
spectrum of the Lorentzian form is observed as the microwave is absorbed during
the process.
In spin wave resonance, FMR is a unique phenomenon where the spins precess
uniformly at the same phase, i.e. the wave vector k = 0 [180]. The collection of spins
is considered to be a single entity (i.e. macrospin approximation), and therefore can
be derived from the Landau-Lifshitz-Gilbert (LLG) equation. The following example
draws its solution laid out by Bilzer [181], but examines the case of a thin film with
PMA. The conditions set for the material of interest has an OOP easy axis along the
z-axis. Assuming that a strong external magnetic field H ext is applied in the z-axis that
aligns all magnetic moments to achieve saturation magnetization M s , the addition
of a small alternating field h ac in the x-axis (through an AC microwave source) will
perturb the magnetization M, which can be expressed as:
M = M s m ≈ m x ˆ
x + m y ˆ
y + M s ˆ
z,
(40)
where ˆ
x, ˆ
y and ˆ
z are unit vectors in Cartesian form. H eff is further defined as
H e f f = h ac ˆ
x + (H ext − M e f f )ˆ z
(41)