Abstract
The review is focused on the use of small-angle polarized-neutron diffraction to describe the orientation of local magnetization vector in spatially ordered magnetic metamaterials. The objects of study are direct and inverse opals; these materials are synthesized for diverse applications in magnetooptics, micro- and nanoelectronics, and photonics. The methodology of experiments and the theoretical base for processing experimental results are considered in detail. It is shown that the method of small-angle diffraction of polarized neutrons is unique in solving such problems; it is used at the limit of its possibilities when studying the magnetic structure under an applied field on the scale of ~400–800 nm. The questions of frustration of local magnetization vectors are discussed using the structural data on direct and inverse opals, obtained by ultra-small-angle diffraction of synchrotron radiation. The existing methods for synthesizing direct and inverse opals, which make it possible to obtain metamaterials with a three-dimensional ordered structure of nanoparticles, are also described.
Similar content being viewed by others
REFERENCES
S. John, Phys. Rev. Lett. 58 (23), 2486 (1987). https://doi.org/10.1103/PhysRevLett.58.2486
E. Yablonovitch, Phys. Rev. Lett. 58 (20), 2059 (1987). https://doi.org/10.1103/PhysRevLett.58.2059
J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton Univ. Press, Princeton, 1995).
T. F. Krauss and R. M. De La Rue, Prog. Quantum Electron. 23 (2), 51 (1999). https://doi.org/10.1016/S0079-6727(99)00004-X
Z. Cheng, W. B. Russel, and P. M. Chaikin, Nature 401 (6756), 893 (1999). https://doi.org/10.1038/44785
L. Meng, H. Wei, A. Nagel, et al., Nano Lett. 11 (8), 2249 (2006). https://doi.org/10.1021/nl061626b
J. H. J. Thijssen, A. V. Petukhov, D. C. Hart, et al., Adv. Mater. 18 (13), 1662 (2006). https://doi.org/10.1002/adma.200502732
A. van Blaaderen and P. Wiltzius, Science 270 (5239), 1177 (1995). https://www.jstor.org/stable/2889216.
A. L. Rogach, N. A. Kotov, D. S. Koktysh, et al., Chem. Mater. 12 (9), 2721 (2000). https://doi.org/10.1021/cm000274l
H. Wei, L. Meng, Y. Jun, and D. J. Norris, App. Phys. Lett. 89 (24), 241913 (2006). https://doi.org/10.1063/1.2404973
Yu. A. Vlasov, V. N. Astratov, A. V. Baryshev, et al., Phys. Rev. E 61, 5784 (2000). https://doi.org/10.1103/PhysRevE.61.5784
R. Rengarajan, D. Mittleman, Ch. Rich, and V. Colvin, Phys. Rev. E 71, 016615 (2005). https://doi.org/10.1103/PhysRevE.71.016615
S. V. Grigor’ev, K. S. Napol’skii, and N. A. Sapoletova, et al. RF Patent No. RU 2371525 C2 (2009), Byull. Izobret., 2009, no. 31, p. 42.
J. Hilhorst, V. V. Abramova, A. Sinitskii, et al., Langmuir 25 (17), 10408 (2009). https://doi.org/10.1021/la900983v
A. A. Eliseev, D. F. Gorozhankin, K. S. Napol’skii, et al., JETP Lett. 90 (4), 272 (2009). https://doi.org/10.1134/S0021364009160103
K. S. Napolskii, N. A. Sapoletova, D. F. Gorozhankin, et al., Langmuir 26 (4), 2346 (2010). https://doi.org/10.1021/la902793b
A. V. Vasil’eva, S. V. Grigor’ev, N. A. Grigor’eva, et al., Phys. Solid State 52 (5), 1087 (2010). https://doi.org/10.1134/S1063783410050409
N. A. Sapoletova, N. A. Martynova, K. C. Napol’skii, et al., Phys. Solid State 53 (6), 1126 (2011). https://doi.org/10.1134/S106378341106031X
N. A. Grigor’eva, A. V. Petukhov, and G. Ya. Vruge, Nondestructive Methods for Studying the Structure of Nanomaterials: A Teaching and Methodical Textbook (Solo, St. Petersburg, 2011) [in Russian].
A. K. Samusev, I. S. Sinev, K. B. Samusev, et al., Phys. Solid State 54 (10), 2073 (2012).
A. K. Samusev, K. B. Samusev, I. S. Sinev, et al., Light and Small Angle X-ray Diffraction from Opal-Based Structures, in Optical Properties of Photonic Structures: Interplay of Order and Disorder, Ed. by M. F. Limonov and R. De La Rue (Taylor and Francis, 2012).
A. V. Chumakova, A. A. Mistonov, A. A. Vorobiev, et al., J. Surf. Invest.: X-ray, Synchrotron Neutron Tech. 7 (6), 1234 (2013). https://doi.org/10.1134/S1027451013130041
V. M. Masalov, E. A. Kudrenko, N. A. Grigoryeva, et al., NANO 8, 1350036 (2013). https://doi.org/10.1142/S1793292013500367
K. S. Napolskii, A. S. Sinitskii, S. V. Grigoriev, et al., Physica B 397, 23 (2007). https://doi.org/10.1016/j.physb.2007.02.072
S. V. Grigor’ev, K. S. Napol’skii, N. A. Grigor’eva, et al., JETP Lett. 87 (1), 12 (2008). https://doi.org/10.1134/S0021364008010049
V. V. Abramova, A. S. Sinitskii, N. A. Grigor’eva, et al., JETP 109 (1), 29 (2009).
S. V. Grigoriev, K. S. Napolskii, N. A. Grigoryeva, et al., Phys. Rev. B 79, 045123 (2009). https://doi.org/10.1103/PhysRevB.79.045123
A. Sinitskii, V. Abramova, N. Grigorieva, et al., Europhys. Lett. 89, 14002 (2010). https://doi.org/10.1209/0295-5075/89/14002
S. V. Grigoriev, K. S. Napolskii, N. A. Grigoryeva, et al., J. Phys.: Conf. Ser. 247, 012029 (2010). https://doi.org/10.1088/1742-6596/247/1/012029
N. A. Grigoryeva, A. A. Mistonov, K. S. Napolskii, et al., Phys. Rev. B 84 (6), 064405 (2011). https://doi.org/10.1103/PhysRevB.84.064405
M. Kostylev, A. A. Stashkevich, Y. Roussigne, et al., Phys. Rev. B 86 (18), 184431 (2012). https://doi.org/10.1103/PhysRevB.86.184431
A. A. Mistonov, N. A. Grigoryeva, A. V. Chumakova, et al., Phys. Rev. B 87 (22), 220408 (2013). https://doi.org/10.1103/PhysRevB.87.220408
A. V. Chumakova, G. A. Valkovskiy, A. A. Mistonov, et al., Phys. Rev. B 90 (22), 144103 (2014). https://doi.org/10.1103/PhysRevB.90.144103
A. A. Mistonov, I. S. Shishkin, I. S. Dubitskii, et al., JETP 120 (5), 844 (2015). https://doi.org/10.7868/S0044451015050122
I. S. Shishkin, A. A. Mistonov, N. A. Grigor’eva, et al., Poverkhn.: Rentgenovskie, Sinkhrotronnye Neitr. Issled. 10 (1), 156 (2016). https://doi.org/10.7868/S020735281602013X
I. S. Shishkin, A. A. Mistonov, I. S. Dubitskiy, et al., Phys. Rev. B 94, 064424 (2016). https://doi.org/10.1103/PhysRevB.94.064424
I. S. Dubitskiy, A. V. Syromyatnikov, N. A. Grigoryeva, et al., J. Magn. Magn. Mater. 441, 609 (2017). https://doi.org/10.1016/j.jmmm.2017.06.036
I. S. Dubitskii, N. A. Grigor’eva, A. A. Mistonov, et al., Phys. Solid State 59 (12), 2464 (2017). https://doi.org/10.21883/FTT.2017.12.45245.071
I. S. Dubitskiy, AA. Mistonov, N. A. Grigoryeva, and S. V. Grigoriev, Physica B 549, 107 (2018). https://doi.org/10.1016/j.physb.2017.10.093
A. A. Mistonov, I. S. Dubitskiy, I. S. Shishkin, et al., J. Magn. Magn. Mater. 477, 99 (2019). https://doi.org/10.1016/j.jmmm.2019.01.016
A. A. Bykov, D. M. Gokhfeld, N. E. Savitskaya, et al., Supercond. Sci. Technol. 32 (11), 115004 (2019). https://doi.org/10.1088/1361-6668/ab3db7
W. Stober, A. Fink, and E. Bohn, J. Colloid Interface Sci. 26 (1), 62 (1968).
V. N. Bogomolov, L. S. Parfen’ev, A. V. Prokof’ev, et al., Fiz. Tverd. Tela 37, 3411 (1995).
V. M. Masalov, N. S. Sukhinina, E. A. Kudrenko, and G. A. Emelchenko, Nanotechnology 22, 275718 (2011). https://doi.org/10.1088/0957-4484/22/27/275718
J. W. Goodwin, J. Hearn, C. C. Ho, and R. H. Ottewill, Colloid Polym. Sci. 252 (6), 464 (1974). https://doi.org/10.1007/BF01554752
H. Miguez, C. Lopez, F. Meseguer, et al., App. Phys. Lett. 71 (9), 1148 (1997). https://doi.org/10.1063/1.119849
P. Jiang, J. F. Bertone, K. S. Hwang, and V. L. Colvin, Chem. Mater. 11 (8), 2132 (1999). https://doi.org/10.1021/cm990080+
D. J. Norris, E. G. Arlinghaus, L. Meng, et al., Adv. Mater. 16 (16), 1393 (2004). https://doi.org/10.1002/adma.200400455
A. I. Plekhanov, D. V. Kalinin, and V. V. Serdobintseva, Ross. Nanotechnol. 1, 245 (2006).
D. W. McComb, B. M. Treble, C. J. Smith, et al., J. Mater. Chem. 11 (1), 142 (2001). https://doi.org/10.1039/B003191G
O. D. Velev, T. A. Jede, R. F. Lobo, and A. M. Lenfoff, Chem. Mater. 10 (11), 3597 (1998). https://doi.org/10.1021/cm980444i
C. F. Blanford, T. N. Do, B. T. Holland, and A. Stein, Mater. Res. Soc. Symp. Proc. 549, 61 (1999). https://doi.org/10.1557/PROC-549-61
A. Richel, N. P. Johnson, and D. W. McComb, Appl. Phys Lett. 76 (14), 1816 (2000). https://doi.org/10.1063/1.126175
B. T. Holland, C. F. Blanford, and A. Stein, Chem. Mater. 11 (3), 795 (1999). https://doi.org/10.1021/cm980666g
S. H. Park and Y. Xia, Chem. Mater. 10 (7), 1745 (1998). https://doi.org/10.1021/cm020100z
H. Yan, C. F. Blanford, J. C. Lytle, et al., Chem. Mater. 13 (11), 4314 (2001). https://doi.org/10.1021/cm0105716
B. T. Holland, C. F. Blanford, and A. Stein, Science 281 (5376), 538 (1998). https://doi.org/10.1126/science.281.5376.538
J. E. G. J. Wijnhoven and W. L. Vos, Science 281 (5378), 802 (1998). https://doi.org/10.1126/science.281.5378.802
S. A. Johnson, P. J. Ollivier, and T. E. Mallouk, Science 283, 963 (1999). https://doi.org/10.1126/science.283.5404.963
B. Gates, Y. Yin, and Y. Xia, Chem. Mater. 11 (10), 2827 (1999). https://doi.org/10.1021/cm990195d
J. F. Bertone, P. Jiang, K. S. Hwang, et al., Phys. Rev. Lett. 83, 300 (1999). https://doi.org/10.1103/PhysRevLett.83.300
M. Deutsch, Y. A. Vlasov, and D. J. Norris, Adv. Mater. 12 (16), 1176 (2000). https://doi.org/10.1002/1521-4095(200008)12:16<1176::AID-ADMA1176>3.0.CO;2-H
H. Miguez, F. Meseguer, C. Lopez, et al., Adv. Mater. 13 (6), 393 (2001). https://doi.org/10.1002/1521-4095(200103)13:6<393::AID-ADMA393>3.0.CO;2-4
M. E. Turner, T. J. Trentler, and V. L. Colvin, Adv. Mater. 13 (6), 180 (2001). https://doi.org/10.1002/1521-4095(200102)13:3<180::AID-ADMA180>3.0.CO;2-Y
P. V. Braun and P. Wiltzius, Adv. Mater. 13 (7), 482 (2001). https://doi.org/10.1002/1521-4095(200104)13:7<482::AID-ADMA482>3.0.CO;2-4
T. Sumida, Y. Wada, T. Kitamura, and S. Yanagida, Chem. Lett. 30 (1), 38 (2001). https://doi.org/10.1246/cl.2001.38
Y. C. Lee, T. J. Kuo, C. J. Hsu, et al., Langmuir 18, 9942 (2002). https://doi.org/10.1021/la020296h
J. E. G. J. Wijnhoven, S. J. M. Zevenhuizen, M. A. Hendriks, et al., Adv. Mater. 12 (12), 888 (2000). https://doi.org/10.1002/1521-4095(200006)12:12<888::AID-ADMA888>3.0.CO;2-T
L. Xu, W. L. Zhou, C. Frommen, et al., Chem. Commun. 12, 997 (2000). https://doi.org/10.1039/B000404I
Q. Luo, Z. Liu, L. Li, et al., Adv. Mater. 13 (4), 286 (2001). https://doi.org/10.1002/1521-4095(200102)13:4<286::AID-ADMA286>3.0.CO;2-5
P. N. Bartlett, J. J. Baumberg, S. Coyle, and M. E. Abdelsalam, Faraday Discussion. 125, 117 (2004). https://doi.org/10.1039/B304116F
S. Nikitenko, A. M. Beale, A. M. J. van der Eerden, et al., J. Synchrotron Radiat. 15, 632 (2008). https://doi.org/10.1107/S0909049508023327
A. V. Petukhov, J. H. J. Thijssen, D. C. Hart, et al., J. Appl. Crystallogr. 39, 137 (2006). https://doi.org/10.1107/S0021889805041774
A. Snigirev, V. Kohn, I. Snigireva, and B. Lengeler, Nature 384 (6604), 49 (1996). https://doi.org/10.1038/384049a0
M. Drakopoulos, A. Snigirev, I. Snigireva, and J. Schilling, Appl. Phys. Lett. 86 (1), 014102 (2005). https://doi.org/10.1063/1.1843282
W. L. Bragg, Proc. Cambridge Philos. Soc. 17, 43 (1914).
J. M. Cowley, Diffraction Physics (Elsevier, Amsterdam, 1995).
P. Debye, Ann. Physik 43, 49 (1914).
J. Waller, Z. Physik 17, 398 (1923).
M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1969; Nauka, Moscow, 1970).
D. I. Svergun and L. A. Feigin, X-ray and Small-Angle Neutron Scattering (Nauka, Moscow, 1986) [in Russian].
L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 3: Quantum Mechanics (Gostekhizdat, Moscow, 1948; Pergamon, New York, 1977).
G. V. Wulff, Nature 1, 16 (1913).
A. Guinier and G. Fournet, Small-Angle Scattering of X-rays (Wiley, New York, 1955).
G. Porod, Acta Phys. Austriaca 2, 255 (1948).
O. Kratky and G. Porod, J. Colloid Sci. 4, 35 (1949).
M. Trau, D. A. Saville, and I. A. Aksay, Langmuir 13 (24), 6375 (1997). https://doi.org/10.1021/la970568u
W. D. Ristenpart, I. A. Aksay, and D. A. Saville, Phys. Rev. Lett. 90 (12), 128303 (2003). https://doi.org/10.1103/PhysRevLett.90.128303
A. Yethiraj, A. Wouterse, B. Groh, and A. van Blaaderen, Phys. Rev. Lett. 92 (5), 058301 (2004). https://doi.org/10.1103/PhysRevLett.92.058301
W. Loose and B. J. Ackerson, J. Chem. Phys. 101 (9), 7211 (1994). https://doi.org/10.1063/1.468278
M. Kobas, T. Weber, and W. Steurer, Phys. Rev. B 71 (22), 224205 (2005). https://doi.org/10.1103/PhysRevB.71.224205
T. R. Welberry, Diffuse X-ray Scattering and Models of Disorder (Oxford Univ. Press, Oxford, 2004).
H. Versmold, Phys. Rev. Lett. 75 (4), 763 (1995). https://doi.org/10.1103/PhysRevLett.75.763
A. J. C. Wilson, Proc. Roy. Soc. London A 180, 277 (1941).
I. I. Novikov, Defects of the Crystalline Structure of Metals (Metallurgiya, Moscow, 1975) [in Russian].
A. I. Akhiezer and I. Ya. Pomeranchuk, Certain Problems of Nuclear Theory (Gostekhizdat, Moscow, 1950) [in Russian].
Y. Toyozawa, Progr. Theor. Phys. 20 (1), 53 (1958).
Yu. A. Izyumov, Fiz. Met. Metalloved. 11 (5), 801 (1961).
Yu. A. Izyumov, Usp. Fiz. Nauk 80 (1), 41 (1963).
E. U. Condon and G. H. Shortley, Theory of Atomic Spectra (Cambridge Univ. Press, Cambridge, 1935; Inostrannaya Literatura, Moscow, 1949).
G. T. Trammell, Phys. Rev. 92, 1387 (1953).
S. V. Maleev, Zh. Eksp. Teor. Fiz. 40 (4), 1224 (1961).
O. Halpern and M. H. Jonson, Phys. Rev. 55, 898 (1939).
A. W. Saenz, Phys. Rev. 119, 1542 (1960).
S. V. Grigor’ev, N. A. Grigor’eva, A. V. Syromyatnikov, et al., JETP Lett. 85 (9), 449 (2007). https://doi.org/10.1134/S0021364007090081
S. Muhlbauer, A. Heinemann, A. Wilhelm, et al., Nucl. Instrum. Methods Phys. Res. A 832, 297 (2016). https://doi.org/10.1016/j.nima.2016.06.105
C. D. Dewhurst, I. Grillo, D. Honecker, et al., J. Appl. Crystallogr. 49, 1 (2016). https://doi.org/10.1107/S1600576715021792
ACKNOWLEDGMENTS
We are deeply grateful to all co-authors of the papers that were reviewed:
N.A. Sapoletov, K.S. Napol’skii, Andrei A. Eliseev, Artem A. Eliseev, A.S. Sinitskii, V.V. Abramov, A.V. Lukashin (staff and students of the Faculty of Materials Science of Moscow State University), A.K. Samusev, I.S. Sinev, K.B. Samusev, M.V. Rybin, M.F. Limonov, E.Yu. Trofimov, D.A. Kurdyukov, and V.G. Golubev (Ioffe Institute, Russian Academy of Sciences) for the preparation of the samples, participation in experiments, and fruitful discussions;
A.V. Petukhov, D.V. Belov, J. Hilhorst (Eindhoven University of Technology, the Netherlands), and W.G. Bouwman (Reactor of the Delft University of Technology, the Netherlands) for the participation in experiments and fruitful discussions;
D.Yu. Chernyshov and K. Kvashnina (BM-01 and DUBBLE, respectively; European Synchrotron Radiation Facility, ESRF, France), H. Eckerlebe (SANS-2, Helmholtz-Zentrum Geesthacht, Germany), D. Menzel (Technische Universität Braunschweig, Germany), A. Heinemann (SANS-1, Forschungsreaktor Technische Universität München (FRM-II), Germany), A. Vorob’ev and D. Honnecker (SuperAdam and small-angle neutron scattering instrument D33, respectively; Institut Laue–Langevin (ILL), France) for the provided experimental time at the research facilities and help in carrying out experiments;
I.S. Shishkin, I.S. Dubitskii, and G.A. Val’kovskii (staff and postgraduates of St. Petersburg State University) and А. Vasil’eva (Petersburg Nuclear Physics Institute) for processing experimental data, help in carrying out experiments, and discussion of the results.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
The authors declare that they have no conflicts of interest.
Additional information
Translated by Yu. Sin’kov
Rights and permissions
About this article
Cite this article
Grigoryeva, N.A., Mistonov, A.A. & Grigoriev, S.V. Small-Angle Neutron Diffraction for Studying Ferromagnetic Inverse Opal-Like Structures. Crystallogr. Rep. 67, 93–117 (2022). https://doi.org/10.1134/S1063774522010060
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063774522010060