C. Desvaux, C. Amiens, P. Fejes, P. Renaud, M. Respaud, P. Lecante, E. Snoeck, and C. Bruno.
Multimillimetre-large superlattices of air-stable iron-cobalt nanoparticles.
Nat. Mater. 4, 750 (2005).

S. Sun, C. B. Murray, D. Weller, L. Folks, and A. Moser.
Monodisperse FePt nanoparticles and ferromagnetic FePt nanocrystal superlattices.
Science 287, 1989 (2000).

S. Rusponi, T. Cren, N. Weiss, M. Epple, P. Buluschek, L. Claude, and H. Brune.
The remarkable difference between surface and step atoms in the magnetic anisotropy of two-dimensional nanostructures.
Nat. Mater 2, 546 (2003).

P. Tartaj, M. del Puerto Morales, S. Veintemillas-Verdaguer, T. González-Carreño, and C. J. Serna.
The preparation of magnetic nanoparticles for applications in biomedicine.
J. Phys. D: Appl. Phys. 36, R182 (2003).

A. K. Gupta and M. Gupta.
Synthesis and surface engineering of iron oxide nanoparticles for biomedical applications.
Biomaterials 26, 3995 (2005).

V. Skumryev, S. Stoyanov, Y. Zhang, G. Hadjipanayis, D. Givord, and J. Nogues.
Beating the superparamagnetic limit with exchange bias.
Nature 423, 850 (2003).

R. F. L. Evans, R. Yanes, O. Mryasov, R. W. Chantrell, and O. Chubykalo-Fesenko.
On beating the superparamagnetic limit with exchange bias.
Europhys. Lett. 88, 57004 (2009).

F. Luis, J. M. Torres, L. M. García, J. Bartolomé, J. Stankiewicz, F. Petroff, F. Fettar, J.-L. Maurice, and A. Vaurès.
Enhancement of the magnetic anisotropy of nanometer-sized Co clusters: Influence of the surface and of interparticle interactions.
Phys. Rev. B 65, 094409 (2002).

J. Bartolomé, L. M. García, F. Bartolomé, F. Luis, R. López-Ruiz, F. Petroff, C. Deranlot, F. Wilhelm, A. Rogalev, P. Bencok, N. B. Brookes, L. Ruiz, and J. M. González-Calbet.
Magnetic polarization of noble metals by Co nanoparticles in M -capped granular multilayers ( $ {M}={C}u$ , Ag, and Au): An X-ray magnetic circular dichroism study.
Phys. Rev. B 77, 184420 (2008).

F. Luis, F. Bartolomé, F. . Petroff, J. Bartolomé, L. M. García, C. Deranlot, H. Jaffrès, M. J. Martínez, P. Bencok, F. Wilhelm, A. Rogalev, and N. B. Brookes.
Tuning the magnetic anisotropy of Co nanoparticles by metal capping.
Europhys. Lett. 76, 142 (2006).

F. Garcia-Sanchez, O. Chubykalo-Fesenko, O. Mryasov, P. Asselin, and R. W. Chantrell.
Switching and thermal stability properties of bilayer thin films: Single versus multigrain cases.
J. Appl. Phys. 103, 07F505 (2008).

G. R. Aranda, O. Chubykalo-Fesenko, R. Yanes, J. Gonzalez, J. J. del Val, R. W. Chantrell, Y. K. Takahashi, and K. Hono.
Coercive field and energy barriers in partially disordered FePt nanoparticles.
J. Appl. Phys. 105, 07B514 (2009).

G. Salazar-Alvarez, J. Qin, V. Sepelák, I. Bergmann, M. Vasilakaki, K. N. Trohidou, J. D. Ardisson, W. A. A. Macedo, M. Mikhaylova, M. Muhammed, M. D. Baró, and J. Nogués.
Cubic versus spherical magnetic nanoparticles: The role of surface anisotropy.
J. Am. Chem. Soc. 130, 13234 (2008).

M. Jamet, W. Wernsdorfer, C. Thirion, V. Dupuis, P. Mélinon, A. Pérez, and D. Mailly.
Magnetic anisotropy in single clusters.
Phys. Rev. B 69, 024401 (2004).

X. Batlle and A. Labarta.
Finite-size effects in fine particles: magnetic and transport properties.
J. Phys. D: Appl. Phys. 35, R15 (2002).

A. Weddemann, I. Ennen, A. Regtmeier, C. Albon, A. Wolf, K. Eckstädt, N. Mill, J. Peter, Michaeland Mattay, C. Plattner, and A. Sewald, Norbert andfd Hütten.
Review and outlook: from single nanoparticles to self-assembled monolayers and granular GMR sensors.
Beilstein J. Nanotechnol. 1, 75 (2010).

J. Frenkel and J. Doefman.
Spontaneous and induced magnetisation in ferromagnetic bodies.
Nature 126, 274 (1930).

R. Evans, U. Nowak, F. Dorfbauer, T. Shrefl, O. Mryasov, R. W. Chantrell, and G. Grochola.
The influence of shape and structure on the Curie temperature of Fe and Co nanoparticles.
J. Appl. Phys. 99, 08G703 (2006).

A. G. Roca, R. Costo, A. F. Rebolledo, S. Veintemillas-Verdaguer, P. Tartaj, T. González-Carreño, M. P. Morales, and C. J. Serna.
Progress in the preparation of magnetic nanoparticles for applications in biomedicine.
J. Phys. D: Appl. Phys. 42, 224002 (2009).

M. Jamet, W. Wernsdorfer, C. Thirion, D. Mailly, V. Dupuis, P. Mélinon, and A. Pérez.
Magnetic anisotropy of a single cobalt nanocluster.
Phys. Rev. Lett. 86, 4676 (2001).

J. M. D. Coey, K. Wongsaprom, J. Alaria, and M. Venkatesan.
Charge-transfer ferromagnetism in oxide nanoparticles.
J. Phys. D: Appl. Phys. 41, 134012 (2008).

L. F. Cotica, I. A. Santos, E. M. Girotto, E. V. Ferri, and A. A. Coelho.
Surface spin disorder effects in magnetite and poly(thiophene)-coated magnetite nanoparticles.
J. Appl. Phys. 108, 064325 (2010).

W. H. Meiklejohn and C. P. Bean.
New magnetic anisotropy.
Phys. Rev. 105, 904 (1957).

S. A. Makhlouf, H. Al-Attar, and R. Kodama.
Particle size and temperature dependence of exchange bias in NiO nanoparticles.
Solid State Commun. 145, 1 (2008).

W. H. Meiklejohn and C. P. Bean.
New magnetic anisotropy.
Phys. Rev. 102, 1413 (1956).

J. Nogués and I. K. Schuller.
Exchange bias.
J. Magn. Magn. Mat. 192, 203 (1999).

O. Iglesias, X. Batlle, and A. Labarta.
Modelling exchange bias in core/shell nanoparticles.
J. Phys.: Condens. Matter 19, 406232 (2007).

F. Liu, M. R. Press, S. N. Khanna, and P. Jena.
Magnetism and local order: Ab initio tight-binding theory.
Phys. Rev. B 39, 6914 (1989).

S. N. Khanna and S. Linderoth.
Magnetic behavior of clusters of ferromagnetic transition metals.
Phys. Rev. Lett. 67, 742 (1991).

S. E. Apsel, J. W. Emmert, J. Deng, and L. A. Bloomfield.
Surface-enhanced magnetism in nickel clusters.
Phys. Rev. Lett. 76, 1441 (1996).

K. W. Edmonds, C. Binns, S. H. Baker, S. C. Thornton, C. Norris, J. B. Goedkoop, M. Finazzi, and N. B. Brookes.
Doubling of the orbital magnetic moment in nanoscale Fe clusters.
Phys. Rev. B 60, 472 (1999).

M. Respaud, J. M. Broto, H. Rakoto, A. R. Fert, L. Thomas, B. Barbara, M. Verelst, E. Snoeck, P. Lecante, A. Mosset, J. Osuna, T. O. Ely, C. Amiens, and B. Chaudret.
Surface effects on the magnetic properties of ultrafine cobalt particles.
Phys. Rev. B 57, 2925 (1998).

A. E. Berkowitz, W. J. Schuele, and P. J. Flanders.
Influence of crystallite size on the magnetic properties of acicular $ \gamma $- $ Fe_{2}O_{3}$ particles.
J. Appl. Phys. 39, 1261 (1968).

J. M. D. Coey.
Noncollinear spin arrangement in ultrafine ferrimagnetic crystallites.
Phys. Rev. Lett. 27, 1140 (1971).

R. H. Kodama.
Magentic nanoparticles.
J. Magn. Magn. Mat. 200, 359 (1999).

F. Bødker, S. Mørup, and S. Linderoth.
Surface effects in metallic iron nanoparticles.
Phys. Rev. Lett. 72, 282 (1994).

E. Tronc, A. Ezzir, R. Cherkaoui, C. Chanéac, M. Noguès, H. Kachkachi, D. Fiorani, A. Testa, J. Grenèche, and J. Jolivet.
Surface-related properties of $ \gamma $- $ {F}e_{2}o_{3}$ nanoparticles.
J. Magn. Magn. Mat. 221, 63 (2000).

J. E. Lima, E. D. Biasi, M. V. Mansilla, M. E. Saleta, F. Effenberg, L. M. Rossi, R. Cohen, H. R. Rechenberg, and R. D. Zysler.
Surface effects in the magnetic properties of crystalline 3 nm ferrite nanoparticles chemically synthesized.
J. Appl. Phys. 108, 103919 (2010).

M. Hamedoun, K. Bouslykhane, H. Bakrim, A. Hourmatallah, and N. Benzakour.
Coupling and surface effects in magnetic thin films.
Physica A 358, 102 (2005).

L. Szunyogh, L. Udvardi, J. Jackson, U. Nowak, and R. Chantrell.
Atomistic spin model based on a spin-cluster expansion technique: Application to the IrMn$ _{3}$/Co interface.
Phys. Rev. B 83, 024401 (2011).

I. Apostolova and J. M. Wesselinowa.
Possible low-Tc nanoparticles for use in magnetic hyperthermia treatments.
Solid State Commun. 149, 986 (2009).

J. H. van Vleck.
On the anisotropy of cubic ferromagnetic crystals.
Phys. Rev. 52, 1178 (1937).

U. Gradmann.
Magnetism in oligatomic films.
J. Appl. Phys. 40, 1182 (1969).

J. G. Gay and R. Richter.
Spin anisotropy of ferromagnetic films.
Phys. Rev. Lett. 56, 2728 (1986).

P. Bruno.
Tight-binding approach to the orbital magnetic moment and magnetocrystalline anisotropy of transition-metal monolayers.
Phys. Rev. B 39, 865 (1989).

R. H. Victora and J. M. MacLaren.
Theory of magnetic interface anisotropy.
Phys. Rev. B 47, 11583 (1993).

L. Néel.
Anisotropie magnétique superficielle et surstructures d'orientation.
J. Phys. Radium 15, 225 (1954).

L. Stöhr and H. Siegmann.
Magnetism from: fundamentals to nanoscale dynamics (Springer, 2006).

C. Andersson, B. Sanyal, O. Eriksson, L. Nordström, O. Karis, D. Arvanitis, T. Konishi, E. Holub-Krappe, and J. H. Dunn.
Influence of ligand states on the relationship between orbital moment and magnetocrystalline anisotropy.
Phys. Rev. Lett. 99, 177207 (2007).

G. Schütz, W. Wagner, W. Wilhelm, P. Kienle, R. Zeller, R. Frahm, and G. Materlik.
Absorption of circularly polarized x-rays in iron.
Phys. Rev. Lett. 58, 737 (1987).

J. Stöhr.
Exploring the microscopic origin of magnetic anisotropies with X-ray magnetic circular dichroism (XMCD) spectroscopy.
J. Magn. Magn. Mat. 200, 470 (1999).

A. Ney, P. Poulopoulos, M. Farle, and K. Baberschke.
Absolute determination of Co magnetic moments: Ultrahigh-vacuum high-$ T_{c}$ SQUID magnetometry.
Phys. Rev. B 62, 11336 (2000).

W. F. Brown.
Thermal fluctuations of a single-domain particle.
Phys. Rev. 130, 1677 (1963).

P. Bruno and J. P. Renard.
Magnetic surface anistropy of transition metal ultrathin films.
Appl. Phys. A 49, 499 (1989).

H. J. Elmers and U. Gradmann.
Magnetic anisotropies in Fe(110) films on W(110).
Appl. Phys. A 51, 255 (1990).

A. P. N. Dinia and H. Danan.
Spectral-density method for classical systems: Heisenberg ferromagnet.
J. App. Phys. 84, 5668 (1998).

E. Tronc, D. Fiorani, M. Noguès, A. Testa, F. Lucari, F. D'Orazio, J. Grenèche, W. Wernsdorfer, N. Galvez, C. Chanéac, D. Mailly, and J. Jolivet.
Surface effects in non-interacting and interacting $ \gamma $- $ {F}e_{2}{O}_{3}$ nanoparticles.
J. Magn. Magn. Mat. 262, 6 (2003).

U. Gradmann.
Magnetic surface anisotropies.
J. Magn. Magn. Mat. 54-57, 733 (1986).

G. Bochi, C. A. Ballentine, H. E. Inglefield, C. V. Thompson, and R. C. O'Handley.
Evidence for strong surface magnetoelastic anisotropy in epitaxial Cu/Ni/Cu(001) sandwiches.
Phys. Rev. B 53, R1729 (1996).

Z. Kurant, R. Gieniusz, A. Maziewski, M. Tekielak, W. Stefanowicz, I. Sveklo, V. Zablotskii, A. Petroutchik, L. Baczewski, and A. Wawro.
Changes in magnetic properties of ultrathin cobalt films as induced by Mo, V, Au overlayers.
J. Magn. Magn. Mat. 316, e511 (2007).

T. Shinjo, N. Nakayama, I. Moritani, and Y. Endoh.
Monolayer of ferromagnetic MnSb.
J. Phys. Soc. Jpn. 55, 2512 (1986).

F. den Broeder, W. Hoving, and P. Bloemen.
Magnetic anisotropy of multilayers.
J. Magn. Magn. Mat. 93, 562 (1991).

B. Schulz and K. Baberschke.
Crossover from in-plane to perpendicular magnetization in ultrathin Ni/Cu(001) films.
Phys. Rev. B 50, 13467 (1994).

D. Wilgocka-Slezak, K. Freindl, A. Kozio\l, K. Matlak, M. Rams, N. Spiridis, M. Slezak, T. Slezak, M. Zajac, and J. Korecki.
Thickness-driven polar spin reorientation transition in ultrathin Fe/Au(001) films.
Phys. Rev. B 81, 064421 (2010).

N. C. Koon, B. T. Jonker, F. A. Volkening, J. J. Krebs, and G. A. Prinz.
Direct evidence for perpendicular spin orientations and enhanced hyperfine fields in ultrathin Fe(100) films on Ag(100).
Phys. Rev. Lett. 59, 2463 (1987).

R. Allenspach and A. Bischof.
Magnetization direction switching in Fe/Cu(100) epitaxial films: Temperature and thickness dependence.
Phys. Rev. Lett. 69, 3385 (1992).

Y. Yafet and E. M. Gyorgy.
Ferromagnetic strip domains in an atomic monolayer.
Phys. Rev. B 38, 9145 (1988).

C. Won, Y. Z. Wu, J. Choi, W. Kim, A. Scholl, A. Doran, T. Owens, J. Wu, X. F. Jin, H. W. Zhao, and Z. Q. Qiu.
Magnetic stripe melting at the spin reorientation transition in $ Fe/Ni/Cu(001)$.
Phys. Rev. B 71, 224429 (2005).

M. Carubelli, O. V. Billoni, S. A. Pighín, S. A. Cannas, D. A. Stariolo, and F. A. Tamarit.
Spin reorientation transition and phase diagram of ultrathin ferromagnetic films.
Phys. Rev. B 77, 134417 (2008).

A. Hubbert and R. Schaffer.
Magnetic domains (Springer, 1998).

Y. Xie and J. A. Blackman.
Magnetocrystalline anisotropy and orbital polarization in ferromagnetic transition metals.
Phys. Rev. B 69, 172407 (2004).

Y. Xie and J. A. Blackman.
Magnetic anisotropy of nanoscale cobalt particles.
J. Phys.: Condens. Matter 16, 3163 (2004).

H. Kachkachi.
Effects of spin non-collinearities in magnetic nanoparticles.
J. Magn. Magn. Mat. 316, 248 (2007).

D. A. Garanin and H. Kachkachi.
Surface contribution to the anisotropy of magnetic nanoparticles.
Phys. Rev. Lett. 90, 065504 (2003).

H. Kachkachi and H. Mahboub.
Surface anisotropy in nanomagnets: transverse or Néel?
J. Magn. Magn. Mat. 278, 334 (2004).

R. Yanes, O. Chubykalo-Fesenko, H. Kachkachi, D. A. Garanin, R. Evans, and R. Chantrell.
Effective anisotropies and energy barriers of magnetic nanoparticles with Néel surface anisotropy.
Phys. Rev. B 76, 064416 (2007).

L. Berger, Y. Labaye, M. Tamine, and J. M. D. Coey.
Ferromagnetic nanoparticles with strong surface anisotropy: Spin structures and magnetization processes.
Phys. Rev. B 77, 104431 (2008).

J. Mazo-Zuluaga, J. Restrepo, F. Munoz, and J. Mejia-Lopez.
Surface anisotropy, hysteretic, and magnetic properties of magnetite nanoparticles: A simulation study.
J. Appl. Phys. 105, 123907 (2009).

A. Cabot, A. P. Alivisatos, V. F. Puntes, L. Balcells, O. Iglesias, and A. Labarta.
Magnetic domains and surface effects in hollow maghemite nanoparticles.
Phys. Rev. B 79, 094419 (2009).

O. Chubykalo-Fesenko and R. W. Chantrell.
Multidimensional energy barrier distributions of interacting magnetic particles evaluated at different magnetization states.
J. Appl. Phys. 97, 10J315 (2005).

O. Chubykalo-Fesenko, K. Guslienko, T. Klemmer, X. Wu, R. Chantrell, and D. Weller.
A computational and experimental study of exchange coupling in FePt self-organized magnetic arrays.
Physica B: Condensed Matter 382, 235 (2006).

H. Kronmüller, R. Fischer, M. Seeger, and A. Zern.
Micromagnetism and microstructure of hard magnetic materials.
J. Phys. D: Appl. Phys. 29, 2274 (1996).

F. Garcia-Sanchez, O. Chubykalo-Fesenko, O. Mryasov, R. W. Chantrell, and K. Y. Guslienko.
Exchange spring structures and coercivity reduction in FePt/FeRh bilayers: A comparison of multiscale and micromagnetic calculations.
Appl. Phys. Lett. 87, 122501 (2005).

R. Evans, F. Dorfbauer, O. Myrasov, O. Chubykalo-Fesenko, T. Schrefl, and R. Chantrell.
The effects of surface coating on the structural and magnetic properties of CoAg core-shell nanoparticles.
IEEE Trans. Magn. 43(6), 3106 (2007).

F. Dorfbauer, R. Evans, M. Kirschner, O. Chubykalo-Fesenko, R. Chantrell, and T. Schrefl.
Effects of surface anisotropy on the energy barrier in cobalt-silver core-shell nanoparticles.
J. Magn. Magn. Mat. 316, e791 (2007).

L. Szunyogh, B. Újfalussy, and P. Weinberger.
Magnetic anisotropy of iron multilayers on Au(001): First-principles calculations in terms of the fully relativistic spin-polarized screened KKR method.
Phys. Rev. B 51, 9552 (1995).

H. Kachkachi and E. Bonet.
Surface-induced cubic anisotropy in nanomagnets.
Phys. Rev. B 73, 224402 (2006).

J. M. Vargas and R. D. Zysler.
Tailoring the size in colloidal iron oxide magnetic nanoparticles.
Nanotechnology 16, 1474 (2005).

G. Chouhan, D. Wang, and H. Alper.
Magnetic nanoparticle-supported proline as a recyclable and recoverable ligand for the CuI catalyzed arylation of nitrogen nucleophiles.
R. Soc. Chem. (Suppl. Mater. (ESI)Chem. Communic.) (2007).

H. Kachkachi and M. Dimian.
Hysteretic properties of a magnetic particle with strong surface anisotropy.
Phys. Rev. B 66, 174419 (2002).

H. Kachkachi, A. Ezzir, M. Noguès, and E. Tronc.
Surface effects in nanoparticles: application to maghemite.
Eur. Phys. J. B 14, 681 (2000).

O. Iglesias and A. Labarta.
Finite-size and surface effects in maghemite nanoparticles: Monte Carlo simulations.
Phys. Rev. B 63, 184416 (2001).

D. Fiorani, ed.
Surface effects in magentic nanoparticles (Springer Science, 2005).

R. H. Kodama and A. E. Berkowitz.
Atomic-scale magnetic modeling of oxide nanoparticles.
Phys. Rev. B 59, 6321 (1999).

M. S. Daw and M. I. Baskes.
Semiempirical, quantum mechanical calculation of hydrogen embrittlement in metals.
Phys. Rev. Lett. 50, 1285 (1983).

F. Dorfbauer, T. Schrefl, M. Kirschner, G. Hrkac, D. Suess, O. Ertl, and J. Fidler.
Nanostructure calculation of CoAg core-shell clusters.
J. Appl. Phys. 99, 08G706 (2006).

H. Kachkachi and D. M. Garanin.
Unpublished .

A. Aharoni.
Introduction to the theory of ferromagnetism (Oxford University Press, 1996).

E. Paz, F. Garcia-Sanchez, and O. Chubykalo-Fesenko.
Numerical evaluation of energy barriers in nano-sized magnetic elements with lagrange multiplier technique.
Physica B: Condens. Matter 403, 330 (2008).

F. Bartolomé, F. Luis, F. Petroff, L. M. García, J. Bartolomé, V. Cros, and H. Jaffrès.
XMCD study of the anisotropy of nanometric Co clusters in insulating and metallic matrices.
J. Magn. Magn. Mater. 272-276, E1275 (2004).
Proceedings of the International Conference on Magnetism (ICM 2003).

F. Luis, J. Bartolome, F. Bartolome, M. J. Martinez, L. M. Garcia, F. Petroff, C. Deranlot, F. Wilhelm, and A. Rogalev.
Enhancement of the magnetic anisotropy of Co clusters by Au capping.
J. Appl. Phys. 99, 08G705 (pages 3) (2006).

Y. Labaye, O. Crisan, L. Berger, J. M. Greneche, and J. M. D. Coey.
Surface anisotropy in ferromagnetic nanoparticles.
J. Appl. Phys. 91, 8715 (2002).

D. A. Dimitrov and G. M. Wysin.
Magnetic properties of spherical fcc clusters with radial surface anisotropy.
Phys. Rev. B 51, 11947 (1995).

G. H. O. Daalderop, P. J. Kelly, and M. F. H. Schuurmans.
Magnetic anisotropy of a free-standing Co monolayer and of multilayers which contain Co monolayers.
Phys. Rev. B 50, 9989 (1994).

B. Újfalussy, L. Szunyogh, P. Bruno, and P. Weinberger.
First-principles calculation of the anomalous perpendicular anisotropy in a co monolayer on au(111).
Phys. Rev. Lett. 77, 1805 (1996).

H. Callen and E. Callen.
The present status of the temperature dependence of magnetocrystalline anisotropy, and the $ \textit{l(l+1)/2}$ law.
J. Phys. Chem. Solids 27, 1271 (1966).

O. N. Mryasov, U. Nowak, K. Y. Guslienko, and R. W. Chantrell.
Temperature-dependent magnetic properties of FePt: Effective spin Hamiltonian model.
Europhys. Lett. 69, 805 (2005).

R. Skomski, A. Kashyap, and D. Sellmyer.
Finite-temperature anisotropy of PtCo magnets.
IEEE Trans. Magn. 39, 2917 (2003).

H. F. Hamann, Y. C. Martin, and H. K. Wickramasinghe.
Thermally assisted recording beyond traditional limits.
Appl. Phys. Lett. 84, 810 (2004).

R. Rottmayer, S. Batra, D. Buechel, W. Challener, J. Hohlfeld, Y. Kubota, L. Li, B. Lu, C. Mihalcea, K. Mountfield, K. Pelhos, C. Peng, T. Rausch, M. Seigler, D. Weller, and X. Yang.
Heat-assisted magnetic recording.
IEEE Trans. Magn. 42, 2417 (2006).

T. W. McDaniel.
Ultimate limits to thermally assisted magnetic recording.
J. Phys.: Condens. Matter. 17, R315 (2005).

A. Lyberatos and K. Y. Guslienko.
Thermal stability of the magnetization following thermomagnetic writing in perpendicular media.
J. Appl. Phys. 94, 1119 (2003).

F. G. Sanchez, O. Chubykalo-Fesenko, O. Mryasov, and R. Chantrell.
Multiscale modelling of hysteresis in FePt/FeRh bilayer.
Physica B: Condensed Matter 372, 328 (2006).

J.-U. Thiele, S. Maat, and E. E. Fullerton.
FeRh/FePt exchange spring films for thermally assisted magnetic recording media.
Appl. Phys. Lett. 82, 2859 (2003).

K. Y. Guslienko, O. Chubykalo-Fesenko, O. Mryasov, R. Chantrell, and D. Weller.
Magnetization reversal via perpendicular exchange spring in FePt/FeRh bilayer films.
Phys. Rev. B 70, 104405 (2004).

U. Atxitia, O. Chubykalo-Fesenko, N. Kazantseva, D. Hinzke, U. Nowak, and R. W. Chantrell.
Micromagnetic modeling of laser-induced magnetization dynamics using the Landau-Lifshitz-Bloch equation.
Appl. Phys. Lett. 91, 232507 (2007).

A. Berger and H. Hopster.
Nonequilibrium magnetization near the reorientation phase transition of Fe/Ag(100) films.
Phys. Rev. Lett. 76, 519 (1996).

I.-G. Baek, H. G. Lee, H.-J. Kim, and E. Vescovo.
Spin reorientation transition in Fe(110) thin films: The role of surface anisotropy.
Phys. Rev. B 67, 075401 (2003).

A. Enders, D. Peterka, D. Repetto, N. Lin, A. Dmitriev, and K. Kern.
Temperature dependence of the surface anisotropy of Fe ultrathin films on Cu(001).
Phys. Rev. Lett. 90, 217203 (2003).

M. Farle.
Ferromagnetic resonance of ultrathin metallic layers.
Rep. Progr. Phys. 61, 755 (1998).

N. Kazantseva, D. Hinzke, U. Nowak, R. W. Chantrell, U. Atxitia, and O. Chubykalo-Fesenko.
Towards multiscale modeling of magnetic materials: Simulations of FePt.
Phys. Rev. B 77, 184428 (2008).

B. C. Chuang D.S. and O. R.C.
Surface and step magnetic anisotropy.
Phys. Rev. B 51, 11947 (1995).

N. Metropolis, A. Rosenbluth, M. Rosembluth, A. Teller, and E. Teller.
Equation of state calculations by fast computing machines.
J. Chem. Phys. 21, 1087 (1953).

J. M. González, O. A. Chubykalo, and R. S. Rueda.
A micromagnetic approach, based on the Monte Carlo algorithm, to the thermally activated magnetization reversal processes.
J. Magn. Magn. Mat. 203, 18 (1999).

Ph.D. thesis, University of York,UK (2009).

P. Asselin, R. F. L. Evans, J. Barker, R. W. Chantrell, R. Yanes, O. Chubykalo-Fesenko, D. Hinzke, and U. Nowak.
Constrained Monte Carlo method and calculation of the temperature dependence of magnetic anisotropy.
Phys. Rev. B 82, 054415 (2010).

L. S. Campana, A. C. D'Auria, M. D'Ambrosio, U. Esposito, L. De Cesare, and G. Kamieniarz.
Spectral-density method for classical systems: Heisenberg ferromagnet.
Phys. Rev. B 30, 2769 (1984).

G. A. Baker, H. E. Gilbert, J. Eve, and G. S. Rushbrooke.
High-temperature expansions for the spin 1/2 Heisenberg model.
Phys. Rev. 164, 800 (1967).

C. Zener.
Classical theory of the temperature dependence of magnetic anisotropy energy.
Phys. Rev. 96, 1335 (1954).

K. Binder and P. C. Hohenberg.
Surface effects on magnetic phase transitions.
Phys. Rev. B 9, 2194 (1974).

T. Kaneyoshi.
Surface magnetism; magnetization and anisotropy at a surface.
J. Phys.: Condens. Matter 3, 4497 (1991).

C. Chappert and P. Bruno.
Magnetic anisotropy in metallic ultrathin films and related experiments on cobalt films.
J. Appl. Phys. 64, 5736 (1988).

G. André, A. Aspelmeier, B. Schulz, M. Farle, and K. Baberschke.
Temperature dependence of surface and volume anisotropy in Gd/W(110).
Surface Science 326, 275 (1995).

M. Farle, W. Platow, A. N. Anisimov, B. Schulz, and K. Baberschke.
The temperature dependence of magnetic anisotropy in ultra-thin films.
J. Mag. Magn. Matt. 165(74), 4 (1997).

A. Buruzs, P. Weinberger, L. Szunyogh, L. Udvardi, P. I. Chleboun, A. M. Fischer, and J. B. Staunton.
Ab initio theory of temperature dependence of magnetic anisotropy in layered systems: Applications to thin Co films on Cu(100).
Phys. Rev. B 76, 064417 (2007).

J. B. Staunton, L. Szunyogh, A. Buruzs, B. L. Gyorffy, S. Ostanin, and L. Udvardi.
Temperature dependence of magnetic anisotropy: An ab initio approach.
Phys. Rev. B 74, 144411 (2006).

D. Pescia and V. L. Pokrovsky.
Perpendicular versus in-plane magnetization in a 2D Heisenberg monolayer at finite temperatures.
Phys. Rev. Lett. 65, 2599 (1990).

B. Dieny and A. Vedyayev.
Crossover from easy-plane to perpendicular anisotropy in magnetic thin films: canted anisotropy due to partial coverage or interfacial roughness.
Europhys. Lett. 25, 723 (1994).

U. Atxitia, D. Hinzke, O. Chubykalo-Fesenko, U. Nowak, H. Kachkachi, O. N. Mryasov, R. F. Evans, and R. W. Chantrell.
Multiscale modeling of magnetic materials: Temperature dependence of the exchange stiffness.
Phys. Rev. B 82, 134440 (2010).



L. Udvardi, L. Szunyogh, K. Palotás, and P. Weinberger.
First-principles relativistic study of spin waves in thin magnetic films.
Phys. Rev. B 68, 104436 (2003).

P. Hohenberg and W. Kohn.
Inhomogeneous Electron Gas.
Phys. Rev. 136, B864 (1964).

W. Kohn and L. J. Sham.
Self-consistent equations including exchange and correlation effects.
Phys. Rev. 140, A1133 (1965).

L. Hedin and B. I. Lundqvist.
Explicit local exchange-correlation potentials.
J. Phys. C: Solid State Phys. 4, 2064 (1971).

J. P. Perdew, J. A. Chevary, S. H. Vosko, K. A. Jackson, M. R. Pederson, D. J. Singh, and C. Fiolhais.
Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation.
Phys. Rev. B 46, 6671 (1992).

U. von Barth and L. Hedin.
A local exchange-correlation potential for the spin polarized case.
J. Phys. C: Solid State Phys. 5, 1629 (1972).

J. Korringa.
On the calculation of the energy of a Bloch wave in a metal.
Physica 13, 392 (1947).

W. Kohn and N. Rostoker.
Solution of the Schrödinger equation in Periodic Lattices with an Application to Metallic Lithium.
Phys. Rev. 94, 1111 (1954).

L. Szunyogh, B. Újfalussy, P. Weinberger, and J. Kollár.
Self-consistent localized KKR scheme for surfaces and interfaces.
Phys. Rev. B 49, 2721 (1994).

M. C. Muñoz, V. R. Velasco, and F. Garcia-Moliner.
Surface and interface electronic structure calculations with empirical tight binding models.
Physica Scripta 35, 504 (1987).

M. P. L. Sancho, J. M. L. Sancho, J. M. L. Sancho, and J. Rubio.
Highly convergent schemes for the calculation of bulk and surface green functions.
J. Phys. F: Met. Phys. 15(4), 851 (1985).

M. C. Muñoz, V. R. Velasco, and F. García-Moliner.
Electronic structure of AlAs-GaAs superlattices.
Phys. Rev. B 39, 1786 (1989).

P. Lloyd.
Wave propagation through an assembly of spheres: II. The density of single-particle eigenstates.
Proc. Phys.l Soc. 90(1), 207 (1967).

J. Zabloud, R. Hammerling, L. Szunyogh, and P. Weinberger.
Electron Sacttering in Solid Matter: A Theoretical and Computational treatise, vol. 147 of Series in solid state science (Springer, 2005).

N. S. González, S. Gallego, and M. C. Muñoz.
Private communication .

H. B. Michaelson.
The work function of the elements and its periodicity.
J. Appl. Phys. 48, 4729 (1977).

R. Smoluchowski.
Anisotropy of the electronic work function of metals.
Phys. Rev. 60, 661 (1941).

N. D. Lang and W. Kohn.
Theory of metal surfaces: Work function.
Phys. Rev. B 3, 1215 (1971).

P. Söderlind, O. Eriksson, B. Johansson, R. C. Albers, and A. M. Boring.
Spin and orbital magnetism in Fe-Co and Co-Ni alloys.
Phys. Rev. B 45, 12911 (1992).

M. Tischer, O. Hjortstam, D. Arvanitis, J. Hunter Dunn, F. May, K. Baberschke, J. Trygg, J. M. Wills, B. Johansson, and O. Eriksson.
Enhancement of orbital magnetism at surfaces: Co on Cu(100).
Phys. Rev. Lett. 75, 1602 (1995).

O. Eriksson, A. M. Boring, R. C. Albers, G. W. Fernando, and B. R. Cooper.
Spin and orbital contributions to surface magnetism in 3d elements.
Phys. Rev. B 45, 2868 (1992).

R. Wu, D. Wang, and A. J. Freeman.
First principles investigation of the validity and range of applicability of the X-ray magnetic circular dichroism sum rule.
Phys. Rev. Lett. 71, 3581 (1993).

N. Nakajima, T. Koide, T. Shidara, H. Miyauchi, H. Fukutani, A. Fujimori, K. Iio, T. Katayama, M. Nývlt, and Y. Suzuki.
Perpendicular magnetic anisotropy caused by interfacial hybridization via enhanced orbital moment in $ {C}o/{P}t$ multilayers: Magnetic circular x-ray dichroism study.
Phys. Rev. Lett. 81, 5229 (1998).

H. A. Dürr, S. S. Dhesi, E. Dudzik, D. Knabben, G. van der Laan, J. B. Goedkoop, and F. U. Hillebrecht.
Spin and orbital magnetization in self-assembled Co clusters on Au(111).
Phys. Rev. B 59, R701 (1999).

N. Jaouen, F. Wilhelm, A. Rogalev, J. Goulon, L. Ortega, J. M. Tonnerre, and A. Yaresko.
Electronic and magnetic interfacial states of Ag in an $ {N}i_{81} {F}e_{19} /{A}g$ coupled multilayer.
J. Phys.: Condens. Matter 20, 095005 (2008).

A. I. Liechtenstein, M. I. Katsnelson, V. P. Antropov, and V. A. Gubanov.
Local spin density functional approach to the theory of exchange interactions in ferromagnetic metals and alloys.
J. Magn. Magn. Mat. 67, 65 (1987).

B. L. Gyorffy, A. J. Pindor, J. Staunton, G. M. Stocks, and H. Winter.
A first-principles theory of ferromagnetic phase transitions in metals.
J. Phys. F: Metal Phys. 15, 1337 (1985).

V. P. Antropov, M. I. Katsnelson, B. N. Harmon, M. van Schilfgaarde, and D. Kusnezov.
Spin dynamics in magnets: Equation of motion and finite temperature effects.
Phys. Rev. B 54, 1019 (1996).

L. Szunyogh and L. Udvardi.
Ab initio calculation of Heisenberg parameters in thin magnetic films.
Philosophical Magazine B 78, 617 (1998).

L. Szunyogh and L. Udvardi.
Ab initio calculation of Heisenberg parameters and Curie temperatures in thin magnetic films.
J. Magn. Magn. Mat. 198-199, 537 (1999).

P. Mavropoulos.
Multiscale modelling of magnetic materials: From the total energy of the homogeneous electron gas to the Curie temperature of ferromagnets.
Multiscale Sim. Met. Mol. Science 42, 271 (2009).

L. Szunyogh, B. Lazarovits, L. Udvardi, J. Jackson, and U. Nowak.
Giant magnetic anisotropy of the bulk antiferromagnets IrMn and $ {I}r{M}n_{3}$ from first principles.
Phys. Rev. B 79, 020403 (2009).

J. B. Staunton, S. Ostanin, S. S. A. Razee, B. L. Gyorffy, L. Szunyogh, B. Ginatempo, and E. Bruno.
Temperature dependent magnetic anisotropy in metallic magnets from an ab initio electronic structure theory: $ {L}1_{0}$-ordered FePt.
Phys. Rev. Lett. 93, 257204 (2004).

I. Dzyaloshinsky.
A thermodynamic theory of "weak" ferromagnetism of antiferromagnetics.
J. Phys. Chem. Solids 4, 241 (1958).

T. Moriya.
Anisotropic superexchange interaction and weak ferromagnetism.
Phys. Rev. 120, 91 (1960).

A. Crépieux and C. Lacroix.
Dzyaloshinsky-Moriya interactions induced by symmetry breaking at a surface.
J. Magn. Magn. Mat. 182, 341 (1998).

A. Antal, B. Lazarovits, L. Balogh, L. Udvardi, and L. Szunyogh.
Multiescale studies of complex magnetism of nanostructures based on first principles.
Philosoph. Magazine 88, 2715 (2008).

D.-S. Wang, R. Wu, and A. J. Freeman.
First-principles theory of surface magnetocrystalline anisotropy and the diatomic-pair model.
Phys. Rev. B 47, 14932 (1993).

C. Kittel.
Theory of the structure of ferromagnetic domains in films and small particles.
Phys. Rev. 70, 965 (1946).

R. Drautz and M. Fähnle.
Spin-cluster expansion: Parametrization of the general adiabatic magnetic energy surface with ab initio accuracy.
Phys. Rev. B 69, 104404 (2004).

R. Drautz and M. Fähnle.
Parametrization of the magnetic energy at the atomic level.
Phys. Rev. B 72, 212405 (2005).

M. Pajda, J. Kudrnovský, I. Turek, V. Drchal, and P. Bruno.
Ab initio calculations of exchange interactions, spin-wave stiffness constants, and Curie temperatures of Fe, Co, and Ni.
Phys. Rev. B 64, 174402 (2001).

R. Skomski.
J. Phys.: Condens. Matter 15(20), R841 (2003).

A. B. Shick and O. N. Mryasov.
Coulomb correlations and magnetic anisotropy in ordered $ {L}1_{0}$ CoPt and FePt alloys.
Phys. Rev. B 67, 172407 (2003).

Rocio Yanes