Thickness-dependent electronic and magnetic properties of $\gamma'$-Fe$_{\mathrm 4}$N atomic layers on Cu(001)

TL;DR

This study investigates how the electronic and magnetic properties of $ ext{Fe}_4 ext{N}$ atomic layers on Cu(001) vary with thickness, revealing layer-dependent electronic states and magnetic moments through experimental and first-principles methods.

Contribution

It provides new insights into the thickness-dependent electronic and magnetic properties of $ ext{Fe}_4 ext{N}$ layers on Cu(001), combining experimental observations with first-principles calculations.

Findings

Thicker $ ext{Fe}_4 ext{N}$ layers show increased magnetic moments.

Layer-resolved density of states explains electronic structure changes.

Continuous trilayer films are successfully grown and characterized.

Abstract

Growth, electronic and magnetic properties of $\gamma'$-Fe$_{4}$N atomic layers on Cu(001) are studied by scanning tunneling microscopy/spectroscopy and x-ray absorption spectroscopy/magnetic circular dichroism. A continuous film of ordered trilayer $\gamma'$-Fe$_{4}$N is obtained by Fe deposition under N$_{2}$ atmosphere onto monolayer Fe$_{2}$N/Cu(001), while the repetition of a bombardment with 0.5 keV N$^{+}$ ions during growth cycles results in imperfect bilayer $\gamma'$-Fe$_{4}$N. The increase in the sample thickness causes the change of the surface electronic structure, as well as the enhancement in the spin magnetic moment of Fe atoms reaching $\sim$ 1.4 $\mu_{\mathrm B}$/atom in the trilayer sample. The observed thickness-dependent properties of the system are well interpreted by layer-resolved density of states calculated using first principles, which demonstrates the strongly layer-dependent electronic states within each surface, subsurface, and interfacial plane of the $\gamma'$-Fe$_{4}$N atomic layers on Cu(001).

Tables

Table 1. Table 1: Calculated atomic magnetic moments of the Fe atoms at each site (in units of μ B subscript 𝜇 B \mu_{\rm B} /atom). The site notation is the same as that used in Fig. 7 .

	Surface Fe2N		Subsurface Fe		Interfacial Fe2N
	Fe1	Fe2	Fe3	Fe4	Fe5	Fe6
Monolayer	1.1	1.1	-	-	-	-
Trilayer	1.8	1.8	2.0	3.0	0.62	0.62

Table 2. Table 2: Experimental and calculated Fe (N) edge jump values for the monolayer, dot-like bilayer, trilayer, and quadlayer γ ′ superscript 𝛾 ′ \bf{\gamma}^{\prime} -Fe 4 N on Cu(001). In the calculation, each γ ′ superscript 𝛾 ′ \bf{\gamma}^{\prime} -Fe 4 N is assumed to have the atomic structure presented in the text and fully cover the entire surface. For the quadlayer one, an Fe 2 N/Fe 2 /Fe 2 N/Fe 2 /Cu(001) structure is assumed.

	Fe edge jump		N edge jump
	Experiment	Calculation	Experiment	Calculation
Monolayer	0.12 (exp.)		0.015 (exp.)
Bilayer dot	-	0.19	-	0.015
Trilayer	0.32	0.40	0.032	0.034
Quadlayer	-	0.57	-	0.034

Full text

I Introduction

Iron nitrides, especially in iron-rich phases, have been under intense research due to the strong ferromagnetism and interest in its physical origin Coey and Smith (1999); Frazer (1958). The difficulty in obtaining a single phase has been a long-standing problem for ferromagnetic iron nitrides, to hinder fundamental understanding of intrinsic physical properties Coey (1994); Komuro et al. (1990); Ortiz et al. (1994). Recently, the successful epitaxial growth of single-phase ferromagnetic $\bf{\gamma}^{\prime}$-Fe4N has been reported on various substrates, which helps to comprehend a crucial role for the hybridization between Fe and N states in the ferromagnetism of $\bf{\gamma}^{\prime}$-Fe4N Atiq et al. (2008); Borsa et al. (2001); Gallego et al. (2004a); Ito et al. (2011); Nikolaev et al. (2003); Kokado et al. (2006); Ito et al. (2015). The robust Fe-N bonding also renders an Fe2N layer strongly two-dimensional Fang et al. (2014), which possibly facilitates a layer-by-layer stacking of $\bf{\gamma}^{\prime}$-Fe4N on metals. This contrasts with the case of elemental 3$d$ transition metals (TMs) deposited on 3$d$ TM substrates, in which inevitable atom intermixing and exchange of constituents prevent the formation of ordered overlayers Kim et al. (1997); Nouvertné et al. (1999); Torelli et al. (2003). Therefore, the investigation into the electronic and magnetic states of $\bf{\gamma}^{\prime}$-Fe4N atomic layers can not only elucidate the layer-/site-selective electronic and magnetic states of $\bf{\gamma}^{\prime}$-Fe4N, but unravel the origin of the strongly thickness-dependent physical properties in a thin-film limit of 3$d$ TM ferromagnets Srivastava et al. (1997); Farle et al. (1997a, b); Schulz and Baberschke (1994); Li et al. (1994); Straub et al. (1996); Weber et al. (1996); Meyerheim et al. (2009).

Here, we report two growth modes of $\bf{\gamma}^{\prime}$-Fe4N/Cu(001) depending on preparation methods. The scanning tunneling microscopy/spectroscopy (STM/STS) observations indicated a successful growth of ordered trilayer $\bf{\gamma}^{\prime}$-Fe4N, without extra nitrogen bombardment onto the existing structures. X-ray absorption spectroscopy/magnetic circular dichroism (XAS/XMCD) measurements revealed the thickness dependence of the magnetic moments of Fe atoms, the origin of which was well explained by the first-principles calculations. Based on an atomically-resolved structural characterization of the system, the layer-by-layer electronic and magnetic states of the $\bf{\gamma}^{\prime}$-Fe4N atomic layers have been understood from both experimental and theoretical points of view.

II Methods

A clean Cu(001) surface was prepared by repetition of sputtering with Ar*+* ions and subsequent annealing at 820 K. Iron was deposited at room temperature (RT) in a preparation chamber under an ultrahigh vacuum (UHV) condition ($<1.0\times 10^{-10}$ Torr), using an electron-bombardment-type evaporator (EFM, FOCUS) from a high-purity Fe rod (99.998 %). The STM measurements were performed at 77 K in UHV ($<3.0\times 10^{-11}$ Torr) using electrochemically etched W tips. The differential conductance d$I$/d$V$ was recorded for STS using a lock-in technique with a bias-voltage modulation of 20 mV and 719 Hz. The XAS and XMCD measurements were performed at BL 4B of UVSOR-III Gejo et al. (2003); Nakagawa et al. (2008) in a total electron yield (TEY) mode. The degree of circular polarization was $\sim 65\ \%$, and the x-ray propagation vector lay within the (11̄0) plane of a Cu(001) substrate. All the XAS/XMCD spectra were recorded at $\sim 8\ {\rm K}$, with external magnetic field $B$ up to $\pm 5$ T applied parallel to the incident x-ray. The symmetry and quality of the surface were also checked by low energy electron diffraction (LEED) in each preparation chamber. First-principles calculations were performed within the density functional theory in the local density approximation Perdew and Wang (1992), using a self-consistent full-potential Green function method specially designed for surfaces and interfaces Lüders et al. (2001); Geilhufe et al. (2015).

III Results and Discussion

III.1 Monolayer and bilayer-dot $\bf{\gamma}^{\prime}$-Fe4N

Monolayer Fe2N on Cu(001) was prepared prior to any growth of multilayer $\bf{\gamma}^{\prime}$-Fe4N by the following cycle: N*+* ion bombardment with an energy of 0.5 keV to a clean Cu(001) surface, subsequent Fe deposition at RT, and annealing at 600 K. Note that the monolayer Fe2N is identical to Fe4N on Cu(001) in a monolayer limit, and thus referred to as also ”monolayer $\bf{\gamma}^{\prime}$-Fe4N” hereafter. A topographic image of the sample after one growth cycle is shown in Fig. 1(a). The monolayer $\bf{\gamma}^{\prime}$-Fe4N is formed on the Cu terraces at $\sim$ 0.85 ML coverage. An atomically-resolved image of that surface displayed in Fig. 1(b) reveals a clear dimerization of the Fe atoms, typical of ordered $\bf{\gamma}^{\prime}$-Fe4N on Cu(001) Gallego et al. (2005); Takahashi et al. (2016). A LEED pattern of the surface is shown in Fig. 1(c), which exhibits sharp spots with the corresponding $p4g(2\times 2)$ symmetry. It is known that Gallego et al. (2005, 2004b); Navio et al. (2007); Takahashi et al. (2016) the topmost layer of the $\bf{\gamma}^{\prime}$-Fe4N on Cu(001) always consists of the Fe2N plane in a bulk Fe4N crystal shown in Fig. 1(d). A schematic model of the monolayer $\bf{\gamma}^{\prime}$-Fe4N is given in Fig. 1(e), composed of a single Fe2N plane on Cu(001). Accordingly, the surface Fe2N plane takes reconstruction to the $p4g(2\times 2)$ coordination Gallego et al. (2005), in which the Fe atoms dimerize in two perpendicular directions as illustrated in Fig. 1(f).

After repeating the growth cycles, we found a new structure different from the monolayer $\bf{\gamma}^{\prime}$-Fe4N. Figure 2(a) displays the surface after two growth cycles in total, namely, another cycle of the N*+* ion bombardment, Fe deposition, and annealing onto the existing monolayer $\bf{\gamma}^{\prime}$-Fe4N surface. Then, the surface becomes mostly covered with the monolayer $\bf{\gamma}^{\prime}$-Fe4N, which contains a small number of bright dots. For a structural identification of these dots, we measured atomically-resolved topographic images and line profiles at different $V_{\rm s}$ as shown in Fig. 2(b) and 2(c). The dot structure imaged at $V_{\rm s}=-0.1\ V$ reveals the dimerization of the Fe atoms as the monolayer $\bf{\gamma}^{\prime}$-Fe4N surface. This indicates that the topmost part of the dot consists of the reconstructed Fe2N. At positive $V_{\rm s}$ of +0.1 V, in contrast, the dot is recognized as a single protrusion both in the topographic image and line profile, while the surrounding monolayer $\bf{\gamma}^{\prime}$-Fe4N still shows the Fe dimerization. This implies the different electronic structure of the dot compared to the monolayer $\bf{\gamma}^{\prime}$-Fe4N, which comes from the difference in a subsurface atomic structure.

The observed height difference between the dot and the monolayer $\bf{\gamma}^{\prime}$-Fe4N ranges from 4 to 10 pm depending on $V_{\rm s}$. These values are in the same order of a lattice mismatch between the bulk crystals of the $\bf{\gamma}^{\prime}$-Fe4N/Cu(001) (380 pm) and Cu(001) (362 pm) Gallego et al. (2005), but an order of magnitude smaller than the lattice constant of the $\bf{\gamma}^{\prime}$-Fe4N/Cu(001). This suggests that the topmost layer of the dot is not located above the monolayer $\bf{\gamma}^{\prime}$-Fe4N surface, but shares the Fe2N plane with. Furthermore, the bright dot is composed of only four pairs of the Fe dimer as imaged in Fig. 2(b), indicating that the difference in the atomic and/or electronic structures is restricted within a small area. Considering the above, it is most plausible that one Fe atom is embedded just under the surface N atom at the dot center, and thus a bilayer $\bf{\gamma}^{\prime}$-Fe4N dot is formed as schematically shown in Fig. 2(d). This structure corresponds to a minimum unit of the bilayer $\bf{\gamma}^{\prime}$-Fe4N on Cu(001).

This bilayer dot formed clusters by a further repetition of the growth cycles. Figure 3(a) shows an enlarged view of the iron-nitride surface after two growth cycles. The coverage of the dot is estimated to be $\sim$ 5 % of the entire surface. Another growth cycle onto this surface led to an increase in a dot density up to $\sim$ 40 %, as shown in Fig. 3(b). However, further repetitions of the cycles resulted in neither a considerable increase in the dot density nor the formation of a continuous bilayer film. This can be attributed to an inevitable sputtering effect in every growth cycle: an additional N*+* ion bombardment to the existing surface not only implanted N*+* ions but also sputtered the surface, which caused the loss of the iron nitrides already formed at the surface, as well as the increase in the surface roughness.

To compensate this loss of surface Fe atoms by the sputtering effect, we also tried to increase the amount of deposited Fe per cycle. Nonetheless, the number of Fe atoms, which remained at the surface after annealing, did not increase possibly because of the thermal metastability of Fe/Cu systems Detzel and Memmel (1994); Memmel and Detzel (1994); Shen et al. (1995); Bayreuther et al. (1993). The isolated Fe atoms without any bonding to N atoms were easily diffused and embedded into the Cu substrate during the annealing process. As a result, only the imperfect bilayer $\bf{\gamma}^{\prime}$-Fe4N was obtained through this method.

III.2 Trilayer $\bf{\gamma}^{\prime}$-Fe4N film

Multilayer $\bf{\gamma}^{\prime}$-Fe4N films were obtained by the following procedure. First, the monolayer $\bf{\gamma}^{\prime}$-Fe4N was prepared on Cu(001) as above. Then, 2 ML Fe was deposited under N2 atmosphere (5.0$\times$10*-8* Torr) 111We checked the ionization of nitrogen molecules/atoms without bombardment using an ion gun. The ion flux monitored for the Fe evaporator increased in proportion to the rise in the N2 pressure, far below the parameters at which Fe started to be evaporated. This indicates the ionization of the N2 molecules and/or N atoms around the evaporator possibly by thermal electrons created inside it. Then, the N*+* and N${}_{2}^{+}$ ions could reach to the surface together with the evaporated Fe atoms, or iron nitride was already formed before landing. at RT, and the sample was annealed at 600 K. Figures 4(a) and 4(b) show topographic images after two and three above mentioned cycles, respectively. In the images, the coverage of new bright area, different from the imperfect bilayer dot, monotonously increases with repeating the cycles. A close view of that new surface is displayed in Fig. 4(c), revealing the dimerized (or even $c(2\times 2)$-like dot) structures. Because a LEED pattern shown in the inset of Fig. 4(c) exhibits the $p4g(2\times 2)$ symmetry without extra spots, the topmost layer of this surface is composed of the reconstructed Fe2N plane Takahashi et al. (2016). Therefore, these observations suggest that the new area would consist of $\bf{\gamma}^{\prime}$-Fe4N other than both of the monolayer and bilayer dot.

In order to determine the structure of this newly obtained $\bf{\gamma}^{\prime}$-Fe4N, a typical height profile of the surface was recorded as shown in Fig. 4(d). It is clear that the new structure is higher than both the Cu surface and the surface including the monolayer/dot-like bilayer $\bf{\gamma}^{\prime}$-Fe4N. This suggests that the new area is composed of $\bf{\gamma}^{\prime}$-Fe4N thicker than bilayer. Quantitative information on the thickness of the new structure could be obtained from Fe $L\ (2p\rightarrow 3d)$ edge jump spectra shown in Fig. 4(e), whose intensity is roughly proportional to the amount of surface/subsurface Fe atoms. The sample prepared in the same procedure as that shown in Fig. 4(b) reveals an edge jump value of 0.32, while the monolayer $\bf{\gamma}^{\prime}$-Fe4N 0.12 222The amount of the Fe atoms detected in the edge-jump spectra was smaller than that expected from the initially deposited ones. This implies that a certain amount of Fe atoms, not participating in forming any $\bf{\gamma}^{\prime}$-Fe4N structures, was embedded into the Cu substrate during annealing, at least several nms (probing depth in the TEY mode) below the surface.. Considering that the new area occupies $\sim$ 60 % of the entire surface as deduced from Fig. 4(b), the thickness of this $\bf{\gamma}^{\prime}$-Fe4N must be less than quadlayer to meet the experimental edge jump value of 0.32 (See Appendix A). Hence, the newly obtained structure is identified as a trilayer $\bf{\gamma}^{\prime}$-Fe4N film. An atomic structure expected for the trilayer $\bf{\gamma}^{\prime}$-Fe4N on Cu(001) is presented in Fig. 4(f). The growth without any ion bombardment to the monolayer surface possibly stabilizes the subsurface pure Fe layer, which could promote the formation of the trilayer $\bf{\gamma}^{\prime}$-Fe4N film in a large area.

Finally, let us mention another growth method of the $\bf{\gamma}^{\prime}$-Fe4N film. We previously report a possible layer-by-layer growth of the $\bf{\gamma}^{\prime}$-Fe4N atomic layers on Cu(001), by the N*+* ion bombardment with a relatively low energy of 0.15 kV Takagi et al. (2010). This soft implantation of N*+* ions successfully avoids extra damage to the existing $\bf{\gamma}^{\prime}$-Fe4N structures during the repetition of the growth cycles. The reported different electronic/magnetic states could then originate from the difference in the fabrication processes. Another finding is that, in the current study, only the monolayer and trilayer $\bf{\gamma}^{\prime}$-Fe4N could be obtained in a continuous film form. This implies that an Fe2N-layer termination would be preferable through the present methods, possibly due to the metastability of an interface between Cu and pure Fe layers Detzel and Memmel (1994); Memmel and Detzel (1994); Shen et al. (1995); Bayreuther et al. (1993).

III.3 Electronic and magnetic properties of $\bf{\gamma}^{\prime}$-Fe4N atomic layers

The surface electronic structures of $\bf{\gamma}^{\prime}$-Fe4N showed large dependence on the sample thickness. Figure 5 displays experimental d$I$/d$V$ spectra measured on the surfaces of the trilayer and monolayer $\bf{\gamma}^{\prime}$-Fe4N. The peaks located at $V_{\rm s}\sim$ +0.20, +0.55, and +0.80 V, mainly originating from the unoccupied states in the down-spin band characteristic of Fe local density of states (LDOS), are observed for both the trilayer and monolayer surfaces. A significant difference between the spectra is a dominant peak located around $V_{\rm s}=-50\ {\rm mV}$ observed only for the trilayer surface. This peak possibly originates from the LDOS peak located around $E-E_{\rm F}=-0.2\ {\rm eV}$, calculated for the Fe atoms not bonded to N atoms in the subsurface Fe layer [corresponding site of Fe4 shown in Fig. 7(b)]. Because of the $d_{\rm 3z^{2}-r^{2}}$ orbital character, this peak could be dominantly detected in the STS spectrum for the trilayer surface. Thus, the appearance of this additional peak could support the different subsurface structure of the trilayer sample, especially, the existence of the subsurface Fe layer proposed above.

The entire electronic and magnetic properties of the sample, including both surface and subsurface information, were investigated by using XAS and XMCD techniques at the Fe $L_{2,3}\ (2p_{1/2,3/2}\rightarrow 3d)$ absorption edges. Figure 6(a) shows XAS ($\mu_{+},\ \mu_{-}$) and XMCD ($\mu_{+}-\mu_{-}$) spectra under $B=\pm 5\ T$ of the trilayer and monolayer samples in the grazing ($\theta=55^{\circ}$) and normal incidence ($\theta=0^{\circ}$). Here, $\mu_{+}\ (\mu_{-})$ denotes a x-ray absorption spectrum with the photon helicity parallel (antiparallel) to the Fe 3$d$ majority spin, and an incident angle $\theta$ is defined as that between the sample normal and incident x-ray. The trilayer (monolayer) sample was prepared in the same procedure as that shown in Fig. 4(b) [Fig. 1(a)]. It is clear that the XMCD intensity is larger in the trilayer one, indicating an enhancement of magnetic moments with increasing thickness.

For a further quantitative analysis on the magnetic moments, we applied XMCD sum rules Carra et al. (1993); Thole et al. (1992) to the obtained spectra and estimated spin ($M_{\rm spin}$) and orbital ($M_{\rm orb}$) magnetic moments separately. Note that the average number of 3$d$ holes ($n_{\rm hole}$) of 3.2 was used in the sum-rule analysis, which was estimated by comparing the area of the experimental XAS spectra with that of a reference spectrum of bcc Fe/Cu(001) ($n_{\rm hole}=3.4$) Chen et al. (1995). The thickness dependence of the $M_{\rm spin}$ and $M_{\rm orb}$ values is summarized in Fig. 6(b). The value of $M_{\rm spin}$ increases monotonously with increasing the Fe $L$-edge jump value, namely, an average sample thickness, and finally saturates at $\sim 1.4\ \mu_{\rm B}$/atom in the trilayer sample (corresponding edge jump value of 0.32). The change in $M_{\rm orb}$ is not so systematic relative to $M_{\rm spin}$, however, the $M_{\rm orb}$ values seem to be enhanced in the grazing incidence. This implies an in-plane easy magnetization of the $\bf{\gamma}^{\prime}$-Fe4N atomic layers on Cu(001), also consistent with the previous reports on the $\bf{\gamma}^{\prime}$-Fe4N thin films on Cu(001) Gallego et al. (2004a); Takagi et al. (2010). Figure 6(c) shows magnetization curves of the monolayer sample, whose intensity corresponds to the $L_{3}$-peak XAS intensity normalized to the $L_{2}$ one. The curve recorded in the normal incidence shows negligible remanent magnetization. On the other hand, that in the grazing one draws a rectangular hysteresis loop, which confirms the in-plane easy magnetization. The coercivity of the monolayer sample is estimated to be $\sim$ 0.05 T at 8.0 K, larger than $\sim$ 0.01 T for 5 ML Fe/Cu(001) Li et al. (1994), $\sim$ 1 mT for 5 ML Fe/GaAs(100)-(4$\times$6) Xu et al. (1998) and the 30 nm thick $\bf{\gamma}^{\prime}$-Fe4N film Gallego et al. (2004a) at RT.

III.4 Theoretical analysis on the electronic and

magnetic states of $\bf{\gamma}^{\prime}$-Fe4N atomic layers on Cu(001)

The observed thickness dependence of the magnetic moments can be well understood with a help of first-principles calculations. Figures 7(a) and 7(b) show layer-resolved DOS of the monolayer and trilayer $\bf{\gamma}^{\prime}$-Fe4N on Cu(001), respectively. Here, non-equivalent Fe sites in each layer are distinguished by different numbering. In particular, the Fe atoms at the Fe3 (Fe4) site in the trilayer $\bf{\gamma}^{\prime}$-Fe4N correspond to those with (without) a bond to N atoms 333The difference of DOS between (Fe1, Fe2) in the monolayer $\bf{\gamma}^{\prime}$-Fe4N, (Fe1, Fe2) and (Fe5, Fe6) in the trilayer one is just a switch of the orbital assignment between $d_{\rm yz}$ and $d_{\rm zx}$. Therefore, the DOS of Fe2 in the monolayer $\bf{\gamma}^{\prime}$-Fe4N, Fe2 and Fe6 in the trilayer one is not presented here.. In Table 1, calculated values of an atomic magnetic moment $M_{\rm atom}$, corresponding to $M_{\rm{spin}}$ + $M_{\rm{orb}}$ along the easy magnetization direction, are also listed. In the monolayer case, the calculated $M_{\rm atom}$ is 1.1 $\mu_{\rm B}$/atom, which is in perfect agreement with the experimental value. This supports an ideal atomic structure of our monolayer sample.

Interestingly, the value of $M_{\rm atom}$ for the Fe atoms in the monolayer $\bf{\gamma}^{\prime}$-Fe4N is more than 1.5 times smaller than that in the topmost layer of the trilayer one (1.83 $\mu_{\rm B}$/atom). In comparison with the DOS shown at the top of Fig. 7(b), the impact of the hybridization with the Cu states on the Fe DOS can be seen in Fig. 7(a): First, the DOS in the up-spin band, especially with $d_{\rm 3z^{2}-r^{2}}$ and $d_{\rm yz}$ orbitals, becomes to have a tail toward a higher-energy side across the $E_{\rm F}$. This change deviates the 3$d$ electrons in the up-spin band from a fully-occupied nature. Moreover, the spin asymmetry of the occupied 3$d$ electrons, the difference between the electron occupation into each spin band normalized by the sum of them, reduces especially for the DOS with $d_{\rm xy}$, $d_{\rm 3z^{2}-r^{2}}$ and $d_{\rm yz}$ orbitals. These changes could decrease $M_{\rm spin}$ of the Fe atoms. Note that the similar reduction in the magnetic moments of 3$d$ TMs due to the hybridization with Cu states is reported, for example, in Ref. Tersoff and Falicov, 1982; Hjortstam et al., 1996.

Then, by comparing two different Fe2N interfaces with the Cu substrate, it turns out that $M_{\rm atom}$ of the monolayer $\bf{\gamma}^{\prime}$-Fe4N (1.1 $\mu_{\rm B}$/atom) is almost twice compared to that of the trilayer one (0.62 $\mu_{\rm B}$/atom). In the monolayer case, the Fe2N layer faces to a vacuum and the Fe atoms are under reduced atomic coordination. This results in the narrower band width, and thus the DOS intensity increases in the vicinity of $E_{\rm F}$. Accordingly, a larger exchange splitting can be possible and the spin asymmetry of the occupied 3$d$ electrons increases as shown in Fig. 7(a), compared to the interfacial Fe2N layer of the trilayer $\bf{\gamma}^{\prime}$-Fe4N [bottom panel of Fig. 7(b)]. This leads to larger magnetic moments at the surface. As a result, the competition between the enhancement at the surface and the decrease at the interface would make $M_{\rm atom}$ values quite layer-sensitive.

In the subsurface Fe layer of the trilayer $\bf{\gamma}^{\prime}$-Fe4N, the value of $M_{\rm atom}$ becomes largest due to the bulk coordination of the Fe atoms. Especially the Fe atoms not bonded to the N ones possess $M_{\rm atom}$ of 3.0 $\mu_{\rm B}$/atom, which is comparable to the values of Fe atoms at the same site in the bulk $\bf{\gamma}^{\prime}$-Fe4N Frazer (1958). Consequently, by averaging the layer-by-layer $M_{\rm atom}$ values of the trilayer $\bf{\gamma}^{\prime}$-Fe4N, the total magnetic moment detected in the XMCD measurement is expected to be 1.7 $\mu_{\rm B}$/Fe, with the electron escape depth taken into account (See Appendix A). Considering the composition expected to the trilayer sample, this value can well explain the experimental one of $\sim$ 1.5 $\mu_{\rm B}$/Fe.

The theory also demonstrates the direction of an easy magnetization axis. The in-plane easy magnetization of our $\bf{\gamma}^{\prime}$-Fe4N samples was confirmed by the magnetization curves as well as the incidence dependence of the $M_{\rm orb}$ value. In contrast, the pristine ultrathin Fe films, which form either fct or fcc structures on Cu(001), show uncompensated out-of-plane spins over a few surface layers Pescia et al. (1987); Meyerheim et al. (2009). This shift of magnetic anisotropy by nitridation can be understood from the orbital-resolved Fe DOS shown in Figs. 7(a) and 7(b). Unlike the pure Fe/Cu(001) system Lorenz and Hafner (1996), the occupation of 3$d$ electrons in states with out-of-plane-oriented orbitals ($d_{\rm yz},\ d_{\rm zx},\ d_{\rm 3z^{2}-r^{2}}$) is considerably larger than that with in-plane-oriented ones ($d_{\rm xy},\ d_{\rm x^{2}-y^{2}}$). This could make $M_{\rm orb}$ prefer to align within a film plane, resulting in the in-plane magnetization of the system Bruno (1989).

IV Summary

In conclusion, we have conducted a detailed study on the growth, electronic and magnetic properties of the $\bf{\gamma}^{\prime}$-Fe4N atomic layers on Cu(001). The ordered trilayer film of $\bf{\gamma}^{\prime}$-Fe4N can be prepared by the Fe deposition under N2 atmosphere onto the existing monolayer surface. On the other hand, the repetition of the growth cycles including the high-energy N*+* ion implantation resulted in the imperfect bilayer $\bf{\gamma}^{\prime}$-Fe4N. The STM and STS observations revealed the change in the surface topography and electronic structures with increasing the sample thickness. The XAS and XMCD measurements also showed the thickness dependence of the spectra, and the corresponding evolution of the $M_{\rm spin}$ values. All the thickness dependence of the electronic and magnetic properties is well explained by the layer-resolved DOS calculated using the first principles. Structural perfection of the system makes it possible to fully comprehend the layer-by-layer electronic/magnetic states of the $\bf{\gamma}^{\prime}$-Fe4N atomic layers.

V Acknowledgement

This work was partly supported by the JSPS Grant-in-Aid for Young Scientists (A), Grant No. 16H05963, for Scientific Research (B), Grant No. 26287061, the Hoso Bunka Foundation, Shimadzu Science Foundation, Iketani Science and Technology Foundation, and Nanotechnology Platform Program (Molecule and Material Synthesis) of the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan. Y. Takahashi was supported by the Grant-in-Aid for JSPS Fellows and the Program for Leading Graduate Schools (MERIT). A.E. acknowledges funding by the German Research Foundation (DFG Grants No. ER 340/4-1).

Appendix A Conversion of XAS edge jump values to the thickness of $\bf{\gamma}^{\prime}$-Fe4N

The escape probability of electrons from inside a sample to a vacuum depends on the depth at which the electrons are excited. For a numerical interpretation of the XAS edge jump, the following factors should be mainly considered in principle: the penetration length of an incident x-ray ($\lambda_{x}$) and electron escape depth ($\lambda_{e}$), both energy-dependent. In the case of a few atomic layers of 3$d$ transition metals, the attenuation of the incident x-ray intensity is almost negligible because $\lambda_{x}$ is orders of magnitude longer than the sample thickness Nakajima et al. (1999). Therefore, in the present case, only the electron escape probability at the depth $z$ from the surface, namely, a factor of $\exp{(-z/\lambda_{e})}$ is taken into account. As for the $\lambda_{e}$ value of Fe, 17 Å was tentatively assumed in our analysis, which is experimentally determined for Fe thin films Nakajima et al. (1999). Then, based on the experimental Fe (N) edge jump values of 0.12 (0.015), those for the full-coverage dot-like bilayer, trilayer, and quadlayer $\bf{\gamma}^{\prime}$-Fe4N on Cu(001) are calculated as summarized in Table 2.