268
M. Becherer
(more generally a universal threshold gate) was theoretically predicted by Papp et al.
in [31] and experimentally demonstrated by Breitkreutz et al. in [17]. It demonstrates
the very efficient implementation of complex boolean functions in pNML, as in terms
of magnet counts it is the most compact design: only 5 magnets for 3 inputs and 2
outputs are deployed.
In order to control the signal flow in DW conductors, two gate magnets close to a
constriction are applied in the DW gate of Breitkreutz et al. in [32] and Breitkreutz
et al. in [33]. By applying two DW gates in series, the structure is extended to
a device similar to latches in conventional CMOS, which is an essential building
block for data processing and synchronization. This is a very important finding, as
it highlights that the nonvolatile computing state of a ferromagnet not automatically
results in integrated memory devices.
2.4 Foundations for Digital Computation
The preceding section introduced the concept of digital computation in pNML
together with experimental demonstration of the basic pNML building blocks. At
this point it is adequate to raise the question, if the demonstrated pNML devices
fulfill all prerequisites for digital computation. For that, the well known 5 tenets for
digital computation systems [34] are adapted for pNML as follows:
1. Nonlinear device characteristics. Nonlinear hysteresis of the nanomagnetic
switching, i.e. nucleation event, overcoming an energy barrier, rapid DW motion.
The switching is first blocked by an energy barrier due to a step in magnetic
anisotropy at the edges of the ANC. Suddenly, when overcoming the barrier, the
magnetization of an island is reversed by a domain wall spreading out.
2. Enable functionally complete Boolean logic set. The majority gate [16] or threshold majority gate [17] fulfill this. With this device, NAND/NOR and hence inverters as well as all other functions can be implemented. However, we argue, that
also latching behavior (integrated memory of non-volatile type) together with
complex functions like the demonstrated full-adder shall be exploited for area,
time and power efficient circuits and architectures.
3. Power amplification (gain). An external magnetic field together with nonlinear switching provides the energy. Ferromagnetism itself is an ensemble effect,
refreshing the computing state due to exchange energy (magnetic spins tend to
align in the same direction) [30]. Compared to electronic switches, magnetic states
stabilize each other, and for switching, only tens of k B T are needed. By contrast,
each electron in an electronic switch dissipates thousands of k B T .
4. Output of one device must drive another, fan-out. This is realized by fork like
branching of DW conductors (elongated magnets, stripes) [25]. Proper design of
the fork-like structures are necessary in order not to pin a domain wall at the
slits/notches, especially when switching at low fields and on short time-scales.
M. Becherer
(more generally a universal threshold gate) was theoretically predicted by Papp et al.
in [31] and experimentally demonstrated by Breitkreutz et al. in [17]. It demonstrates
the very efficient implementation of complex boolean functions in pNML, as in terms
of magnet counts it is the most compact design: only 5 magnets for 3 inputs and 2
outputs are deployed.
In order to control the signal flow in DW conductors, two gate magnets close to a
constriction are applied in the DW gate of Breitkreutz et al. in [32] and Breitkreutz
et al. in [33]. By applying two DW gates in series, the structure is extended to
a device similar to latches in conventional CMOS, which is an essential building
block for data processing and synchronization. This is a very important finding, as
it highlights that the nonvolatile computing state of a ferromagnet not automatically
results in integrated memory devices.
2.4 Foundations for Digital Computation
The preceding section introduced the concept of digital computation in pNML
together with experimental demonstration of the basic pNML building blocks. At
this point it is adequate to raise the question, if the demonstrated pNML devices
fulfill all prerequisites for digital computation. For that, the well known 5 tenets for
digital computation systems [34] are adapted for pNML as follows:
1. Nonlinear device characteristics. Nonlinear hysteresis of the nanomagnetic
switching, i.e. nucleation event, overcoming an energy barrier, rapid DW motion.
The switching is first blocked by an energy barrier due to a step in magnetic
anisotropy at the edges of the ANC. Suddenly, when overcoming the barrier, the
magnetization of an island is reversed by a domain wall spreading out.
2. Enable functionally complete Boolean logic set. The majority gate [16] or threshold majority gate [17] fulfill this. With this device, NAND/NOR and hence inverters as well as all other functions can be implemented. However, we argue, that
also latching behavior (integrated memory of non-volatile type) together with
complex functions like the demonstrated full-adder shall be exploited for area,
time and power efficient circuits and architectures.
3. Power amplification (gain). An external magnetic field together with nonlinear switching provides the energy. Ferromagnetism itself is an ensemble effect,
refreshing the computing state due to exchange energy (magnetic spins tend to
align in the same direction) [30]. Compared to electronic switches, magnetic states
stabilize each other, and for switching, only tens of k B T are needed. By contrast,
each electron in an electronic switch dissipates thousands of k B T .
4. Output of one device must drive another, fan-out. This is realized by fork like
branching of DW conductors (elongated magnets, stripes) [25]. Proper design of
the fork-like structures are necessary in order not to pin a domain wall at the
slits/notches, especially when switching at low fields and on short time-scales.