Epitaxial NiCo₂O₄ film as an emergent spintronic material: Magnetism and transport properties

Transition-metal complex oxides with perovskite (ABO₃) and spinel (AB₂O₄) structures exhibit diverse functional properties such as magnetism, ferroelectricity, and superconductivity, which are highly tunable due to the close interplay between the charge, spin, orbital, and lattice degrees of freedom.¹ NiCo₂O₄ (NCO) belongs to the family of spinel oxides made of magnetic transition-metal elements Fe, Co, and/or Ni [see Fig. 1(a) and Table I].^2–8 Each crystal unit cell (u.c.) consists of 16 octahedral (O_h) sites and 8 tetrahedral (T_d) sites for the cations [Figs. 1(b) and 1(c)]. The complex chemical/oxygen environment makes these materials highly susceptible to chemical disorder.^9–11 Compared with other members of this family, NCO stands out for its high conductivity (∼$103Ω−1cm−1$⁠),¹² potentially half metallicity,¹³ fast spin dynamics,¹⁴ and large magnetoelastic effects.¹⁵ The last effect leads to strain tunable magnetic anisotropy, which can result in strong perpendicular magnetic anisotropy (PMA) in epitaxial thin films.¹⁵ In addition, the multi-cation, mixed valence character makes NCO surface active in charge storage and catalytic processes.^{10,11,16–18}

To date, NCO of spinel structure has been synthesized in the forms of polycrystalline powders and nanocrystals using the wet chemical method^{10,11,18,24,25,31–33} and, more recently, epitaxial thin films using physical vapor deposition (pulsed laser deposition and RF magnetron sputtering),^{9,12,15,22,32,34–40} while the preparation of large single crystals has not been reported yet. Previous studies of NCO have mainly focused on the electrochemical properties of NCO nanocrystals for catalysis and energy applications.^{10,11,41–44} There are emerging interests in single-crystalline epitaxial thin films of NCO, which can not only facilitate the fundamental exploration and nanoscale control of its intrinsic physical properties but also provide a versatile platform for developing high speed spintronic applications. In this Perspective, we discuss the recent advances in the study of epitaxial NiCo₂O₄ thin films, focusing on the understanding of their unusual magnetic and transport properties, the impacts of crystal structure and electronic structure, the effects of disorder, strain, and film thickness on property tuning, and their potential for spintronic applications.

It is known that the chemical configurations of NCO, including cation stoichiometry, valency, and site occupancy, depend sensitively on the material preparation conditions.^{22,23,35,45–48} In the optimal configuration, NCO possesses a saturation magnetization (M_S) of about 2 μ_B/formula unit (f.u.), magnetic Curie temperature (T_C) of about 420 K, and conductivity of about $103Ω−1cm−1$⁠.^{12,23,45–47} In this section, we discuss the optimal structure of NCO and compare its properties with other spinel materials (Table I).

As shown in Fig. 1(b), the unit cell of spinel oxide has 8 T_d sites and 16 O_h sites for cations.⁴⁹ Regarding the atomic distances, the nearest neighbors are between the edge-sharing O_h sites, and the next nearest neighbors are between the corner-sharing O_h and T_d sites [Fig. 1(c)]. The third nearest neighbors are between the T_d sites, which are not directed connected. NCO can be viewed as Co₃O₄^19,50–52 with one Co replaced by Ni per formula unit. In Co₃O₄, the O_h sites are occupied by Co³⁺ and the T_d sites are occupied by Co²⁺, making Co₃O₄ a normal spinel.⁵³ For NCO, instead of having all the Ni (Co) ions on the T_d (O_h) sites, the T_d sites are actually occupied by eight Co ions, leaving the O_h sites shared by eight Ni and eight Co ions.^22,47 This type of arrangement is known as spinel inversion.

For NCO, eight O_h sites in the unit cell are occupied by Co³⁺, and the other eight O_h sites are occupied by Ni ions with mixed valence (Ni²⁺ and Ni³⁺) (Fig. 2).^9,22 The 3d states of Ni are split into t_2g and e_g groups due to the crystal field generated by the surrounding oxygen octahedron, with the t_2g states at lower energy [Fig. 2(a)].⁵⁴ In comparison, the T_d sites are occupied by the Co ions with mixed valence (Co²⁺ and Co³⁺), with the e_g states at the lower energy [Fig. 2(b)].⁵⁴ 

The magnetic properties of NCO hinge on the magnetic moments on the Ni and Co ions, which are related to the site occupancy, valence, and spin states of these ions. The spin state of the ions depends on the local oxygen environment (O_h or T_d), as shown in Table II. For the same local environment symmetry, the spin state is determined by the competition between the crystal field splitting energy and the electrostatic energy between two electrons of opposite spins in the same state. When the crystal field splitting energy is small, the electronic configuration follows Hund's rule to maximize the total spin (high spin). Otherwise, the electrons prefer filling the low-lying energy states, corresponding to the low-spin states.

For spinel oxides (Table I) of smaller lattice constants, such as Co₃O₄ and NCO, the higher crystal field splitting between the t_2g and e_g states on the O_h site favors low-spin state [Fig. 2(a)]. In contrast, the crystal field splitting of the T_d sites is typically smaller than that of the O_h sites because of the smaller spatial overlap between the 3d states of the cation and the 2p states of neighboring oxygen ions. The T_d sites thus prefer the high-spin states. For example, due to the large crystal field splitting, Co³⁺ on the O_h sites are at the low-spin state carrying zero magnetic moment. In Co₃O₄, all O_h sites are occupied by the nonmagnetic Co³⁺, making Co²⁺ on the T_d sites the only magnetic ions.⁵³ This explains the low magnetic transition temperature (40 K) of Co₃O₄, since the T_d sites are far away from each other [Fig. 1(c)].¹⁹ On the other hand, for those of larger lattice constants in Table I (NiFe₂O₄, CoFe₂O₄, and Fe₃O₄), the larger octahedron and tetrahedron lead to smaller crystal field splitting, making the high-spin states more energetically favorable.^4,20,21,55 The sensitive dependence on lattice constants also means the magnetic states of spinel materials can be effectively altered using epitaxial strain.⁵⁶ 

As shown in Fig. 2, for NCO, the magnetic moments are carried by Ni²⁺ and Ni³⁺ on the O_h sites and Co²⁺ and Co³⁺ on the T_d sites. Here, Ni²⁺ and Ni³⁺ are in their low-spin states, giving rise to an average magnetic moment of 1.5 μ_B/Ni. Co²⁺ and Co³⁺ are in their high-spin states, corresponding to an average magnetic moment of 3.5 μ_B/Co.

The strongest exchange interaction in magnetic spinels is between the corner-sharing T_d and O_h sites.⁵⁷ The approximately 125° cation–oxygen–cation bond angle leads to antiferromagnetic interaction.^58,59 The second largest exchange interaction is between the edge-sharing O_h sites, where the 90° cation–oxygen–cation bond angle corresponds to ferromagnetic (FM) interaction, which is weaker than the antiferromagnetic interactions in general.^58,59 The mixed valence on the O_h sites also enables the potential double exchange interaction, which is related to the metallicity of NCO.²² 

Since the magnetic Ni and Co ions occupy the corner-sharing O_h and T_d sites, respectively, their magnetic moments are expected to be antiparallel [Fig. 2(c)]. The cancellation between the two spin sub-lattices is incomplete due to the different magnetic moments on Ni and Co ions, resulting in ferrimagnetism [Fig. 3(a)].²³ Given that the average spin magnetic moments are 1.5 μ_B/Ni on O_h sites and 3.5 μ_B/Co on T_d sites, the optimal magnetic moment per formula unit is 2.0 μ_B, which is consistent with the experimental observation of high quality epitaxial thin films [Fig. 3(b)].^12,23

Figure 3(b) shows the magnetic properties of (001) NCO films deposited on Mg₂AlO₄ (MAO) substrates. The magnetic Curie temperature is about 420 K for the 30 u.c. film, as deduced by extrapolating M(T) beyond 400 K [Fig. 3(b)].¹² It is lower than many other spinels listed in Table I, such as Fe₃O₄, NiFe₂O₄, and CoFe₂O₄.^4,7 According to the mean field theory, this is likely related to the coordination number for the magnetic ions. Considering only the strongest T_d–O_h exchange interactions, each T_d site has 12 neighboring O_h sites. When 50% of the O_h sites are occupied by the nonmagnetic (NM) Co³⁺, the magnetic coordination number is reduced by 50%, meaning the pair of strongest exchange interaction per unit cell is reduced by 50%. This is consistent with the roughly 50% reduction in T_C compared with that of other compounds in Table I except Co₃O₄.

Besides being ferrimagnetic above room temperature, one appealing property of NCO is its high magnetic anisotropy energy (MAE), which can be sensitively tuned by epitaxial strain. Since NCO has a cubic structure (lattice constant of 0.8114 nm),²⁷ using the minimum number of terms, the free energy of magnetic anisotropy can be described by⁶⁰ 

where $m^=(mx,my,mz)$ is the unit magnetization vector and $mx,my,andmz$ are the projection of $m^$ on the $x^$⁠, $y^$⁠, and $z^$ axes (Σm_i² = 1), respectively. The coefficient K₁ measures the MAE. If K₁ > 0, the easy axes are along the {100} directions. Otherwise, the easy axes are along the {111} directions.

As bulk single crystals of NCO are not available, single-crystalline NCO can only be synthesized in the form of epitaxial films, which are slightly deformed from the cubic symmetry by the epitaxial strain. In these systems, the MAE can be determined by measuring epitaxial thin films grown along different crystalline orientations. For a strained epitaxial film, the free energy can be modified to include the magnetoelastic effects,⁶⁰ 

where e_ij (i, j = x, y, z) are the components of the strain tensor, and $B1$ and $B2$ are the longitudinal and shear magnetoelastic coupling constants, respectively. Figure 4 shows schematically the non-zero strain components e_ij for NCO films grown on substrates of different orientations.

For the (001) oriented substrates, the non-zero components of the strain tensor are $ezz$⁠, and $exx=eyy$⁠. The free energy of the in-plane and out-of-plane directions are $FME(x^)=B1exx$ and $FME(z^)=B1ezz$⁠, respectively.

For the (110) oriented substrates, the non-zero components of the strain tensor are $exx=eyy$⁠, $ezz$⁠, and $exy$⁠. The free energy of the out-of-plane direction is $FME(m^(110))=K14+B1exx+B22exy$⁠. For the in-plane [001] direction, $FME(m^(001))=B1ezz$⁠.

For the (111) oriented substrates, the non-zero components of the strain tensor are $exy=eyz=ezx$⁠. The free energy of the out-of-plane direction is $FME(m^(111))=K13+B2exy$⁠. For the two in-plane directions, one has $FME(m^(1¯10))=K14−B22exy$⁠, and $FME(m^(11¯2))=K14−B22exy$⁠.

Experimentally, when the NCO films are grown on MAO substrates (lattice constant of 8.09 Å),^61,62 the substrates exert an in-plane compressive strain $ein=−0.3%$ on the film. For the NCO (001) films, the strain can be measured as $exx=ein<0$ and $ezz=eout>0$⁠, where $eout$ reflects the difference between the spacing of the (001) plane for the strained film and that of the bulk values. As shown in Fig. 5(a), the easy axis is along the out-of-plane [001] direction, while the in-plane [100] direction becomes a hard axis. Defining the energy integral $I=∫0Hsat⁡MdH$⁠, where H, H_sat, and M are the magnetic field, saturation magnetic field for the hard axis, and magnetization, respectively, the free energy different between the in-plane [100] direction and out-of-plane [001] direction can be calculated as $Ea=I[100]−I[001]$⁠, which is equal to $FME(x^)−FME(z^)=B1(exx−ezz$⁠). This means that $B1=Eaein−eout$⁠.

For NCO (110) films, the strain can be measured as $exx=eyy=eout+ein2>0$⁠, $exy=eout−ein2>0$⁠, and $ezz=ein<0$⁠. As shown in Fig. 5(b), both the in-plane [$11¯0$] and out-of-plane [110] directions are hard axes. Hence, the free energy difference between the [110] and [001] directions is $Ea=I[110]−I[001]$⁠, which is equal to $FME(m^(110))−FME(z^)=K14+(2B1+B2)eout−ein4$⁠. This can be measured using the hysteresis loops in Fig. 5(b). Considering $eout−ein≪1$⁠, $Ea=K14+(2B1+B2)eout−ein4≈K14$⁠.

For the NCO (111) films, the strain can be measured as $exy=eyz=ezx=−2ein<0$⁠. As shown in Fig. 5(c), the hysteresis loops taken along the in-plane [$11¯0$] and [$112¯$] directions as well as the out-of-plane [111] direction are similar. By equating the free energy, one has $K1=−18B2exy=−36B2eout$⁠.

By measuring $eout$ and $Ea$ of the (001) and (110) films at 20 K, one finds $K1≈0.76MJ/m3$⁠, $B1≈−28MJ/m3$⁠, and $B2≈-7.0MJ/m3$⁠. These values are comparable to those of CoFe₂O₄, which is well-known for the high MAE and the magnetoelastic effects.⁶⁰ The room temperature values of these constants are about 40% of the low-temperature values, as determined by the reduced magnetization [Fig. 3(b)].

Figures 5(d)–5(f) display the simulated free energy using the extracted $K1$⁠, $B1$⁠, and $B2$ values and the measured strain. As shown in Fig. 5(d), as $B1<0$⁠, the compressive strain increases the energy along the [100] and [010] directions, making them the hard axes. Meanwhile, the energy along the [001] direction is reduced, making it a global easy axis. Hence, NCO(001)/MAO(001) possesses uniaxial PMA. For the NCO(110) films, the strain mainly makes the [001] direction a local easy axis. For the NCO(111) films, the [100], [010], and [001] remain easy axes, while the energy of the [111] axis is reduced to be comparable to that of the [$1¯10$] axis.

This section discusses the tuning of the magnetic properties in NCO thin films by the structural and chemical variations from the optimal configurations.

The large magnetoelastic constant suggests that the magnetic properties of NCO are highly tunable using mechanical means via spin–lattice coupling. Conversely, it is also possible to change the shape of NCO slightly using the magnetic field. In particular, NCO(001) films strained on MAO exhibits a strong PMA, with K_u = 0.45 MJ/m³ at 20 K and 0.21 MJ/m³ at 300 K^47,63 (Table III).

The ability to achieve high magnetic anisotropy has significant impact on developing energy and information applications. For example, electrodes with strong PMA are highly desired for nanoscale spintronic devices to achieve high thermal stability and energy-efficient switching.⁷¹ Most materials or heterostructures of high PMA are based on intermetallic compounds,^72–76 multilayers,^68,69 or metal/oxide interfaces,⁷¹ with many of them involving high-cost elements such as Au and Pt. In contrast, transition-metal oxide conductors, despite their advantages of low-cost as well as structural and chemical stabilities, have rarely been reported to exhibit high PMA (Table III).

Magnetic anisotropy originates from structural anisotropy and spin–orbit coupling (SOC). In ordered intermetallic compounds containing strong SOC nonmagnetic (NM) metals (e.g., Pd, Au, and Pt) and ferromagnetic (FM) metals (e.g., Fe and Co), anisotropic crystal structures lead to anisotropic hybridization between the states in the NM and FM elements and consequently high magnetic anisotropy (about 5 MJ/m³).^72–77 The structural anisotropy can also be introduced by stacking NM and FM layers for high PMA (about 1 MJ/m³).⁶⁹ On the other hand, remarkable PMA has been demonstrated in Co/Ni multilayers (about 0.5 MJ/m³)⁶⁸ and FM/oxide interfaces (about 0.2 MJ/m³)^65,71,78 without the need of strong SOC NM. Here, the electronic degeneracy and occupancy are adjusted such that the 3d states in FM with a large orbital angular momentum (in-plane states) determine the magnetic anisotropy. In particular, at the FM/oxide interface, the 3d electronic states are tuned via the hybridization with oxygen states. This suggests the possibility of having transition-metal oxides with high magnetic anisotropy.

In 3d transition-metal oxides, the hybridization of the metal 3d and oxygen 2p states generates a crystal field splitting of Δ ∼ 1 eV; the SOC (ξ ∼ 50 meV) couples these split states and modifies the energy by ≈ ⟨L_z⟩ξ²/Δ, where ⟨L_z⟩ is the average angular momentum projected along the out-of-plane direction. This energy modification, which gives rise to the MAE, can reach ∼1 meV for ⟨L_z⟩ ∼ 1. This is the origin of the large magnetic anisotropy (∼1 MJ/m³) and strong spin–lattice coupling in CoFe₂O₄, an insulator that exhibits PMA in strained films.^66,78–88 For oxide conductors, however, room temperature ferromagnetism is already rare, not to mention high magnetic anisotropy. Most widely studied FM oxide conductors, such as (La,Sr)MnO₃, have low magnetic anisotropy^64,89,90 and weak spin lattice coupling due to the dominant z² state, which has a low orbital angular momentum.⁹¹ 

The microscopic origin of the large magnetoelastic constants has to do with the electronic structure of NCO and particularly the effect of strain on the single-ion MAE via SOC. A model Hamiltonian can be written using a one-electron picture,

Here, $HCF$ is the Hamiltonian including the crystal field, $l→$ and $s→$ are the orbital and spin angular momentum, respectively, and E_ex and $A^$ are parameters for simulating the exchange interaction between the ion with the neighboring magnetic ions with spins along the direction $A^$⁠. The magnetoelastic coupling can be understood as follows: when strain modifies the electronic orbital states by changing the local environment of the magnetic ions (H_CF), the preferred spin orientation also changes due to the SOC.

In one unit cell of NCO, there are eight low-spin Ni^2.5 ions in the NiO₆ octahedron [Fig. 6(a), O_h symmetry] and eight high-spin Co^2.5 ions in the CoO₄ tetrahedron [Fig. 6(b), T_d symmetry], where the fractional valence reflects the mixed valence state.^22,34 The Co and Ni 3d states are split into doubly degenerate e_g states and triply degenerate t_2g states due to the corresponding H_CF. Under the biaxial compressive strain, which reduces the cubic symmetry to tetragonal, these states further split [Figs. 6(a) and 6(b)].

Figure 6(c) shows the simulated single-ion magnetic anisotropy E_SIMA as a function of strain in (001) NCO films, assuming ξ, crystal field splitting, and E_ex as 0.05, 1, and 5 eV, respectively. The crystal field is simulated by replacing the oxygen atoms with point charges in NiO₆ and CoO₄. The total energy on a magnetic ion E_t is calculated by summing the energy of the individual electrons⁶⁸ according to the population of d-orbitals [Figs. 7(a) and 7(b)]. The single-ion magnetic anisotropy is manifested in the dependence of E_t on the direction of $A^$⁠, defined as E_SIMA = E_t,x − E_t,z for (001) NCO, where E_t,x and E_t,z are the total energy for $A^=x^$ (in-plane) and $A^=z^$ (out-of-plane), respectively. The epitaxial strain Δa/a, where a is the bulk lattice constant, is introduced by distorting the NiO₆ and CoO₄ local environment according to the lattice constant change, which are Δa and −2Δa for in-plane and out-of-plane axes, respectively. For both Ni^2.5 and Co^2.5, under the tetragonal distortion due to the compressive strain (Δa < 0), E_SIMA is positive. This means that the c axis (out-of-plane direction) is the easy axis, which is consistent with the experimental observation.^12,15,37

A microscopic understanding of the effect of strain on magnetic anisotropy can be gained using the Co^2.5O₄ tetrahedron as an example [Fig. 6(c)]. In this case, the tetragonal distortion generates an S₄ symmetry [Fig. 6(b)]. The 3d electronic configuration can thus be viewed as a half-filled shell plus an electron in the |x²−y²〉 state and a fractional occupation of the z² state. Since the half-filled shell is not expected to contribute to the magnetic anisotropy, the electron in the |x²−y²〉 state dominates the anisotropy energy. As illustrated in Fig. 7(a), if the spin is along the z axis, the |x²−y², s_z = 1/2〉 state couples to the |xy, s_z = 1/2〉 state to lower its energy, with a coupling strength 〈x²−y², s_z = 1/2|$ξℏ2s→i⋅l→i$| xy, s_z = 1/2〉 = ξ. On the other hand, when the spin is along the x axis, the |x²−y², s_x = 1/2〉 state couples to the |xz, s_x = 1/2〉 state to lower its energy, with a coupling strength 〈x²−y², s_x = 1/2|$ξℏ2s→i⋅l→i$| xz, s_x = 1/2〉 = ξ/2, which is smaller than that when the spin is along the c axis. Therefore, the compressive strain results in an out-of-plane magnetic anisotropy. Hence, the 3d |x²−y²〉 state of Co in the Co^2+δO₄ tetrahedron plays a key role in the magnetoelastic coupling of NCO due to its potentially large orbital angular momentum along the z axis. Assuming the magnitude of ξ, crystal field splitting, and E_ex as 0.05, 1, and 5 eV, respectively, the single-ion magnetic anisotropy is found to be about 1 meV/f.u. [Fig. 6(c)]. This translates to about 1 MJ/m³ in MAE, in good agreement with the observed values in Table III. Recent studies further show that the tetragonal distortion is responsible for the spin reorientation transition from PMA to an easy cone anisotropy in NCO at low temperature.⁹² The dominant contribution of Co to the PMA has been confirmed by a recent study using XMCD, which reveals orbital magnetic moments of 0.14 μ_B/Co and 0.07 μ_B/Ni [Fig. 7(b)].²³ In addition, the orbital magnetic moment of Co is along the out-of-plane direction, while that of Ni is more isotropic.²³ 

Ever since the first stabilization of NCO in the form of epitaxial thin films, the high tunability of its physical properties by the growth condition has gained attention.^9,22,35–40 For example, NCO can be tuned from a conductor to an insulator by changing the growth temperature;^22,35 the magnetic transition temperature and saturation magnetization can be varied substantially using different O₂ pressure during film growth.⁴⁷ Chemical disorders such as cation/oxygen vacancies, valence disorder, and cation inversion can have significant impacts on the electronic and magnetic properties of NCO.⁹³ In this section, we discuss the effects of cation stoichiometry, valence, and site occupancy on the observed property variation.

NCO can be viewed as Co₃O₄ with one Co atom replaced by Ni atom per formula unit. For Co₃O₄, Co³⁺ occupies the O_h site, which has a higher coordination number. As Co³⁺ is less stable than Co²⁺, such a configuration enhances its bonding and stability. For NCO, the site occupancy is complicated by the additional species of cations (Ni²⁺ and Ni³⁺) and their chemical stability. In principle, Ni may replace up to all the Co²⁺ on the T_d sites and up to 50% of the Co³⁺ on the O_h sites. The large number of possible configurations of NCO involving four types of cations (Ni²⁺, Ni³⁺, Co²⁺, and Co³⁺) and two sites (O_h and T_d) and the subtle differences in cation stability all depend sensitively on the growth condition, which provides an effective means to tune the properties of NCO.

To describe the stoichiometry and valency of NCO, we use the chemical formula $[Nin12+Nin23+Con32+Con43+]Co3+O4$⁠, where $Σni≤2$⁠. Here, the Co³⁺ outside the bracket occupies the O_h sites. The site occupancy can be described using the fractions of these cations on the O_h sites $xi$⁠, where $xi≤1$⁠. The additional restriction of charge neutrality requires $2n1+3n2+2n3+3n4=5−2Vo$⁠, where $Vo$ is the number of oxygen vacancy per formula unit.

Following the rules of spin states in Table II, one can calculate the total spin magnetization per formula unit in terms of the structure configuration parameters,

Note that $n1x1+n2x2+n3x3+n4x4$ is the occupancy of the O_h sites combining all cations. Therefore, if the number of each ionic specie (⁠$ni$⁠) and the occupancy of the O_h sites are fixed, the individual $xi$ does not matter. In other words, swapping the cations between the O_h and T_d sites (degree of spinel inversion) would not change magnetization. This can be inferred in Table II: for all four cations, moving a cation from an O_h site to a T_d site increases the magnetic moment by $2μB$⁠. Swapping two cations between the O_h and T_d sites would thus increase magnetization for one cation and reduce the contribution of the other by the same amount, with the net magnetization unchanged.

The effect of valency can be examined by changing the oxygen stoichiometry of NCO, which has been realized by growing NCO films under optimal condition and carrying out post-growth annealing at the growth temperature to generate oxygen vacancies.⁴⁵ As shown in Figs. 8(a) and 8(b), the valency of cations in NCO was characterized using x-ray absorption spectroscopy.⁴⁵ After annealing in vacuum at 315 °C, the valence of Co remains mostly unchanged, while for Ni an obvious increase of Ni²⁺ is observed.

Starting from nearly optimal structural configuration, annealing in vacuum does not change the total site occupation, or $n1x1+n2x2+n3x3+n4x4=1$ in Eq. (4). Since Co cations are not affected, $n3$ and $n4$ are constants. Therefore, Eq. (4) becomes

Clearly, when $Vo$ increases, $Ms$ decreases. This can be understood considering that the contribution of Ni³⁺ to magnetization is larger than that of the Ni²⁺, according to Table II. This is consistent with the observation in Fig. 8(c), where $Ms$ decreases after post-growth annealing in vacuum.⁴⁵ In addition, T_C also reduces slightly, reflecting the change of exchange interaction when Ni³⁺ is converted to Ni²⁺.⁴⁵ 

Change of cation stoichiometry of NCO has been observed in epitaxial thin films grown in different oxygen pressure (Fig. 9).⁴⁷ As shown in Figs. 9(a) and 9(b), when the O₂ growth pressure decreases, the occupancy of Ni cation on the O_h site decreases substantially. In contrast, the small occupancy of Ni cation on the T_d site remains approximately constant. Overall, when the O₂ pressure decreases, total population of the Ni cation decreases. This is consistent with the observation in Fig. 8: Ni³⁺ originally occupies the O_h site in the optimal NCO structure and becomes unstable when oxygen stoichiometry is changed.⁴⁵ The change of oxygen vacancy due to the reduced O₂ pressure during film deposition further weakens the bonding of Ni cations with the surrounding oxygen, which leads to the reduction of Ni cation population.

Another important observation for NCO films grown in reduced O₂ pressure is the cation vacancy on the T_d sites [Fig. 10(a)],^40,48 which can even result in the formation of the rock salt (Ni,Co)O phase.⁹⁴ The T_d sites are mainly occupied by Co cations in the optimal NCO structure. First-principles calculations indicate that the energy of the Co³⁺ on the T_d site is higher than that of Ni²⁺ on the O_h site, while the latter is slightly higher than that of Co³⁺ on the O_h sites.⁴⁰ Given that no clear O_h vacancy is observed during the growth of NCO in reduced O₂ pressure, it is likely that the Co³⁺, which occupies the T_d site in the optimal NCO structure, tends to occupy the O_h site instead when the fractional occupancy of Ni is reduced on the O_h site [Fig. 10(b)].

According to Eq. (5), when the total occupancy on the O_h site is fixed, the cation vacancy is expected to significantly reduce M_s, which is consistent with the observation in Fig. 9(c).⁴⁷ Since the Co cation on the T_d site is mostly responsible for the magnetic anisotropy (Fig. 7), the reduction of Co occupancy on the T_d site is expected to decrease the MAE, which is indeed observed experimentally [Fig. 9(d)].⁴⁷ Furthermore, when there is cation vacancy on the T_d site, the effective coordination number for the exchange interaction is reduced, which lowers T_C⁴⁷ according to the mean field theory. As shown in Fig. 9(c), the change of T_C follows that of M_s closely, suggesting the key role played by the cation vacancy on the T_d site.

Besides cation vacancy, inhomogeneous site occupancy has also been observed in NCO films grown in low O₂ pressure. More specifically, the T_d site vacancy occurs in a phase-separated fashion, effectively consisting of regions with optimal phase and regions with T_d-vacant phase [Fig. 10(a)].^40,48 In the optimal NCO phase, M_s is parallel to the moments on the T_d site and antiparallel to that on the O_h site. This is because the moments on the O_h and T_d sites are antiferromagnetically coupled, and all cations (Ni²⁺, Ni³⁺, Co²⁺, and Co³⁺) have higher spin magnetic moments when they are on the T_d site (Table II). For the T_d-vacant phase, the magnetic contribution may be dominated by the O_h sites, and M_s may be aligned with the magnetic moment on the O_h sites.

Given the antiferromagnetic coupling between the moments on the O_h and T_d sites, the magnetization between the neighboring optimal phase and the T_d-vacant phase are expected to be antiparallel when there is no external field [Fig. 10(c)]. This is observed in the “exchange spring”-type^95,96 magnetic hysteresis loops [Fig. 10(d)].⁴⁸ There are clearly two contributions to the hysteresis loop that are antiferromagnetically coupled. When the external field is large enough, both contributions are aligned by the field; when the external field is removed, the two contributions become anti-aligned, manifested as a reduction in magnetization near zero field.

Optimal NCO exhibit low resistivity (about 0.8 mΩ cm at 50 K) with weak temperature dependence, making it an appealing choice as transparent conductors.^{10,11,18,24,25} The electronic properties of NCO can be sensitively tuned by disorder,⁹ which can lead to a metal–insulator transition. Figures 11(a) and 11(b) show the temperature dependence of resistivity ρ(T) for NCO films on (001) MAO substrates deposited at different temperatures.³⁵ The films at high growth temperatures (500 °C and higher) exhibit insulating behaviors, while optimal resistivity is observed in the film deposited at 350 °C. There is a clear relation between the metallicity of the sample and its structural and magnetic properties, with the most conductive sample possessing the highest M_s and T_C.^35,40 Studies have shown that the metallic behavior of NCO is well correlated with the Ni³⁺ concentration [Fig. 11(c)],^22,97 suggesting that the charge itinerancy in NCO originates from the Ni³⁺–O²⁻–Ni³⁺ double exchange.

Besides growth temperature, disorder can also be introduced into epitaxial thin films via strain. Figure 11(d) shows ρ(T) for NCO(111) films deposited on MAO(111) and Al₂O₃(001) substrates,³⁴ which are subject to 0.3% and 4% compressive strain, respectively. The insulating behavior of the film on Al₂O₃ shows moderate improvement upon post-growth annealing, ruling out the contributions of valence mixing and spinel inversion. It has been suggested that the possible culprit is the presence of antiphase boundaries upon structural relaxation. This scenario is corroborated by the large magnetoresistance (MR), as will be discussed in Sec. VI.

For epitaxial thin films, film thickness is a powerful control knob for property tuning.^12,37,98 For example, ferroic materials are known to show the finite size effect, i.e., the suppression of ferroic order at the ultrathin limit. Figure 12(a) shows the temperature dependence of sheet resistance R_□(T) taken on 1.5–30 unit cell thick NCO films deposited on (001) MAO substrates.^12,99 The thicker films (20–30 u.c.) show optimal conduction, with metallic behavior and ρ  ∼ 0.8 mΩ cm at 50 K [Fig. 12(b)]. A resistance upturn occurs at low temperature, which can be due to weak localization or enhanced charge correlation.¹⁰⁰ The films become progressively more resistive with reduced thickness, transitioning to the strongly localized insulating behavior at 2 u.c., with the sheet resistance reaching the two-dimensional quantum resistance of h/e².^100–102 Similar thickness driven metal–insulator transition has been widely observed in correlated oxides, including (La,Sr)MnO₃,¹⁰³ RNiO₃ (R: rare earth),^104–106 and SrIrO₃.^100,107,108 Such a transition can be due to the surface/interface induced disorder/distortion,^{105,106,108,109} dimensionality crossover,^{100,104,107,108} or enhanced correlation energy¹⁰⁷ in the ultrathin limit.

The film thickness tuning of charge itinerancy in NCO is accompanied by the modulation of magnetic properties, with T_C and M_s also suppressed in thinner films [Fig. 3(b)].^12,37 On the other hand, a recent study shows for optimal NCO, T_C remains above 300 K in 3 u.c. thick films, and the magnetic dead layer thickness can be below 1.5 u.c. (1.2 nm), making NCO highly competitive for spintronic applications compared with other correlated oxides and various two-dimensional van der Waals magnets.⁹⁹ The film thickness can also effectively tune the coercive field H_c [Figs. 12(b) and 12(d)]. Figure 12(d) shows the switching hysteresis of anomalous Hall resistance at 300 K for 5–30 u.c. (001) NCO films. While all films exhibit strong PMA with T_C above 300 K, H_c decreases significantly in thinner films, which may be due to the reduced magnetic double well energy as T_C is approaching room temperature in these samples [Fig. 11(c)]. Well below T_C, the 30 u.c. film exhibits a T-independent H_c of ∼2 kOe [Fig. 11(c)]. In thinner NCO films, H_c increases exponentially with reducing T,^12,99 suggesting thermally activated domain wall depinning.¹¹⁰ The distinct T-dependences of H_c between the thick and thin films can be attributed to the enhanced contribution from film surface, where domain nucleation and domain wall pinning can be caused by surface roughness, reconstruction, and spin fluctuation.

For magnetic conductors, the magnetotransport properties can reveal critical information about the electronic band and spin scattering mechanisms. In this section, we discuss the intrinsic magnetotransport properties observed in epitaxial NCO films, including linear magnetoresistance and film thickness/temperature-driven sign change in the anomalous Hall effect (AHE). These highly tunable phenomena reflect the complex interplay between band-intrinsic Berry phase, SOC, disorder induced spin scattering, and correlation effect.

The magnetoresistance of NCO films is highly sensitive to disorder and can exhibit distinct magnetic field dependences. With optimal quality, NCO films exhibit very small negative MR in a perpendicular magnetic field with a quasi-linear field dependence. For example, it has been shown that the MR ratio (MRR) of high quality NCO films exhibit very weak T-dependence, with the out-of-plane MRR remaining less than 1% at 5 T over a wide temperature range (300 mK–300 K).¹² Figures 13(a) and 13(b) show the MR taken on 10 u.c. NCO films at two different temperatures. Switching hysteresis is observed in out-of-plane MR upon magnetization switching. Above H_c, the sample can sustain the linear MR up to 17 T [Fig. 13(b)]. In contrast, the in-plane MR shows a typical parabolic dependence at low magnetic field [Fig. 13(a)], which can be attributed to magnetization rotation to a hard axis. It has been suggested that the linear MR shares similar origins as the intrinsic contribution to the AHE,¹² which originates from the band-intrinsic Berry curvature in systems with a broken inversion system. It is favored in magnetic conductors with large SOC and can persist to higher magnetic fields in more disordered materials. It is also noted that at ultra-low temperature, there are sharp spikes appearing in MR at low magnetic field [Fig. 13(b)], which may signal the emergence of unusual spin texture in the presence of strong SOC.

For highly disordered NCO films, on the other hand, the MR is significantly enhanced and exhibits strong temperature dependence [Figs. 13(c) and 13(d)],^34,40,94,111 and the magnitude and temperature dependence of MR strongly resemble those of nano-crystalline NCO samples.¹¹² It has been attributed to spin-polarized transport through antiphase boundaries³⁴ or spin filtering effect in phase-separated samples,^40,48 with the latter similar to that of the colossal magnetoresistive manganites.¹¹³ The magnitude of MR can thus be effectively tuned by the level of disorder via changing the growth condition or substrate strain [Fig. 13(d)].^34,40,111

Epitaxial NCO films also exhibit intriguing AHE that can be tuned by film thickness,^12,99,114 as well as topological Hall-like features.¹¹¹ Figure 14(a) shows the Hall resistance R_xy in out-of-plane magnetic field taken on the 30 u.c. NCO film shown in Fig. 3(b), which exhibits clockwise switching hysteresis of AHE.¹² The anomalous Hall resistance R_AHE shows a non-monotonic temperature dependence, peaking close to room temperature. For a 10 u.c. NCO film, R_AHE also peaks at ∼300 K and gradually diminishes with reducing temperature, reaching zero at about 190 K [Fig. 14(b)].¹² When the temperature is further lowered, the AHE re-emerges with counterclockwise hysteresis, corresponding to a sign change in R_AHE from negative to positive. Such temperature-driven sign change does not correspond to any abrupt change in the magnetic state [Fig. 3(b)] or the change of carrier-type. Unlike the sign change phenomena observed in SrRuO₃,^115,116 there is no universal scaling relation between the anomalous Hall conductivity $σxy$ and magnetization,^12,114 ruling out the impact of sign reversal in the Berry curvature. It has thus been proposed that the sign change is due to the competing effects of different AHE mechanisms, which possess different signs and temperature dependences.^12,117,118

Previous theoretical studies have shown that for multi-band magnetic conductors, the scaling behavior of AHE can be divided into three regimes depending on how clean the system is.^119,120 For dirty metals, with the relaxation rate $ℏ/τ$ exceeding Fermi energy E_F, $σxy$ is dominated by impurity spin scattering and exhibits a power-law dependence on the longitudinal conductivity $σxx:σxy∼σxx1.6$⁠.¹²¹ For moderately dirty systems (⁠$ℏ/τ≤EF$⁠), $σxy$ is dominated by the band-intrinsic Berry phase effect and becomes insensitive to scattering, remaining a constant (⁠$σxx(0)$⁠). For super-clean systems, skew scattering dominates and $σxy$ scales linearly with $σxx$⁠. As the conductivity of optimal NCO films is close to the boundary between the dirty metal and moderately dirty regimes (⁠$σxx∼103Ω−1cm−1$⁠), it has been suggested that both impurity scattering and Berry phase effect can contribute to the AHE. The relative strength of these two can be tuned by temperature and film thickness [Figs. 14(a) and 14(b)], leading to sign change. As shown in Fig. 14(c), the $σxy$ vs $σxx$ scaling relation for 5–30 u.c. NCO films can be well described by

Here, the first and second terms depict the Berry phase and impurity scattering contributions, respectively, and A is a fitting parameter that increases with reducing film thickness.¹² It has been further showed that Eq. (6) is sustained down to the 2 u.c. films in the metallic phase, while the Berry phase contribution vanishes as the samples transition to the insulating phase.⁹⁹ In contrast, for samples with $σxx$ well above $103Ω−1cm−1$⁠, the Berry phase contribution dominates $σxy$ [Fig. 14(d)].¹¹⁴ The clear correlation between the metallicity of sample and the relative strength between the first and second terms in Eq. (6) yields strong support to this scenario. Another interesting observation is the emergence of another scattering independent $σxy$ regime at low temperature [Fig. 14(c)], where the conduction is dominated by disorder enhanced correlation effect and the side-jump mechanism may also contribute to AHE.^122–124 

NCO is a versatile material with robust magnetic order and close to half metallicity. It hosts a plethora of cation configurations in terms of local oxygen environments (O_h and T_d), cation species (Ni and Co), and valence states (2+ and 3+). The small energy difference between these configurations leads to high electrochemical activity, making NCO appealing for catalysis and energy storage applications.¹¹ While the inverse spinel structure is unstable in the large single crystal form, there has been rapid development of high quality epitaxial thin films in recent years, leveraging the strong spin–lattice coupling. Its electronic and magnetic properties depend sensitively on the strain and disorder levels—substrate type, growth condition, and film thickness have been exploited to effectively control the metallicity, magnetic transition temperature, magnetization, coercive field, magnetic anisotropy, and magnetotransport of the samples. The highly tunable nature yields NCO distinct advantages for manipulating spin using nonmagnetic means, which is highly desirable for developing energy-efficient spintronic applications.

One promising application for NCO is to serve as the spin-injection layer for epitaxial magnetic tunnel junctions (MTJs). It has been predicted theoretically that spinel MTJs with MAO tunnel barriers can facilitate spin filtering and enhance tunnel magnetoresistance.^125,126 Studies of epitaxial MTJs composed of MAO and NCO also reveal high-spin polarization of −73%.¹³ The above room temperature T_C, strain tunable PMA,¹⁵ film thickness dependent H_c, close to half metallicity, and fast spin dynamics¹⁴ make NCO films ideal for constructing high efficiency, high speed MTJs.

Another possible device concept for NCO is magnetic field sensors.¹²⁷ Optimal NCO exhibits linear MR with weak temperature dependence that can persist to high magnetic field [Figs. 13(a) and 13(b)].^12,48 The magnitude of MR can be further tuned by disorder and strain,^34,40 which can be exploited to design field sensing devices with high sensitivity.

Epitaxial NCO films also present a rich playground to explore the AHE.¹²⁸ The conductivity of optimal NCO is close to the boundary between the dirty metal and moderately dirty regimes, where multiple mechanisms can contribute to AHE.^119,120 As the electronic properties can be sensitively tuned by the disorder level via changing substrate type, growth condition, and film thickness, the relative strength between the contributions from the band-intrinsic Berry phase effect, impurity scattering, and correlation energy can be varied. The anomalous Hall conductivity of NCO is comparable with that of magnetic semiconductors,¹²⁹ while it can persist well above room temperature. These versatile features make NCO an appealing material choice for exploring AHE-based device applications.

As an emerging spintronic material, there are three major directions for future studies of NCO. The first one involves further improving the material quality, particularly magnetic properties. It is of both fundamental and technological interest to explore the finite size limit of magnetism in NCO. To date, the thinnest NCO films with T_C > 300 K is 3 u.c. (2.4 nm).⁹⁹ Robust PMA has been observed in NCO films as thin as 1.5 u.c. (1.2 nm), where T_C is suppressed to about 170 K.⁹⁹ The thickness scaling behavior of these ultrathin NCO films outperform the widely investigated magnetic oxides such as SrRuO₃¹³⁰ and (La,Sr)MnO₃¹⁰³ and are comparable to the two-dimensional van der Waals magnets with PMA.¹³¹ The scalable growth method via physical vapor deposition make them highly competitive for developing high density magnetic memories. It is thus important to explore material strategies to enhance T_C and engineer the magnetic parameters in the ultrathin NCO films.

The second direction centers on gaining microscopic understanding of the unusual properties of these materials. High quality epitaxial NCO thin films only became available over the last ten years. Due to its relatively large unit cell, theoretical computation of band properties of spinels is lagging behind the perovskite oxides.³⁹ For example, the emergence of unconventional low field spikes in MR [Fig. 13(b)] and possible topological Hall signal¹¹¹ suggest the existence of non-coplanar spin textures, which may be associated with non-trivial topology. To elucidate the origin of these effects, it requires combined theoretical and experimental efforts to map out the band structure, determine the strength of SOC and Dzyaloshinskii–Moriya interaction, and identify the possible existence of chiral spin textures. It has also been shown that the thermoelectric coefficients of NCO films is much smaller than other spinel oxides,¹³² while whether it is intrinsic to NCO or compromised by the sample quality remains to be investigated.

The third direction lies on developing novel device concepts, exploiting the magnetotransport anomaly and strain tunable properties in NCO films. The fact that the magnitude and size of the anomalous Hall resistance as well as the switching field can be sensitively tuned opens the door for developing novel information storage devices using AHE. It is desirable to explore possible electric field effect control of AHE, which can be built on the field effect transistor device architechture.^133,134 The field effect can also be exploited to tune the topological Hall effect and, if confirmed, chiral spin textures, which can be of interest for topological computing. As the PMA in NCO can be effectively tuned by strain, it is also conceivable to interface NCO-based MTJ with a piezoelectric substrate, exploring electric control of the switching characteristics of the tunneling magnetoresistance.⁶⁷ 

In conclusion, in this Perspective, we summarize the recent advancements on understanding the intriguing properties of epitaxial NCO films, discussing both the optimal configuration and the strong tunability. These understandings allow us to outline a few promising directions of research, aiming at inspiring future studies of this emerging material system for high density, high speed, and energy-efficient spintronic and nanoelectronic applications.

The authors acknowledge the primary support from the National Science Foundation (NSF) through EPSCoR RII Track-1: Emergent Quantum Materials and Technologies (EQUATE), Award No. OIA-2044049. Additional support was from NSF Grant Nos. DMR-1454618 and DMR-1710461. Work by Z.G.C. was supported by the National Key R&D Program of China under Grant No. 2018YFA0305604 and the National Science Foundation of China (NSFC) under Grant No. 11874403.

The authors have no conflicts to disclose.

Xiaoshan Xu: Conceptualization (equal); Writing – original draft (equal); Writing – review and editing (equal). Corbyn Mellinger: Data curation (equal); Writing – review and editing (equal). Zhi Gang Cheng: Data curation (equal); Writing – review and editing (equal). Xuegang Chen: Data curation (equal); Writing – review and editing (equal). Xia Hong: Conceptualization (equal); Writing – original draft (equal); Writing – review and editing (equal).

The data that support the findings of this study are available from the corresponding authors upon reasonable request.