Direct observation of the magnetic anisotropy of an Fe(II) spin crossover molecular thin film

In this work, we provide clear evidence of magnetic anisotropy in the local orbital moment of a molecular thin film based on the SCO complex [Fe(H2B(pz)2)2(bipy)] (pz = pyrazol−1−yl, bipy = 2,2′−bipyridine). Field dependent x-ray magnetic circular dichroism measurements indicate that the magnetic easy axis for the orbital moment is along the surface normal direction. Along with the presence of a critical field, our observation points to the existence of an anisotropic energy barrier in the high-spin state. The estimated nonzero coupling constant of ∼2.47 × 10−5 eV molecule−1 indicates that the observed magnetocrystalline anisotropy is mostly due to spin–orbit coupling. The spin- and orbital-component anisotropies are determined to be 30.9 and 5.04 meV molecule−1, respectively. Furthermore, the estimated g factor in the range of 2.2–2.45 is consistent with the expected values. This work has paved the way for an understanding of the spin-state-switching mechanism in the presence of magnetic perturbations.


Introduction
Some of the transition metal complexes exhibit a spin state transition between a high-spin state and a low-spin state due to external stimuli [1][2][3][4][5][6][7][8]. Spin crossover (SCO) materials, in particular the molecule [Fe(H 2 B(pz) 2 ) 2 (bipy)] (pz = pyrazol−1−yl, bipy = 2,2 ′ −bipyridine) shown in figure 1, undergo spin state switching when stimulated by light, temperature, pressure, or magnetic field [2,4,[6][7][8][9][10]. The ligand crystal field causes the 3d-orbitals of the central Fe(II) to split into the e g and t 2g orbitals. When the molecule is in the low-spin configuration, the t 2g orbital is fully populated by six electrons, so that S = 0 and diamagnetism are observed. Well above the critical temperature T C ≈ 160 K, the [Fe(H 2 B(pz) 2 ) 2 (bipy)] molecule is expected to be in the high-spin state with two unpaired electrons in the e g orbital and the remaining four electrons in the t 2g orbital, [9] so that S = 2. It has been previously demonstrated that the [Fe(H 2 B(pz) 2 ) 2 (bipy)] molecule may undergo a non-volatile, isothermal, reversible spin-state transition even at room temperature when coupled to a ferroelectric thin film [7,10]. More importantly, the change in conductivity in the SCO molecular layer, which is associated with this spin state transition, provides a facile readout mechanism for potential molecular-based memory devices [7,10]. When changing the spin state, an energy barrier must be overcome to switch the SCO molecule from a low-spin state to a high-spin state or vice versa [11]. Previous work estimated an activation energy of ∼60 meV molecule −1 (3.55 × 10 3 kJ m −3 ) by conducting temperature dependent measurements for [Fe(H 2 B(pz) 2 ) 2 (bipy)] thin films on SiO 2 [7,12]. For molecular SCO materials, including [Fe(H 2 B(pz) 2 ) 2 (bipy)] thin films, studies have confirmed that the activation energy to change the spin state is significantly reduced by an external magnetic field [6,[13][14][15][16][17][18][19][20]. Octahedral Fe(II) spin crossover molecule [Fe(H2B(pz)2)2(bipy)] (pz = pyrazol−1−yl, bipy = 2,2 ′ −bipyridine) structure with electron distribution [21]. The imperfect symmetry of the six ligands connected to the central Fe(II) ion implies a non-zero orbital moment when the Fe ion is not in the S = 0 spin configuration.
The question arises as to whether the effect of the magnetic field on an SCO molecule is influenced by magnetic anisotropy [22]. In other words, does an anisotropic energy barrier exist? Studying the magnetic anisotropy for SCO molecules in high-spin states is important for understanding the substrate interactions of spin crossover molecular thin films [7,8,23,24]. Here, we present a study of the magnetic anisotropy of an SCO thin film based on [Fe(H 2 B(pz) 2 ) 2 (bipy)] using x-ray magnetic circular dichroism (XMCD). XMCD is an ideal probe to study the element specific magnetic anisotropy, as it distinguishes between the spin and orbital moments for each molecule. We clearly demonstrate the existence of magnetic anisotropy and determine the spin and orbital contributions to the magnetic anisotropy when the SCO molecules are in the high-spin state.

Methods
[Fe(H 2 B(pz) 2 ) 2 (bipy)] was synthesized following established methods [2,4,[6][7][8][9][10], and its molecular structure with electron distribution envelope is shown in figure 1 [25,26]. Following previous methods [6][7][8][9][10], a [Fe(H 2 B(pz) 2 ) 2 (bipy)] thin film, measured to be 65 nm thick by a Bruker DektakXT profilometer, was thermally evaporated under high vacuum (3.8 × 10 −7 Torr) onto a P/B-doped Si substrate with a native oxide at the surface. The molecular integrity is preserved during this process, as confirmed by the previously published x-ray diffraction data [27]. Field and temperature dependent XMCD measurements were performed at Argonne National Laboratory's Advanced Photon Source beamline 4-ID-C with a beam diameter of 1 mm in total electron yield (TEY) mode [28]. Incident x-rays were parallel to the applied magnetic field. Each XMCD spectrum was obtained by first characterizing the sample with left and right circularly polarized light, while the magnetic field direction was kept constant, then characterizing the sample again with left and right circularly polarized light and the magnetic field polarity reversed. This technique allows artifacts to be removed from a weak XMCD signal by obtaining a net XMCD signal that is the difference between XMCD spectra obtained with the spin of the photon parallel with either the spin majority or spin minority.
Three XMCD measurements, namely field-orientation dependent XMCD, field-strength dependent XMCD, and temperature-dependent XMCD, were performed to characterize the Fe L 2,3 -edge of the nominally 65 nm thick [Fe(H 2 B(pz) 2 ) 2 (bipy)] thin film on a Si substrate with a native SiO 2 oxide surface. These XMCD spectra were then analyzed using the sum rules introduced by Chen et al [29,30]. To obtain the average spin moment ⟨S z ⟩ and average orbital moment ⟨L z ⟩, we sum the contributions from the 2p 3/2 (L 2 ) and 2p 1/2 (L 3 ) orbitals by integrating the XMCD and x-ray absorption spectroscopy (XAS) spectra respectively over the incident photon energy range as shown in figure 2. We then apply the XMCD sum rule equations ⟨S z ⟩ = −(6p − 4q)(10 − n 3d )/r and ⟨L z ⟩ = −4q(10 − n 3d )/3r where r =´(µ + + µ − ) dω and q =´(µ + − µ − ) dω are integrated over the L 3 + L 2 edges, and p =´(µ + − µ − ) dω is integrated over the L 3 edge only [29,30]. The µ + and µ − values are proportional to the XAS intensities collected with the spin of the photons aligned parallel and anti-parallel to the spin majority, respectively. After background subtraction, the XAS signal for each XMCD signal was integrated, and the total area under the curve was parameterized as r as shown in figure 2(a). The determination of p and q is shown in figure 2(b), where the error bar for p is the standard deviation of the integrated signal values after the L 3 edge and the error bar for q is the standard deviation of the integrated signal values after the L 3 + L 2 edges. The p, q, and r values are then used in the XMCD sum rules [29,30]. For Fe(II), the average number of valence electrons in the 3d orbital, n 3d , is taken to be 6.61 [29,31].

Results and discussion
The magnetic moment of the SCO [Fe(H 2 B(pz) 2 ) 2 (bipy)] molecule originates from the core Fe(II) ion. In addition to a spin moment ⟨S z ⟩, an Fe(II) SCO molecule in the high-spin state is expected to have a small orbital moment ⟨L z ⟩ due to the asymmetry of the ligand field [11,32], as indicated in figure 1. The details of the spin and orbital moment contributions in the [Fe(H 2 B(pz) 2 ) 2 (bipy)] molecule are of particular interest.
To obtain the field-orientation dependent XMCD data, a 2.0 T magnetic field was applied approximately parallel to the [Fe(H 2 B(pz) 2 ) 2 (bipy)] molecular thin film at a temperature of 200 K for the in-plane (IP) measurement and then nearly perpendicular to the sample surface for the out-of-plane (OOP) measurement at the same temperature. Both the IP and OOP XMCD spectra are plotted in figure 3(a). The average orbital moment ⟨L z ⟩ and spin moment ⟨S z ⟩ were calculated for both the IP and OOP magnetic field orientations using the XMCD sum rules. These values are plotted as a function of the magnetic field angle in figure 3(b). The orbital moment for the OOP orientation is found to be slightly larger than that of the IP orientation, while the spin moment shows a small variation with the opposite trend. The increase in the OOP measurement compared to the IP measurement implies that the hard axis for the orbital moment is IP. An OOP easy axis suggests that anisotropy is dominated by the magnetocrystalline anisotropy, which in turn suggests a certain preferential orientation of [Fe(H 2 B(pz) 2 ) 2 (bipy)] in the molecular thin film on the SiO 2 native oxide surface of the Si substrate [30].
Our data indicate that the orbital moment is locked at some degree relative to the substrate, while the spin moment is free to rotate compared to the orbital magnetic moment, implying spin-orbit coupling. Soft x-ray MCD experiments in the TEY mode are surface sensitive with a probing depth of ∼2 nm, but substrate effects could still be observed due to cooperative interaction between molecules [33,34]. Figure 3(c) shows the ratio of spin moment to orbital moment for the two different applied magnetic field orientations. The IP ratio ⟨S z ⟩/⟨L z ⟩ is almost twice that of the OOP ratio. This is due to a small increase in the orbital moment, while the spin moment remains relatively constant, indicating a hard orbital moment and a soft spin moment. Reduced cubic symmetry enhances the orbital moment, and the orbital moment of transition metals is highly sensitive to external fields [35]. Our field-strength dependent XMCD measurement (vide infra) shows that the 2.0 T applied magnetic field is far from the saturation field. Therefore, the true orbital moment value of the molecule is expected to potentially be much larger than the average value measured for the thin film sample [34]. Additional measurements for [Fe(H 2 B(pz) 2 ) 2 (bipy)] were conducted along the easy axis with the field OOP; the magnitude of the anisotropy values reported from these data are expected to approximate the maximum values possible for the system.
The first-order magnetic anisotropy energy density of a thin film is expressed as E ani = K 1 sin 2 γ, where K 1 is the first-order anisotropy constant and γ is the polar angle, as measured from the sample's surface normal [36]. The anisotropy constant K 1 can be further decomposed into the contributions from the shape anisotropy, K s , and the magnetocrystalline anisotropy, K u [36]. The shape anisotropy is typically a negative value for thin film samples. The positive anisotropy demonstrated by the magnetic field orientation dependent XMCD data suggests that the anisotropy is dominated by the magnetocrystalline anisotropy rather than the shape anisotropy of the molecule. Using the standard energy expression for spin-orbit coupling, the magnetocrystalline anisotropy energy can be expressed as where L is the orbital moment, S is the spin moment, m o is the orbital moment along the hard or easy axis (in our estimation we used the values shown in figure 3(b)), and ζ is the spin-orbit coupling constant with the dimension of energy [30]. Accordingly, for our sample, the magnetocrystalline anisotropy has a maximum value when measured along the OOP easy axis [30]. With the spin-orbit coupling constant for Fe(II) ζ = 400 cm −1 [37], ∆E SO is estimated to be ∼2.47 × 10 −5 eV molecule −1 . Because the magnetic moment is far from saturation, as the applied magnetic field strength increases, the expected energy difference between the hard-axis and soft-axis will remain constant, even as the total energy required to align molecules with the externally applied field increases. Given that the average volume of an [Fe(H 2 B(pz) 2 ) 2 (bipy)] molecule is 2710 Å 3 , the anisotropy constant was determined to be K 1 = ∆E SO volume-per-molecule −1 = 1.47 kJ m −3 [25]. This is approximately one-order of magnitude smaller than the previously reported K 1 = 45 kJ m −3 value for bulk bcc-Fe [38].
The material dependent spectroscopic g factor correlates the spin-orbit coupling and the alignment of the magnetic moment with an external magnetic field. When the molecular z-axis is taken to align with the external magnetic field, the g z component may be calculated from Kittel's formula expressed as g z = 2 (⟨L z ⟩ / ⟨S z ⟩ + 1) where ⟨L z ⟩ is the average orbital moment and ⟨S z ⟩ is the average spin moment along the z-axis [39]. In figure 3(d), the g factor is larger for the OOP measurement than for the IP measurement. When the external magnetic field is orientated along the OOP direction, the magnetic g factor is g z = 2.41. This agrees with the previously reported values for related Fe(II) SCO complexes in the high-spin state under a magnetic field [40,41].
The spin and orbital moments determined from the XMCD data for [Fe(H 2 B(pz) 2 ) 2 (bipy)] thin films are seen to depend on the strength of the externally applied magnetic field. With an OOP magnetic field applied along the easy axis of the orbital moment, the sample was characterized by field magnitudes [0.5 T, 1.0 T, 1.5 T, 2.0 T] at constant temperature T = 200 K with the sample in a high-spin dominated state due to x-ray excitation. The high-spin state fraction is estimated to be near 85%, and this is determined by the agreement of the XAS spectra shown in figure 2(a) with previously published results [7]. The field-strength dependent XMCD spectra are shown in figure 4(a), where the XMCD signal strength increases with the applied field strength for both the L 2 and L 3 edges. In figure 4(b), the spin and orbital moments calculated with the XMCD sum rules show an approximately linear dependence on the applied magnetic field strength. The non-zero y-axis intercept of the ⟨S z ⟩ trend line indicates that the magnetic anisotropy favors spontaneous spin moment alignment and therefore the molecule possesses some net spin moment. The non-zero x-axis intercept of the measured orbital moment ⟨L z ⟩, as a function of an applied magnetic field, indicates a nonzero critical field. This nonzero critical field for the measured orbital moment implies that an energy barrier is present for orbital moments to align parallel with the external magnetic field in [Fe(H 2 B(pz) 2 ) 2 (bipy)] thin films. This indication of an anisotropy barrier has been recently observed in other SCO molecular systems [19].
The anisotropy of the orbital moment in [Fe(H 2 B(pz) 2 ) 2 (bipy)] thin films may be determined from the x-axis intercepts of the spin moment and orbital moment trend lines, respectively. As shown in figure 4(b), the x-axis intercept indicates the magnitude of the external magnetic field required to overcome the internal energy barrier. For the spin moment trend line, the x-intercept occurs at −0.11 T, while the orbital moment trend line intercepts the x-axis at +0.13 T. The anisotropy constant can then be determined from ∆E = B·µ where ∆E is the energy required to align a magnetic moment with the external field, µ is the spin or orbital moment of the molecule and B is the magnetic field [36,42,43]. The predicted spin moment for an Fe(II) ion is 4.89 µ B , yielding an energy barrier of 3.11 × 10 −2 meV molecule −1 with an external field of 0.11 T and a spin-moment anisotropy of 30.9 meV molecule −1 (1.83 kJ m −3 ) when accounting for the volume of a single molecule. This is the same order-of-magnitude as the spin-orbit coupling anisotropy estimated from figure 3. An orbital moment of 0.668 µ B is estimated from Kittel's formula for the orbital moment using the predicted spin moment of a single Fe(II) ion s = 4.89 µ B and a g factor of 2.27 (as estimated by the linear In figure 4(c), the ratio of the spin and orbital moments is shown as a function of an external magnetic field; the size of the error bars decreases as the magnetic field increases due to a better signal-to-noise ratio at a higher field. As field strength increases, the ratio of the spin moment to the orbital moment decreases, indicating a stronger spin-orbit interaction as the field increases. The g z factor values determined by Kittel's formula are shown in figure 4(d) as a function of field strength with a linear regression, predicting a zero-field g-factor along the z-axis of the thin film to be g z = 2.26. A typical value for a metal ion with six electrons in the d-orbital is g z = 2.20, while previously reported g factor values for Fe(II) range from 2.2 to 2.3 [3,44,45]. The g factor for a Fe(II) ion deviates from the spin-only value of g = 2.00 due to the presence of a small amount of orbital moments. The magnetic anisotropy could be due to various causes including substrate interactions, intermolecular cooperative effects, the inclusion of substrate-induced strain, and a preferential molecular orientation induced by the substrate, but is expected to be temperature dependent regardless of cause [12,22,32]. For the temperature-dependent XMCD measurement, the magnetic field strength was kept at 2.0 T and oriented OOP along the orbital moment easy axis. Figure 5(a) shows the change in the XMCD signal for two temperatures near and slightly above the critical temperature of [Fe(H 2 B(pz) 2 ) 2 (bipy)], where the L 3 edge signal decreases with increasing temperature. As the thermal energy increases, the SCO molecules experience phonon and magnon effects preventing alignment with the external magnetic field; this causes the net spin moment to decrease due to dynamic spin canting [46]. In figure 5(b), the orbital and spin moments are shown to decrease with increasing temperature, with the spin moment decreasing more quickly than the orbital moment. The [Fe(H 2 B(pz) 2 ) 2 (bipy)] thin film is high-spin state dominated for the entire temperature range due to the excitation effects of x-ray source during the measurements [7,9,10]. Because the orbital moment of the [Fe(H 2 B(pz) 2 ) 2 (bipy)] sample is magnetically hard, the orbital moment demonstrates less temperature dependence.
In figure 5(c), the ⟨S z ⟩ / ⟨L z ⟩ ratio increases with increasing temperature. The measured orbital moment depends on the orientation of the molecule with respect to the magnetic field, and the orientation of the molecule is fixed during deposition due to substrate effects [34,47,48]. Here, strong interaction between the SCO molecule electric dipole moment and the SiO 2 substrate surface dipole layer is both likely and plausible. This suggests that the orbital moment is insensitive to changes in temperature and confirms that the molecule has a preferential orientation on the substrate, as previously reported elsewhere [48,49]. For a magnetocrystalline anisotropy originating from spin-orbit coupling and substrate effects, there is a possibility of tuning the anisotropy barrier through the use of different substrates [43].
The magnitudes of the K s and K u constants for Fe(II) were previously reported to be ∼10 −1 meV atom −1 and ∼10 −3 meV atom −1 respectively [30,38]. Our data are in good agreement with these studies. The volume of a single Fe atom is 11.8 Å 3 while the volume of a single [Fe(H 2 B(pz) 2 ) 2 (bipy)] molecule is 2710 Å 3 due to the addition of ligands on the central metal ion [25,30]. The molecule's larger volume results in a decreased coupling between the central Fe(II) ions of the [Fe(H 2 B(pz) 2 ) 2 (bipy)] molecules. Since the magnetic field from a dipole decreases with a cubic dependency, this provides insight into the origin of the different magnitudes for the magnetic anisotropic constants. Previous studies of [Fe(H 2 B(pz) 2 ) 2 (bipy)] in a molecular thin film estimated the activation energy to be ∼102 meV molecule −1 and experimentally measured the activation energy to be 60 meV molecule −1 [4,7,12]. The difference in magnitude between the magnetic anisotropy constants and the activation energy suggests that including crystal field effects and substrate interactions does not substantially change the energy required to change the molecular spin state.

Conclusion
Field strength-, field orientation-, and temperature-dependent XMCD studies show that the SCO molecules [Fe(H 2 B(pz) 2 ) 2 (bipy)] in a thin film have a preferential alignment with the easy axis along the surface normal, on a SiO 2 substrate, and possess a magnetic anisotropy barrier. The observed magnetic anisotropy dominated by magnetocrystalline anisotropy is due to the coupling between the orbital moment and spin moment in the high-spin state, as evidenced by a zero-field g factor of g z = 2.26. The spin-orbit coupling energy is determined to be 1.47 kJ m −3 and the spin and orbital moment anisotropies were estimated to be 30.9 and 5.04 meV molecule −1 , respectively. The magnetic anisotropy suggests a preferential orientation for the molecule relative to the substrate, but intermolecular interactions and strain could be implicated as well. The spin moment is shown to be soft with respect to external magnetic field orientation and substrate interactions, while the orbital moment shows a preferential direction.

Data availability statement
All data that support the findings of this study are included within the article (and any supplementary files).