Structure and tunneling magneto-dielectric properties of Co–SrF₂ nano-granular thin films

In the age of the internet of things, applications of magneto-electric (ME) and quantum effects have experienced explosive growth. In general, the ME effect, which was first introduced by Röntgen in 1888,¹ implies the coupling of magnetic and electric properties of a material. It is traditionally derived from the coupling of spatial-inversion and time-reversal symmetrical properties in multiferroic materials. However, previous studies of the ME effect suffer from the limitation of low application temperature, which restricts its applicable capacity.^2–5 

As one of the ME effects, the magneto-dielectric (MD) effect was first considered by Landau et al.⁶ in 1960 based on the magnetic crystal symmetry, which was then discovered on Cr₂O₃ by Folen et al.⁷ in 1961. Similarly, the design that couples magnetic and dielectric properties through a certain property, such as crystal symmetry, enlightened subsequent research of the MD effect with various mechanisms, such as spin–orbit coupling,^8,9 spin–lattice coupling,¹⁰ Jahn–Teller distortion with spin–orbit coupling,^11,12 coupling of uniform polarization and q-dependent spin–spin correlation,¹³ and unusual commensurate–incommensurate magnetic transition coupling.¹⁴ Their chemical compositions were limited to oxides, especially manganate,^10–12,14 and high crystallinity is indispensable. Their preparation processes were complicated, and a strong magnetic field above 1 T was usually necessary. However, in terms of applications, the largest limitation was the very low operating temperature.

In 2014, a new effect was realized in our early work on the structure of nano-granular thin films.^15–18 This was described as the tunneling magneto-dielectric (TMD) effect. The thin film can be prepared easily by the sputtering method. Its chemical composition can be oxide, fluoride, and other insulating materials. Moreover, it can be observed and measured at room temperature. The granule–matrix structure plays a vital role in the mechanism of the TMD effect. In this structure, the superparamagnetism (SPM) of magnetic nano-granules provides freely controllable electron spin directions, and the magnetized nano-granules and insulator matrix spacing provide the condition for the tunneling effect. As the most common quantum effect, tunneling is a common phenomenon of particle volatility in spintronics.⁴ In particular, two noted effects, the giant magnetoresistance (GMR) effect^19,20 and the tunneling magnetoresistance (TMR) effect,^21–23 have been discovered based on the structure of the magnetic tunnel junction (MTJ), which is similar to the granule–matrix structure in the TMD effect. Therefore, the quality of this structure should directly determine the existence and efficiency of the TMD effect. This structure also possesses giant dielectric properties^15,24 and good high-frequency magnetic properties.²⁵ 

In order to make the following research content easy to understand, the physical mechanism of the TMD effect will be introduced. In Mott’s model, the importance of the granule–matrix structure is to maintain localized hopping conductivity states of electrons in this type of disordered system. The criterion for localization is defined by the width and quality of the energy interval (mobility gap) in a pair of energy traps.²⁶ In the granule–matrix structure (Co granules and Sr–F ceramic matrix) of this study, the mobility gap width is the thickness of the matrix between two granules, and the mobility gap quality is interpreted as the decay rate of the hopping electron wave function in the insulating barrier region and is affected by the matrix crystallinity. The primary aim of this study is to investigate the effect of matrix crystallinity.

Co was chosen as the granule material owing to its high magnetization and excellent thermal stability.²⁷ Given the standard enthalpy of formation (Δ_fH^ϴ_298K) of CoF₂ of −672.69 kJ/mol,²⁸ alkaline-earth fluorides, for which Δ_fH^ϴ_298K is always below −1100 kJ/mol, would be the best choice. As shown in Fig. 1,^29,30 BeF₂ was excluded owing to its severe toxicity. The upper-right image in Fig. 1 shows that SrF₂ should provide the best choice of the matrix, owing to its high resistivity and low Δ_fH^ϴ_298K. The purpose of using SrF₂ as the new composition was to improve the mobility gap quality by improving the matrix crystallinity. The consequent lower decay rate of the hopping electron wave function will provide better localized hopping conductivity states for the tunneling effect and thereby a higher TMD response. The localized hopping conductivity in Mott’s model can be considered equivalent to the tunneling conductivity in the tunneling effect. The overall structure of this study was divided into three parts: (1) composition and structure evaluation, (2) permittivity and magnetization evaluation, and (3) TMD response evaluation.

Co–SrF₂ nano-granular thin films were deposited at room temperature on substrates of Si(100), Pt(100 nm)/Ti(50 nm)/Si(100), and quartz glass using the co-sputtering method with a SrF₂ ceramic target (radio frequency source) (thickness of 3 mm) and a Co magnetic metal target (direct current source) (thickness of 1.5 mm). Background pressure and sputtering Ar gas pressure were 2 × 10⁻⁴ and 0.65 Pa, respectively. The power of the SrF₂ target was fixed at 300 W, so the chemical composition of the thin film was controlled by adjusting the power of the Co target from 0 to 205 W.

The structure and morphology of the Co–SrF₂ thin films were observed by transmission electron microscopy [TEM; Topcon EM-002B (200 kV, LaB₆)] on the Si(100) substrate. Chemical composition was examined by x-ray fluorescence (XRF; Rigaku ZSX Primus II) on the quartz glass substrate. Thickness was tested using a stylus profilometer (Dektak 6M). Electrical resistivity was measured by the conventional four-terminal sensing and concentric ring methods on the quartz glass substrate. Hystereses of magnetization were obtained using a vibrating sample magnetometer (VSM; TOEISI PV-M20-5S) on the quartz glass substrate. Dielectric properties were evaluated by a digital bridge, LCR meter (Keysight E4980A) from 1 kHz to 1 MHz with and without an external magnetic field up to 10 kOe on the Pt(100 nm)/Ti(50 nm)/Si(100) substrate. All measurements reported in this study were carried out at room temperature.

With the increasing Co content from 0 to 19 at. %, the stoichiometric ratio, Sr:F, was maintained constant at 1:2, which is the same as that of the SrF₂ target composition. The thickness of the Co–SrF₂ thin films was controlled to 1000 nm. The morphologies and diffraction patterns were analyzed by Gatan DigitalMicrograph and ImageJ software and are shown in Fig. 2. In Fig. 2, (a) is the diffraction pattern of the Co₁₆–(SrF₂)₈₄ thin film, where five-ring patterns of SrF₂ were observed because of its high crystallinity. However, no diffraction rings were clearly observed for the Co granules. In Fig. 2 (b)–(d) are TEM graphs of Co₉–(SrF₂)₉₁, Co₁₆–(SrF₂)₈₄, and Co₁₉–(SrF₂)₈₁ thin films, respectively. When the Co content was below 9 at. %, the granules were still relatively small and could not be easily perceived. As the Co content increased from 9 to 19 at. %, the Co granules became clearer and their average diameter increased from 3.0 to 3.7 nm. As the Co content approached 19 at. %, the Co granules became elliptical along the film growth direction and their TEM images probably overlapped.

Before evaluating the TMD property, the magnetic hystereses of the thin films were measured, as shown in Fig. 3(a). The hystereses of all thin films showed superparamagnetic properties because the average diameters of the Co granules observed by TEM were all smaller than 4 nm, which is less than the superparamagnetic critical diameter of Co of 8 nm²⁷ at room temperature. Regarding the magnetization (M) under the external magnetic field (H) of 10 kOe as the saturation magnetization (M_S = M_H=10kOe), as the Co content increased from 0 to 9 at. %, M_S increased from 0 to 0.55 kG; thereafter, when the Co content almost doubled to 19 at. %, M_S increased by more than five times to 3.1 kG. This dependence of M_S on the Co content is consistent with the results observed by TEM. At Co contents below 9 at. %, M_S was low because the granules were not well formed; above 9 at. %, the number of formed granules began to increase and the resultant M_S also increased rapidly.

The dependence of permittivity (ε′) and dielectric loss (ε″) on frequency (f) with H = 0 is shown in Fig. 3(b). Dielectric relaxation occurred between 1 and 1000 kHz. The permittivity values at 1 and 1000 kHz (ε′_f=1kHz and ε′_f=1MHz) were regarded as the parameters to evaluate the dielectric constant at low and high frequency. Similar to the dependence of M_S, as the Co content increased from 0 to 9 at. %, ε′_f=1kHz and ε′_f=1MHz increased to 26 and 5, respectively; when the Co content almost doubled to 19 at. %, ε′_f=1kHz and ε′_f=1MHz increased by more than 25 times to 648 and 139, respectively. The origin of this polarization is different from the classic polarization, such as space charge relaxation or dipolar relaxation. In this study, in a nano-granular pair system, the metallicity of two granules formed two electric potential traps, and insulation of the Sr–F ceramic matrix formed a thin electric potential barrier. With thermal excitation, electrons will tunnel from one granule to the other with a transition probability, which is different owing to the external magnetic field. Based on the Debye–Fröhlich model,³¹ the different occupation probabilities can be calculated by the transition probability. Finally, the difference of occupation probabilities defines the electric polarization by p = ed₁₂(P₁ − P₂), where e is the element charge, d₁₂ is the distance between the centers of two granules, and P₁ and P₂ are the occupation probabilities in granule 1 and granule 2 of the nano-granular pair system, respectively.

The dependences of ε′ on f with H = 0 and 10 kOe of the Co₉–(SrF₂)₉₁, Co₁₆–(SrF₂)₈₄, and Co₁₉–(SrF₂)₈₁ thin films are shown in Figs. 4(a)–4(c). A permittivity shift was confirmed, which can be more clearly observed in the upper-right enlarged graph. The clearest shift can be observed in Fig. 4(b) of the Co₁₆–(SrF₂)₈₄ thin film. In Fig. 4(b), the almost unchanged permittivity at both ends indicates that the shift direction was to the right. Owing to the presence of dielectric relaxation, the permittivity at the same frequency seemed to shift upward near 20 kHz. The relative permittivity percentage increment at the same frequency is defined as Δε′/ε′₀ = (ε′_H=10kOe–ε′₀)/ε′₀, which is referred to as the TMD response, where ε′₀ and ε′_H=10kOe are the measured permittivity with H = 0 and 10 kOe, respectively. The dependence of TMD response on frequency is shown in Fig. 4(d) for the Co₁₆–(SrF₂)₈₄ thin film, which shows a peak curve with a maximum TMD response of ∼3.5% at a frequency of ∼20 kHz.

Given the confirmation of the permittivity shift caused by the external magnetic field (H), the dependence of the TMD response on H from −10 to 10 kOe is shown in Fig. 5(a). Theoretically speaking, the superparamagnetism (SPM) is indispensable to the TMD response (refer to the research of Inoue and Maekawa).³² In addition, Sheng et al.³³ suggested that only when the magnetic granules behave as superparamagnets, the relative angle between two granules can be defined for tunneling events that occur in a period of time, which is much shorter than the characteristic period of the thermal fluctuation of the magnetic moments of the granules. As a result, it is necessary to confirm the superparamagnetism, and the fitting function is a Langevin function, which is an approximation of the Brillouin function. As a result, the fitted solid curve matches well with the experimental scatter curve. In the fitting process, the TMD response is proportional to the square of the normalized magnetization, (M/M_S)², and the dependence of M on H can be described by a Langevin function, L(x), where x is proportional to H.

The TMD responses were fitted as the solid curves shown in Fig. 5(a). Figure 5(b) shows that the dependences of the TMD response on the Co contents of Co–SrF₂, Co–Al–O, and Fe–Co–Mg–F¹⁵ thin films exhibited bell-shaped curves. The dependence curve of the Co–SrF₂ thin films was the narrowest and highest, indicating that this gave the largest TMD response of 3.5% with a minimal Co content of 16 at. %. Because SPM is indispensable to the TMD effect, when the Co content is larger than 16 at. %, the agglomeration and fusion of Co nano-granules lead to fewer Co nano-granular pairs actually participating in the TMD effect. That is why there will be a peak at 16 at. % in the dependence of the TMD response on the Co content.

Considering all results, the new ceramic matrix material, SrF₂, improved various properties of these thin films due to its high electrical resistivity and low enthalpy of formation. The most important and direct result is the high matrix crystallinity shown in Fig. 2(a) with a stable stoichiometric ratio. This stable stoichiometric ratio of Sr:F = 1:2 is the same as that of the SrF₂ target, which was first observed in TMD studies. In the TMD theory, the charging energy (γ₁₂) of a granule pair (granule 1 and granule 2) is defined in Eq. (1), which determines whether thermally activated electrons will tunnel from one granule to the other. γ₁₂ can be divided into two parts: the magnetic term, 1 + P²m², defined by the spin polarization (P) and the normalized magnetization (m) of the granular system, and the exponential attenuation term, exp[–2κs₁₂–E₁₂/(k_BT)], defined by the decay rate of the hopping electron wave function (κ), the distance between the surfaces of nano-granule 1 and nano-granule 2(s₁₂), temperature (T), and the thermal activation energy (E₁₂) in the tunneling process. E₁₂ is defined in Eq. (2), which is determined by the diameters of nano-granules (d₁, d₂).

In summary, according to Eqs. (1) and (2), the TMD response is closely related to the hyperfine structure of the nano-granular pair system, including s₁₂, d₁, d₂, and κ. s₁₂, d₁, and d₂ represent the spatial structure relationship of the hyperfine structure. Then, κ quantifies the influence of the hyperfine structure on electron tunneling. As a result, the quality of the mobility gap in hopping conductivity is very important, which means the lower the κ, the better the localized hopping conductivity states for tunneling and the higher the tunneling conductivity. In this study, the mobility gap is the spacing matrix of the superparamagnetic granule pair, which is why matrix crystallinity is important to ensure a TMD response. Indeed, Co–SrF₂ thin films with high matrix crystallinity achieved a higher TMD response, as shown in Fig. 5(b),

where

This study sets out to evaluate a new composition design, Co–SrF₂, and explores the influence of matrix crystallinity on the nano-granular structure. TEM results showed that Co–SrF₂ thin films exhibited a homogeneous nano-granular structure with high matrix crystallinity. TEM, magnetization, and permittivity results all showed that two states existed: with a Co content below 9 at. %, the Co granules were not formed well and M_S, ε′_f=1kHz, and ε′_f=1MHz increased to 0.55 kG, 26, and 5, respectively; when the Co content doubled to 19 at. %, the number of granules increased and these parameters increased to 3.1 kG (5× increase), 648 (25× increase), and 139 (28× increase), respectively. These results prove that as the Co content increased, the formation and the increase in the number of Co granules occurred separately in two stages. The improved spacing material, SrF₂, the high matrix crystallinity of which provided a better mobility gap in hopping conductivity and higher tunneling conductivity, gave a higher TMD response. TMD results showed that the TMD response peaked at 3.5% at a Co content of 16 at. % and a frequency of 20 kHz, which is higher than that reported in previous work.

With respect to the TMD effect, these findings indicate the importance of matrix crystallinity and stoichiometric ratio and illustrate the influence of the matrix material on the nano-granular structure. Further studies may focus on the achievement of higher crystallinity of superparamagnetic Co granules without reducing the crystallinity of the matrix material.

This work was supported by the Japan Society for the Promotion of Science (JSPS) KAKENHI under Grant-in-Aid Nos. 20H02447 and 21K18810. Mr. Shun ITOH from Analytical Research Core for Advanced Materials, Institute for Materials Research, Tohoku University, is greatly acknowledged for assistance with the TEM observations.

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