Zero Field Cooled Exchange Bias Effect in Nano-Crystalline Mg-Ferrite Thin Film

I report, Zero Field Cooled (ZFC) Exchange Bias (EB) effect in a single phase nanocrystalline Mg-ferrite thin film, deposited on an amorphous quartz substrate using pulsed laser ablation technique. The film showed a high ZFC EB shift (HE~ 190 Oe) at 5 K. The ZFC EB shift decreased with increasing temperature and disappeared at higher temperatures (T>70 K). This Mg-ferrite thin film also showed Conventional Exchange Bias (CEB) effect, but unlike many CEB systems, the film showed decrease in the coercivity (HC) under the Field Cooled (FC) measurements. The film also showed training effect in ZFC measurements which followed the frozen spin relaxation behaviour. The observed exchange bias could be attributed to the pinning effect of the surface spins of frozen glassy states at the interface of large ferrimagnetic grains.

reported ZFC EB effect in few more bulk materials. [9][10][11] All these studies had broadly pointed out that a unidirectional anisotropy is introduced to the system during the initial magnetization process. While, the microscopic origin of the ZFC EB effect is not yet fully understood. This paper focuses on the exchange bias effect in Mg-ferrite nanocrystalline thin film. The cubic spinel ferrites such as Mg, Ni, Mn -ferrites are well known magnetic materials for the high frequency applications. 12,13 The ferrimagnetic ordering in these ferrite systems is mainly due to the anti-parallel alignment of cation spins at the tetrahedral (A) and the octahedral (B) sites. The chemical formula of these cubic spinel ferrites is expressed as (M1-xFex)A(MxFe2x)BO4 based on their cation occupancy. 14 In Mg-ferrite bulk sample, a (x = ~ 0.89) faction of Fe 3+ ions occupy the A sites while other (2-x) in the B sites and this leads to the ferrimagnetic ordering in it. 14,15 However, it is to be noted that these single phase bulk spinel ferrites (MFe2O4, M = Mg, Mn, Co, Ni) do not show exchange bias effect. Though, there are few reports on conventional exchange bias effect in thin films of some ferrites. Like, Venzke et al. 16 observed the CEB effect in as deposited Ni-ferrite thin films. Alaan et al. also reported exchange bias effect in MnZn -ferrite thin films. 17,18 While in case of Mg-ferrite thin films, some inconsistent and self-contradicting data on exchange bias effect were also reported earlier. 19,20 Therefore, the details and true behaviour of the exchange bias effect in Mg-ferrite thin films are still unknown. Here, I have presented the detail study of the exchange effect in Mg-ferrite thin film. The data presented in this paper, shows some distinguishably deferent features compared to the CEB effect. These features are compared with the other exchange bias systems and discussed in this paper.

II. Experimental details a. Details of the thin film growth conditions
Nanocrystalline Mg-ferrite thin film was deposited using pulsed laser ablation technique. A single phase high density Pulsed Laser Deposition (PLD) target was prepared through solid state reaction route. The film was deposited using a Nd:YAG pulsed laser with energy density 2 Joule/cm 2 . The pulsed laser repetition rate was kept at 10 shots/sec and the film was deposited on quartz substrate using 18000 pulsed laser shots. The clean amorphous quartz substrate was kept 4.5 cm away from the PLD target and was heated to 500 °C while taking the deposition.
The deposited film was ex-situ annealed at 250 °C for 2 hrs in air and cooled down to room temperature (RT) through atmospheric cooling in closed furnace. All the measurements were performed using this annealed film.

b. Magnetization loops (M-H) measurement details
The field dependence of magnetization (M-H) of the film was measured using two protocols, ZFC and FC. For the ZFC measurements, the film was cooled down in zero magnetic field from RT. The ZFC M-H loops were collected by sweeping the magnetic field in two different ways. In the first way (p-type), the field was swept from 0 Oe → +50 kOe → -50 kOe → +50 kOe . In the second way (n-type), the field was swept from 0 Oe → -50 kOe → +50 kOe → -50 kOe. In these measurements the initial 0 Oe → ±50 kOe, magnetization curve is termed as virgin M-H curve.
The FC M-H loops were collected by cooling the film in an applied field HFC, from RT and the M-H loops were measured by sweeping the field as HFC → -50 kOe → +50 kOe. Prior to all the measurements the film was subjected to a damped oscillating magnetic field (centred at 0 Oe) which gradually becomes zero at RT. This process ensured the zero magnetization state of the film at RT. All the measurements were performed by applying the magnetic field along the film's plane.    show any additional peak correspond to alien elements, which confirms the elemental purity of the deposited film. Fig. 3   The Fe 2p core level spectra shows two satellite peaks at 719.5 eV and ~733.6 eV. These satellite peaks confirm the presence of Fe 3+ ionic state in the system. A similar Fe 2p spectra was also obtained for Fe 3+ ions by other research groups. [21][22][23] The oxygen 1s core level spectra shows two peaks (at 530.2 eV and 532.3 eV) correspond to surface absorbed oxygen (532.3 eV) 24 and 1s core level spectra (530.2 eV) of oxygens of the MgFe2O4. The GIXRD, FEG-SEM and the XPS results suggest that the film is single phase nano-crystalline and impurity free MgFe2O4.

b. Zero field Cooled (ZFC) and Field Cooled Exchange Bias effect
The also reported in some bulk ZFC EB systems. 7, 8 25 This behaviour was speculated due to a field induced ordering in the system. 7,9 Here one need to note that the shifted asymmetric M-H loops were also observed not only due to the exchange bias effect but also due to minor loop and experimental artefacts. 26       and the coercivity (HC) of the film, measured at 5 K. The exchange bias shift showed a large increase for HFC = 5 kOe as compared to the ZFC value. However as HFC increased beyond 5 kOe, the exchange bias field (HE) decreased almost monotonically and a lower than ZFC EB shift was observed for HFC = 50 kOe. While the coercivity (HC) of the film decreased rapidly with the increasing cooling field for HFC ≤ 10 kOe and as the HFC increased beyond 10 kOe it shows almost a constant value. Previously, Wang et al. 7 and Nayak et al. 8 had also showed that the coercivity of the bulk ZFC EB systems decreased in the FC measurements. However, it is known that in CEB systems the coercivity generally increased in the FC measurements. 28

c. Zero Field Cooled (ZFC) training effect
Another important feature of the exchange bias effect is training effect. The training effect is extensively used to understand the exchange coupling behaviour at the interface of the conventional exchange bias systems. 31,[33][34][35] I have also studied the training effect in this Mgferrite thin film to understand the origin of the ZFC EB effect in the system. Here unlike the CEB systems (in CEB systems, training effect is studied in Field cooled mode), the film was cooled down to 10 K from RT without a magnetic field. Then consecutive training M-H loops were collected by sweeping the magnetic field at 10 K. Fig. 8 (a) shows low field part these M-H loops. The complete M-H loops are shown in the inset of Fig. 8 (a). The Fig. 8

(a) clearly shows that the exchange bias shift (HE) and coercivity (HC) of the M-H loops decrease as a result of consecutive M-H loop iterations (loop number 'n'). Similar behaviour is also observed
in Conventional Exchange Bias (CEB) systems. 30,36 Though the CEB systems necessarily require to field cool before the training measurements. 30,36 It is also interesting to note that the remanence magnetizations (both |Mr1| and |Mr2|) of the film increased with the increasing 'n'.
Whereas in case of the CEB systems, the training effect of the M-H loop (that shifted along negative field axis), generally shows a decrease in the |Mr1| value with increasing 'n'. 32,34,37,38 While the |Mr2| has both decreasing and increasing tendencies depending on the CEB systems. 34,[37][38][39] The decrease in the exchange bias field (HE) of the training M-H loops were extensively studied in different CEB systems 30,33,36  Where, HE is the exchange bias field for the nth M-H loop, HE∞ is the EB field for n = ∞ and KE is a proportionality constant. This behaviour was attributed to the thermodynamic relaxation of the interfacial spins and it is found that most of the CEB systems obey this behaviour for n > 1. 32,40 The HC and the ME (= |M r2 |−|M r1 | 2 ) of the training M-H loops of these CEB systems also show similar trend for n >1. 30 40, 41 Mishra et al. 35 had proposed another mechanism for the training effect. They had considered the frozen spin relaxation and the spin rotation at the interface of the CEB systems during training effect measurements and the exchange bias shift was formulated as 35 Where, Af and Pf are the parameters related to the frozen spin relaxation, Ai and Pi are the parameters related to the spin rotation. The A factors are the weight factor and have the dimension of magnetic field, the P is a dimensionless parameter related to relaxation rate. 35,40,42,43 The exchange bias field (HC) and coercivity (HC) of the Mg-ferrite thin film are plotted as a function of the training loop index number 'n' in the Fig. 8 (b). Fig. 8 (c) and (d) show the ME and average Mr of the film with 'n', respectively. The exchange bias field (HE) can be fitted with the equation 1 for n > 1.Whereas the HE of the film shows good fitting with only one exponent of equation 2 for all 'n'. Similar to the HE, the HC, ME and Mr of the film are also fitted with the equation 1 for n > 1 and with one exponent of equation 2 for all 'n'. The dimension and notation of the parameters of the equations 1 and 2 are changed accordingly for the fitting of HC, ME and Mr. Table 1 shows the parameters obtained from the fittings of exchange bias field, HE. The fitting with equation 1 for HE yield HE∞ = -50 Oe. Here one needs to note that, previously the negative HE∞ was also obtained in Fe3O4 film. 40
There are also some single phase (crystallographic phase) materials that show CEB effect. 30,41,48 However, these single phase materials show coexistence of different magnetic orders within them and the exchange coupling at the interface of these magnetic orders resulted in exchange bias effect. 30,41,48 The XRD of our thin film shows single phase of Mg-ferrite cubic spinel structure. The XPS data also supported it, since no impurity element was found. Therefore to understand the exchange bias phenomenon in this film one needs to know the magnetic orderings within it. The thermomagnetic measurements were performed to address this. Fig. 9  modes (in Fig. 9 (a)). We can see that the ZFC M-T data deviates from the FC M-T data at Tirr (indicated with arrow in the Fig. 9 (a)).  This behaviour is generally attributed to the freezing of the moments of smaller grains. 45,49 Below Tirr the spin of the smaller nanocrystalline grains frozen to the random direction as the crystalline anisotropy of the grains overcome the thermal fluctuation. 49 The value of Tirr decreases as the applied magnetic field increases. The decrease of Tirr with the increasing magnetic field followed the famous Thouless and de Almeida line 50,51 (Tirr ∝ H 2/3 ) for spin glass systems, shown in the inset of the Fig. 9 (a).
The high field FC M-T data is shown in the Fig. 9 (b). These FC M-T data shows good fit with the Bloch's law 52 (M(T) = M 0 (1 − BT 3 2 )), for temperature dependence magnetization of a ferrimagnetic system, above Td (indicated by arrow). As temperature decreased below Td, an upturn in the magnetization is observed. It is also observed that the value of Td increased with the applied magnetic field. I assumed that this behaviour is due to the coexistence of , the low temperature data shows a tendency towards saturation as compared to the fitted data. This behaviour could be due to a weak ordering of the SPM grains under application of high magnetic field. The similar field induced ordering of the SPM grains were also predicted in different ZFC EB systems. 7, 25 Therefore, it is likely that the smaller grains of this Mg-ferrite nanocrystalline thin film were frozen into a spin glass like state as the temperature decreased much below the Tirr. The pinning effect of the surface spins of these frozen glassy states at the interface of ferrimagnetic grains could possibly leads to the observed exchange bias effect. Earlier, exchange bias effect was also reported in different single phase ferrite thin films such as Ni-ferrite, MnZn-ferrite thin films. [16][17][18] The observed EB effect in these systems was also speculated due to the pinning effect of the surface spins of a disordered

V. Conclusion
A single layer Mg-ferrite thin film was deposited on amorphous quartz substrate using pulsed laser ablation technique. This film showed ZFC EB effect along with the ZFC training effect.
The film also showed CEB effect in field cooled measurements. The observed exchange bias effect is attributed to the pinning effect of the surface spins of frozen glassy states at the interface of ferrimagnetic grains. The decrease in the coercivity of the field cooled M-H loop is speculated due to a weak field induce ordering of the superparamagnetic grains.