Magnetic bodies interact with each other through magnetic dipolar fields that depend on the instantaneous magnetization vectors of the coupled magnetic bodies in a system. Previous studies have shown that reliable, deterministic coupling can be achieved in identical two-magnet systems and is a function of the longitudinal and perpendicular components of the dipolar field. In this work, we extend previous work significantly by developing analytic models that map the regions of dipolar field driven magnetization reversal of a non-identical two-magnet system. Models are obtained for mono-domain magnetic bodies with biaxial magnetic anisotropy. The analytic models presented map the necessary requirements for a deterministically coupled two-magnet system. In these deterministic, stable reversals, the two-magnet system stabilizes in an anti-parallel configuration along the natural free-axis of the system, regardless of thermal effects. However, non-deterministic reversals can also occur in certain non-identical systems. These pseudo-reversals occur because only one of the nanomagnets meets the critical field requirements. In this case, the system reversal is a result of thermal drift and therefore complex function system parameters and observation time. We also note that multi-magnet systems may find steady-state orientations away from the free-axis if the perpendicular components of the dipolar field are too large. We present models which accurately map the field magnitudes which result in these meta-stable reversals. Lastly, models to interpret the impact of dipolar coupling on the critical current requirement for spin-transfer-torque driven magnetization switching are also presented in this manuscript. This work greatly expands our understanding of the complex-field interaction in multi-magnet systems and is crucial when evaluating complex magnetic devices.

1.
S.
Datta
,
S.
Salahuddin
, and
B.
Behin-Aein
, “
Non-volatile spin switch for boolean and non-boolean logic
,”
Appl. Phys. Lett.
101
,
252411
(
2012
).
2.
R.
Cowburn
and
M.
Welland
, “
Room temperature magnetic quantum cellular automata
,”
Science
287
,
1466
1468
(
2000
).
3.
A.
Imre
,
G.
Csaba
,
L.
Ji
,
A.
Orlov
,
G.
Bernstein
, and
W.
Porod
, “
Majority logic gate for magnetic quantum-dot cellular automata
,”
Science
311
,
205
208
(
2006
).
4.
F. M.
Spedalieri
,
A. P.
Jacob
,
D. E.
Nikonov
, and
V. P.
Roychowdhury
, “
Performance of magnetic quantum cellular automata and limitations due to thermal noise
,”
IEEE Trans. Nanotechnol.
10
,
537
546
(
2011
).
5.
D.
Nikonov
and
I.
Young
, “
Benchmarking of beyond-CMOS exploratory devices for logic integrated circuits
,”
IEEE J. Explor. Solid-State Comput. Devices Circuits
1
,
3
11
(
2015
).
6.
S.
Chikazumi
and
C. D.
Graham
,
Physics of Ferromagnetism 2e
(
Oxford University Press
,
2009
), Vol.
94
.
7.
I. D.
Mayergoyz
,
G.
Bertotti
, and
C.
Serpico
,
Nonlinear Magnetization Dynamics in Nanosystems
(
Elsevier
,
2009
).
8.
G.
Bertotti
,
C.
Serpico
, and
I.
Mayergoyz
, “
Probabilistic aspects of magnetization relaxation in single-domain nanomagnets
,”
Phys. Rev. Lett.
110
,
147205
(
2013
).
9.
W. T.
Coffey
and
Y. P.
Kalmykov
, “
Thermal fluctuations of magnetic nanoparticles: Fifty years after brown
,”
J. Appl. Phys.
112
,
121301
(
2012
).
10.
N.
Kani
,
S.
Dutta
, and
A.
Naeemi
, “
Analysis of coupling strength in multi-domain magneto-systems
,” in
2015 73rd Annual Device Research Conference (DRC)
(IEEE,
2015
), pp.
111
112
.
11.
N.
Kani
and
A.
Naeemi
, “
Analytical models for coupling reliability in identical two-magnet systems during slow reversals
,”
J. Appl. Phys.
122
,
223902
(
2017
).
12.
J. C.
Slonczewski
, “
Current-driven excitation of magnetic multilayers
,”
J. Magn. Magn. Mater.
159
,
L1
L7
(
1996
).
13.
L. D.
Landau
and
E.
Lifshitz
, “
On the theory of the dispersion of magnetic permeability in ferromagnetic bodies
,”
Phys. Z. Sowjetunion
8
,
101
114
(
1935
).
14.
T. L.
Gilbert
, “
A phenomenological theory of damping in ferromagnetic materials
,”
IEEE Trans. Magn.
40
,
3443
3449
(
2004
).
15.
L.
Berger
, “
Emission of spin waves by a magnetic multilayer traversed by a current
,”
Phys. Rev. B
54
,
9353
(
1996
).
16.
M.
Stiles
and
J.
Miltat
, “
Spin transfer torque and dynamics
,” in
Spin Dynamics in Confined Magnetic Structures III
(
Spinger
,
2006
), pp.
225
308
.
17.
R.
Engel-Herbert
and
T.
Hesjedal
, “
Calculation of the magnetic stray field of a uniaxial magnetic domain
,”
J. Appl. Phys.
97
,
074504
(
2005
).
18.
N.
Kani
,
S.-C.
Chang
,
S.
Dutta
, and
A.
Naeemi
, “
A model study of an error-free magnetization reversal through dipolar coupling in a two-magnet system
,”
IEEE Trans. Magn.
52
(2),
1
12
(
2016
).
19.
S.
Ament
,
N.
Rangarajan
, and
S.
Rakheja
, “
A practical guide to solving the stochastic Landau-Lifshitz-Gilbert-Slonczewski equation for macrospin dynamics
,” preprint arXiv:1607.04596 (
2016
).
20.
M.
Donahue
and
D.
Porter
, “
OOMMF user's guide, version 1.0
,”
Interagency Report No. NISTIR 6376
, National Institute of Standards and Technology, Gaithersburg, MD,
1999
.
21.
H.
Liu
,
D.
Bedau
,
J.
Sun
,
S.
Mangin
,
E.
Fullerton
,
J.
Katine
, and
A.
Kent
, “
Dynamics of spin torque switching in all-perpendicular spin valve nanopillars
,”
J. Magn. Magn. Mater.
358
,
233
258
(
2014
).
22.
G.
Bertotti
,
I. D.
Mayergoyz
,
M.
d'Aquino
,
S.
Perna
, and
C.
Serpico
, “
Phase-flow interpretation of magnetization relaxation in nanomagnets
,”
IEEE Trans. Magn.
50
,
1
4
(
2014
).
23.
J.
Sun
, “
Spin-current interaction with a monodomain magnetic body: A model study
,”
Phys. Rev. B
62
,
570
(
2000
).
24.
D.
Pinna
,
A. D.
Kent
, and
D. L.
Stein
, “
Thermally assisted spin-transfer torque dynamics in energy space
,”
Phys. Rev. B
88
,
104405
(
2013
).
25.
N.
Kani
, “
Modeling of magnetization dynamics and applications to spin-based logic and memory devices
,” Ph.D. thesis,
Georgia Institute of Technology
,
2017
.
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