A. Fernandez-pacheco, R. Streubel, O. Fruchart, R. Hertel, P. Fischer et al., Three-dimensional nanomagnetism, Nature Communications, vol.87, p.15756, 2017.
DOI : 10.1103/PhysRevB.87.144401

URL : https://hal.archives-ouvertes.fr/hal-01536109

A. Mourachkine, Nano Lett, vol.8, p.11, 2008.

X. Kou, Memory Effect in Magnetic Nanowire Arrays, Advanced Materials, vol.44, issue.11, p.1393, 2011.
DOI : 10.1109/TMAG.2008.2001814

M. F. Contreras, Int. J. Nanomedicine, vol.10, p.2141, 2015.

K. Pitzschel, J. Bachmann, S. Martens, J. M. Montero-moreno, J. Kimling et al.,

K. Escrig, D. Nielsch, and . Görlitz, J. Appl. Phys, vol.109, p.33907, 2011.

S. Da-col, M. Darques, O. Fruchart, and L. Cagnon, Reduction of magnetostatic interactions in self-organized arrays of nickel nanowires using atomic layer deposition, Applied Physics Letters, vol.98, issue.11, p.112501, 2011.
DOI : 10.1063/1.2928202

URL : https://hal.archives-ouvertes.fr/hal-00553589

S. S. Parkin, Science, vol.320, issue.190, 2008.

A. Berganza, C. Bran, M. Jaafar, M. Vazquez, and A. , Domain wall pinning in FeCoCu bamboo-like nanowires, Scientific Reports, vol.114, issue.1, p.29702, 2016.
DOI : 10.1063/1.4816479

S. Da-col, S. Jamet, M. Stano, B. Trapp, S. Le-denmat et al.,

. Fruchart, Appl. Phys. Lett, vol.109, p.62406, 2016.

M. Yan, A. Kákay, S. Gliga, and R. Hertel, Beating the Walker Limit with Massless Domain Walls in Cylindrical Nanowires, Physical Review Letters, vol.3, issue.5, p.57201, 2010.
DOI : 10.1103/PhysRevB.79.094402

S. Moretti, V. Raposo, E. Martinez, and L. Lopez-diaz, Domain wall motion by localized temperature gradients, Physical Review B, vol.95, issue.6, p.64419, 2017.
DOI : 10.1063/1.335644

E. Berganza, M. Jaafar, C. Bran, and J. A. Fernández-roldán,

A. Vázquez, . Asenjo, . Sci, and . Rep, , p.11576, 2017.

N. Biziere, R. L. Ballier, M. C. Clochard, M. Viret, T. L. Wade et al.,

. Wegrowe, J. Appl. Phys, vol.110, p.63906, 2011.

A. S. Esmaeily, M. Venkatesan, A. S. Razavian, and J. M. Coey, J. Appl. Phys, vol.113, pp.17-327, 2013.

O. Iglesias-freire, C. Bran, and E. Berganza,

N. Asenjo, , 2015.

E. M. Palmero, C. Bran, R. P. Del-real, and M. Vázquez, Synthesis and magnetism of modulated FeCo-based nanowires, Journal of Physics: Conference Series, vol.755, p.12001, 2016.
DOI : 10.1088/1742-6596/755/1/012001

V. Mohanan, P. , and P. S. Kumar, Chirality dependent pinning and depinning of magnetic vortex domain walls at nano-constrictions, Journal of Magnetism and Magnetic Materials, vol.422, p.419, 2017.
DOI : 10.1016/j.jmmm.2016.09.004

P. Bruno, Geometrically Constrained Magnetic Wall, Physical Review Letters, vol.78, issue.12, p.2425, 1999.
DOI : 10.1103/PhysRevLett.78.3773

S. Allende, D. Altbir, and K. Nielsch, Magnetic cylindrical nanowires with single modulated diameter, Physical Review B, vol.22, issue.17, p.174402, 2009.
DOI : 10.1038/nmat931

S. Allende and R. Arias, Transverse domain wall propagation in modulated cylindrical nanostructures and possible geometric control, Physical Review B, vol.83, issue.17, p.174452, 2011.
DOI : 10.1063/1.3466747

M. Franchin, A. Knittel, M. Albert, D. Chernyshenko, and T. Fischbacher,

. Fangohr, Phys. Rev. B, vol.84, p.94409, 2011.

M. Sturma, J. Toussaint, and D. Gusakova, Geometry effects on magnetization dynamics in circular cross-section wires, Journal of Applied Physics, vol.117, issue.24, p.243901, 2015.
DOI : 10.1063/1.4891276

URL : https://hal.archives-ouvertes.fr/cea-01745409

L. C. Arzuza, R. Lopez-ruiz, D. Salazar-aravena, M. Knobel, F. Beron et al., , p.309, 2017.

F. Alouge, E. Kritsikis, J. Steiner, and J. Toussaint, A convergent and precise finite element scheme for Landau???Lifschitz???Gilbert equation, Numerische Mathematik, vol.2, issue.1, p.407, 2014.
DOI : 10.1007/BF03167039

A. Hubert, R. Schäfer, and M. Domains, , 1998.

A. Thiaville and Y. Nakatani, Nanomagnetism and Spintronics, 2009.

A. A. Thiele, Steady-State Motion of Magnetic Domains, Physical Review Letters, vol.29, issue.6, p.230, 1973.
DOI : 10.1103/PhysRevLett.29.1679

, The so-called dynamical Thiele's domain wall width definition is obtained for the stationary domain wall displacement without changing its profile along the invariable crosssection wire axis. It reads ? ? = 2 " / X c/c# , where S is the cross-section surface and the expression is

R. , Computational micromagnetism of magnetization processes in nickel nanowires, Journal of Magnetism and Magnetic Materials, vol.249, issue.1-2, p.251, 2002.
DOI : 10.1016/S0304-8853(02)00539-5

S. Jamet, N. Rougemaille, J. Toussaint, and O. Fuchart, Magnetic Nano-and Microwires : Design, synthesis, 2015.

A. Thiaville and Y. Nakatani, Dynamics in Confined Magnetic Structures III, Topics Applied Physics, vol.106, p.161, 2006.

Y. Nakatani, A. Thiaville, and J. Miltat, Faster magnetic walls in rough wires, Nature Materials, vol.35, issue.2, pp.521-537, 2003.
DOI : 10.1143/JJAP.35.6065

E. Martines, L. Lopez-diaz, L. Torres, C. Tristan, and O. , Thermal effects in domain wall motion: Micromagnetic simulations and analytical model, Physical Review B, vol.242, issue.245, p.174409, 2007.
DOI : 10.1063/1.367113

A. Mougin, M. Cormier, J. P. Adam, P. Metaxas, and J. Ferré, Domain wall mobility, stability and Walker breakdown in magnetic nanowires, Europhysics Letters (EPL), vol.78, issue.5, p.57007, 2007.
DOI : 10.1209/0295-5075/78/57007

URL : https://hal.archives-ouvertes.fr/hal-00267331

B. Krüger, The interaction of transverse domain walls, Journal of Physics: Condensed Matter, vol.24, issue.2, p.24209, 2012.
DOI : 10.1088/0953-8984/24/2/024209

C. A. Ferguson, D. A. Maclaren, S. Mcvitie, and J. Magn, Metastable magnetic domain walls in cylindrical nanowires, Journal of Magnetism and Magnetic Materials, vol.381, p.457, 2015.
DOI : 10.1016/j.jmmm.2015.01.027

R. Hertel, A. Kakay, and J. Magn, Analytic form of transverse head-to-head domain walls in thin cylindrical wires, Journal of Magnetism and Magnetic Materials, vol.379, p.45, 2015.
DOI : 10.1016/j.jmmm.2014.11.073

E. Durand, E. Et-magnétostatique, and C. Masson, , 1953.

, ? is estimated by comparing the slopes of the circlebased wire profile used in numerical simulations and of the analytical tanh-based profile close to the modulation center

, For the gently sloping modulation with ? ? this expression reduces to 4? ?

, 316 the relative error made by tahn-based shape approximation is less than 10%, which is suitable for a large range of modulation sizes In the extreme cases of very abrupt diameter transition the disagreement between circle-based and tanh-based modulation shapes is more pronounced. Nevertheless this mismatch is largely overtopped by such model imperfection as, for example, the omission of the magnetostatic domain wall repulsion from the modulation

J. Kimling, Magnetization Reversal in Cylindrical Nanowires and in Nanowires with Perpendicular Magnetic Anisotropy

Y. P. Ivanov, M. Vazquez, and O. Chubykalo-fesenko, Magnetic reversal modes in cylindrical nanowires, Journal of Physics D: Applied Physics, vol.46, issue.48, p.485001, 2013.
DOI : 10.1088/0022-3727/46/48/485001

A. A. Ivanov and V. A. Orlov, A comparative analysis of the mechanisms of pinning of a domain wall in a nanowire, Physics of the Solid State, vol.75, issue.8, p.2441, 2011.
DOI : 10.1103/PhysRevB.75.054421