Magnetic oxide thin films and heterostructures

Single oxide films

Interface magnetism presupposes a well-defined, albeit structurally imperfect interface. Synthesis of ultrathin films is a limiting test of perfection. When it is clean enough morphologically, the film has two continuous interfaces, one of which may be vacuum or air. The interfaces are not independent—they are coupled in some way. Quantum confinement (see the article by Stemmer and Millis in this issue) is a common form of coupling, but electric polarization can also couple interfaces at larger separations. A summary of some of the changes in magnetism found in thin films and heterostructures is given in Figure 2 .

Figure 2.

Schematic magnetic structures and hysteresis loops of thin films and heterostructures. (a) Change of magnetic order when the conducting bulk ferromagnet La_-0.7Sr_0.3MnO₃ is made into an ultrathin insulating film. (b) A bilayer of a Pauli paramagnet (CaRuO₃) and an insulating antiferromagnet (CaMnO₃) becomes ferromagnetic at the interface. (c) A bilayer of two antiferromagnets LaMnO₃ and LaCrO₃ becomes ferromagnetic at the interface. (d) Exchange coupling in a bilayer between a ferromagnet and an antiferromagnet produces a loop shift of the ferromagnet (exchange bias).

A consequence of quantum confinement can be a metal-insulator transition with changing film thickness. Explanations as to why films of an oxide that is metallic in bulk form (LaNiO₃, for example) may become insulating when they are only a few unit cell layers thick ^{Reference Scherwitzl, Gariglio, Gabay, Zubko, Gibert and Triscone13} or confined between layers of an insulator (LaAlO₃, for example) ^{Reference Blanca-Romero and Pentcheva14} include the following: (1) The bandwidth in the perpendicular direction vanishes, increasing electron correlation effects; (2) 3d crystal field degeneracy is lifted by the lower symmetry; and (3) strain and structural distortions alter the electronic structure. Such a change of electronic properties upon reducing the number of layers has been studied in SrVO₃/STiO₃ ^{Reference Pardo and Pickett15,Reference Kim, Kim, Kang, Noh, Lee, Lee and Lee16} and in VO₂/TiO₂ ^{Reference Pardo and Pickett17} ( Figure 3 ). These changes will naturally modify the magnetic properties. ^{Reference Scherwitzl, Gariglio, Gabay, Zubko, Gibert and Triscone13}

Figure 3.

(a) Majority spin band structures of m = 1 to 5 unit cells of VO₂ encased by TiO₂ (001), illustrating the progression from ferromagnetic insulator (m = 1 and 2), through “semi-Dirac” half metal (m = 3 and 4) to half metal at m ≥ 5. The semi-Dirac phases have 2D point Fermi surfaces such as graphene, highlighted by the red circles, where the dispersion is linear (“massless”) along the ⟨1,1⟩ directions, but is quadratic (“massive”) along a perpendicular line through the crossing point. Each added layer brings in more V 3d bands in the vicinity of the Fermi level, which eventually results in metallic behavior. (b) Surfaces of equal spin density (equal to the charge density since there is full polarization on each V d ^{Reference Zubko, Gariglio, Gabay, Ghosez and Triscone1} ion) illustrating the different orbital polarization in the first, second, and subsequent V layers from the TiO₂ interface. Figure adapted with permission from Reference 21.

A good example is the ever-popular mixed-valence manganite La_0.7Sr_0.3MnO₃, a conducting ferromagnet in bulk form with a Curie temperature of T _c = 370 K. Thin films of this manganite are insulating, ^{Reference Huijben, Martin, Chu, Holcomb, Yu, Rijnders, Blank and Ramesh18} and when deposited on SrTiO₃ (110) in thicknesses less than 10 unit cells (4 nm), they have a noncollinear, canted spin structure with T _c = 540 K. ^{Reference Boschker, Kautz, Houwman, Siemons, Blank, Huijben, Koster, Vailionis and Rijnders19} Even higher Curie temperatures (650 K) are achieved by strain control of e _g orbital occupancy in superlattices with BaTiO₃. ^{Reference Sadoc, Mercey, Simon, Grebille, Prellier and Lepetit20} Strain introduced by an appropriate choice of substrate can be propagated in a superlattice.

Interface symmetry lowering and quantum confinement lead to orbital polarization at the interface, arising from the lifting of the orbital degeneracy of the d electrons. The effect is distinct from orbital ordering due to spontaneous symmetry breaking. Orbital polarization is crucial for interfacial magnetism; it influences which bands are occupied, their widths, and the strength and character of the magnetic coupling. It is directly observable by x-ray linear dichroism or angle-resolved photoelectron spectroscopy.

When a complex combination of d orbitals is occupied, the orbital polarization may give rise to an orbital moment. A representation with an angular momentum quantum number L = 1 of the t _2g orbitals in trigonal symmetry is

(1) $$\left| {{\Psi _m} > } \right. = {{\left( {\left. {\zeta _m^0} \right|{d_{xy}} > + \left. {\zeta _m^1} \right|{d_{yz}} > + \left. {\zeta _m^2} \right|{d_{zx}} > } \right)} \mathord{\left/ {\vphantom {{\left( {\left. {\zeta _m^0} \right|{d_{xy}} > + \left. {\zeta _m^1} \right|{d_{yz}} > + \left. {\zeta _m^2} \right|{d_{zx}} > } \right)} {\sqrt 3 }}} \right. \kern-\nulldelimiterspace} {\sqrt 3 }};\;{\zeta _m} = {e^{{{2\pi im} \mathord{\left/ {\vphantom {{2\pi im} 3}} \right. \kern-\nulldelimiterspace} 3}}}.$$

|Ψ_{m = 0}> is the real combination with a _1g symmetry and zero magnetic quantum number, but the others, |Ψ_{m = ±1}>, are two complex combinations, which may possess an unusually large orbital moment and give rise to exotic ordered states. Such surprises emerged in first-principles calculations, initially for VO₂ (001) thin films confined within TiO₂, where a 3d ^{Reference Zubko, Gariglio, Gabay, Ghosez and Triscone1} orbital moment of 0.2 μ_B appears on the V⁴⁺ions. ^{Reference Pardo and Pickett21} Orbital moments on 3d ions are normally an order of magnitude smaller than this. When SrVO₃, a correlated metal in the bulk, is confined between SrTiO₃ (001) layers, the predicted moment for the interfacial V⁴⁺ is huge, 0.75 μ_B ^{Reference Pardo and Pickett15} and unprecedented even in 5d oxides, where spin-orbit coupling is much larger but quenching effects are also increased. The largest effects are expected for a single t _2g electron or hole. Consequences of the orbital moments include large interfacial magnetocrystalline anisotropy and magnetic coupling that is governed by the total angular momentum of the ion J, rather than the spin angular momentum S.

A different principle is illustrated by ZnFe₂O₄. Zinc ferrite is an insulating, fully frustrated antiferromagnet in the bulk, wherein zinc and iron cations occupy different sublattices in the spinel structure; the spin freezing temperature is 10 K. Thin films, however, have a more random cation distribution with antiferromagnetic intersublattice exchange, and they are conducting canted ferrimagnets with a Curie temperature of 600 K. ^{Reference Chen, Spoddig and Ziese22} In this case, it is the bulk material that is insulating and the thin films that are conducting.

Interface mismatch between materials with different magnetic character is the basis of spintronics. An ultrathin ferromagnetic insulating film between two normal metals provides a spin filter tunnel junction. ^{Reference Lüders, Bibes, Bouzehouane, Jacquet, Contour, Fusil, Bobo, Fontcuberta, Barthélémy and Fert23} The different energy gaps seen by ↑ and ↓ electrons tunneling through the insulating ferromagnetic barrier can provide vastly different tunneling rates, resulting in a spin polarized current. Nonmagnetic oxide barriers are used with ferromagnetic electrodes in conventional magnetic tunnel junctions, most notably Fe/MgO/Fe (001).

Dilute magnetic oxides and d ⁰ magnetism

It has been known for over a decade that thin films of transparent oxides such as TiO₂, ZnO, SnO₂, and HfO₂ may show signs of high-temperature ferromagnetism. ^{Reference Coey, Tsymbal and Žutić29} This effect is absent in well-crystallized, defect-free films. ^{Reference Chambers30} At first, the magnetism was associated with doping with 3d cations, and the films were regarded as uniformly magnetized dilute magnetic semiconductors where the dopant cations are coupled ferromagnetically by spin-polarized conduction electrons. ^{Reference Ando31} This view has turned out to be mistaken, for several reasons. A search for magnetic order, based on element-specific techniques such as x-ray magnetic dichroism ^{Reference Tietze, Gacic, Schütz, Jakob, Brück and Goering32} and Mössbauer spectroscopy ^{Reference Coey, Stamenov, Gunning, Venkatesan and Paul33} failed to find it for the dopants, which remain paramagnetic. Analysis of the magnetization curves in terms of dipolar interactions ^{Reference Coey, Mlack, Venkatesan and Stamenov34} indicated that only a few percent of the film volume is magnetically ordered, although the magnetization of this small fraction was comparable to that of nickel. Furthermore, analysis of the magnetic moment as a function of film thickness failed to reveal any clear relation between the moment and the thickness of the film. Values of the areal moment density on the order of 100–200 µ_B nm^–2 in the oxide films are common. ^{Reference Coey, Tsymbal and Žutić29} As there are about 15 atoms per nm ^{Reference Hwang, Iwasa, Kawasaki, Keimer, Nagaosa and Tokura2} , this indicates that the moment is distributed over at least several unit cells from the interface.

It is unfortunate that much effort was devoted to Co-doped ZnO films in these studies, because cobalt is the element with the highest Curie temperature. Cobalt nanoclusters tend to form in the wurtzite lattice, and they are a potential source of the observed magnetism in these films. ^{Reference Coey, Tsymbal and Žutić29} A better choice of dopant would have been Sc or V, since these elements do not form high-temperature ferromagnetic phases.

One reason for the decline of interest in thin films of dilute magnetic oxides has been the lack of a generally accepted, nontrivial explanation of the phenomenon. Both the origin of the moment and a mechanism of exchange coupling that would produce high-temperature ordering between distant moments are perplexing. While it is easy to detect very small magnetic moments, it is important to pinpoint the source of magnetism, whether in the film or in the substrate near the interface. Progress has been hampered by problems with reproducibility of the results. The magnetism often depends on uncontrolled aspects of film synthesis, which influence the defect content; quantitative results differ from group to group, and even from run to run in the same laboratory.

Defects seem to be the critical factor. Cation vacancies that create strongly correlated holes on the surrounding 2p oxygen ions have been suggested as a source of magnetism. ^{Reference Elfimov, Yunoki and Sawatzky35} The behavior of Ta-doped TiO₂ has been discussed in these terms. ^{Reference Rusydi, Dhar, Barman, Ariando, Qi, Motapothula, Yi, Santoso, Feng, Yang, Dai, Yakovlev, Ding, Wee, Neuber, Breese, Ruebhausen, Hilgenkamp and Venkatesan36} Nitrogen substitution for oxygen has a similar effect. ^{Reference Elfimov, Rusydi, Csiszar, Hu, Hsieh, Lin, Chen, Liang and Sawatzky37} An alternative suggestion is that oxygen vacancies, which trap electrons to create F-centers, are principally involved. ^{Reference Coey, Tsymbal and Žutić29}

A different model associates the magnetization with electrons in a defect-based impurity band that occupies only a small fraction of the sample volume. ^{Reference Edwards and Katsnelson38} The density of states of this band can have a maximum near the Fermi level, and split spontaneously if the Stoner model criterion is satisfied. ^{Reference Coey4} The role of the 3d dopants in this case is only to act as an electron reservoir, exchanging electrons with the impurity band, provided the 3D ions coexist in two different valence states. ^{Reference Coey, Stamenov, Gunning, Venkatesan and Paul33}

There are many experimental reports of ordered magnetism in films of oxides with no magnetic doping. ^{Reference Venkatesan, Fitzgerald and Coey11,Reference Coey, Tsymbal and Žutić29} When the effect is not directly attributable to the substrate ^{Reference Khalid, Setzer, Ziese, Esquinazi, Spemann, Pöppl and Goering5} or an obvious impurity phase, it can be discussed in terms of one of these models. The magnetic response looks like that of an anhysteretic soft ferromagnet. It is remarkable that after correction for the background diamagnetism, as shown in Figure 1, the saturation magnetization is often found not to vary with temperature between 4 K and 300 K. This behavior is illustrated for Sc-doped ZnO in Figure 4 . This lack of temperature dependence suggested ferromagnetism with an exceedingly high Curie temperature (high energy scale), which is compatible with a half-metallic impurity band where spin-wave excitations are suppressed. ^{Reference Edwards and Katsnelson38}

Figure 4.

Magnetization of a typical d ⁰ material, a thin film of zinc oxide doped with scandium. The magnetization curves measured at temperatures between 4 K and 300 K exhibit a ferromagnetic-like saturation, with magnetization curves that superpose, after correction for the high-field slope. Figure adapted with permission from Reference 66.

A quite different view is that these peculiar systems are not ferromagnetic at all, but rather that the magnetic response is a manifestation of giant orbital paramagnetism. ^{Reference Hernando, Crespo, García, Coey, Ayuela and Echenique39} A new theory of the phenomenon ^{Reference Coey, Ackland and Sen40} predicts saturation as

(2) $$m = {{{m_0}\,x} \mathord{\left/ {\vphantom {{{m_0}\,x} {{{\left( {1 + {x^2}} \right)}^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}}}}}} \right. \kern-\nulldelimiterspace} {{{\left( {1 + {x^2}} \right)}^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}}}}},$$

where x is a ratio of energies, one of them proportional to the applied field, which does not depend on temperature. Unlike a Langevin function where the initial susceptibility varies as 1/T, which would be an indication of superparamagnetism, there is no temperature dependence in this model, in agreement with experimental observations.

Magnetism at interfaces of nonmagnetic oxides

Finally, we turn to the emergence of conductivity and magnetism at the interface of two nonmagnetic insulators. ^{Reference Millis41} Electronic reconstruction needed to create a uniform electric field in the polar oxide and avoid polarization catastrophe ^{Reference Nakagawa, Hwang and Muller42} accounts for the appearance of a 2DEG at the interface between TiO₂-terminated SrTiO₃ and LaAlO₃. LaAlO₃ consists of a polar stack of positively charged (LaO)⁺ and negatively charged (AlO₂)^– layers along the (100) direction, while the layers in SrTiO₃ have no intrinsic charge dipole. A net electric field and diverging electrostatic energy due to the dipole layers in LAO are avoided by transferring 0.5 electrons per unit cell from the upper surface of LaAlO₃ to the Ti 3d band in SrTiO₃ at the interface (see the article by Hilgenkamp in this issue). The n-type interface conductivity of the 2DEG is sensitive to oxygen vacancy creation during growth, ^{Reference Kalabukhov, Gunnarsson, Börjesson, Olsson, Claeson and Winkler43} cation intermixing at the interface, ^{Reference Willmott, Pauli, Herger, Schlepütz, Martoccia, Patterson, Delley, Clarke, Kumah, Cionca and Yacoby44} and strain. ^{Reference Bark, Felker, Wang, Zhang, Jang, Folkman, Park, Baek and Zhou45} Both charge transfer and oxygen vacancies may be necessary. ^{Reference Liu, Li, Lü, Huang, Huang, Zeng, Qiu, Huang, Annadi, Chen, Coey, Venkatesan and Ariando46} The cation stoichiometry of the LaAlO₃ grown on SrTiO₃ is also found to influence the conducting behavior. ^{Reference Breckenfeld, Bronn, Karthik, Damodaran, Lee, Mason and Martin47,Reference Warusawithana, Richter, Mundy, Roy, Ludwig, Paetel, Heeg, Pawlicki, Kourkoutis, Zheng, Lee, Mulcahy, Zander, Zhu, Schubert, Eckstein, Muller, Hellberg, Mannhart and Schlom48}

The first suggestions of a ferromagnetic state at this interface came from calculations that considered charge order with orbital polarization of the electrons occupying d _xy states on alternate Ti sites in an interface layer—a ¼-filled band, ^{Reference Pentcheva and Pickett49} similar to that calculated for the LaTiO₃/SrTiO₃ interface. ^{Reference Okamoto, Millis and Spaldin50} Experiments ^{Reference Brinkman, Huijben, van Zalk, Huijben, Zeitler, Maan, van der Wiel, Rijnders, Blank and Hilgenkamp51} then revealed magnetic hysteresis in the sheet resistance, measured at 0.3 K, as well as a resistivity minimum at about 50 K that was tentatively ascribed to Kondo scattering of the conduction electrons by magnetic ions ( Figure 5 ).

Figure 5.

Evidence for magnetism of the two-dimensional electron gas at the LaAlO₃/SrTiO₃ interface. (a) Resistance showing a minimum associated with Kondo scattering for samples deposited at various oxygen pressures. Figure adapted with permission from Reference 51. (b) Magnetic moment measured with SQUID-VSM. Figure adapted with permission from Reference 52. (c) Direct imaging of a magnetic stray field using a scanning SQUID microscope. Figure adapted with permission from Reference 7. (d) Moment detected by torque magnetometry. Figure adapted with permission from Reference 54.

This observation of magnetic character at the interface of non-magnetic oxides has stimulated much interest and ongoing controversy. Films grown at high oxygen pressures ^{Reference Ariando, Wang, Baskaran, Liu, Huijben, Yi, Annadi, Barman, Rusydi, Dhar, Feng, Ding, Hilgenkamp and Venkatesan52} have been found to induce electronic phase separation at the interface, with the coexistence of a ferromagnetic phase, which persists to room temperature (Figure 5), and a superconducting-like diamagnetic phase below 60 K. These different phases may be associated with the selective occupancy of the Ti 3d sub-bands at the interface, arising from symmetry breaking that lifts their degeneracy. Further evidence for coexisting superconductivity and magnetism came from transport measurements ^{Reference Dikin, Mehta, Bark, Folkman, Eom and Chandrasekhar53} and torque magnetometry. ^{Reference Li, Richter, Mannhart and Ashoori54} Direct imaging using a scanning SQUID probe (Figure 5) ^{Reference Bert, Kalisky, Bell, Kim, Hikita, Hwang and Moler7} revealed ferromagnetic and superconducting puddles a few microns in size, but it was concluded that the ferromagnetism did not require mobile electrons. ^{Reference Kalisky, Bert, Klopfer, Bell, Sato, Hosoda, Hikita, Hwang and Moler55} These observations beg the question of whether the 2DEG is intrinsically ferromagnetic, ^{Reference Michaeli, Potter and Lee56} or if the ferromagnetism is somehow associated with oxygen vacancies or other defects near the interface. ^{Reference Pavlenko, Kopp, Tsymbal, Mannhart and Sawatzky57}

In Figure 6 , we illustrate the effect of crystal field splitting of the d orbitals; the t _2g and e _g orbitals are separately degenerate in octahedral symmetry. However, near the interface, tetragonal symmetry partly lifts the degeneracy, and in-plane d _xy orbitals may have lower energy than out-of-plane d _xz, d _yz orbitals. The first available states at the interface, according to measurements of x-ray linear dichroism ^{Reference Salluzzo, Cezar, Brookes, Bisogni, De Luca, Richter, Thiel, Mannhart, Huijben, Brinkman, Rijnders and Ghiringhelli58} and electronic structure calculations, ^{Reference Popović, Satpathy and Martin59} are d _xy. A ferromagnetic moment of ∼0.1µ_B per Ti has been associated with these oxygen-hybridized Ti d _xy orbitals using surface-sensitive x-ray magnetic dichroism measurements. ^{Reference Lee, Xie, Sato, Bell, Hikita, Hwang and Kao60} Quenching of the magnetism upon annealing in oxygen suggests that oxygen vacancies have a decisive influence. ^{Reference Salluzzo, Gariglio, Stornaiuolo, Sessi, Rusponi, Piamonteze, De Luca, Minola, Marr, Gadaleta, Brune, Nolting, Brookes and Ghiringhelli61}

Figure 6.

(a) Schematic of the one-electron Ti 3d orbitals, which are occupied near the interface in SrTiO₃. The cubic crystal field due to the surrounding oxygen octahedron splits the t _2g and e _g states, and further splitting of the t _2g states arises from the local tetragonal symmetry at the LaAlO₃/SrTiO₃ interface. (b) The d _xy orbitals form a two-dimensional in-plane band, and the d _yz and d _xz orbitals form orthogonal one-dimensional bands.

The effective interface volume in a sample can be enhanced by one to two orders of magnitude by using a multilayer, although it should be emphasized that thin films and bulk crystals are not identical. The bandgap in thin-film SrTiO₃ is 0.6 eV greater than the single-crystal value. ^{Reference Bao, Yao, Wakiya, Shinozaki and Mizutani62,Reference Panomsuwan, Takai and Saito63} Small-angle polarized neutron reflectometry ^{Reference Fitzsimmons, Hengartner, Singh, Zhernenkov, Bruno, Santamaria, Brinkman, Huijben, Molegraaf, de la Venta and Schuller64} has set a limit on the interface moment of about 0.3 µ_B per two-dimensional unit cell for LaAlO₃/SrTiO₃ multilayers, which might be spread over several layers. Larger moments were found in direct magnetic measurements of the samples, which include any contributions that arise from the substrate. ^{Reference Fitzsimmons, Hengartner, Singh, Zhernenkov, Bruno, Santamaria, Brinkman, Huijben, Molegraaf, de la Venta and Schuller64}

By tuning the electron density at the oxide interface using a top gate while imaging the sample by magnetic force microscopy, ^{Reference Bi, Huang, Bark, Ryu and Eom8} it was demonstrated that room-temperature ferromagnetism appears as the electrons in the conduction band were depleted. The conduction electron spins align antiparallel to the magnetization, destabilizing magnetic order as the conductive state is reached. Gate control of ferromagnetism at the oxide interface opens a new vista for spintronic applications.

Magnetism at this interface has spurred various theoretical suggestions of its origin, most agreeing that the magnetic electrons reside in Ti 3d t _2g orbitals. One view is that a layer of localized d _xy electrons at the interface ^{Reference Michaeli, Potter and Lee56,Reference Salluzzo, Cezar, Brookes, Bisogni, De Luca, Richter, Thiel, Mannhart, Huijben, Brinkman, Rijnders and Ghiringhelli58,Reference Lee, Xie, Sato, Bell, Hikita, Hwang and Kao60} is magnetically coupled by mobile electrons in the d _xz, d _yz bands, while other data suggest that itinerant electrons are unnecessary, or ineffective, in coupling the local moments. For an intrinsic, electronically reconstructed interface, first-principles calculations indicate a ground state of d _xy moments coupled by direct exchange, ^{Reference Pentcheva and Pickett49} though this is unlikely to account for high-temperature ferromagnetism. Another view is that localized Ti e _g spins induced by neighboring oxygen vacancies result in ferromagnetic order. ^{Reference Pavlenko, Kopp, Tsymbal, Mannhart and Sawatzky57} A different idea is that the magnetism is itinerant ^{Reference Chen and Balents65} and appears at low occupancy of quasi-one-dimensional d _xz, d _yz orbitals via the Stoner mechanism, which leads to spin splitting of bands when the density of states at the Fermi level is sufficiently high. ^{Reference Coey4} Another viewpoint is that the magnetism arises within a narrow impurity band comprised of oxygen vacancy-related orbitals, which are unstable with respect to Stoner splitting.

More systematic study of the magnitude of the magnetization, Curie temperature, and dependence on interface perfection and orientation, including oxygen vacancies and electron density, is required to resolve many of these controversial issues. A cogent question is: why have the 2DEG and emergent interface magnetism only been found in SrTiO₃? The magnetism seems very likely to be related to the availability of Ti 3d states highly susceptible to moment formation, while the 2DEG may be related to the feature, unusual for any oxide, such that an electron density of 10^–4/cell in the bulk results in high-mobility conducting behavior (and superconductivity).