Temperature dependence of exchange bias in (NiFe/IrMn)_n multilayer films studied through static and dynamic techniques Open Access

The phenomenon of exchange bias discovered over 60 years ago¹ remains a topic of interest in applications and basic research. Marked by a shifted major hysteresis loop (MHL), exchange-biased systems display subtle properties requiring deeper exploration, including a non-monotonic variation of the ferromagnetic resonance (FMR) linewidth (ΔH) as a function of temperature. This property had been observed in rare-earth (RE)-doped iron garnets,^2–7 and a theory was developed by Teale and Tweedale² and Van Vleck and Orbach⁸ based on earlier work of Galt⁹ and Clogston,¹⁰ describing a slow-relaxation due to the paramagnetic impurities.

The slow-relaxer theory was later adapted by McMichael et al.¹¹ and supported by Lubitz et al.¹² to explain these occurrences in exchange-biased systems, identifying the slow-relaxing impurities as antiferromagnetic grains. Others have suggested that the impurities are paramagnetic ions present at the interface of the ferromagnetic and antiferromagnetic layers.^13–15 In this work, the theory of paramagnetic ion relaxation is used to describe experimental observations.

Three multilayer samples of [Ni₈₀Fe₂₀ (t nm)/IrMn (20 nm)]_n were deposited on silicon wafers by the method described in Ref. 16. A 250 Oe magnetic field was applied in the plane of the samples during deposition to induce a magnetic anisotropy. The thickness of each antiferromagnetic layer in all samples was 20 nm. The thickness of ferromagnetic layers was adjusted between the samples according to the number of layers to hold the total sample thickness constant. Thickness of the individual ferromagnetic layers and number of repetitions across the samples are given by t = 20, 60, 80 nm and n = 10, 5, 4, and the samples are named S1, S2, S3, respectively (see Table 1 in Ref. 16). The samples were cut to similar sizes for experiments. Room temperature studies of these samples are presented in Refs. 16 and 17.

MHLs were measured along the exchange bias (H_EB) axis using a Quantum Design Magnetic Properties Measurement System (MPMS) in the temperature range 300 K to 2 K. In the dynamic regime, FMR was measured using a NanOsc CryoFMR spectrometer capable of broadband FMR by individually probing a continuous range of frequencies. Integration of CryoFMR with Quantum Design’s Physical Properties Measurement System (PPMS) using a probe with a coplanar waveguide (CPW) allows for low-temperature FMR measurements. FMR was measured in the range 3 GHz to 16 GHz at temperatures from 300 K to 2 K in 25 K increments. The sample was placed on the CPW with microwave magnetic field perpendicular to the exchange bias and the dc field (H_dc) of the PPMS along the exchange bias, both fields in the plane of the films. H_dc was ramped from 3000 Oe to -3000 Oe while probing the transmission coefficient.

The temperature-dependence of the MHLs is seen in Fig. 1 at selected temperatures, from which H_EB can be extracted. The similar coercivities between samples at room temperature but largely differing H_EB values are consistent with previous studies.¹⁶ H_EB can be determined dynamically from the FMR measurements taking half of the sum of resonance fields, H_R, at a given frequency for fields along (0°) H_EB as well as antiparallel to (180°) H_EB.

Fig. 2 shows a comparison between the values of H_EB determined through FMR and MHL. Near room temperature, static and dynamic measurements produce similar values of H_EB. This agreement is broken for temperatures below 250 K. Static measurements yield an expected increase in the value of H_EB as temperature decreases which has been explained as temperature dependence of the number of grains contributing to H_EB.^14,18 FMR shows a gradual decrease in H_EB after reaching some peak value, the most obvious peak observed in the sample with the most layer repetitions. The difference in H_EB determined through static and dynamic techniques can be explained based on the results of Gloanec et al.^14,15

Another feature of the FMR measurements is an increase of the linewidth (ΔH) as temperature decreases, leading to a broad peak which occurs for both 0° and 180°, as seen in Fig. 3. The clearest peak occurs in the sample with the highest number of repetitions. This feature is explained through the slow-relaxer mechanism as an anisotropic exchange field between the ferromagnet and the impurities.⁸ 

Reminiscent of the work of Teale and Tweedale for iron-garnets containing Yb,² we define a dynamic shift S_D(ω,T) (see Fig. 4 in Ref. 4) as,

where H_EB(ω,T) and H_EB(0,T) are obtained through FMR and MHL, respectively. The field-shift is anisotropic, therefore affecting H_EB(ω,T) and likely causing the disagreement between the static and dynamic determinations of H_EB.

It has been shown that S_D and ΔH take the form

where C is the impurity concentration, ω is the FMR frequency, T is temperature.^4,13 As these terms share constants of proportionality (see Eqs (1) and (2) in Ref. 4 or Eqs (3-16) and (3-17) in Ref. 10), it is clear that

where τ is the relaxation time. The ratio 2|S_D|/ΔH is plotted in Fig. 4. The relaxation time

is taken from Orbach’s derivation of spin-lattice relaxation time,^19,20 and is used in fitting the data in Fig. 4. Of the suggested models, this seems to give the best fit, supporting the theory of slow relaxation by paramagnetic ions as suggested by others.^13–15 This model is consistent with that used in Refs. 14 and 15. Fits seen in Fig. 4(b) are examples of other suggested relaxation behaviors. The dotted red line corresponds to exponential dependence of τ from Néel²¹ which would indicate slow relaxation of antiferromagnetic grains.^11,12 The solid red line is the thermal dependence suggested by Dubowik et al. who used the form τ∼T^-2, although for a more limited temperature range.¹³ Based on these results, our work supports that the slow-relaxing impurities are paramagnetic ions at the surface boundaries.

It is clear that the model better fits S1 than S2 or S3. The subtle differences in the shape of the curve between samples can be expected since ωτ is dependent on ΔH, which becomes flatter as number of layers in the sample is decreased. The fact that this fit is still imperfect may be attributed to difficulties in obtaining an accurate value for ΔH since the FMR spectra for these samples was somewhat asymmetric.

In summary, our work gives support to one of the current theories of the slow-relaxer mechanism. We have investigated this model for multilayered samples, which to our knowledge, is the first study of this type to use samples other than bilayers. Another advantage of our study is that a wider range of FMR frequencies is probed. Other studies have been limited to smaller numbers of FMR frequencies, with many using only an X-band frequency between 9 and 10 GHz. The signatures of the slow-relaxation mechanism, namely, enhanced ΔH at low temperature and peak below 100 K and an anisotropic shift are most apparent in the sample with most repetitions and therefore the highest number of surface boundaries, i.e. more possible sites for paramagnetic ions to act as impurities.

D.J.A. and L.S. thank NanOsc Instruments AB for providing the CryoFMR option used for FMR measurements in this work. D.J.A acknowledges support from the University of New Orleans Graduate School scholarship. LS thanks National Science Foundation for the support through the Independent Research and Development Program.