Perpendicular magnetic anisotropy in Co x Mn 4 − x N ( x = 0 and 0 . 2 ) epitaxial films and possibility of tetragonal Mn 4 N phase

We grow 25-nm-thick Mn4N and Co0.2Mn3.8N epitaxial films on SrTiO3(001) by molecular beam epitaxy. These films show the tetragonal structure with a tetragonal axial ratio c/a of approximately 0.99. Their magnetic properties are measured at 300 K, and perpendicular magnetic anisotropy is confirmed in both films. There is a tendency that as the Co composition increases, an anisotropy field increases, whereas saturation magnetization and uniaxial magnetic anisotropy energy decrease. First-principles calculation predicts the existence of tetragonal Mn4N phase. This explains the c/a ∼ 0.99 in the Mn4N films regardless of their film thickness and lattice mismatch with substrates used.


I. INTRODUCTION
To realize high-performance magnetic recording devices and spintronics devices, extensive search has been conducted on ferromagnetic materials possessing outstanding features such as a large spin polarization and perpendicular magnetic anisotropy (PMA).][5][6][7][8][9][10][11][12] Mn 4 N is one of the anti-perovskite ferrimagnetic nitrides, and PMA was reported for films grown on glass, 13 Si(001), 14 MgO(001), [15][16][17][18][19] and SrTiO 3 (STO)(001) 16 substrates.Figure 1 shows the lattice structure of Mn 4 N.One N atom is located at body center and Mn atoms are located at corner (I) site and face-centered (II) site of the cube. 3Mn 4 N bulk has a lattice constant of a 0 = 0.387 nm, and is ferrimagnetic metal (M S = 182 emu/cm 3 at 77 K) with the Curie temperature of 745 K. 3 The magnetic moments of Mn atoms were evaluated to be 3.85 µ B at I sites and −0.90 µ B at II sites from the neutron diffraction measurement at 77 K, 3 where µ B is the Bohr magneton.For Mn 4 N thin films in Refs.15-19, the in-plane lattice constant (a) and perpendicular lattice constant (c) were evaluated by x-ray diffraction (XRD), and the tetragonal structure (c/a ∼ 0.99) was reported regardless of layer thickness and substrate used.6][17][18][19] However, c/a ∼ 0.99 and PMA were reported even in the Mn 4 N film on MgO(001), in which misfit dislocations were observed immediately above the interface between the film and the substrate. 17The lattice mismatch between them is −8.2%.It is reasonable to consider that tensile strain is not likely to remain in such films.Thus, the origin of the observed tetragonal Mn 4 N films is an open question.In addition, despite a number of studies on anti-perovskite nitrides so far, there have been no reports on magnetic properties of single crystalline Co x Mn 4−x N films.In this study, we evaluated the c/a ratio, electrical resistivity (ρ), M S , and uniaxial magnetic anisotropy energy (K u ) in approximately 25-nm-thick Mn 4 N and Co 0.2 Mn 3.8 N epitaxial thin films grown on STO(001) substrates by molecular beam epitaxy (MBE).Our objective is to clarify the effect of Co substitution for Mn site on the magnetic properties of Mn 4 N.In addition, we investigated the possibility of tetragonal Mn 4 N phase using the first-principles calculation.

II. EXPERIMENTS AND CALCULATION
We grew approximately 25-nm-thick Mn 4 N and Co 0.2 Mn 3.8 N epitaxial films on STO(001) substrates at 450 o C by MBE using solid sources of Co and Mn, and radio-frequency N plasma.The details of growth procedure are described in Ref. 16.The sample structures are Al/Mn 4 N/STO and Al/Co 0.2 Mn 3.8 N/STO, where 10-nm-thick Al capping layers were deposited to prevent oxidation.We also prepared those without the Al capping layers for resistivity measurement.The crystalline quality of the grown films was characterized by reflection high-energy electron diffraction (RHEED) and out-of-plane (ω-2θ) XRD measurement.c/a of the films was deduced from x-ray reciprocal lattice mapping.We used Rutherford back scattering spectrometry and electron probe microanalyzer measurements to evaluate x in Co x Mn 4−x N. We also measured temperature dependences of ρ at temperatures from 10 to 300 K by four-point probe method.Magnetization versus magnetic field curves were measured by superconducting quantum interference device (SQUID) magnetometer at 300 K. External magnetic field (H) of −50 to 50 kOe was applied parallel and perpendicular to the film surface.To calculate M S per unit volume, the grown layer thickness was determined from x-ray reflectivity and its area was deduced by a top-view photo.Magnetic torque (T) curves were measured at room temperature (RT) under H varied as 7. 5,  9, 12, 15, 17, 19, 21, 23, or 25 kOe, by rotating the electromagnet clockwise (cw) and counterclockwise (ccw).The K u values were deduced by so-called the 45 • -torque method. 20We performed the first-principles calculations on Mn 4 N by using the Bader analysis 21 and the Vienna ab initio simulation package 22 (VASP) with the projected-augment wave pseudopotential 23 and a spin-polarized Perdew-Burke-Ernzerhof generalized gradient approximations and Perdew-Wang exchange-correlation function. 24The convergence in the total electron energy (E tot ) was better than 10 −7 eV/cell using the energy cut off of 400 eV.The k-points sampling of 11 × 11 × 11 were used for the calculation of the charge density with VASP.In the calculation, we assumed two types of Mn 4 N, type A and type B. In type A Mn 4 N, the spin magnetic moment (m spin ) of Mn atoms located at I sites is anti-parallel to that at both IIA and IIB sites.On the other hand, in type B Mn 4 N, the m spin at I sites is parallel to that at IIB sites and anti-parallel to that at IIA sites.We calculated the

III. RESULTS AND DISCUSSION
Epitaxial growth of Mn 4 N and Co 0.2 Mn 3.8 N films was confirmed by c-axis-oriented XRD peaks such as (002) and (004) together with streaky RHEED patterns.Figures 2(a The resistivity ρ of the Mn 4 N and Co 0.2 Mn 3.8 N films decreased with decreasing temperature and became almost constant in the low temperature region.This is a typical behavior in metals.The ρ values at 10 and 300 K were 26 and 164 µΩ•cm in Mn 4 N, and 79 and 166 µΩ•cm in Co 0.2 Mn 3.8 N, respectively.The larger ρ at low temperatures in Co 0.2 Mn 3.8 N than in Mn 4 N is likely caused by alloy scattering due to disordered arrangement of Co and Mn atoms, because ordered structures are probable only when x = 1, 2, or 3 in the Co x Mn 4−x N system.The temperature dependence of ρ was already reported in Mn 4 N films formed on MgO(001) by pulsed laser deposition (PLD) 17 and by MBE. 18The ρ value of the Mn 4 N film in the present work is slightly larger than that in Ref. 17, and is approximately 8 times larger than that in Ref. 18 at 300 K. We think that the difference of N content in the film may affect the magnitude of ρ. to the film in both samples, showing the occurrence of PMA.The anisotropy field (H k ) value of the Co 0.2 Mn 3.8 N films was larger than that of the Mn 4 N film.The M S values of Mn 4 N and Co 0.2 Mn 3.8 N were 80 and 60 emu/cm 3 , respectively, showing that M S was reduced by the slight addition of Co into Mn 4 N.This value is smaller than those already reported such as 145 emu/cm 3 in approximately 30-nm-thick Mn 4 N on STO(001) formed by MBE, 16 and 157 emu/cm 3 in Mn 4 N on MgO(001) grown by PLD. 17 It is reported that the value of M S in Mn 4 N changed depending on N 2 gas supply during the growth. 19We speculate that the N vacancy may affect the M S value in Mn 4 N.In this experiment, we set the total deposition amount of 3d element and N 2 gas flow to be the same for the Mn 4 N and Co 0.2 Mn 3.8 N films.Therefore, the change in M S between the two samples is attributed to the addition of Co.We performed first-principles calculations for CoMn 3 N and found the reason for this M S reduction.The details will be explained elsewhere., normal to the sample surface.These curves exhibit two-hold symmetry because of PMA.The amplitude of the torque curves increases with increasing H, whereas the hysteresis loss observed around θ = 0 • and 180 • is reduced.Since the hysteresis loss is observed even at 25 kOe, H k is greater than 25 kOe in both samples.This result is consistent with the results shown in Fig. 3.The sawtooth-like curves show that the magnetization was not saturated.Since the magnetization direction was not parallel to H, K u values were underestimated when we derived them from the maximum amplitude of the torque curves.Thus, we used the 45 • -torque method to estimate K u from unsaturated magnetic torque curves.Figure 4(c) shows the (T/H) 2 -T plots using the averaging-out absolute values at θ = 45 • , 135 • , 225 • , and 315 • .The M S and K u eff values were obtained from the intersections of the fitting lines with the vertical and horizontal axes, respectively. 20Using the equation K u = K u eff + 2πM S 2 , the K u values were calculated to be 1.0 × 10 6 and 8.9 × 10 5 erg/cm 3 for Mn 4 N and Co 0.2 Mn 3.8 N, respectively.This result shows that the addition of a small amount of Co into Mn 4 N decreased both M S and K u .The obtained K u for Mn 4 N is comparable  to those reported for Mn 4 N on MgO(001) grown by PLD (1.6 × 10 6 erg/cm 3 ) determined from the magnetization measurement, 17 and that grown by sputtering (8.8 × 10 5 erg/cm 3 ) determined from magnetic torque measurement. 19e next discuss the calculation results.Figure 5 shows the E tot versus c/a plots in both type A and B Mn 4 N. Here, E tot was compared with respect to type B Mn 4 N with c/a = 0.98.E tot of type A and B Mn 4 N reached a minimum at c/a = 1.00 and 0.98, respectively, and E tot of type A Mn 4 N are higher than that of type B. This means that the type B Mn 4 N with the tetragonal structure of c/a = 0.98 is predicted to be an energetically stable phase.Table I shows the lattice constants a and c, m spin of each site, and M S in the type A and B Mn 4 N when their E tot 's show a minimum.6][17][18][19] Tetragonal-structured Mn atoms (fct-Mn), possessing the anti-ferromagnetic configuration similar to that of type B Mn 4 N, was confirmed both experimentally (c/a = 0.945) 25 and theoretically (c/a = 0.90). 26It might be possible that intrinsic tetragonal Mn 4 N was realized by the same mechanism as that of fct-Mn described in Ref. 26.On the other hand, the bulk Mn 4 N possesses cubic structure 3 and it seems to be inconsistent with our calculated results.[17][18][19]

IV. CONCLUSION
We grew approximately 25-nm-thick Mn 4 N and Co 0.2 Mn 3.8 N epitaxial thin films on STO(001) substrates by MBE.Both samples showed PMA, and M S values were 80 and 60 emu/cm 3 , Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions.Download to IP: 130.158.56.102On: Mon, 25 Jul 2016 06:01:57 respectively, at 300 K.The ratio c/a ∼ 0.99 was confirmed from the x-ray reciprocal lattice mapping.The K u values determined from the magnetic torque measurement were 1.0 × 10 6 and 8.9 × 10 5 erg/cm 3 , respectively.H k value increased, and both K u and M S values decreased as the Co composition increased.The first-principles calculations suggested that there is the intrinsic tetragonal Mn 4 N.This explains the reason why the c/a ∼ 0.99 was reported in the Mn 4 N films epitaxially grown on MgO(001) and STO(001) substrates regardless of the Mn 4 N film thickness and lattice mismatch on these substrates.
) and 2(b) show the reciprocal lattice mapping of STO(024) and Co x Mn 4−x N(024) (x = 0 and 0.2) spots, respectively.The white dotted line in the figures passes the origin of the reciprocal lattice map and the diffraction spot of STO(024).The diffraction spot of Co x Mn 4−x N(024) is located on the left side of the line in Figs.2(a) and 2(b), meaning the tetragonal structure of the grown layers.The lattice constants (a = 0.389 nm and c = 0.385 nm) and the tetragonal axial ratio of c/a ∼ 0.99 was obtained in both samples.The lattice constants of the Mn 4 N layer was almost the same as those in Ref.16  (a = 0.390 nm and c = 0.386 nm).

Figures 3 (
FIG. 3. Magnetization curves of (a) Mn 4 N and (b) Co 0.2 Mn 3.8 N films.The hysteresis was open when H was applied normal to the sample surface in both cases.

Figures 4 (
a) and 4(b) show torque curves of Mn 4 N and Co 0.2 Mn 3.8 N films measured at RT under various H values. θ is the angle between H and the plane of the film; θ = 0 • means that H is applied in parallel to Co x Mn 4−x N[100], the in-plane direction, and θ = 90 • shows that H is parallel to Co x Mn 4−x N[001]

FIG. 4 .
FIG. 4. Magnetic torque curves of (a) Mn 4 N and (b) Co 0.2 Mn 3.8 N films measured at RT under various H values. (c) (T /H ) 2 versus T plots.

TABLE I .
First-principles calculation results for Mn 4 N.