SpringerLink
Log in

Electronic Phase Separation in Magnetic Materials

  • ELECTRICAL AND MAGNETIC PROPERTIES
  • Published:
Physics of Metals and Metallography Aims and scope Submit manuscript

Abstract

A review of the basic concepts and mechanisms related to the electronic phase separation and the formation of nanoscale inhomogeneities in magnetic materials is given. We put the main emphasis onto strongly correlated electron systems such as manganites, where phase separation occurs due to the competition of ferro- and antiferromagnetic states, as well as cobaltites, where the spin-state transitions play an important role. Special attention is paid to the mechanism of phase separation related to the imperfect nesting of sheets of the Fermi surface, which is especially important for systems with spin density waves, a striking example of which are iron-containing pnictides.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.
Fig. 9.
Fig. 10.
Fig. 11.
Fig. 12.
Fig. 13.
Fig. 14.
Fig. 15.
Fig. 16.
Fig. 17.
Fig. 18.
Fig. 19.
Fig. 20.
Fig. 21.
Fig. 22.

Similar content being viewed by others

REFERENCES

  1. E. Dagotto, Nanoscale Phase Separation and Colossal Magnetoresistance: The Physics of Manganites and Related Compounds (Springer, Berlin, 2013).

    Google Scholar 

  2. E. Nagaev, Colossal Magnetoresistance and Phase Separation in Magnetic Semiconductors (Imperial College, London, 2001).

    Google Scholar 

  3. E. Dagotto, T. Hotta, and A. Moreo, “Colossal magnetoresistant materials: the key role of phase separation,” Phys. Rep. 344, 1–153 (2001).

    Article  CAS  Google Scholar 

  4. E. Nagaev, “Colossal magnetoresistance materials: manganites and conventional magnetic semiconductors,” Phys. Rep. 346, 388–513 (2001).

    Article  Google Scholar 

  5. M. Yu. Kagan and K. I. Kugel, “Inhomogeneous charge distributions and phase separation in manganites,” Phys. Usp. 44, 553 (2001).

    Article  CAS  Google Scholar 

  6. M. Yu. Kagan, K. I. Kugel, and A. L. Rakhmanov, “Electronic phase separation: recent progress in the old problem,” Phys. Rep. 916, 1–106 (2021).

    Article  CAS  Google Scholar 

  7. N. G. Bebenin, R. I. Zainullina, and V. V. Ustinov, “Colossal magnetoresistance manganites,” Phys. Usp. 61, 719 (2018).

    Article  CAS  Google Scholar 

  8. E. L. Nagaev, “Ground states and anomalous magnetic moment of conduction electrons in an antiferromagnetic semiconductor,” Pis’ma Zh. Eksp. Teor. Fiz. 6, 484–486 (1967).

    CAS  Google Scholar 

  9. E. L. Nagaev, “Ferromagnetic microregions in a semiconductor antiferromagnet,” Zh. Eksp. Teor. Fiz. 54, 228–238 (1968).

    CAS  Google Scholar 

  10. T. Kasuya, A. Yanase, and T. Takeda, “Stability condition for the paramagnetic polaron in a magnetic semiconductor,” Solid State Commun. 8, 1543–1546 (1970).

    Article  CAS  Google Scholar 

  11. M. Hennion, F. Moussa, G. Biotteau, et al., “Liquidlike spatial distribution of magnetic droplets revealed by neutron scattering in La1 – xCaxMnO3,” Phys. Rev. Lett. 81, 1957–1960 (1998).

    Article  CAS  Google Scholar 

  12. M. Hennion, F. Moussa, G. Biotteau, et al., “Evidence of anisotropic magnetic polarons in La0.94Sr0.06MnO3 by neutron scattering and comparison with Ca-doped manganites,” Phys. Rev. B 61, 9513–9522 (2000).

    Article  CAS  Google Scholar 

  13. S. L. Ogarkov, M. Y. Kagan, A. O. Sboychakov, et al., “Formation of long-range spin distortions by a bound magnetic polaron,” Phys. Rev. B 74, 014436 (2006).

    Article  CAS  Google Scholar 

  14. A. O. Sboychakov, A. L. Rakhmanov, K. I. Kugel, M. Yu. Kagan, and I. V. Brodskii, “Tunnel magnetoresistance of phase-separated manganites,” J. Exp. Theor. Phys. 93, 753–761 (2002).

    Google Scholar 

  15. M. Y. Kagan, A. Klaptsov, I. Brodsky, et al., “Nanoscale phase separation in manganites,” J. Phys. A: Math. Gen. 36, 9155.

  16. I. Gonzalez, J. Castro, D. Baldomir, et al., “Magnetic polarons in a doped one-dimensional antiferromagnetic chain,” Phys. Rev. B 69, 224409 (2004).

    Article  CAS  Google Scholar 

  17. A. O. Sboychakov, A. L. Rakhmanov, K. I. Kugel, et al., “Evolution with temperature of the magnetic polaron state in an antiferromagnetic chain with impurities,” Phys. Rev. B 72, 014438 (2005).

    Article  CAS  Google Scholar 

  18. A. M. Balagurov, V. Y. Pomjakushin, D. V. Sheptyakov, et al., “Long-scale phase separation versus homogeneous magnetic state in (La1 – yPry)0.7Ca0.3MnO3: A neutron diffraction study,” Phys. Rev. B 64, 024420 (2001).

    Article  CAS  Google Scholar 

  19. M. Uehara, S. Mori, C. H. Chen, and S. -W. Cheong, “Percolative phase separation underlies colossal magnetoresistance in mixed-valent manganites,” Nature 399, 560–563 (1999).

    Article  CAS  Google Scholar 

  20. M. Kagan, K. Kugel, and D. Khomskii, “Phase separation in systems with charge ordering,” J. Exp. Theor. Phys. 93, 415–423 (2001).

    Article  CAS  Google Scholar 

  21. S. Mori, C. H. Chen, and S. -W. Cheong, “Pairing of charge-ordered stripes in (La,Ca)MnO3,” Nature 392, 473–476 (1998).

    Article  CAS  Google Scholar 

  22. P. G. Radaelli, D. E. Cox, L. Capogna, et al., “Wigner-crystal and bi-stripe models for the magnetic and crystallographic superstructures of La0.333Ca0.667MnO3,” Phys. Rev. B 59, 14440–14450 (1999).

    Article  CAS  Google Scholar 

  23. B. Raveau, M. Hervieu, A. Maignan, and C. Martin, “The route to CMR manganites: What about charge ordering and phase separation?,” J. Mater. Chem. 11, 29–36 (2001).

    Article  CAS  Google Scholar 

  24. D. I. Khomskii and K. I. Kugel, “Elastic interactions and superstructures in manganites and other Jahn‒Teller systems,” Phys. Rev. B 67, 134401 (2003).

    Article  CAS  Google Scholar 

  25. J. Bala, P. Horsch, and F. Mack, “Manganites at quarter filling: Role of Jahn-Teller interactions,” Phys. Rev. B 69, 094415 (2004).

    Article  CAS  Google Scholar 

  26. M. Gulacsi, A. Bussmann-Holder, and A. R. Bishop, “Spin and lattice effects in the Kondo lattice model,” Phys. Rev. B 71, 214415 (2005).

    Article  CAS  Google Scholar 

  27. G. V. Pai, S. R. Hassan, H. R. Krishnamurthy, and T. V. Ramakrishnan, “Zero-temperature insulator-metal transition in doped manganites,” Europhys Lett. 64, 696 (2003).

    Article  CAS  Google Scholar 

  28. T. V. Ramakrishnan, H. R. Krishnamurthy, S. R. Hassan, and G. V. Pai, “Theory of insulator-metal transition and colossal magnetoresistance in doped manganites,” Phys. Rev. Lett. 92, 157203 (2004).

    Article  CAS  Google Scholar 

  29. O. Cepas, H. R. Krishnamurthy, and T. V. Ramakrishnan, “Do** and field-induced insulator-metal transitions in half-doped manganites,” Phys. Rev. Lett. 94, 247207 (2005).

    Article  CAS  Google Scholar 

  30. C. Zener, “Interaction between the d-shells in the transition metals. II. Ferromagnetic compounds of manganese with perovskite structure,” Phys. Rev. 82, 403–405 (1951).

    Article  CAS  Google Scholar 

  31. Yu. A. Izyumov and Yu. N. Skryabin, “Double exchange model and the unique properties of the manganites,” Phys. Usp. 44, No. 2, 109–134 (2001).

    Article  CAS  Google Scholar 

  32. K. I. Kugel, A. L. Rakhmanov, and A. O. Sboychakov, “Phase separation in Jahn‒Teller systems with localized and itinerant electrons,” Phys. Rev. Lett. 95, 267210 (2005).

    Article  CAS  Google Scholar 

  33. P.-G. de Gennes, “Effects of double exchange in magnetic crystals,” Phys. Rev. 118, 141–154 (1960).

    Article  CAS  Google Scholar 

  34. L. M. Falicov and J. C. Kimball, “Simple model for semiconductor-metal transitions: SmB6 and transition-metal oxides,” Phys. Rev. Lett. 22, 997–999 (1969).

    Article  CAS  Google Scholar 

  35. J. K. Freericks, E. H. Lieb, and D. Ueltschi, “Phase separation due to quantum mechanical correlations,” Phys. Rev. Lett. 88, 106401 (2002).

    Article  CAS  Google Scholar 

  36. A. S. Alexandrov and N. F. Mott, Polarons & Bipolarons (World Scientific, Singapore, 1995).

    Google Scholar 

  37. K. I. Kugel and D. I. Khomskii, “Polaron effects and exchange interaction in magnetic dielectrics with jahn-teller ions,” Zh. Eksp. Teor. Fiz. 79, 987–1005 (1980).

    Google Scholar 

  38. J. S. Smart, Effective Field in Theory of Magnetism (Saunders, Philadelphia, 1966).

  39. E. L. Nagaev, “Concentration phase transition to a noncollinear magnetic state,” Zh. Eksp. Teor. Fiz. 57, 1274–1279 (1969) [Sov. Phys. JETP 30, 693–695 (1970)].

    Google Scholar 

  40. A. O. Sboychakov, K. I. Kugel, and A. L. Rakhmanov, “Jahn‒Teller distortions and phase separation in doped manganites,” Phys. Rev. B 74, 014401 (2006).

    Article  CAS  Google Scholar 

  41. L. D. Landau and E. M. Lifshitz, Statistical Physics. Part 1 (Elsevier, Amsterdam, 2013).

    Google Scholar 

  42. A. L. Rakhmanov, K. I. Kugel, Ya. M. Blanter, and M. Yu. Kagan, “Resistivity and 1/f noise in nonmetallic phase-separated manganites,” Phys. Rev. B 63, 174424 (2001).

    Article  CAS  Google Scholar 

  43. K. I. Kugel, A. L. Rakhmanov, A. O. Sboychakov, et al., “Characteristics of the phase-separated state in manganites: relationship with transport and magnetic properties,” J. Exp. Theor. Phys. 98, 572–581 (2004).

    Article  CAS  Google Scholar 

  44. A. Sboychakov, A. Rakhmanov, K. Kugel, et al., “Tunnelling magnetoresistance and 1/f noise in phase-separated manganites,” J. Phys.: Condens. Matter 15, 1705 (2003).

    CAS  Google Scholar 

  45. M. Hennion, F. Moussa, G. Biotteau, et al., “Liquidlike spatial distribution of magnetic droplets revealed by neutron scattering in La1 – xCaxMnO3,” Phys. Rev. Lett. 81, 1957–1960 (1998).

    Article  CAS  Google Scholar 

  46. M. Hennion, F. Moussa, G. Biotteau, et al., “Evidence of anisotropic magnetic polarons in La0.94Sr0.06MnO3 by neutron scattering and comparison with Ca-doped manganites,” Phys. Rev. B 61, 9513–9522 (2000).

    Article  CAS  Google Scholar 

  47. G. Allodi, R. De Renzi, G. Guidi, et al., “Electronic phase separation in lanthanum manganites: Evidence from 55Mn NMR,” Phys. Rev. B 56, 6036–6046 (1997).

    Article  CAS  Google Scholar 

  48. J. M. D. Teresa, M. R. Ibarra, P. A. Algarabel, et al., “Evidence for magnetic polarons in the magnetoresistive perovskites,” Nature 386, 256–259 (1997).

    Article  Google Scholar 

  49. N. I. Solin, V.V. Mashkautsan, A.V. Korolev, et al., “Magnetic polarons, clusters, and their effect on the electric properties of weakly doped lanthanum manganites,” JETP Lett. 77, 230–235 (2003).

    Article  CAS  Google Scholar 

  50. N. I. Solin, “Intrinsic inhomogeneities of low-doped lanthanum manganites in the paramagnetic temperature range,” J. Exp. Theor. Phys. 114, 96–106 (2012).

    Article  CAS  Google Scholar 

  51. M. Fath, S. Freisem, A. Menovsky, et al., “Spatially inhomogeneous metal-insulator transition in doped manganites,” Science 285, 1540–1542 (1999).

    Article  CAS  Google Scholar 

  52. N. Babushkina, E. Chistotina, K. Kugel, et al., “Magnetoresistance and magnetic susceptibility of phase-separated La–Pr–Ca manganites,” J. Phys.: Condens. Matter 15, 259 (2002).

    Google Scholar 

  53. L. Fisher, A. Kalinov, I. Voloshin, et al., “Phase separation and isotope effect in the ferromagnetic insulating state of the Pr1 – xCaxMnO3 system (0.2 < x < 0.33),” Phys. Rev. B 68, 174403 (2003).

    Article  CAS  Google Scholar 

  54. P. Wagner, I. Gordon, V. Moshchalkov, et al., “Spin-dependent hop** in the paramagnetic state of the bilayer manganite (La0.4Pr0.6)1.2Sr1.8Mn2O7,” Europhys. Lett. 58, 285 (2002).

    Article  CAS  Google Scholar 

  55. J. Zhao, H. Kunkel, X. Zhou, and G. Williams, “Magnetic and transport properties, and the phase diagram of hole-doped La1 – xMgxMnO3 (x < 0.4),” J. Phys.: Condens. Matter 13, 9349 (2001).

    CAS  Google Scholar 

  56. K. I. Kugel, A. L. Rakhmanov, A. O. Sboychakov, and D. I. Khomskii, “Doped orbitally ordered systems: Another case of phase separation,” Phys. Rev. B 78, 155113 (2008).

    Article  CAS  Google Scholar 

  57. K. Kugel, A. Sboychakov, and D. Khomskii, “Inhomogeneous states in strongly correlated electron systems with orbital degrees of freedom,” J. Supercond. Nov. Magn. 22, 147‒153 (2009).

    Article  CAS  Google Scholar 

  58. P. M. Raccah and J. B. Goodenough, “First-order localized-electron ↔ collective-electron transition in LaCoO3,” Phys. Rev. B 55, 932–943 (1967).

    Article  Google Scholar 

  59. S. Yamaguchi, Y. Okimoto, H. Taniguchi, and Y. Tokura, “Spin-state transition and high-spin polarons in LaCoO3,” Phys. Rev. B 53, R2926–R2929.

  60. S. Yamaguchi, Y. Okimoto, and Y. Tokura, “Local lattice distortion during the spin-state transition in LaCoO3,” Phys. Rev. B 55, 8666–8669 (1997).

    Article  Google Scholar 

  61. M. A. Korotin, S. Y. Ezhov, I. V. Solovyev, et al., “Intermediate-spin state and properties of LaCoO3,” Phys. Rev. B 54, 5309–5316 (1996).

    Article  CAS  Google Scholar 

  62. N. B. Ivanova, S. G. Ovchinnikov, M. M. Korshunov, I. M. Eremin, and N. V. Kazak, “Specific features of spin, charge, and orbital ordering in cobaltites,” Phys. Usp. 52, 789 (2009).

    Article  CAS  Google Scholar 

  63. M. Pouchard, A. Villesuzanne, and J.-P. Doumerc, “Spin state behavior in some cobaltites(III) and (IV) with perovskite or related structure,” J. Solid State Chem. 162, 282‒292 (2001).

    Article  CAS  Google Scholar 

  64. D. I. Khomskii and U. Low, “Superstructures at low spin—high spin transitions,” Phys. Rev. B 69, 184401 (2004).

    Article  CAS  Google Scholar 

  65. A. Maignan, V. Caignaert, B. Raveau, et al., “Thermoelectric power of HoBaCo2O5.5: possible evidence of the spin blockade in cobaltites,” Phys. Rev. Lett. 93, 026401 (2004).

    Article  CAS  Google Scholar 

  66. L. N. Bulaevskii, E. L. Nagaev, and D. I. Khomskii, “A new type of self-trapped state of a conduction electron in an antiferromagnetic semiconductor,” Zh. Eksp. Teor. Fiz. 54, 1562‒1565 (1968) [Sov. Phys. JETP 27, 836–838 (1968)].

    CAS  Google Scholar 

  67. A. O. Sboychakov, K. I. Kugel, A. L. Rakhmanov, and D. I. Khomskii, “Phase separation in doped systems with spin-state transitions,” Phys. Rev. B 80, 024423 (2009).

    Article  CAS  Google Scholar 

  68. A. Podlesnyak, M. Russina, A. Furrer, et al., “Spin-state polarons in lightly hole-doped LaCoO3,” Phys. Rev. Lett. 101, 247603 (2008).

    Article  CAS  Google Scholar 

  69. R. Caciuffo, D. Rinaldi, G. Barucca, et al., “Structural details and magnetic order of La1 – xSrxCoO3 (x \( \lesssim \) 0.3),” Phys. Rev. B 59, 1068‒1078 (1999).

    Article  CAS  Google Scholar 

  70. N. N. Loshkareva, E. A. Gan’shina, B. I. Belevtsev, et al., “Spin states and phase separation in La1 – xSrxCoO3 (x = 0.15, 0.25, 0.35) films: Optical, magneto-optical, and magnetotransport studies,” Phys. Rev. B 68, 024413 (2003).

    Article  CAS  Google Scholar 

  71. D. Phelan, D. Louca, K. Kamazawa, et al., “Spin incommensurability and two phase competition in cobaltites,” Phys. Rev. Lett. 97, 235501.

  72. S. R. Giblin, I. Terry, D. Prabhakaran, et al., “Local matrix-cluster interactions in a phase separated perovskite,” Phys. Rev. B 74, 104411 (2006).

    Article  CAS  Google Scholar 

  73. C. He, M. A. Torija, J. Wu, et al., “Non-Griffiths-like clustered phase above the Curie temperature of the doped perovskite cobaltite La1 – xSrxCoO3,” Phys. Rev. B 76, 014401 (2007).

    Article  CAS  Google Scholar 

  74. D. I. Khomskii, Basic Aspects of the Quantum Theory of Solids: Order and Elementary Excitations (Cambridge University, 2010).

    Book  Google Scholar 

  75. G. Gruner, “The dynamics of charge-density waves,” Rev. Mod. Phys. 60, 1129–1181 (1988).

    Article  Google Scholar 

  76. P. Monceau, “Electronic crystals: an experimental overview,” Adv. Phys. 61, 325–581 (2012).

    Article  CAS  Google Scholar 

  77. A. W. Overhauser, “Spin density waves in an electron gas,” Phys. Rev. 128, 1437–1452 (1962).

    Article  Google Scholar 

  78. G. Gruner, “The dynamics of spin-density waves,” Rev. Mod. Phys. 66, 1–24 (1994).

    Article  CAS  Google Scholar 

  79. A. Shibatani, K. Motizuki, and T. Nagamiya, “Spin density wave in chromium and its alloys,” Phys. Rev. 177, 984–1000 (1969).

    Article  CAS  Google Scholar 

  80. A. Shibatani, “Effect of magnetic field on spin density wave in chromium,” J. Phys. Soc. Jpn. 26, 299–308 (1969).

    Article  CAS  Google Scholar 

  81. A. Shibatani, “Néel temperature of the spin density wave in chromium and its alloys,” J. Phys. Soc. Jpn. 29, 93–101 (1970).

    Article  Google Scholar 

  82. T. Rice, “Band-structure effects in itinerant antiferromagnetism,” Phys. Rev. B 2, 3619 (1970).

    Article  Google Scholar 

  83. J. Ruvalds, C. Rieck, S. Tewari, et al.,  “Nesting mechanism for d-symmetry superconductors,” Phys. Rev. B 51, 3797 (1995).

    Article  CAS  Google Scholar 

  84. A. Gabovich, A. Voitenko, J. Annett, and M. Ausloos, “Charge- and spin-density-wave superconductors,” Supercond. Sci. Technol. 14, R1 (2001).

    Article  CAS  Google Scholar 

  85. K. Terashima, Y. Sekiba, J. H. Bowen, et al., “Fermi surface nesting induced strong pairing in iron-based superconductors,” Proc. Natl. Acad. Sci. 106, 7330–7333 (2009).

    Article  CAS  Google Scholar 

  86. Y. -D. Chuang, A. Gromko, D. Dessau, et al., “Fermi surface nesting and nanoscale fluctuating charge/orbital ordering in colossal magnetoresistive oxides,” Science 292, 1509–1513 (2001).

    Article  CAS  Google Scholar 

  87. I. Eremin and A. V. Chubukov, “Magnetic degeneracy and hidden metallicity of the spin-density-wave state in ferropnictides,” Phys. Rev. B 81, 024511 (2010).

    Article  CAS  Google Scholar 

  88. A. Chubukov, “Renormalization group analysis of competing orders and the pairing symmetry in Fe-based superconductors,” Phys. C 469, 640–650 (2009).

    Article  CAS  Google Scholar 

  89. S. Graser, T. Maier, P. Hirschfeld, and D. Scalapino, “Near-degeneracy of several pairing channels in multiorbital models for the Fe pnictides,” New J. Phys. 11, 025016 (2009).

    Article  CAS  Google Scholar 

  90. M. Vavilov, A. Chubukov, and A. Vorontsov, “Coexistence between superconducting and spin density wave states in iron-based superconductors: Ginzburg‒Landau analysis,” Supercond. Sci. Technol. 23, 054011 (2010).

    Article  CAS  Google Scholar 

  91. T. Kondo, R. M. Fernandes, R. Khasanov, et al., “Unexpected Fermi-surface nesting in the pnictide parent compounds BaFe2As2 and CaFe2As2 revealed by angle-resolved photoemission spectroscopy,” Phys. Rev. B 81, 060507 (2010).

    Article  CAS  Google Scholar 

  92. P. Brydon, J. Schmiedt, and C. Timm, “Microscopically derived Ginzburg‒Landau theory for magnetic order in the iron pnictides,” Phys. Rev. B 84, 214510 (2011).

    Article  CAS  Google Scholar 

  93. J. Schmiedt, P. Brydon, and C. Timm, “Do** dependence of antiferromagnetism in models of the pnictides,” Phys. Rev. B 85, 214425 (2012).

    Article  CAS  Google Scholar 

  94. Yu. A. Izyumov, M. I. Katsnel’son, and Yu. N. Skryabin, Magnetism of Collectivized Electrons (Fizmatlit, Moscow, 1994).

    Google Scholar 

  95. N. I. Kulikov and V. V. Tugushev, “Spin density waves and band antiferromagnetism in metals,” Usp. Fiz. Nauk 144, No. 12. 643–680 (1984) [Sov. Phys. Usp. 27, 954–976 (1984)].

    Article  CAS  Google Scholar 

  96. E. Fawcett, “Spin-density-wave antiferromagnetism in chromium,” Rev. Mod. Phys. 60, 209 (1988).

    Article  CAS  Google Scholar 

  97. A. L. Rakhmanov, A. V. Rozhkov, A. O. Sboychakov, and F. Nori, “Phase separation of antiferromagnetic ground states in systems with imperfect nesting,” Phys. Rev. B 87, 075128 (2013).

    Article  CAS  Google Scholar 

  98. A. O. Sboychakov, A. V. Rozhkov, K. I. Kugel, et al., “Electronic phase separation in iron pnictides,” Phys. Rev. B 88, 195142 (2013).

    Article  CAS  Google Scholar 

  99. A. A. Gorbatsevich, Yu. V. Kopaev, and I. V. Tokatly, “Zone theory of phase stratification,” Zh. Eksp. Teor. Fiz. 101, 971‒994 (1992) [JETP 74, 521–532 (1992)].

    Google Scholar 

  100. J. T. Park, D. S. Inosov, C. Niedermayer, et al., “Electronic phase separation in the slightly underdoped iron pnictide superconductor Ba1 – xKxFe2As2,” Phys. Rev. Lett. 102, 117006 (2009).

    Article  CAS  Google Scholar 

  101. D. S. Inosov, A. Leineweber, X. Yang, et al., “Suppression of the structural phase transition and lattice softening in slightly underdoped Ba1 – xKxFe2As2 with electronic phase separation,” Phys. Rev. B 79, 224503 (2009).

    Article  CAS  Google Scholar 

  102. G. Lang, H. -J. Grafe, D. Paar, et al., “Nanoscale electronic order in iron pnictides,” Phys. Rev. Lett. 104, 097001 (2010).

    Article  CAS  Google Scholar 

  103. T. Goko, A. A. Aczel, E. Baggio-Saitovitch, et al., “Superconducting state coexisting with a phase-separated static magnetic order in (Ba,K)Fe2As2, (Sr,Na)Fe2As2, and CaFe2As2,” Phys. Rev. B 80, 024508 (2009).

    Article  CAS  Google Scholar 

  104. C. Bernhard, C. N. Wang, L. Nuccio, et al., “Muon spin rotation study of magnetism and superconductivity in Ba(Fe1 – xCox)2As2 single crystals,” Phys. Rev. B 86, 184509 (2012).

    Article  CAS  Google Scholar 

  105. X. Lu, D. W. Tam, C. Zhang, et al., “Short-range cluster spin glass near optimal superconductivity in BaFe2 – xNixAs2,” Phys. Rev. B 90, 024509 (2014).

    Article  CAS  Google Scholar 

  106. E. Civardi, M. Moroni, M. Babij, et al., “Superconductivity emerging from an electronic phase separation in the charge ordered phase of RbFe2As2,” Phys. Rev. Lett. 117, 217001 (2016).

    Article  CAS  Google Scholar 

  107. B. Shen, B. Zeng, G. Chen, et al., “Intrinsic percolative superconductivity in KxFe2 – ySe2 single crystals,” Europhys. Lett. 96, 37010 (2011).

    Article  CAS  Google Scholar 

  108. A. Ricci, N. Poccia, G. Campi, et al., “Nanoscale phase separation in the iron chalcogenide superconductor K0.8Fe1.6Se2 as seen via scanning nanofocused X-ray diffraction,” Phys. Rev. B 84, 060511 (2011).

    Article  CAS  Google Scholar 

  109. A. Ricci, N. Poccia, B. Joseph, et al., “Direct observation of nanoscale interface phase in the superconducting chalcogenide KxFe2 – ySe2 with intrinsic phase separation,” Phys. Rev. B 91, 020503 (2015).

    Article  CAS  Google Scholar 

  110. P. Dai, J. Hu, and E. Dagotto, “Magnetism and its microscopic origin in iron-based high-temperature superconductors,” Nat. Phys. 8, 709‒718 (2012).

    Article  CAS  Google Scholar 

  111. A. Narayanan, A. Kiswandhi, D. Graf, et al., “Coexistence of spin density waves and superconductivity in (TMTSF)2PF6,” Phys. Rev. Lett. 112, 146402 (2014).

    Article  CAS  Google Scholar 

  112. G. Campi, A. Bianconi, N. Poccia, et al., “Inhomogeneity of charge-density-wave order and quenched disorder in a high-Tc superconductor,” Nature 525, 359‒362 (2015).

    Article  CAS  Google Scholar 

  113. A. L. Rakhmanov, K. I. Kugel, and A. O. Sboychakov, “Coexistence of spin density wave and metallic phases under pressure,” J. Supercond. Nov. Magn. 33, 2405–2413 (2020).

    Article  CAS  Google Scholar 

  114. R. Y. Chen, B. F. Hu, T. Dong, and N. L. Wang, “Revealing multiple charge-density-wave orders in TbTe3 by optical conductivity and ultrafast pump-probe experiments,” Phys. Rev. B 89, 075114 (2014).

    Article  CAS  Google Scholar 

  115. J. Zaanen and O. Gunnarsson, “Charged magnetic domain lines and the magnetism of high-Tc oxides,” Phys. Rev. B 40, 7391‒7394 (1989).

    Article  CAS  Google Scholar 

  116. R. S. Akzyanov and A. V. Rozhkov, “Generation of localized magnetic moments in the charge-density-wave state,” Eur. Phys. J. B 88, 1‒9 (2015).

    Article  CAS  Google Scholar 

  117. S. V. Kokanova, P. A. Maksimov, A. V. Rozhkov, and A. O. Sboychakov, “Competition of spatially inhomogeneous phases in systems with nesting-driven spin-density wave state,” Phys. Rev. B 104, 075110 (2021).

    Article  CAS  Google Scholar 

  118. P. Igoshev, M. Timirgazin, V. Gilmutdinov, et al., “Spiral magnetism in the single-band Hubbard model: the Hartree‒Fock and slave-boson approaches,” J. Phys.: Condens. Matter 27, 446002 (2015).

    CAS  Google Scholar 

  119. P. Igoshev, M. Timirgazin, V. Gilmutdinov, et al., “Correlation effects and non-collinear magnetism in the doped Hubbard model,” J. Magn. Magn. Mater. 383, 2‒7 (2015).

    Article  CAS  Google Scholar 

  120. M. J. Calderon, G. Leon, B. Valenzuela, and E. Bascones, “Magnetic interactions in iron superconductors studied with a five-orbital model within the Hartree‒Fock and Heisenberg approximations,” Phys. Rev. B 86, 104514 (2012).

    Article  CAS  Google Scholar 

  121. Q. Luo and E. Dagotto, “Magnetic phase diagram of a five-orbital Hubbard model in the real-space Hartree‒Fock approximation varying the electronic density,” Phys. Rev. B 89, 045115 (2014).

    Article  CAS  Google Scholar 

  122. P. Fulde and R. A. Ferrell, “Superconductivity in a strong spin-exchange field,” Phys. Rev. 135, 550 (1964).

    Article  Google Scholar 

  123. A. I. Larkin and Yu. N. Ovchinnikov, “Inhomogeneous state of superconductors,” Zh. Eksp. Teor. Fiz. 47, 1136–1146 (1964) [Sov. Phys. JETP 20, 762–770 (1965)].

    CAS  Google Scholar 

  124. A. O. Sboychakov, A. V. Rozhkov, A. L. Rakhmanov, and F. Nori, “Antiferromagnetic states and phase separation in doped AA-stacked graphene bilayers,” Phys. Rev. B 88, 045409 (2013).

    Article  CAS  Google Scholar 

  125. D. E. Sheehy and L. Radzihovsky, “BEC‒BCS crossover, phase transitions, and phase separation in polarized resonantly-paired superfluids,” Ann. Phys. 322, 1790‒1924 (2007).

    Article  CAS  Google Scholar 

  126. L. P. Gor’kov and G. B. Teitel’baum, “Spatial inhomogeneities in iron pnictide superconductors: The formation of charge stripes,” Phys. Rev. B 82, 020510 (2010).

    Article  CAS  Google Scholar 

  127. Q. Luo, D.-X. Yao, A. Moreo, and E. Dagotto, “Charge stripes in the two-orbital Hubbard model for iron pnictides,” Phys. Rev. B 83, 174513 (2011).

    Article  CAS  Google Scholar 

  128. Y. Matsuda and H. Shimahara, “Fulde‒Ferrell‒Larkin‒Ovchinnikov state in heavy fermion superconductors,” J. Phys. Soc. Jpn. 76, 051005 (2007).

    Article  CAS  Google Scholar 

  129. C. Mora and R. Combescot, “Transition to Fulde‒Ferrell‒Larkin‒Ovchinnikov phases in three dimensions: A quasiclassical investigation at low temperature with Fourier expansion,” Phys. Rev. B 71, 214504 (2005).

    Article  CAS  Google Scholar 

  130. H. Burkhardt and D. Rainer, “Fulde‒Ferrell‒Larkin‒Ovchinnikov state in layered superconductors,” Ann. Phys. 506, 181‒194 (1994).

    Article  Google Scholar 

  131. S. Takada, “Superconductivity in a molecular field. II Stability of Fulde‒Ferrel phase,” Prog. Theor. Phys. 43, 27‒38 (1970).

    Article  CAS  Google Scholar 

  132. Y. Kamihara, T. Watanabe, M. Hirano, and H. Hosono, “Iron-based layered superconductor La[O1 – xFx]FeAs (x = 0.05‒0.12) with T c = 26 K,” J. Am. Chem. Soc. 130, 3296‒3297 (2008).

    Article  CAS  Google Scholar 

  133. M. Rotter, M. Tegel, and D. Johrendt, “Superconductivity at 38 K in the iron arsenide (Ba1 – xKx)Fe2As,” Phys. Rev. Lett. 101, 107006 (2008).

    Article  CAS  Google Scholar 

  134. X. Wang, Q. Liu, Y. Lv, et al., “The superconductivity at 18 K in LiFeAs system,” Solid State Commun. 148, 538‒540 (2008).

    Article  CAS  Google Scholar 

  135. G. R. Stewart, “Superconductivity in iron compounds,” Rev. Mod. Phys. 83, 1589–1652 (2011).

    Article  CAS  Google Scholar 

  136. P. Dai, “Antiferromagnetic order and spin dynamics in iron-based superconductors,” Rev. Mod. Phys. 87, 855–896 (2015).

    Article  CAS  Google Scholar 

  137. F. Rullier-Albenque, D. Colson, A. Forget et al., “Hole and electron contributions to the transport properties of Ba(Fe1 – xRux)2As2 single crystals,” Phys. Rev. B 81, 224503 (2010).

    Article  CAS  Google Scholar 

  138. Y. Laplace, J. Bobroff, V. Brouet, et al., “Nanoscale-textured superconductivity in Ru-substituted BaFe2As2: A challenge to a universal phase diagram for the pnictides,” Phys. Rev. B 86, 020510 (2012).

    Article  CAS  Google Scholar 

  139. P. Richard, T. Sato, K. Nakayama, et al., “Fe-based superconductors: an angle-resolved photoemission spectroscopy perspective,” Rep. Prog. Phys. 74, 124512 (2011).

    Article  CAS  Google Scholar 

  140. A. Kordyuk, “Iron-based superconductors: Magnetism, superconductivity, and electronic structure,” Low Temp. Phys. 38, 888‒899 (2012).

    Article  CAS  Google Scholar 

  141. I. A. Nekrasov, N. S. Pavlov, and M. V. Sadovskii, “Electronic structure of NaFeAs superconductor: LDA + DMFT Calculations compared with ARPES experiment,” J. Supercond. Nov. Magn. 29, 1117‒1122 (2016).

    Article  CAS  Google Scholar 

  142. S. Graser, A. F. Kemper, T. A. Maier, et al., “Spin fluctuations and superconductivity in a three-dimensional tight-binding model for BaFe2As2,” Phys. Rev. B 81, 214503 (2010).

    Article  CAS  Google Scholar 

  143. I. I. Mazin, “Superconductivity gets an iron boost,” Nature 464, 183‒186 (2010).

    Article  CAS  Google Scholar 

  144. J. Fink, S. Thirupathaiah, R. Ovsyannikov, et al., “Electronic structure studies of BaFe2As2 by angle-resolved photoemission spectroscopy,” Phys. Rev. B 79, 155118 (2009).

    Article  CAS  Google Scholar 

  145. K. Kugel, A. Rakhmanov, A. Sboychakov, et al., “A two-band model for the phase separation induced by the chemical mismatch pressure in different cuprate superconductors,” Supercond. Sci. Technol. 22, 014007 (2009).

    Article  CAS  Google Scholar 

  146. J. Lorenzana, C. Castellani, and C. Di Castro, “Phase separation frustrated by the long-range Coulomb interaction. I. Theory,” Phys. Rev. B 64, 235127 (2001).

    Article  CAS  Google Scholar 

  147. J. Lorenzana, C. Castellani, and C. Di Castro, “Phase separation frustrated by the long-range Coulomb interaction. II. Applications,” Phys. Rev. B 64, 235128 (2001).

    Article  CAS  Google Scholar 

  148. R. Jamei, S. Kivelson, and B. Spivak, “Universal aspects of Coulomb-frustrated phase separation,” Phys. Rev. Lett. 94, 056805 (2005).

    Article  CAS  Google Scholar 

  149. Y. Laplace, J. Bobroff, F. Rullier-Albenque, et al., “Atomic coexistence of superconductivity and incommensurate magnetic order in the pnictide Ba(Fe1 – xCox)2As2,” Phys. Rev. B 80, 140501 (2009).

    Article  CAS  Google Scholar 

  150. P. Bonville, F. Rullier-Albenque, D. Colson, and A. Forget, “Incommensurate spin density wave in Co-doped BaFe2As2,” Europhys. Lett. 89, 67008 (2010).

    Article  CAS  Google Scholar 

  151. D. K. Pratt, M. G. Kim, A. Kreyssig, et al., “Incommensurate spin-density wave order in electron-doped BaFe2As2 superconductors,” Phys. Rev. Lett. 106, 257001 (2011).

    Article  CAS  Google Scholar 

  152. H. Luo, R. Zhang, M. Laver, et al., “Coexistence and competition of the short-range incommensurate antiferromagnetic order with the superconducting state of BaFe2 – xNixAs2,” Phys. Rev. Lett. 108, 247002 (2012).

    Article  CAS  Google Scholar 

  153. C. H. Lee, K. Kihou, H. Kawano-Furukawa, et al., “Incommensurate spin fluctuations in hole-overdoped superconductor KFe2As2,” Phys. Rev. Lett. 106, 067003 (2011).

    Article  CAS  Google Scholar 

  154. J.-P. Castellan, S. Rosenkranz, E. A. Goremychkin, et al., “Effect of Fermi surface nesting on resonant spin excitations in Ba1 – xKxFe2As2,” Phys. Rev. Lett. 107, 177003 (2011).

    Article  CAS  Google Scholar 

  155. R. J. Birgeneau, C. Stock, J. M. Tranquada, and K. Yamada, “Magnetic neutron scattering in hole-doped cuprate superconductors,” J. Phys. Soc. Jpn. 75, 111003 (2006).

    Article  CAS  Google Scholar 

  156. J. M. Tranquada, “Neutron scattering studies of antiferromagnetic correlations in cuprates,” in Handbook of High-Temperature Superconductivity (Springer, Berlin, 2007), pp. 257‒298.

    Google Scholar 

  157. A. O. Sboychakov, K. I. Kugel, and A. L. Rakhmanov, “Phase separation in a two-band model for strongly correlated electrons,” Phys. Rev. B 76, 195113 (2007).

    Article  CAS  Google Scholar 

  158. G. D. Mahan, Many-Particle Physics (Springer, Berlin, 2013).

    Google Scholar 

Download references

Funding

This study was supported by the Russian Science Foundation, project no. 20-62-46047. The work of K.I. Kugel on the structure of inhomogeneities was partially supported by the Russian Foundation for Basic Research, project no. 20-02-00015.

Author information

Authors and Affiliations

  1. Institute for Theoretical and Applied Electrodynamics, Russian Academy of Sciences, 125412, Moscow, Russia

    K. I. Kugel, A. L. Rakhmanov & A. O. Sboychakov

  2. Mikheev Institute of Metal Physics, Ural Branch, Russian Academy of Sciences, 620990, Ekaterinburg, Russia

    K. I. Kugel

  3. Moscow Institute of Physics and Technology (National Research University), 141700, Dolgoprudnyi, Moscow oblast, Russia

    A. L. Rakhmanov

Authors
  1. K. I. Kugel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. L. Rakhmanov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. O. Sboychakov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to K. I. Kugel.

Ethics declarations

The authors declare that they have no conflicts of interest.

Additional information

Translated by K. Kugel

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kugel, K.I., Rakhmanov, A.L. & Sboychakov, A.O. Electronic Phase Separation in Magnetic Materials. Phys. Metals Metallogr. 123, 674–708 (2022). https://doi.org/10.1134/S0031918X22070134

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0031918X22070134

Keywords:

Search

Navigation