Temperature gradient-induced magnetization reversal of single ferromagnetic nanowires

In this study, we investigate the temperature- and temperature gradient-dependent magnetization reversal process of individual, single-domain Co39Ni61 and Fe15Ni85 ferromagnetic nanowires via the magneto-optical Kerr effect and magnetoresistance measurements. While the coercive fields (HC) and therefore the magnetic switching fields (HSW) generally decrease under isothermal conditions at elevated base temperatures (Tbase), temperature gradients (ΔT) along the nanowires lead to an increased switching field of up to 15% for ΔT  = 300 K in Co39Ni61 nanowires. This enhancement is attributed to a stress-induced, magneto-elastic anisotropy term due to an applied temperature gradient along the nanowire that counteracts the thermally assisted magnetization reversal process. Our results demonstrate that a careful distinction between locally elevated temperatures and temperature gradients has to be made in future heat-assisted magnetic recording devices.

(Some figures may appear in colour only in the online journal) Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. need to overcome this limit, alternative concepts for future magnetic data storage have emerged. One of the most distinct approaches is heat-assisted magnetic recording (HAMR) [4,5], where the shape or crystal anisotropy enhances the magn etic switching fields, H SW , (and therefore the coercivity, H C ) and suppresses the superparamagnetic limit, while a heating laser pulse that decreases H C for a short period of time is used to allow for a magnetic bit writing process. In fact, for highly anisotropic FePt HAMR devices, a data storage areal density of 1.4 Tb in −2 has recently been demonstrated in a laboratory environment [6].
Parallel to the efforts to incorporate heat pulses into magnetic memory devices, the research field of spin-caloritronics [7] evolved, seeking a fundamental understanding of the interplay between charge, spin and heat. While the HAMR technique basically relies on induced magnetic switching at elevated temper ature pulses, temperature gradients were also found to generate numerous spin-caloritronic effects. Currently, classical thermoelectric effects in ferromagnetic materials systems are quite well-established. The so-called spin-dependent Seebeck effect has been observed in anisotropic magnetoresist ance (MR) [8,9], giant MR [10,11] and tunnel MR [12,13] regimes. The spin-Seebeck effect (SSE) [14,15], which describes the generation of a pure spin current due to a temperature gradient in a ferromagnetic material, is currently under intense investigation. Furthermore, the thermal spin transfer torque (TSTT) has attracted much attention because the effect on the magnetic switching behavior of magnetic tunnel junctions is three orders of magnitude larger than its spintronic equivalent effect (the spin transfer torque) can account for, due to charge currents generated by the spin-dependent Seebeck effect [16].
In this study, we directly compare the influence of the base temperature, T base , and temperature gradients, ΔT, on the magnetization reversal of ferromagnetic nanostructures. Therefore, magneto-optical Kerr (MOKE) measurements and MR measurements were performed on individual Co 39 Ni 61 and Fe 15 Ni 85 nanowires under an externally applied magnetic field, µ 0 H, at different ΔT and T base values. We show that H SW generally decreases with increasing T base , while the magnetic switching field of Co 39 Ni 61 nanowires increases for increasing ΔT. We attribute this increase in H SW for increasing ΔT to a stress-induced enhancement of the magneto-elastic anisotropy and develop a simple approach to estimate the H C values as a function of the applied ΔT.
Cylindrical ferromagnetic nanowires with an average diameter of 150 nm and lengths of up to 30 µm were grown by template-assisted electrodeposition into self-ordered, nanoporous alumina (AAO) membranes [17]. Two types of soft magnetic alloy nanowires-Fe 15 Ni 85 and Co 39 Ni 61 -were synthesized according to previously followed procedures from Salem et al [18] and Vega et al [19], respectively. Prior to electrodeposition, the internal walls of the alumina membranes had been coated with an approx. 10 nm thick layer of SiO 2 by atomic layer deposition [20,21]. The SiO 2 cover layer protects the nanowires from oxidation and additionally supplies mechanical stability when the nanowires are suspended in ethanol after being released from the AAO template by selective chemical etching.
Two types of micro-devices (A and B) were designed to measure the optical and electrical properties of the individual nanowires (figures 1(a) and 2(a), respectively). Therefore, the suspended nanowire/ethanol solution was applied dropwise to a 150 µm thick quartz substrate, and the micro-devices were defined by laser beam lithography followed by a metallization process [9].
Micro-device A consists of two Ti/Pt lines-one at each end of the nanowire-which are not in electrical contact with the nanowire (figure 1(a)) and which have been simultaneously used as heater lines and as resistive thermometers. DC currents up to 10 mA generated temperature gradients via Joule heating in the heater line, which led to temperatures up to 680 K at the hot thermometer and 380 K at the cold thermometer. Hence, temperature gradients, ΔT, up to 300 K were generated along the nanowire ( figure 1(b)). We note that the actual temperature difference along the nanowire is slightly below the measured temperature difference, because the nanowire is about 1 µm shorter than the distance between the thermometers.
Micro-device A was used to measure the coercive fields of Co 39 Ni 61 and Fe 15 Ni 85 nanowires as a function of the applied temperature gradients via the longitudinal MOKE [22]. A NanoMOKE ™ 2 from Durham Magneto Optics equipped with an (45°) incidence continuous wave-laser light with a power output of 1.9 mW and with an in-plane focused spot size of approximately 3 µm was used. Alternating magnetic fields up to ±0.08 T could be applied with a quadrupole magnet in the plane of incidental beam of light and thus parallel to the nanowire axis, as described in detail by Vega et al [19]. With a distance of approx. 500 nm between the nanowire and the heater line, the estimated maximum Oersted fields induced by the heater lines to the nanowire were in the order of 10 −4 T and could be excluded from having an impact on the magnetization reversal of the nanowire. Furthermore, the temperature rise due to the incidental laser beam could be neglected in this study due to an estimated heating of less than 1 K. The recorded hysteresis loops show no deviation whether the laser spot was focused on the wire's edges or on its center, and the square-like MOKE hysteresis curves exhibited symmetric Barkhausen jumps for Fe 15 Ni 85 and the Co 39 Ni 61 nanowires. In figure 1(c), the hysteresis loop of the Co 39 Ni 61 nanowire measured at T base = 300 K and for ΔT = 0 K was exemplarily given with a coercive field of 424 G. Due to the low signal-tonoise ratio, it became necessary to successively average data over several hundred single shot hysteresis loops.
Micro-device B (figure 2(a)) corresponded with the typical experimental setup [9,23] for measuring the thermopower, S (S = U th /ΔT, with U th being the thermo-voltage induced by the temperature gradient ΔT), of nanowires. The microdevice consisted of one resistive heater line (yellow) and two resistive thermometers (red and blue for the hot and cold thermometer, respectively). For the thermoelectric characterization, applied DC currents flowing through the resistive heater line generated a temperature gradient along the nanowire. Employing both resistive thermometers, ΔT was determined, and U th was measured along the nanowire. For a general characterization of our sample we determined the resistivity, ρ, and S of the nanowires. Resistance measurements were conducted in a four-point measurement geometry, for which we used the hot and cold thermometers (figure 2(a)) as the electrodes. We observed metallic ρ(T)-curves for both material systems with room temperature values of ρ(Fe 15 Ni 85 ) = 34.5 µΩ cm and ρ(Co 39 Ni 61 ) = 19.7 µΩ cm, which are higher than the corresponding bulk literature values of ρ(Fe 15 Ni 85 , bulk) = 14 µΩ cm and ρ(Co 39 Ni 61 , bulk) = 11 µΩ cm [24]. These enhanced resistivity values of the nanostructures compared to bulk materials are commonly observed and attributed to the nanocrystalline nature of the electrodeposited nanowires [25]. The thermopower of Fe 15  Additionally, micro-device B was also used to determine the temperature-dependent coercive fields of Co 39 Ni 61 and Fe 15 Ni 85 nanowires. In a probe station setup, we therefore performed MR measurements with the externally applied magnetic field up to 0.5 T parallel to the nanowire axis and in the temperature range from 290 K to 350 K. Distinct resistance jumps on the order of 50 mΩ can be observed at the switching field values as exemplarily shown for a Fe 15 Ni 85 nanowire with a coercive field of 178 G (figure 2(c)).
For ΔT = 0 K, H C for Fe 15 Ni 85 as well as Co 39 Ni 61 nanowires decreased in the MR measurements with increasing T base ( figure 3(a)). The reduction of the temperature normalized coercive field, taken as the coercivity measured at any temperature referred to the value at T = 300 K, (H C (T)/H C (300 K)) for Fe 15 Ni 85 nanowires (4% from 300 K to 350 K) is slightly steeper than for the one of Co 39 Ni 61 nanowires (1% from 300 K to 350 K). Such decrease in H C value with increasing T was a consequence of the thermally assisted switching process-the basic concept of HAMR devices.
In a next step, H C of the Co 39 Ni 61 and Fe 15 Ni 85 nanowires as a function of ΔT was investigated in the NanoMOKE setup. Longitudinal MOKE hysteresis loops for Co 39 Ni 61 and Fe 15 Ni 85 nanowires were measured with applied ΔT between 0 K and 300 K along the nanowire axis, and the applied magn etic field µ 0 H parallel to the nanowire axis as shown in figure 3(b). For Fe 15 Ni 85 nanowires, we observed a decrease of H C with increasing ΔT of 4% for ΔT = 100 K. In contrast, we surprisingly found an increasing H C for increasing ΔT for the Co 39 Ni 61 nanowires. This observation remained valid even when we changed the material of the micro-device from Pt to Au to exclude any influence by the electrical contact material ( figure 3(b)). Therefore, we conclude that the increase in H C with increasing ΔT has an intrinsic origin that counteracts the average temperature-assisted switching mechanism.
To explain the unexpected H C (ΔT ) dependence of the Co 39 Ni 61 nanowires, we will discuss possible origins in the following, whereas we start with considering stress-induced changes on the magnetic switching mechanism.
Our first hypothesis is an axial stress-induced enhancement of H C due to an increasing ΔT along the nanowire axis. To establish an easy, quantitative model for H C (ΔT ), we start with [29] with the vacuum permeability µ 0 , the saturation magnetization M S , the angle θ between external magnetic field µ 0 H and the magnetization vector, and the effective anisotropy constant K eff of the nanowires, which is given by K eff ≈. K shape + K me , with the shape anisotropy constant K shape and the magneto-elastic anisotropy constant K me . Note that we neglect the magneto-crystalline anisotropy in our nanowire because it is rather small regarding the magneto-crystalline anisotropy constants [30,31] of 5 kJ m −3 and 7.5 kJ m −3 for Co 39 Ni 61 and Fe 15 Ni 85 , respectively. Due to their high aspect ratio, the magnetization of the nanowires and therefore their magnetization reversal in the relaxed state without induced stress are dominated by shape anisotropy. The shape anisotropy constant of an infinitely long wire is given by [32] Using the literature values [32,33] λ me is the magnetostriction coefficient, and σ is the axial stress given by σ = α Co/Ni/Fe YΔT. Here, Y is the Young's modulus (Y Ni,Co,Fe ≈ 209 GJ m −3 ), and α Co/Ni/Fe reflects the thermal expansion coefficients [35] α Co = 13.0 · 10 −6 K −1 , α Ni = 13.4 · 10 −6 K −1 , and α Fe = 11.8 · 10 −6 K −1 of Co, Ni and Fe at 300 K, respectively. Thus, a temperature gradient of 300 K along the nanowire leads to a stress of about σ(ΔT = 300 K) ≈ 800 MJ m −3 along the nanowire axis in all investigated material systems. Now, for ΔT = 300 K the relatively low magnetostriction coefficient [36] of the Fe 15 Ni 85 (λ me = −5 × 10 −6 ) leads to a minor contribution of K me = −6 kJ m −3 even for the highest thermal stress, such that K eff ≈ K shape . For the Co 39 Ni 61 system with the ten-times higher magnetostriction coefficient [37] λ me = 65 × 10 −6 , however, we obtain K me = 78 kJ m −3 for ΔT = 300 K, which is one order of magnitude higher than K me (Fe 15 Ni 85 ) and provides a significant contribution to the magnetic configuration in the nanowire. In fact, for ΔT = 300 K and using equation (1), we obtain a relative change in the coercive field of HC(∆T=300 K) HC(∆T=0 K) = 1.22 for the Co 39 Ni 61 nanowires as indicated by the dashed line in figure 3(b). We find a very good agreement between our estimation and the experimental data for ΔT < 200 K. At higher ΔT, the measured H C (ΔT) deviates to a less steep increase than that predicted by our model, which we attribute to the heat-assisted magnetization reversal process due to the elevated average temperature of the nanowire caused by the high applied ΔT. For the Co 39 Ni 61 , the deviation between the measured H C (ΔT) and the calculated H C (ΔT) is 7% at ΔT = 300 K. Performing the same estimation of H C (ΔT) for the Fe 15 Ni 85 nanowire only yields a stressinduced decrease of the normalized H C to 0.97 at ΔT = 300 K, as shown by the blue dotted line in figure 3(b). As a result, the heat-assisted switching process determines H C (ΔT) for the Fe 15 Ni 85 nanowires, and the measured H C (ΔT) is significantly smaller than the estimated values regarding the stress-induced magneto-elastic anisotropy component, which leads to a difference of 20% between the measured H C (ΔT) and the normalized H C (ΔT) estimated with our model at ΔT = 300 K.
Extrapolating the H C (T base ) (see figure 3(a)) of the nanowires to T base = 600 K (ΔT = 300 K) gives a decrease of H C (T base ) of 5% for the Co 39 Ni 61 nanowire and 20% for the Fe 15 Ni 85 nanowire, which is for both material systems in good agreement with the difference between measured and calculated values of H C (ΔT) at ΔT = 300 K.
Increasing H C with increasing ΔT for the Co 39 Ni 61 nanowires due to increasing radial stress-induced by the nanowirecore/SiO 2 -shell is unlikely because radial stress is also present for the measurements with increasing base temperature, where we observed a decreasing H C for increasing T base .
To our knowledge, saturation magnetostriction λ S (σ, T ), affecting the hysteretic behavior of ferromagnetic nanowires has so far only been reported for nanowire arrays within the template, which are exposed to uniform temperature enhancements. Kumar et al [34] observed increasing H C with increasing T for Ni nanowires in an AAO template with a thick Al backside. Due to the different thermal expansion coefficients of Ni, AAO and Al, they calculated magnetoelastic aniso tropy constants between −42 kJ m −3 and −96 kJ m −3 . Silva et al [38] investigated Co nanowires in AAO templates and found that longer nanowire segments experience a stronger thermal expansion and therefore more stress in the AAO templates for decreasing T than shorter nanowires, which leads to change in the easy magnetization axis from parallel to perpendicular direction to the nanowire axis that occurs nearer to the electrodeposition temperature of 300 K for longer Co nanowire than for shorter Co segments. Pirota et al [39] intensified this study on Ni nanowires in AAO templates and calculated (thermal) induced stresses between −170 kJ m −3 for short (l = 0.5 µm) nanowires and −780 kJ m −3 for longer (l = 2.2 µm) segments.
Another effect that might have a noticeable influence on the switching mechanism of magnetic nanowires under a temperature gradient is the TSTT. It has been recently demonstrated that the TSTT has a much higher effect on the magnetization reversal characteristics of tunnel MR structures than the STT due to a spin-dependent Seebeck effect accounting for [16]. One underlying mechanism for this observation in our samples geometry could be a pure spin current due to the longitudinal SSE [15] that can have a stabilizing or destabilizing effect on the magnetization of the nanowire and therefore decreases or increases the coercivity H C . Overall, we believe that the interplay of the stress-induced contributions of the  15 Ni 85 nanowires as a function of the applied ΔT at T base = 300 K. Black dots correspond to a Co 39 Ni 61 nanowire contacted with platinum leads, blue dots correspond to a Fe15Ni85 nanowire contacted with platinum leads, and the red dots correspond to a Co 39 Ni 61 nanowire contacted with gold leads. magneto-elastic anisotropy and an intrinsic thermally assisted switching mechanism described in this work fits the data accurately. Thus, we conclude that no major influences of the TSTT and the longitudinal SSE are observed in these samples.
In summary, we synthesized Co 39 Ni 61 and Fe 15 Ni 85 nanowires to investigate temperature-and temperaturegradient dependent magnetization reversal process of ferromagnetic nanostructures. Performing MR measurements, we found that the magnetic switching fields (and therefore their coercivities) decreased with increasing the base temperature for both Co 39 Ni 61 and Fe 15 Ni 85 nanowires. MOKE measurements with applied temperature gradients at room temper ature showed a decrease in the coercive field values for Fe 15 Ni 85 nanowires while H C increases up to 5% per 100 K for Co 39 Ni 61 nanowires. We attribute this increase in H C for Co 39 Ni 61 nanowires to a stress-induced enhancement in the magneto-elastic aniso tropy contribution to the effective anisotropy due to an applied temperature gradient, and we were able to fit the measured H C (ΔT) increase with a simple model. Our results highlight the quite distinct effects of elevated temperatures and applied temperature gradients on the switching fields and therefore on the magnetization reversal mechanisms of ferromagnetic nanostructures and reveal the challenges of future heat-assisted, magnetic recording device design.