[en] We predict the occurrence of a novel type of atomic-scale spin lattice in an Fe monolayer on the Ir(001) surface. Based on density functional theory calculations we parametrize a spin Hamiltonian and solve it numerically using Monte Carlo simulations. We find the stabilization of a three-dimensional spin structure arranged on a (3×3) lattice. Despite an almost vanishing total spin magnetization we predict the emergence of orbital magnetization and large anomalous Hall effect, to which there is a significant topological contribution purely due to the real space spin texture at the surface.
Disciplines :
Physics
Author, co-author :
Hoffmann, Markus
Weischenberg, J.
Dupé, Bertrand ; Université de Liège - ULiège > Département de physique > Physique des matériaux et nanostructures
Freimuth, Frank
Ferriani, Paolo
Mokrousov, Yuriy
Heinze, Stefan
Language :
English
Title :
Topological orbital magnetization and emergent Hall effect of an atomic-scale spin lattice at a surface
Publication date :
2015
Journal title :
Physical Review. B, Condensed Matter and Materials Physics
N. Nagaosa and Y. Tokura, Nat. Nanotechnol. 8, 899 (2013). 1748-3387 10.1038/nnano.2013.243
K.-S. Ryu, L. Thomas, S.-H. Yang, and S. Parkin, Nat. Nanotechnol. 8, 527 (2013). 1748-3387 10.1038/nnano.2013.102
S. Emori, U. Bauer, S.-M. Ahn, E. Martinez, and G. S. D. Beach, Nat. Mater. 12, 611 (2013). 1476-1122 10.1038/nmat3675
M. Hayashi, L. Thomas, R. Moriya, C. Rettner, and S. S. P. Parkin, Science 320, 209 (2008). SCIEAS 0036-8075 10.1126/science.1154587
N. Kiselev, A. N. Bogdanov, R. Schäfer, and U. K. Rößler, J. Phys. D 44, 392001 (2011). JPAPBE 0022-3727 10.1088/0022-3727/44/39/392001
A. Fert, V. Cros, and J. Sampaio, Nat. Nanotechnol. 8, 152 (2013). 1748-3387 10.1038/nnano.2013.29
J. Sampaio, V. Cros, S. Rohart, A. Thiaville, and A. Fert, Nat. Nanotechnol. 8, 839 (2013). 1748-3387 10.1038/nnano.2013.210
I. E. Dzyaloshinskii, Sov. Phys. JETP 5, 1259 (1957).
T. Moriya, Phys. Rev. 120, 91 (1960). PHRVAO 0031-899X 10.1103/PhysRev.120.91
A. Neubauer, C. Pfleiderer, B. Binz, A. Rosch, R. Ritz, P. G. Niklowitz, and P. Böni, Phys. Rev. Lett. 102, 186602 (2009). PRLTAO 0031-9007 10.1103/PhysRevLett.102.186602
S. X. Huang and C. L. Chien, Phys. Rev. Lett. 108, 267201 (2012). PRLTAO 0031-9007 10.1103/PhysRevLett.108.267201
N. Kanazawa, Y. Onose, T. Arima, D. Okuyama, K. Ohoyama, S. Wakimoto, K. Kakurai, S. Ishiwata, and Y. Tokura, Phys. Rev. Lett. 106, 156603 (2011). PRLTAO 0031-9007 10.1103/PhysRevLett.106.156603
P. Bruno, V. K. Dugaev, and M. Taillefumier, Phys. Rev. Lett. 93, 096806 (2004). PRLTAO 0031-9007 10.1103/PhysRevLett.93.096806
C. Franz, F. Freimuth, A. Bauer, R. Ritz, C. Schnarr, C. Duvinage, T. Adams, S. Blügel, A. Rosch, Y. Mokrousov, et al. Phys. Rev. Lett. 112, 186601 (2014). PRLTAO 0031-9007 10.1103/PhysRevLett.112.186601
J. Gayles, F. Freimuth, T. Schena, G. Lani, P. Mavropoulos, R. Duine, S. Blügel, J. Sinova, and Y. Mokrousov, arXiv:1503.04842 [Phys. Rev. Lett. (to be published)].
S. Heinze, K. von Bergmann, M. Menzel, J. Brede, A. Kubetzka, R. Wiesendanger, G. Bihlmayer, and S. Blügel, Nat. Phys. 7, 713 (2011). 1745-2473 10.1038/nphys2045
B. Dupé, M. Hoffmann, C. Paillard, and S. Heinze, Nat. Commun. 5, 4030 (2014).
B. Dupé, G. Bihlmayer, S. Blügel, and S. Heinze, arXiv:1503.08098.
M. Heide, G. Bihlmayer, and S. Blügel, Physica B 404, 2678 (2009). PHYBE3 0921-4526 10.1016/j.physb.2009.06.070
M. Menzel, Y. Mokrousov, R. Wieser, J. E. Bickel, E. Vedmedenko, S. Blügel, S. Heinze, K. von Bergmann, A. Kubetzka, and R. Wiesendanger, Phys. Rev. Lett. 108, 197204 (2012). PRLTAO 0031-9007 10.1103/PhysRevLett.108.197204
N. Romming, C. Hanneken, M. Menzel, J. E. Bickel, B. Wolter, K. von Bergmann, A. Kubetzka, and R. Wiesendanger, Science 341, 636 (2013). SCIEAS 0036-8075 10.1126/science.1240573
X. Zhang, Y. Zhou, and M. Ezawa, arXiv:1504.01198.
J. Barker and O. Tretiakov, arXiv:1505.06156.
H. V. Gomonay and V. M. Loktev, Phys. Rev. B 81, 144427 (2010). PRBMDO 1098-0121 10.1103/PhysRevB.81.144427
S.-H. Yang, K.-S. Ryu, and S. Parkin, Nat. Nanotechnol. 10, 221 (2015). 1748-3387 10.1038/nnano.2014.324
V. Martin, W. Meyer, C. Giovanardi, L. Hammer, K. Heinz, Z. Tian, D. Sander, and J. Kirschner, Phys. Rev. B 76, 205418 (2007). PRBMDO 1098-0121 10.1103/PhysRevB.76.205418
E. Simon, K. Palotàs, L. Ròzsa, L. Udvardi, and L. Szunyogh, Phys. Rev. B 90, 094410 (2014). PRBMDO 1098-0121 10.1103/PhysRevB.90.094410
S. Polesya, S. Mankovsky, S. Bornemann, D. Ködderitzsch, J. Minàr, and H. Ebert, Phys. Rev. B 89, 184414 (2014). PRBMDO 1098-0121 10.1103/PhysRevB.89.184414
P. E. Blöchl, Phys. Rev. B 50, 17953 (1994). PRBMDO 0163-1829 10.1103/PhysRevB.50.17953
G. Kresse and J. Furthmüller, Phys. Rev. B 54, 11169 (1996). PRBMDO 0163-1829 10.1103/PhysRevB.54.11169
G. Kresse and D. Joubert, Phys. Rev. B 59, 1758 (1999). PRBMDO 0163-1829 10.1103/PhysRevB.59.1758
G. Kresse and J. Hafner, Phys. Rev. B 47, 558 (1993). PRBMDO 0163-1829 10.1103/PhysRevB.47.558
G. Kresse and J. Hafner, Phys. Rev. B 49, 14251 (1994). PRBMDO 0163-1829 10.1103/PhysRevB.49.14251
G. Kresse and J. Furthmüller, Comput. Mater. Sci. 6, 15 (1996). CMMSEM 0927-0256 10.1016/0927-0256(96)00008-0
J. P. Perdew, J. A. Chevary, S. H. Vosko, K. A. Jackson, M. R. Pederson, D. J. Singh, and C. Fiolhais, Phys. Rev. B 46, 6671 (1992). PRBMDO 0163-1829 10.1103/PhysRevB.46.6671
J. Kudrnovský, F. Máca, I. Turek, and J. Redinger, Phys. Rev. B 80, 064405 (2009). PRBMDO 1098-0121 10.1103/PhysRevB.80.064405
J. P. Perdew and A. Zunger, Phys. Rev. B 23, 5048 (1981). PRBMDO 0163-1829 10.1103/PhysRevB.23.5048
P. Ferriani, I. Turek, S. Heinze, G. Bihlmayer, and S. Blügel, Phys. Rev. Lett. 99, 187203 (2007). PRLTAO 0031-9007 10.1103/PhysRevLett.99.187203
J. R. Yates, X. Wang, D. Vanderbilt, and I. Souza, Phys. Rev. B 75, 195121 (2007). PRBMDO 1098-0121 10.1103/PhysRevB.75.195121
A. A. Mostofi, J. R. Yates, Y.-S. Lee, I. Souza, D. Vanderbilt, and N. Marzari, Comput. Phys. Commun. 178, 685 (2008). CPHCBZ 0010-4655 10.1016/j.cpc.2007.11.016
F. Freimuth, Y. Mokrousov, D. Wortmann, S. Heinze, and S. Blügel, Phys. Rev. B 78, 035120 (2008). PRBMDO 1098-0121 10.1103/PhysRevB.78.035120
www.flapw.de.
We have obtained the following values of the exchange constants (Equation presented) between (Equation presented)-nearest neighbors in the Fe monolayer on Ir(001): (Equation presented) meV. Note that we can only determine the value (Equation presented) meV from the fitting where (Equation presented) is the nearest-neighbor biquadratic exchange interaction.
F. Máca, J. Kudrnovský, V. Drchal, and J. Redinger, Phys. Rev. B 88, 045423 (2013). PRBMDO 1098-0121 10.1103/PhysRevB.88.045423
We have checked the influence of the Ir film thickness on the energy dispersion of spin spirals up to 15 Ir layers and found convergence of the exchange parameters for 11 Ir layers.
K. von Bergmann, S. Heinze, M. Bode, E. Y. Vedmedenko, G. Bihlmayer, S. Blügel, and R. Wiesendanger, Phys. Rev. Lett. 96, 167203 (2006). PRLTAO 0031-9007 10.1103/PhysRevLett.96.167203
A. Deák, L. Szunyogh, and B. Ujfalussy, Phys. Rev. B 84, 224413 (2011). PRBMDO 1098-0121 10.1103/PhysRevB.84.224413
A. Crépieux and C. Lacroix, J. Magn. Magn. Mater. 182, 341 (1998). JMMMDC 0304-8853 10.1016/S0304-8853(97)01044-5
M. Bode, M. Heide, K. von Bergmann, P. Ferriani, S. Heinze, G. Bihlmayer, A. Kubetzka, O. Pietzsch, S. Blügel, and R. Wiesendanger, Nature (London) 447, 190 (2007). NATUAS 0028-0836 10.1038/nature05802
C. Sürgers, G. Fischer, P. Winkel, and H. Löhneysen, Nat. Commun. 5, 3400 (2014).
H. Chen, Q. Niu, and A. H. MacDonald, Phys. Rev. Lett. 112, 017205 (2014). PRLTAO 0031-9007 10.1103/PhysRevLett.112.017205
T. Tomizawa and H. Kontani, Phys. Rev. B 80, 100401 (2009). PRBMDO 1098-0121 10.1103/PhysRevB.80.100401
T. Tomizawa and H. Kontani, Phys. Rev. B 82, 104412 (2010). PRBMDO 1098-0121 10.1103/PhysRevB.82.104412
Y. Machida, S. Nakatsuji, Y. Maeno, T. Tayama, T. Sakakibara, and S. Onoda, Phys. Rev. Lett. 98, 057203 (2007). PRLTAO 0031-9007 10.1103/PhysRevLett.98.057203
Y. Taguchi, Y. Oohara, H. Yoshizawa, N. Nagaosa, and Y. Tokura, Science 291, 2573 (2001). SCIEAS 0036-8075 10.1126/science.1058161
Y. Machida, S. Nakatsuji, S. Onoda, T. Tayama, and T. Sakakibara, Nature (London) 463, 210 (2010). NATUAS 0028-0836 10.1038/nature08680
R. Shindou and N. Nagaosa, Phys. Rev. Lett. 87, 116801 (2001). PRLTAO 0031-9007 10.1103/PhysRevLett.87.116801
N. Nagaosa, J. Sinova, S. Onoda, A. MacDonald, and N. Ong, Rev. Mod. Phys. 82, 1539 (2010). RMPHAT 0034-6861 10.1103/RevModPhys.82.1539
P. Czaja, F. Freimuth, J. Weischenberg, S. Blügel, and Y. Mokrousov, Phys. Rev. B 89, 014411 (2014). PRBMDO 1098-0121 10.1103/PhysRevB.89.014411
The values of the AHC in units of S/cm can be obtained by dividing the values in Fig. 4 by the thickness of the film, and they lie in the range between several hundreds and several thousands S/cm, depending on the thickness. For example, in the case of a 3-layer-thick Ir substrate (0.82 nm total thickness) the total AHC constitutes (Equation presented) S/cm.
F. Freimuth, S. Blügel, and Y. Mokrousov, Phys. Rev. B 90, 174423 (2014). PRBMDO 1098-0121 10.1103/PhysRevB.90.174423
N. H. Long, P. Mavropoulos, B. Zimmermann, D. S. G. Bauer, S. Blügel, and Y. Mokrousov, Phys. Rev. B 90, 064406 (2014). PRBMDO 1098-0121 10.1103/PhysRevB.90.064406
Z. Fang, N. Nagaosa, K. S. Takahashi, A. Asamitsu, R. Mathieu, T. Ogasawara, H. Yamada, M. Kawasaki, Y. Tokura, and K. Terakura, Science 302, 92 (2003). SCIEAS 0036-8075 10.1126/science.1089408
R. Cheng and Q. Niu, Phys. Rev. B 86, 245118 (2012). PRBMDO 1098-0121 10.1103/PhysRevB.86.245118
O. Gomonay, Phys. Rev. B 91, 144421 (2015). PRBMDO 1098-0121 10.1103/PhysRevB.91.144421
J. Shi, G. Vignale, D. Xiao, and Q. Niu, Phys. Rev. Lett. 99, 197202 (2007). PRLTAO 0031-9007 10.1103/PhysRevLett.99.197202
