Dense inter-particle interaction mediated spontaneous exchange bias in NiO nanoparticles

Abstract

We report the finite size effect and nickel vacancy defects in NiO nanoparticles that result in the formation of magnetic phase separation in uncompensated antiferromagnetic NiO-cores with frustrated and disordered spins at the surface NiO-shell. The inter-particle interaction is probed by analyzing the relaxation dynamics measurements. A significant index for the interaction of n derived from the dynamic magnetization is proposed, which paves the way for the examination of the spontaneous exchange bias mechanism and offers insight into the influence of the particle size and defects.

---

1. Introduction

Nickel oxide (NiO) is an antiferromagnetic (AFM) insulating material having a Néel temperature (T_N = 520 K) above room temperature which has been the object of extensive research attention over the last few decades because of its importance in numerous technological applications (i.e., catalysis, batteries, ceramics etc.). In the last decade, renewed interest has been generated in nanoscale NiO whose unique properties (i.e., high surface to volume ratio, short diffusion paths, enhanced magnetic and electric properties, nickel vacancies etc.) have opened up avenues for its use in diverse fields for catalysis,^1–3 anodic electrochromics,⁴ capacitors,^5,6 smart windows,⁷ fuel and solar cells,^8,9 biosensors¹⁰ and spintronics.^11–13 In particular, intense research effort is being made to combine NiO nanostructures with graphene in order to develop highly functional energy storage systems^14,15 and electrochemical sensors.¹⁶ Saha et al.¹⁷ first explained the zero-field or spontaneous exchange bias (EB) effect by using a micromagnetic simulation in a bilayer system with a polycrystalline AFM. The term spontaneous refers to the case in which the system is not conventionally field cooled. They proposed a mechanism which could induce unidirectional anisotropy (UA) in an otherwise isotropic ferromagnetic–antiferromagnetic (FM–AFM) system just by the simple application of the first field point in the hysteresis loop evaluation without setting any initial bias as was used to observe the spontaneous exchange bias (SEB) effect. Recently, the SEB effect has been observed in various bulk, FM/AFM core/shell, and nanocomposite to pure AFM nanostructure systems. For example, Maity et al.¹⁸ reported on superspin glass mediated giant SEB (300–600 Oe) in an AFM–FM BiFeO₃–Bi₂Fe₄O₉ nanocomposite. They ascribed the observed SEB to spontaneous symmetry breaking and the consequent onset of UA driven by “super interaction bias coupling” between the FM core of Bi₂Fe₄O₉ (∼19 nm) and the canted AFM moment in the coarser BiFeO₃ (∼112 nm) through superspin-glass moments at the interface. Similarly, Lierop et al.¹⁹ observed SEB in Ni₈₀Fe₂₀/Co₃O₄ thin films. Liu et al.²⁰ also observed an absence of AFM state in α-Fe₂O₃ nanocrystals. In their comprehensive measurements and analysis, all the as-synthesized products for different morphologies illustrate magnetic phase transformation at extremely low temperatures, and show no apparent Morin transition in the range 2 to 350 K. We note that, in all the above examples the observed SEB is due to UA driven by coupling at the interface of the FM–AFM component. Ahmadvand et al.²¹ observed SEB in AFM LaFeO₃ nanoparticles (40 to 45 nm) attributing it to exchange coupling between the weak-FM shell and the AFM core of the particles. Chauhan et al.²² reported on the effect of varying particle sizes and maximum applied fields during the initial magnetization on the SEB in AFM hexagonal-YMnO₃ nanoparticles (45 to 90 nm). The observed SEB was attributed to the exchange interaction between the compensated AFM spins and spin-glass-like uncompensated surface spins. In this work, we present that in AFM NiO nanoparticles the inter-coupling between short-range ordered clusters of spins which behave like weak ferromagnetic (FM) NiO-shells and uncompensated AFM NiO-cores lead to a shift in the hysteresis loop known as the SEB phenomenon. To study the anomalous magnetic behavior of AFM NiO nanoparticles, static and dynamic magnetic measurements, including time, temperature and field dependence have been carried out.

2. Experimental details

The structural and morphological analysis of chemically synthesized 16.6(7), 19.5(6), 29(4), 31(1), and 54(6) nm NiO particles has been discussed in detail in our previous work.²³ Nanoparticles of NiO were synthesized by the sol–gel technique followed by annealing in an ambient atmosphere for 1 hour at different temperatures from 400 to 800 °C (at intervals of 100 °C). In a previous work, we utilized confocal Raman spectroscopy to probe the superexchange interaction energy E_2M along the next-nearest-neighbor (NNN) Ni²⁺ ions through oxygen in NiO. The observed exponential decrease of E_2M with particle size was attributed to an increase in the nickel vacancy concentration. In this work we probe the effect of the nickel vacancy concentration and finite size on the magnetic properties of NiO nanoparticles. Detailed temperature, time and field dependent magnetic measurements were carried out using a superconducting quantum interference device (SQUID) magnetometer (Quantum Design, VSM). The morphology was characterized using a transmission electron microscope (TEM, JEM-3010 JEOL) and structural characterization was made from high-resolution TEM (HRTEM) and selective area diffraction patterns (SAED) of all the NiO nanoparticles.

3. Results and discussion

3.1. Morphology and structural analysis

The TEM images in Fig. 1(a)–(e) show the morphology for NiO nanoparticles with various annealing temperatures ranging from 400 to 800 °C, respectively. It can be seen that the nanoparticles obtained after annealing at T_A = 400 °C, as shown in Fig. 1(a), are closely packed and irregular in shape. The effect of further thermal treatments at 500 to 800 °C, resulted in an increase in both the size and dispersity of the nanoparticles. Details about the mean diameter estimated by using a log-normal distribution function and the grain size obtained from a Williamson–Hall plot have been discussed in our previous work.²³ Annealing at low temperature (400 to 600 °C) resulted in the formation of particles with a single domain having grain sizes of 16.6(7), 19.5(6) and 29(4) nm, respectively. Further annealing at higher temperatures, 700–800 °C resulted in the formation of particles with multiple grains having grain sizes of 31(1) and 54(6) nm, respectively. The NiO nanoparticles of all the samples seemed to be pseudo-spherical in shape and retained a perfect Fm3̄m crystalline structure as can be seen in the HRTEM images shown in the inset to Fig. 1(a)–(e). The inter-planar distance d obtained from HRTEM images of 400–800 °C annealed particles are 2.101, 2.095, 2.091, 2.087, and 2.085 Å, respectively, corresponding to the [200] nuclear plane of NiO nanoparticles. The lattice constants (4.202, 4.189, 4.182, 4.174, and 4.170 Å) calculated from the d value for the particles annealed at 400–800 °C matched the XRD analysis very well.²² The observed increase in the lattice constants with the decrease of particle size can be attributed to the effect of nickel vacancy defects and finite size effects, details about which have been discussed in our previous report.²³ The selective-area-electron-diffraction (SAED) patterns of particles annealed at 400–600 °C reveal their poly-crystalline nature; see Fig. 1(f)–(h). The SAED patterns of large sized 31(1) and 54(6) nm NiO particles appearing in Fig. 1(i) and (j) can be ascribed to the existence of cubic NiO along the [001] and [111] reflection zone axes.

Fig. 1 (a)–(e) TEM images and (f)–(j) SAED patterns of the 16.6(7) to 54(6) nm NiO nanoparticles. The insets of (a)–(e) show HRTEM images of the respective NiO nanoparticles.

3.2. Temperature dependent magnetic measurement

The temperature dependence of the field cooling (FC) and zero field cooling (ZFC) magnetization for NiO nanoparticles with a mean diameter 16.6(7) nm with a applied magnetic field H_a = 100 Oe is shown in Fig. 2(a). The ZFC magnetization shows a pronounced board peak, defined as a blocking temperature T_B ∼ 178 K, while FC magnetization increases monotonically with decreasing temperature below T_B. At lower temperature, there is a small peak in the ZFC magnetization visible at around 6 K, called as the freezing temperature T_f which is associated with collective freezing of uncompensated surface NiO moments. A value of T_f ranging from 5 to 15 K has been reported for NiO nanoparticles synthesized by different techniques.^24–31 As shown in Fig. 2(a), a bifurcation between the ZFC and FC is visible above T_B with the data beginning to merge at an irreversible temperature T_irr. The sizes dependence of T_B, T_irr and T_f are depicted in Fig. 2(b), respectively, whereas T_f reveals size independent. The values of T_B and T_irr show a further increase of particle size from 16.6(7) to 31(1) nm for a shift in the T_B from 198 K to 374 K, and the T_irr from 262 to 398 K, respectively. The similar increasing behavior of T_B with the size has also been observed from small size NiO nanoparticles (<10 nm). Duan et al.³¹ reported an increase of T_B from 19.8 to 161 K with increase in the particle size from 3.5 to 12.4 nm. Similarly, Montes et al.³² reported an increase of T_B ∼ 3.5, 53 and 145 K with particle size, 2 to 10 nm. However, Thota et al.²⁶ reported an increase of T_B and T_irr with a decrease of particle size from 22 to 4.1 nm. In the former two studies, it was observed that the set of nanoparticles are non-interacting, whereas in later findings they are interacting. Shim et al.²⁵ compared the size dependency of T_B from non-interacting (oleic acid (OA) coated) and interacting (uncoated) NiO particles (5 to 20 nm). An increase in T_B with size was observed from all the OA coated, non-interacting nanoparticles. In contrast, a decrease of T_B with an increase of particle size up to 8 nm and above, and an increase with size was observed from uncoated nanoparticles. Their findings confirmed that the value of T_B from NiO nanoparticles is not just governed by the size and distribution of the particles, but also by their nature. The observed increase of T_B with particle size signals that the inter-particle interaction in this set of nanoparticles is either weak or absent, which will be discussed later in the text.

Fig. 2 (a) M(T) curves measured with the ZFC–FC protocol in an external magnetic field of 100 Oe for 16.6(7) nm NiO nanoparticles. (b) Blocking (T_B), irreversible (T_irr), and freezing (T_f) temperature as functions of nanoparticle size.

In addition, the magnetic susceptibility of the bulk AFM material increases with temperatures below the Néel temperature but exhibits paramagnetic behavior.³³ The observed decrease in magnetization (from both ZFC–FC curves) with measurement temperature for 31(1) nm particles (see ESI: Fig. S1(a)†) indicates that the AFM moments begin to dominate over the net magnetization. The 54(6) nm (T_A = 800 °C) particles show bulk-like AMF behavior (see ESI: Fig. S1(b)†). A similar increase of magnetization with temperature has been reported by Richardson et al.³⁴ from bulk NiO and by Mandal et al.³³ from quenched NiO particles (size ≥ 60 nm). However, recently Mariana et al.³⁵ observed paramagnetic behavior over temperatures ranging from 2–380 K from 60.3 ± 2.2 nm NiO particles. The observed behavior was attributed to incomplete compensation of the AFM sublattices at the surface. They claimed that the paramagnetic behavior observed from the nanoparticles is typically the same as that observed from bulk NiO, citing references to Jagodič et al.³⁶ and Winkler et al.²⁵ However, Jagodič et al.³⁶ observed a similar kind of surface spin magnetization effect from both nanoparticles and bulk NiO, but only below 25 K. A further increase of measurement temperature of bulk NiO resulted in an increase of susceptibility similar to that observed in Fig. S1(b) (see ESI†). On the other hand, Winkler et al.²⁵ reported observation of the paramagnetic behavior in the high temperature region in 3 nm sized NiO particles which was attributed to highly uncompensated moments of the AFM core. The 3 nm size particle is ∼20 times smaller and at such a small size nickel vacancy defects are too high, resulting in paramagnetic/superparamagnetic behavior due to the breakdown of AFM ordering.³² This argument is consistent with the recently observed breakdown of AFM ordering in ∼2.5 nm NiO particles by Montes et al.³² We also observed a similar breakdown of AFM ordering in the ∼3 nm size NiO nanoparticles (data not published). Furthermore, the M(T) behavior for 3 nm size particles is similar to that observed by Jagodič et al.³⁶ and Duan³¹ and Montes,³² due to freezing of the clusters of surface spins. The M(T) behavior observed from the R-state of samples (size ≥ 60 nm) by Proenca et al.³⁵ is similar to that observed by Mandal et al.³³ and they speculate on the existence of two components, FM and/or paramagnetic and AFM. The former dominates in the low temperature region and the latter in the high temperature region. Furthermore, the invisibility of T_f for the 〈d〉 = 54(6) nm sample strongly suggests the absence of disordered surface moments and nickel vacancies. Therefore, NiO particles with a crystalline size higher than or equal to 54(6) nm behave like bulk NiO and can be considered as ideal AFM NiO.³² Furthermore, the value of the magnetization (M_FC) decreases with the increase of particle size. The observed increase of susceptibility to a decrease of NiO nanoparticle size is in good agreement with the results of Tiwari et al.²⁷

The finite size effect results in disordered spins at the surface were concluded in our previous work from the analysis of two magnon excitation.^23,37 The intensity of magnon excitation in NiO is related to AFM ordering and it decreases with the increase of nickel vacancy concentration.³⁸ There is a monotonic increase in the nickel vacancies with a decrease in the particle size. Therefore, each uncompensated AFM NiO nanoparticle gives rise to a net magnetic moment due to a reduction in the number of exchange coupled moments caused by finite size effects. In such a scenario, at finite temperatures, the uncompensated AFM exhibits superparamagnetic (SPM) behavior. The important characteristic of SPM is the superparamagnetic relaxation time, also called the Néel relaxation time τ_N.³⁹ The τ_N is the average time that the magnetization spends in the minima of the anisotropic energy. Let us consider an assembly of particles with uniaxial anisotropy along the z-axis. A large external field H_a is applied along the z direction, such that all the particles are magnetized to saturation M_S. If the field is removed, the magnetization will decay due to thermal agitation according to the relationship M_S = M_o exp(−t/τ). If τ_N is very large, M_S = M_o and the system will remain in a stable state. The relaxation time τ_N then must be proportional to the Boltzmann's factor, exp(E(θ)/k_BT), since E(θ) = KV sin²(θ)is the energy barrier between the two energy minima. Thus, the relaxation rate can be written as follows: τ_N = τ_o exp(KV/k_BT), where K is the magnetic anisotropic energy density, V is the particle volume, k_B is Boltzmann's constant, and τ_o is the characteristic of the material, called the attempt time, with a typical value in the range of 10⁻¹³ to 10⁻⁹ s. At a certain temperature, T_B, τ_N will become equal to τ_m, the time of measurement. This leads to T_B = (KV/k_B)/ln(τ_m/τ_o) and it then becomes dependent on the measurement time. According to the Néel–Brown model,^39,40 the uniaxial and non-interacting SPM nanoparticles exhibit distribution in the anisotropic energy barrier due to poly-dispersity. In this work, the experimental measurement time is τ_m = 4 s, and τ_o ∼ 10⁻⁹ s, then T_B ≈ KV/22k_B. Using the above expression, the calculated K shows exponential dependency on the nanoparticle volume as shown in Fig. 3 (summarized in Table 1). Furthermore, the solid black line in Fig. 3 indicates the Néel–Brown model, which fits T_B versus V plotted for large size particles using K = 72 864 erg cm⁻³ (K value of 31(1) nm nanoparticles) very well. However, the data points of small size particles (16.6(7) nm and 19.5(6) nm) show significant deviation from linearity and extrapolation to the vertical axis shows a non-zero value even at zero volume. The non-zero value could be due to the inter-particle interaction as small size particles are poly-dispersed, densely packed (as seen from SEM/TEM) and possess the highest amount of nickel vacancies.

Fig. 3 The T_B and K versus the volume of NiO nanoparticles. The black solid line indicates the fit to the experimental data obtained using the Néel–Brown models. The dashed exponential curve is a guide for the eye only.

Table 1 Summary of the freezing temperature (T_f), anisotropic temperature (T₁), blocking temperature (T_B), irreversible temperature (T_irr) and the anisotropy energy density (K) of various sized NiO nanoparticles

TA (°C)	Size (nm)	Tf (K)	TB (K)	Tirr (K)	K (erg cm^−3)
400	16.6(7)	6	178	262	225 852
500	19.5(6)	6	198	325	154 985
600	29(4)	6	306	384	72 821
700	31(1)	6	374	398	72 864
800	54(6)	—	—	—	—

---

3.3. Relaxation dynamics

Ulrich et al.⁴¹ proposed a theoretical model for the characterization of nanoparticle systems involving inter-particle interaction or a spin-glass like behavior. The decay of magnetization relaxation of intermediate and large concentrated poly-dispersed FM particles over time explicitly follows the power law W(t) = t⁻ⁿ, where W(t) = −(d/dt)ln M(t). The value of n defines the state of the system, i.e., if n = 0, then it is a dilute system of mono-dispersed particles, n ∼ 2/3 is a dilute system of poly-dispersed particles, and n ≥ 1 becomes a dense system, independent of size distribution. This theoretical model is based on Monte Carlo simulations and has been used frequently for interpretation of the relaxation dynamics of magnetic clusters^42,43 and nanoparticles.^44–47 The model is useful to probe the strength of the interparticle interactions. To examine the interparticle interaction time dependent magnetization relaxation M(t) measurement was carried out within the blocking state. First, the sample was cooled down from 300 K to 60 K in a small external magnetic field of 100 Oe. Subsequently, the magnetic field was turned off using an oscillator mode (rate 10 Oe s⁻¹) and relaxation of the magnetic moment with respect to time was recorded for a time period of one hour. Fig. 4 shows the plot of ln W(t) versus ln(t) for various sizes of NiO nanoparticles. The solid line represents the fit obtained using ln W(t) = c − n ln(t) and the fitting parameters are depicted. The fitted value of n = 0.93 for the smallest size particles, 16.6(7) nm lies within the dilute system of poly-dispersed particles and dense system of strongly interacting particles. The poly-dispersity is due to the broad size distribution of particles as observed from log-normal fitting and it narrows down with an increase of particle size. As seen from the ZFC–FC measurements, these particles possess the highest magnetic moment and therefore exhibit strong interaction. The value of the relaxation rate n decreases with an increase of particle size, and for 54(6) nm NiO particles it becomes time independent, which is characteristic of an ideal AFM material. For particles with sizes higher than ∼30 nm we obtain qualitatively the same picture as for mono-dispersed systems. Therefore, we can conclude that small size particles are densely packed, poly-dispersed and possess the highest magnetic moment. The enhanced magnetic moment in small size particles could arise from spontaneously formed short-range ordered clusters of spins at the surface in an applied magnetic field, which lose their magnetization with the passage of time and therefore can be regarded as a weak-FM material.

Fig. 4 Plot of ln(t) dependency of ln W(t) measured from all the NiO samples. The straight line shows the a model fit (see the text) to the experimental data after the lapse of a crossover time t_o.

3.4. Spontaneous exchange bias phenomenon

Spontaneous exchange bias (SEB) results from a break in the symmetry across the FM–AFM interface and setting up of the UA during the first field of hysteresis loop measurement. To study the SEB phenomenon magnetization versus applied magnetic field, M(H_a) was measured using a p-type protocol, 0 → (+H_max) → (−H_max) → (+H_max) in ZFC mode at 25 K, as shown in Fig. 5. The M(H_a) loop from 16.6(7) nm particles is highly asymmetric, and shifted toward the negative magnetic axis as can be seen from the portion of the loop near the origin in Fig. 5(a). The non-zero value of the coercivity (H_C) and remanence (M_r) in the low field region clearly point to the existence of a weak-FM component. Care has been taken to avoid a spurious shift from the trapped magnetic field in a superconducting magnet by demagnetization using a low oscillatory field. The loop asymmetry along the applied field axis and magnetization axis can be quantified as a spontaneous exchange bias field (H_SEB = (|H_C1| − |H_C2|)/2) and vertical shift (M_VS = (|M_r1| − |M_r2|)/2), respectively, where H_C1 and H_C2 are the fields corresponding to the points in the forward and reverse branches of the hysteresis loop at where the magnetization reaches zero. Similarly, M_r1 and M_r2 indicate the magnetization corresponding to the points on the forward and reverse branches of the hysteresis loop at which the applied field is zero. The observed shifts in H_SEB and M_VS for 16.6(7) nm particles at 25 K are −48 Oe and 1.394 × 10⁻³ emu g⁻¹, respectively. Observation of the SEB field in the AFM transition metal oxides has not yet been reported on, and this is the first report on NiO nanoparticles.

Fig. 5 (a)–(e) A portion of the M(H_a) loop near the origin of the hysteresis loop measured at 25 K with p- and n-type protocols after zero-field cooling for 16.6(7) to 54(6) nm NiO nanoparticles, respectively. The dashed red colored line represents the virgin magnetization curve. (f) Measured H_SEB field 25 K as a function of the crystalline size of the nanoparticles.

In order to explore the effect of field direction on SEB, we also performed M(H_a) measurements at 25 K with the n-type protocol, 0 → (−H_max) → (+H_max) → (−H_max). Similar to the p-type, the M(H_a) loop of the n-type is also found to be highly asymmetric, but shifted toward the positive magnetic axis, as can be seen in the portion of the loop near the origin in Fig. 5(a). The observed shifts in H_SEB and M_VS are 45 Oe and −1.247 × 10⁻³ emu g⁻¹, respectively. Slightly lower values of H_SEB and M_VS are obtained after the n-type measurements than those of the p-type. Maity et al.^18,48 reported H_SEB of −850 Oe and +615 Oe after p- and n-type hysteresis loop measurements from the Bi₂Fe₄O₉–BiFeO₃ FM/AFM system, respectively. The slight difference observed in the behavior of SEB field obtained using the p- and n-type protocols is a common phenomenon. The reported high value of SEB from Bi₂Fe₄O₉–BiFeO₃ as compared to NiO is due to the inter-coupling between the log-range ordered FM and AFM spins at the interface.^18,48 Furthermore, the p-type and n-type M(H_a) loops measured in the ZFC mode are almost symmetric in nature and exhibit a similar value for SEB, which is within the experimental measurement error. The above findings indicate that the observed spontaneous shifts in the M(H_a) loop are not experimental artifacts, but rather an intrinsic property of NiO nanoparticles induced by the finite size effect. The corresponding full hysteresis loop measured at 25 K with p-type and n-type protocols with ZFC is shown in Fig. S2 (see ESI†). From the M(H_a) loops, it can be inferred that in the high field region, magnetization increases linearly with a magnetic field without saturation. The sample consisted of two magnetic components: the first component is easily magnetized in the low-field region and the second non-saturating component is responsible for the linear increasing behavior of magnetization in the high field region. A similar two-component behavior has been reported from different sized NiO nanoparticles.³³ Similarly, the M(H_a) loop measurement for various sizes of NiO nanoparticles was carried out at 25 K by both the p- and n-type protocols. Fig. 5(b)–(e) show a portion of the M(H_a) loop near the origin and Fig. S2(b)–(e) (see ESI†) show the full hysteresis loop measured with p- and n-type protocols after ZFC measurement of 19.5(6) nm to 54(6) nm NiO nanoparticles. Non-zero coercivity, loop shift and two component behaviors are visible to the naked eye even for the 19.5(6) nm nanoparticles with reduced values and magnetization compared to that of 16.6(7) nm NiO nanoparticles. As expected, with an increase of particle size, the AFM component overcomes the FM component due to reduced number of nickel vacancies and the surface effect, and the M(H_a) curve exhibits a linear increase of magnetization with the field. The M(H_a) loops for nanoparticles ≥30 nm exhibit zero-coercivity and a linear increase in the magnetization, the same as for the bulk AFM material. We note that the value of the magnetization decreases monotonically with the increase in the particle size, which is in excellent agreement with the decrease of nickel vacancies observed in the Raman measurements.²³ The particle size dependency of H_SEB observed at 25 K is shown in Fig. 5(f). Considering that 10 Oe is the error limit of the magnetic field for the MPMS-SQUID magnetometer, the H_SEB decreases with an increase of particle size. As expected, the 31(1) and 54(6) nm NiO nanoparticles do not show any SEB, due to the reduction of the FM component.

To further study the effect of temperature on SEB and the corresponding H_C, the ZFC M(H_a) loop measurement was carried out on a 16.6(7) nm sample at different temperatures, namely, 2, 25, 50, 100, 200 and 300 K, using both the p- and n-type protocols; see Fig. S3(a) and S4(a) (see ESI†), respectively. The M(H_a) loops measured with both protocols are quite similar showing that the two component behavior exists even up to room temperature. We note that the magnetization at ±15 kOe increases with temperature, showing a maximum for M(H_a) at 100 K and then decreases, reaching a minimum for M(H_a) at 300 K. In general, for FM materials, the magnetization should decrease, whereas for AFM materials, it should increase with an increase of thermal energy. The reasons for the observed anomalous behavior are not clear yet and further study needs to be done. The measured M(H_a) loop for the remaining samples, the 19.5(6), 29(4), 31(1) and 54(6) nm nanoparticles with the p- and n-type protocols at 2, 25, 50, 100, 200 and 300 K are shown in Fig. S3(b)–(e) and S4(b)–(e) (see ESI†), respectively. The M(H_a) loop measured with both p- and n-type protocols for nanoparticles ≥30 nm in size shows a linearly increasing behavior, the same as for the bulk AFM material. Furthermore, the magnetization at ±15 kOe increases with temperature, showing a maximum for M(H_a) at 300 K, which is consistent with the increasing susceptibility behavior of the pure AFM material. Similar to H_SEB and M_VS, the values of the coercivity H_C and remanence M_r were obtained from the p- and n-type M(H_a) loops by using (H_C = (|H_C1| + |H_C2|)/2) and (M_r = (|M_r1| + |M_r2|)/2), respectively. The temperature dependencies of H_SEB, H_C, M_VS, and M_r for all the NiO samples are shown in Fig. 6(a)–(d). The shaded area represents the maximum instrumental error. In the conventional exchange bias for mono-dispersed FM/AFM core/shell nanoparticles, the values of H_SEB decrease with the increase of temperature and vanish above the blocking temperature.⁴⁹ In contrast, the reason for the non-zero values observed at 300 K, particularly from small size particles above T_B is not yet clear but could possibly be due to the broad size distribution of the nanoparticles. Furthermore, the H_SEB and M_VS as a function of temperature show a deep valley around 50 K in the p-type M(H_a) loop, and a broad maximum around 25 and 100 K in the n-type M(H_a) loop for the 16.6(7) and 19.5(6) nm nanoparticles, respectively. The edge of the shift in the hysteresis loop occurs with NiO nanoparticles with a size of 29(4) nm; the SEB loop shift disappears with particles above this size, which could be due to reduced FM component.

Fig. 6 (a)–(d) shows the variation in H_SEB, H_C, M_VS, and M_r for different size nanoparticles as a functions of temperature.

As can be noted in Fig. 6(b)–(d), the temperature dependency of H_C and M_r (from both p- and n-type M(H_a)) shifts to higher temperatures with the increase of particle size. For 16.6(7) nm, H_C and M_r show an increasing behavior with a tendency to bend in the low temperature region. A broad maximum is observed around 100 and 200 K in the M(H_a) loop for the 19.5(6) and 29(4) nm nanoparticles, respectively. Maity et al.⁴⁸ also observed a similar deep valley for SEB and coercivity around ∼150 and 50 K, respectively, from the Bi₂Fe₄O₉–BiFeO₃ FM–AFM nano-composites. Even though the reason for this deep valley (broad maximum) after the p-type (n-type) is not clear, the observed loop shift and tendency to approach to zero with temperature confirms the existence of the SEB phenomenon in small size NiO nanoparticles. To further confirm the SEB phenomenon, we also carried out field cooled (FC) hysteresis loop measurement from 0 to 20 kOe. The measurements were performed on 16.6(7) nm NiO nanoparticles which were cooled down from 300 K to 60 K in an external magnetic field. The observed M(H_a) loop (see ESI: Fig. S5†) shows an asymmetric diagonal loop shift. The observed results clearly show that the external cooling field pre-magnetizes the sample and therefore produces a giant CEB field.

4. Conclusions

In summary, the size dependency of the blocking temperature and freezing temperature confirm the occurrence of a two-component behavior from the uncompensated AFM NiO and randomly oriented surface spins, respectively. The relaxation dynamic results reveal that 16.6(7) and 19.6(5) nm are dense/poly-dispersed interacting nanoparticles, 29(4) nm: dilute, poly-dispersed, non-interacting nanoparticles and 31(1) and 54(6) nm are dilute, mono-dispersed, non-interacting nanoparticles. The zero-field-cooled hysteresis loop measured using both the p-type and n-type protocols confirm the initial field direction dependency of the hysteresis loop shift. The maximum H_SEB = −53 Oe and M_VS = 1.943 × 10⁻³ emu g⁻¹ at 50 K and H_C = 903 Oe and M_r = 0.03251 emu g⁻¹ at 2 K were obtained for the p-type M(H_a) loop of a 16.6(7) nm NiO nanoparticles. The values of H_SEB, M_VS, H_C and M_r decrease with the increase of particle size due to reduction of the FM component (i.e., decrease of nickel vacancy concentration). The observed SEB effect is attributed to the inter-coupling of spins at the interface of short-range ordered clusters of spins, which behave like weak FM to the uncompensated AFM.

Acknowledgements

We would like to thank the Ministry of Science and Technology (MOST) of the Republic of China for their financial support of this research through project numbers MOST-103-2112-M-259-005 and MOST-104-2112-M-259-001.

References

1. J. Park, E. Kang, S. U. Son, H. M. Park, M. K. Lee, J. Kim, K. W. Kim, H. J. Noh, J. H. Park, C. J. Bae, J. G. Park and T. Hyeon, Adv. Mater., 2005, 17, 429–434.
2. J. Xiao, B. Chen, X. Liang, R. Zhang and Y. Li, Catal. Sci. Technol., 2001, 1, 999–1005.
3. Y.-H. Pai and S.-Y. Fang, J. Power Sources, 2013, 230, 321–326.
4. E. L. Runnerstrom, A. Llordes, S. D. Lounis and D. J. Milliron, Chem. Commun., 2014, 50, 10555–10572.
5. X. Yan, X. Tong, J. Wang, C. Gong, M. Zhang and L. Liang, Mater. Lett., 2013, 95, 4.
6. J. S. Pilban, A. Pandikumar, B. T. Goh, Y. S. Lim, W. J. Basirun, H. N. Lim and N. M. Huang, RSC Adv., 2015, 5, 14010–14019.
7. R. A. Patil, R. S. Devan, J.-H. Lin, Y.-R. Ma, P. S. Patil and Y. Liou, Sol. Energy Mater. Sol. Cells, 2013, 112, 91–96.
8. X. Wang, Y. Z. Li, S. Wang, Z. Zhang, L. Fei and Y. Qian, Cryst. Growth Des., 2006, 6, 2163–2165.
9. E. A. Gibson, M. Awais, D. Dini, D. P. Dowling, M. T. Pryce, J. G. Vos, G. Boschloo and A. Hagfeldt, Phys. Chem. Chem. Phys., 2013, 15, 2411–2420.
10. M. Tyagi, M. Tomar and V. Gupta, Biosens. Bioelectron., 2013, 41, 6.
11. H. Wang, C. Du, P. C. Hammel and F. Yang, Phys. Rev. Lett., 2014, 113, 097202.
12. H. Christian, D. L. Grégoire, V. N. Vladimir, B. Y. Jamal, K. Olivier and V. Michel, Europhys. Lett., 2014, 108, 57005.
13. R. Vardimon, M. Klionsky and O. Tal, Nano Lett., 2015, 15, 3894–3898.
14. Y. Jiang, D. Chen, J. Song, Z. Jiao, Q. Ma, H. Zhang, L. Cheng, B. Zhao and Y. Chu, Electrochim. Acta, 2013, 91, 173–178.
15. G. Zhou, D.-W. Wang, L.-C. Yin, N. Li, F. Li and H.-M. Cheng, ACS Nano, 2012, 6, 3214–3223.
16. X. Zhu, Q. Jiao, C. Zhang, X. Zuo, X. Xiao, Y. Liang and J. Nan, Microchimica Acta, 2013, 180, 7.
17. J. Saha and R. H. Victora, Phys. Rev. B: Condens. Matter Mater. Phys., 2007, 76, 100405.
18. T. Maity, S. Goswami, D. Bhattacharya, G. C. Das and S. Roy, J. Appl. Phys., 2013, 113, 17D916.
19. J. van Lierop, K. W. Lin, J. Y. Guo, H. Ouyang and B. W. Southern, Phys. Rev. B: Condens. Matter Mater. Phys., 2007, 98, 237201.
20. C. Liu, J. Ma and H. Chen, RSC Adv., 2012, 2, 1009–1013.
21. A. Hossein, S. Hadi, K. Parviz, P. Asok, A. Mehmet and Z. Khalil, J. Phys. D: Appl. Phys., 2010, 43, 245002.
22. S. Chauhan, S. S. Kumar and R. Chandra, Appl. Phys. Lett., 2013, 103, 042416.
23. A. C. Gandhi, J. Pant, S. D. Pandit, S. K. Dalimbkar, T.-S. Chan, C.-L. Cheng, Y.-R. Ma and S. Y. Wu, J. Phys. Chem. C, 2013, 117, 18666–18674.
24. E. Winkler, R. D. Zysler, M. V. Mansilla, D. Fiorani, D. Rinaldi, M. Vasilakaki and K. N. Trohidou, Nanotechnology, 2008, 19, 185702.
25. H. Shim, A. Manivannan, M. S. Seehra, K. M. Reddy and A. Punnoose, J. Appl. Phys., 2006, 99, 08Q503.
26. S. Thota and J. Kumar, J. Phys. Chem. Solids, 2007, 68, 1951–1964.
27. S. D. Tiwari and K. P. Rajeev, Phys. Rev. B: Condens. Matter Mater. Phys., 2005, 72, 104433.
28. M. Ghosh, K. Biswas, A. Sundaresan and C. N. R. Rao, J. Mater. Chem., 2006, 16, 106–111.
29. S. K. Sharma, J. M. Vargas, E. D. Biasi, F. Béron, M. Knobel, K. R. Pirota, C. T. Meneses, K. Shalendra, C. G. Lee, P. G. Pagliuso and R. Carlos, Nanotechnology, 2010, 21, 035602.
30. S. Haas, E. Dagotto, J. Riera, R. Merlin and F. Nori, J. Appl. Phys., 1994, 75, 6340–6342.
31. W. J. Duan, S. H. Lu, Z. L. Wuand and Y. S. Wang, J. Phys. Chem. C, 2012, 116, 26043–26051.
32. N. Rinaldi-Montes, P. Gorria, D. Martinez-Blanco, A. B. Fuertes, B. L. Fernandez, F. J. Rodriguez, I. de Pedro, M. L. Fdez-Gubieda, J. Alonso, L. Olivi, G. Aquilanti and J. A. Blanco, Nanoscale, 2014, 6, 457–465.
33. S. Mandal, K. S. R. Menon, S. K. Mahatha and S. Banerjee, Appl. Phys. Lett., 2011, 99, 232507.
34. J. T. Richardson, D. I. Yiagas, B. Turk, K. Forster and M. V. Twigg, J. Appl. Phys., 1991, 70, 6977–6982.
35. M. P. Proenca, C. T. Sousa, A. M. Pereira, P. B. Tavares, J. Ventura, M. Vazquez and J. P. Araujo, Phys. Chem. Chem. Phys., 2011, 13, 9561–9567.
36. M. Jagodič, Z. Jagličić, A. Jelen, J. Bae Lee, Y.-M. Kim, H. Jin Kim and J. Dolinšek, J. Phys.: Condens. Matter, 2009, 21, 215302.
37. S. Mandal, S. Banerjee and K. S. R. Menon, Phys. Rev. B: Condens. Matter Mater. Phys., 2009, 80, 214420.
38. A. Gandhi, C.-Y. Huang, C. C. Yang, T.-S. Chan, C.-L. Cheng, Y.-R. Ma and S. Y. Wu, Nanoscale Res. Lett., 2011, 6, 1–14.
39. L. Néel, Ann. Geophys., 1949, 5, 37.
40. W. Brown, Phys. Rev., 1963, 130, 1677–1686.
41. M. Ulrich, J. García-Otero, J. Rivas and A. Bunde, Phys. Rev. B: Condens. Matter Mater. Phys., 2003, 67, 024416.
42. F. Rivadulla, M. A. López-Quintela and J. Rivas, Phys. Rev. Lett., 2004, 93, 167206.
43. K. De, S. Majumdar and S. Giri, J. Phys. D: Appl. Phys., 2007, 40, 5810.
44. M. Thakur, M. P. Chowdhury, S. Majumdar and S. Giri, Nanotechnology, 2008, 19, 045706.
45. D. De, A. Karmakar, M. K. Bhunia, A. Bhaumik, S. Majumdar and S. Giri, J. Appl. Phys., 2012, 111, 033919.
46. X. Chen, S. Sahoo, W. Kleemann, S. Cardoso and P. P. Freitas, Phys. Rev. B: Condens. Matter Mater. Phys., 2004, 70, 172411.
47. J.-Y. Ji, P.-H. Shih, T.-S. Chan, Y.-R. Ma and S. Y. Wu, Nanoscale Res. Lett., 2015, 10, 243.
48. T. Maity, S. Goswami, D. Bhattacharya and S. Roy, Phys. Rev. Lett., 2013, 110, 107201.
49. J. Nogués, J. Sort, V. Langlais, V. Skumryev, S. Suriñach, J. S. Muñoz and M. D. Baró, Phys. Rep., 2005, 422, 65–117.

---

Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c5ra24673c

---