Electric Field-Controlled Magnetic Anisotropy …
21
by PMA in a much wider range of N e than in the strong exchange interaction case
(Fig. 3a).
Comparing (29) and (30), it appears that the Fermi sea term can be enhanced
by reducing the k-dependent spin splitting, |b(k)|, which follows from weakening
J , so that the interband contribution has a larger amplitude than the intraband one.
However, near N e = 0 (likewise near N e = 2), the intraband contribution is linear
in N e while the interband one is quadratic, so that the former can overtake the latter,
and thus favors IMA. The MAE from the band energy difference between M||x
and M||z and its decomposition (Fig. 3b) exhibits half of the difference in the SOC
energy that overlaps with the net internal energy difference. The energetic competition between the Rashba SOC and the coupling to the ferromagnetic background is
settled differently when either only one or when both bands are partially filled, due
to an allowed transfer of electronic occupation between the two bands at the Fermi
sea.
In the third case where the exchange energy is compared to the SOC strength
(J = t
), the splitting between the two bands is small. The intraband and interband
contributions to the susceptibility are almost identical leading to a small net value of
the MAE.
6 Conclusions
The pulse-field manipulation by magnetic properties of multilayer magnetic nanostructures is based on an excitation of the coherent electron spin polarization coupled
by the exchange interaction with localized magnetic states and heat-induced demagnetization. The impact of the pulse laser field on magnetic states can occur directly
via the effective bias field of the inverse Faraday magneto-optic effect or indirectly
via the laser-induced heat demagnetization with subsequent action of the effective
bias field. The controlled impact of the strong enough laser field on the magnetic
nanostructures with an antiferromagnetic exchange interaction occur due to the effective bias fields caused by the different time of the heat demagnetization of magnetic
sublattices and the relaxation of the antiferromagnetic exchange interaction.
The electric field control can occur via the spin polarization of an electric
current under the ferromagnetic exchange interaction in ferromagnetic layers and
its exchange interaction with the localized magnetic states. In multilayer magnetic
nanostructures with the spin Hall effect, the electric field control occurs via a spin–
orbit-induced conversion of the electric current to the spin current coupled with the
localized magnetic states by the exchange interaction.
The pure electric field can control the magnetic anisotropy in the magnetic nanostructures, with the Rashba spin–orbit interaction, by the external gate voltage applied
across a dielectric layer. In this case, the connection of the electric field with the
localized magnetic states occurs via the exchange interaction of polarized itinerant
electrons with the localized magnetic states. The corresponding mechanism of the
21
by PMA in a much wider range of N e than in the strong exchange interaction case
(Fig. 3a).
Comparing (29) and (30), it appears that the Fermi sea term can be enhanced
by reducing the k-dependent spin splitting, |b(k)|, which follows from weakening
J , so that the interband contribution has a larger amplitude than the intraband one.
However, near N e = 0 (likewise near N e = 2), the intraband contribution is linear
in N e while the interband one is quadratic, so that the former can overtake the latter,
and thus favors IMA. The MAE from the band energy difference between M||x
and M||z and its decomposition (Fig. 3b) exhibits half of the difference in the SOC
energy that overlaps with the net internal energy difference. The energetic competition between the Rashba SOC and the coupling to the ferromagnetic background is
settled differently when either only one or when both bands are partially filled, due
to an allowed transfer of electronic occupation between the two bands at the Fermi
sea.
In the third case where the exchange energy is compared to the SOC strength
(J = t
), the splitting between the two bands is small. The intraband and interband
contributions to the susceptibility are almost identical leading to a small net value of
the MAE.
6 Conclusions
The pulse-field manipulation by magnetic properties of multilayer magnetic nanostructures is based on an excitation of the coherent electron spin polarization coupled
by the exchange interaction with localized magnetic states and heat-induced demagnetization. The impact of the pulse laser field on magnetic states can occur directly
via the effective bias field of the inverse Faraday magneto-optic effect or indirectly
via the laser-induced heat demagnetization with subsequent action of the effective
bias field. The controlled impact of the strong enough laser field on the magnetic
nanostructures with an antiferromagnetic exchange interaction occur due to the effective bias fields caused by the different time of the heat demagnetization of magnetic
sublattices and the relaxation of the antiferromagnetic exchange interaction.
The electric field control can occur via the spin polarization of an electric
current under the ferromagnetic exchange interaction in ferromagnetic layers and
its exchange interaction with the localized magnetic states. In multilayer magnetic
nanostructures with the spin Hall effect, the electric field control occurs via a spin–
orbit-induced conversion of the electric current to the spin current coupled with the
localized magnetic states by the exchange interaction.
The pure electric field can control the magnetic anisotropy in the magnetic nanostructures, with the Rashba spin–orbit interaction, by the external gate voltage applied
across a dielectric layer. In this case, the connection of the electric field with the
localized magnetic states occurs via the exchange interaction of polarized itinerant
electrons with the localized magnetic states. The corresponding mechanism of the