Paramagnetic molecule induced strong antiferromagnetic exchange coupling on a magnetic tunnel junction based molecular spintronics device

This paper reports our Monte Carlo (MC) studies aiming to explain the experimentally observed paramagnetic molecule induced antiferromagnetic coupling between the ferromagnetic (FM) electrodes. Recently developed magnetic tunnel junction based molecular spintronics devices (MTJMSDs), which were prepared by chemically bonding the paramagnetic molecules between the FM electrodes along the exposed side edges of magnetic tunnel junctions, exhibited molecule induced strong antiferromagnetic coupling. Our MC studies focused on the atomic model analogous to the MTJMSD and studied the effect of molecules magnetic couplings with the two FM electrodes. Simulations show that when a molecule established ferromagnetic coupling with one electrode and antiferromagnetic coupling with the other electrode then theoretical results effectively explained the experimental findings. MC and experimental studies suggest that the strength of exchange coupling between molecule and FM electrode should be 50 percent of the interatomic exchange coupling strength of the FM electrodes.


Introduction: Molecular spintronics devices
(MSDs) have attracted worldwide attention due to their potential to revolutionize logic and memory devices [1,2]. A typical MSD is comprised of two ferromagnetic (FM) electrodes-coupled by molecular channels [3,4]. Molecular channels with a net spin state are the basis of a large number of intriguing studies [5], which were either observed experimentally [6,7] or were calculated theoretically [2]. Porphyrins [8], single molecular magnets [2], and magnetic molecular clusters [9] possess a net spin state and can be synthetically tailored to be employed in a MSD. Single molecular magnetbased MSDs have been widely discussed as the practical architecture for quantum computation [1]. Moreover, paramagnetic molecules strongly coupled to FM electrodes are expected to yield a novel class of magnetic metamaterials and novel device forms. We have recently discussed magnetic tunnel junction (MTJ based MSDs, referred as MTJMSD in this paper, as the most promising, practical, and versatile approach to harness molecule as the device element [3,10]. This approach necessitates the chemical bonding the molecular 3 channels on the FM electrodes of a prefabricated exposed edge MTJ (Fig. 1a) to develop novel MTJMSDs (Fig. 1b). For the first time MTJMSD approach exhibited direct evidence of molecular coupling on the magnetic properties of a MTJ at room temperature. This paper focuses on MC simulations explaining the experimentally observed paramagnetic molecule induced magnetic changes on a prefabricated MTJ. Our MC simulations, which are performed on a theoretical model analogous to MTJMSD, investigated the impact of the nature and magnitude of molecular coupling with the FM electrodes, thermal energy (kT), and MTJMSDs sizes.

Experimental details and simulation methodology:
MTJMSD fabrication protocol involves a flat insulated substrate ( Fig. 1c) with microscopic cavities in the photoresist (Fig. 1d) to do sequential depositions of FM electrodes, and ultrathin insulator (Fig. 1e). This yields several thousand MTJs with exposed sides after the liftoff (Fig. 1f). These MTJs with exposed side edges can be structurally (Fig. 1g) and magnetically (Fig. 1h) characterized before introducing paramagnetic molecular device elements; magnetic force microscopy (MFM) image of a cluster of bare MTJs is shown in figure 1h. In this study we used organometallic molecular clusters (OMC). The OMC molecules utilized in this study were synthesized by the Holmes group [9,11]. In an OMC, the Fe III and Ni II centers positioned in alternate corners of a box and are linked via cyanides (Fig. 1i). Specific details about the thin film depositions [4], MTJ fabrication [12][13][14]. molecule attachment protocol [4] and OMCs [9,11,15] (Fig. 1i) have been published elsewhere. The experimental magnetic studies before and after attaching OMCs-demonstrated unprecedented changes in the magnetic properties of a MTJ [13].
These studies produced strong evidence that molecules are much more than a simple spin or charge carrier. OMCs produced unprecedented, strong antiferromagnetic coupling for the MTJ with Ta (5 nm)/Co (3-5 nm)/NiFe (5-7 nm)/AlOx (2 nm)/NiFe (10 nm) configuration. In this MTJ tantalum (Ta) served as the seed layer. Cobalt (Co) and NiFe(81% Ni/19% Fe) were deposited as the bottom FM electrode followed by the 2 nm alumina (AlOx) tunnel barrier and NiFe top FM electrode. 4 In order to understand the mechanism behind OMC induced strong coupling we have conducted MC simulations on an analogous MTJMSD system designed in the Ising model framework (Fig.1j). Our previous attempt to explain MTJMSD magnetic properties with non-vector spin and 2D Ising model fall short [14]; to overcome the limitation of previous work we conducted MC study with the actual MTJMSD model and used vector form of the spin. To represent the molecules on the edges, (Fig. 1k), a plane containing atoms along the sides and with empty interior was introduced between the two FM electrodes; FM electrodes are represented by the Ising model. The inter-FM electrode magnetic coupling is only occurring via the molecules (Fig. 1k). However, inter-FM electrode coupling via the empty space is considered to be zero. Using this MC model (  (Fig. 1k). Our MC studies utilized a continuous model [16] which allowed spin vectors to settle in any direction according to the equilibrium energy governed by eq. 1. For all MC simulations the boundary condition were selected in such a way that the spin of atoms beyond boundary atom of the MTJMSD model (Fig. 1j) generate a new state. Under the Metropolis algorithm, the spin vector direction of a randomly selected site was changed to produce a new state; energy for the new and old configuration was calculated using eq.1.

∆E<0 or exp (-∆E/kT)≥ r.
Where r is a uniformly distributed random variable whose magnitude range from 0 to 1. To achieve a stable low energy state, every MC simulation was run 10 to 100 million steps, depending upon MTJMSD dimensions. After this MC simulations, further runs were performed to generate an average magnitude of observables; two subsequent recordings for any observables were collected at the time interval comparable to autocorrelation time [16]. The units of total energy E and exchange coupling parameters is same as of kT. To keep discussion generic, the exchange coupling parameters and kT are referred as the unitless parameters throughout this study. Overall magnetic moment of the MTJMSD is the sum of magnetic moment of the two FM electrodes and the magnetic moment of the molecules.
This spin state decreased to S=3 as temperature increased to 60 K. We were unable to estimate the spin state of those OMCs which got integrated in a MTJMSD. To simplify our MC studies we only considered an S=1 spin state for the molecules throughout. Alkane tethers are expected to serve as the perfect spin channel, as compared to ~ 2 nm AlOx tunnel barrier, with low spin orbit and hyperfine splitting to ensure 6 high spin coherence length and time [17]. Hence a sufficient population of OMCs can serve as the highly efficient spin channels producing strong coupling.
The SQUID magnetometer studies, 7 electrode [19], was in 0.5-0.54 range. We concluded that OMC induced antiferromagnetic coupling is of the order of 0.5 times of the interatomic ferromagnetic exchange coupling strengths; we assume that T c corresponds to the interatomic exchange coupling on FMs.
To substantiate our hypothesis that the nature of magnetic interactions of OMCs are opposite with the two FM electrodes -two different types of tunnel junctions were studied. These two tunnel junctions were designed to contain one of the two FM electrode of the MTJMSD and palladium (Pd) as the another electrode. Interestingly, OMCs decreased the magnetic moment of Pd (10 nm)/AlOx (2 nm)/NiFe(12 nm) tunnel junction (Fig. 2b). On the other hand, OMCs increased the magnetic moment of Co(5 nm) /NiFe (5 nm)/AlOx (2nm)/Pd (10 nm) tunnel junction (Fig. 2c). Assuming that OMCs interaction with the Pd was identical in the two cases the results in figure 2b and 2c suggest that OMCs had antiferromagnetic coupling with the NiFe electrode and ferromagnetic coupling with the Co/NiFe electrode. If our interpretation of these experimental studies is correct then MC simulations must exhibit complementary or confirmatory results providing the connection between MTJMSD low magnetization state and necessity of J mT and J mB have opposite sign.
We surmise that such an unprecedented molecule induced antiferromagnetic coupling should also be visible in the other forms of magnetic studies. We performed ferromagnetic resonance (FMR) studies before and after transforming MTJ (Fig. 1a) into MTJMSD (Fig. 1b). It was observed that intensities of typical optical and acoustic resonance modes from the bare MTJs decreased significantly and in some cases disappeared after attaching OMCs on MTJ with Ta (5 nm)/Co (~5 nm)/NiFe (~5 nm)/AlOx (2 nm)/NiFe (~10 nm) configuration; note this MTJ configuration exhibited OMC induced antiferromagnetic coupling during SQUID magnetometer study (Fig. 2a). We also conducted similar experiments on the MTJs with the 4 nm thick AlOx spacer to make sure that OMCs are not able to bridge the gap; no statistical difference was observed due to OMCs. According to Layadi et al. [20], if antiferromagnetic coupling strength between the two FM electrodes increased beyond a critical limit then magnetization of two FM electrodes align antiparallel to each other; in this event two usual resonance modes disappear and 8 only a single mode appear at a higher magnetic field. More importantly, the intensity of the single mode arising after establishing strong antiferromagnetic coupling will be proportional to the square of (t T M T -t B M B ); where t T and t B are the thickness of top and bottom FM electrodes, respectively; M T and M B are the magnetizations of the top and bottom FM electrodes, respectively. Hence, on an OMC affected MTJ with t T ≈ t B the resultant single mode will be appearing at a higher magnetic field and will possess significantly less intensity as compared to the two modes observed on a bare MTJ. This theoretical study provides explanation to the disappearance of FMR modes and strongly suggests that OMC produced strong antiferromagnetic coupling between two FM electrodes.
To further substantiate the presence of OMC induced strong antiferromagnetic coupling magnetic force microscopy (MFM) studies were conducted. Veeco Multimode AFM and Co coated magnetic cantilever (Nanoscience). It is noteworthy that MFM imaging is based on measuring the change in long range dipolar forces between a magnetic sample and MFM cantilever. We observed that in most of the scans at MTJMSD coordinates of the topographical images (Fig. 2f) extremely faint or negligible magnetic contrast was observed (Fig. 2g). This study is important in providing evidence that MTJMSD are physically intact. Interestingly, in some MFM scans coexistence of high MFM contrast and negligible MFM contrast was observed. We believe that high contrast MFM is arising from those MTJs which failed to transform into MTJMSD after interacting with the OMCs. On the positive side, such imperfect MTJMSD serve as a good reference to justify the validity of the MFM imaging parameters.

MC study of MTJMSD:
Molecule's couplings with the top and bottom FM electrodes are the two most important parameters in governing the magnetic properties of a MTJMSD (Fig. 1k). We first varied J mT and J mB at fixed kT to investigate which combination of the molecular couplings yields the antiferromagnetic couplings between FM electrodes leading to the experimental observations on MTJMSD (Fig. 2). A 3D graph for 11x10x10 MTJMSD at kT=0.1 suggests the M (magnetic moment of the MTJMSD model) was approaching the magnitude of net molecular magnetic moment when J mT and J mB were of opposite signs (Fig. 3a); it does not matter if J mT or J mB is positive or negative. This MC result (Fig. 3a) confirms our interpretation of experimental magnetization data (Fig. 2b-c) that OMC developed ferromagnetic (+) coupling with the Co/NiFe electrode and antiferromagnetic (-) coupling with the NiFe electrode; hence, in order to see the near zero MTJMSD magnetization J mT and J mB must be of opposite sign (Fig. 3a).
Our MC studies also investigated the effect of the magnitude of J mT and J mB and MTJMSD device size. For this study M for various MTJMSD sizes was plotted as a function of -equal and opposite values of J mT and J mB , i.e. J mT = -J mB or -J mT = J mB (Fig. 3b-c). We varied the height of MTJMSD with (Hx10x10) size (Fig. 1j)   MC simulations also complement the FMR experimental studies on MTJMSDs (Fig. 2c). Layadi et al. [20] have theoretically described for very strong antiferromagnetic coupling forces two FM electrodes to align in the opposite direction and the resultant FMR spectra from such a system resembles the FMR data obtained from MTJMSD (Fig. 2c). Our MC simulation also showed that MTJMSD with opposite signs of J mT and J mB lead to the opposite alignment of FM electrodes. We also attempted to gain insights about the MFM studies which showed negligible magnetic contrast at the sites of MTJMSDs (Fig. 2g). MFM images are a result of magnetic force (F) experienced by the magnetic tip's magnetization (m) in the stray field (H) generated by the magnetic sample in the ambient of magnetic permittivity (µ) (Fig. 4a). It is given by the following equation.
We hypothesized that the oppositely aligned top FM and bottom FM will produce stray magnetic fields in the opposite direction to yield negligible magnetic contrast from the MTJMSD (Fig. 4b). Our MC simulation generated the atomic and molecule site specific magnetization vector profile; an atomic scale 3D vector plot of 3x5x5 MSD device size for J mT = -J mB =0.5 and kT=0.1 is presented (Fig. 4c). At the first place this 3D view asserts that our MC studies are working on the right model which is analogous to the MTJMSD device (Fig. 1b). We performed similar studies on 11x10x10 MSD size and calculated spatial magnetic moment plot for the MTJMSD and the two FM electrodes (Fig. 4 d-e). For MTJMSD we summed the magnetic moment of atoms of FM electrodes and molecules at each topological site along the height dimension and it turned out be very close the total magnetic moment of the molecules, which is only 6.9% of the total magnetization of FM electrode for the 11x10x10 MTJMSD; 36 molecules per 500 FM atoms. Such a small spatial magnetic moment at each spatial site will produce negligible stray field and magnetic contrast as observed in the experimental MFM image from actual MTJMSD (Fig. 2g). As shown in the schematic stray field, the average magnetization of the oppositely aligned FM electrodes ( Fig. 4b) will cancel each other. However, independent measurement of spatial distribution of the average magnetic moment of the top and bottom FM electrode will still be very high as compared to that of overall MTJMSD (Fig. 4e).
In addition to J mT and J mB the variation of kT produced a pronounced effect on the MTJMSD magnetic state. For J mT = -J mB , as kT increased the MTJMSD's M, dropped close to the total magnetization of molecules (Fig. 5a); however, for higher kT thermal fluctuations forced MTJMSD  (Fig 5b and c). The opposite orientation of the FM electrode vectors directly agrees with the atom specific spatial orientation of the spin vector as shown in figure 4c. We also studied the effect of molecular coupling strength on the magnetization of the molecules (Fig. 5d). It is apparent that molecules were well ordered when molecular coupling strength was ~0.5 or more; for the weaker coupling strengths molecules assumed random spin vectors (Fig. 5d). A MTJMSD experienced difficulty in settling in a low magnetization state when molecular coupling strength was <0.5 (Fig. 5e). This result is in agreement with the study focusing on the variations of the molecular coupling strength in device size ( Fig. 2). We also studied the effect of MSD size on the M vs. kT graph. For J mT = -J mB =1 all the studied MTJMSD sizes settled in near zero magnetization state (Fig. 5f). However, for J mT = -J mB =0.5 only the smaller device sizes tended to settle in the lower magnetization state (inset of Fig. 5f). We also studied χ -1 vs. kT for 11x10x10 MSD size (Fig. 5g). This study suggests that a major transition occurred close to the kT c (or kT c =J T =J B ) for the MTJMSD (Fig. 5g). Zooming on the data enclosed in the gray color lines showed that χ -1 of the overall MTJMSD was more than that of FM electrodes, before the kT c (Inset of Fig.   5g). We believe that this region of kT signifies the dominance of the molecular coupling. However, after the Curie temperature (J T =J B ) χ -1 for the FM electrodes dominated. Presumably kT destroyed the ordering due to J T and J B on the FM electrodes. This study suggests that the effect of molecular coupling (J mT and -J mB ) was functional up to kT=~0.8.

CONCLUSIONS
MC simulations were performed to study the effect of magnetic molecule induced exchange coupling on the magnetic properties of the MTJMSD. We considered all the possible permutations and combinations and nature of interactions between a paramagnetic molecule and the two FM electrodes of a MTJMSD to understand the experimental results. Experimentally observed molecule induced strong antiferromagnetic coupling was only possible when a molecule, with a net spin state, established ferromagnetic coupling with one FM electrode and antiferromagnetic coupling with the other FM electrode. Our MC simulations effectively explain the origin of the experimental data obtained from SQUID magnetometer, ferromagnetic resonance, and MFM studies on MTJMSD. The experimentally estimated molecular coupling strength was in agreement with our results of MC simulations. Increasing MTJMSD size was found to weaken the molecular coupling effect. However it is quite possible that we underestimated the impact of molecular coupling on the MTJMSD size. In this study we mainly focused on the Heisenberg type magnetic interaction among nearest neighbors. In reality, molecules are expected to have other modes of couplings such as biquadratic coupling, dipolar coupling, and most importantly paramagnetic molecules are also capable of invoking spin fluctuation assisted coupling between two FM electrodes. [5] One significant caveat about our MC simulation is that it considers FM electrodes to be 100% spin polarized; however, in actual a FM electrode is nearly 40% spin polarized. [22,23] We surmise that assuming 100% spin polarized FM electrodes is still a good assumption in the context of MTJMSDs. It is because of the fact that OMC induced strong coupling is expected to produce spin filtering leading to highly spin polarized FM electrodes. Molecular channels with small spin -orbit coupling and hyperfine splitting, can ensure high spin coherence as compared to a ~2 nm AlOx insulator with numerous spin scattering defect sites and imperfections. Further experimental and theoretical studies are needed in order to explore the rich physics and novel device forms associated with the MTJMSD approach.