Magnetic Properties of Low Temperature Phase MnBi of Island Structure

The magnetic and structural properties of island-structured LTP MnBi fabricated onto MgO single crystal substrates are discussed. The size and height of the “Volmer-Weber” type islands vary from place to place but are averagely a few microns and sub-microns, respectively. From the wetting angle (40 ∼ 60°) of those islands, the surface energy ΥMnBi of LTP MnBi is found to be 0.5∼0.8 J/m2. Those MnBi islands possesses the magnetic anisotropy constant Ku and saturation magnetization Ms close to those for bulk over a temperature range of 5 to 400 K. There seems to be a correlation between Ku and lattice constant c measured at 300K. The Ku is found to be inversely proportional to Ms5 over the temperature range from 5 K to 400 K, as compared to the Ms8 dependence for those fabricated onto fused silica glass substrates.


I. INTRODUCTION
Among various high magnetic anisotropy materials such as SmCo 5 and Fe 14 Nd 2 B, the low temperature phase (LTP) MnBi exhibits a significant increase of the uniaxial magnetic anisotropy constant K u with temperature T over a temperature range from about 100K to about 500K, in the order of 10 7 erg/cc for T beyond about 250K. [1][2][3][4][5][6] Therefore, the LTP MnBi is attractive for permanent magnet applications operated at elevated temperatures. Much work has been reported in literature to elucidate both experimentally and theoretically this unique temperature dependence of K u . [2][3][4][5][6] A recent experimental work of the temperature dependence of K u in the LTP MnBi thin films deposited onto silica glass substrates showed that K u was inversely proportional to the 8 th power of the saturation magnetization M s . Such a strong (inversely) dependent K u on M s has not been reported in any other materials up till now. It was also found that the K u was proportional to the unit cell volume. 6 The theory based on first principles calculation of magnetic anisotropy energy as function of lattice constants (a and c) was found to be qualitatively in agreement with the experimental results, but the transition at around T = 100K from the in-plane to the out-of plane direction for the easy axis for magnetization is not accounted for. 4,6 Despite the voluminous works reported, the detailed mechanism for the origin of the magnetic anisotropy is still open to question. Since the magnetic anisotropy is significantly dependent on lattice constants a and c, the present study has been motivated to study the effect of the lattice constant on magnetic anisotropy for the LTP MnBi films by choosing single crystal substrates of MgO with various orientations.

II. EXPERIMENTAL
Multilayers of [Mn (x nm) / Bi (y nm)] × N (x=2, y=1∼8, N=1∼10) were deposited onto MgO (100), (110) and (111) single crystal substrates at an ambient temperature by using a DC magnetron sputtering system. The deposition rates for Bi and Mn were 0.07 nm/s and 0.02 nm/s, respectively. Then, the samples thus fabricated were annealed in vacuum better than 10 −8 Torr at various temperatures T a for times t a . A 5nm thick Ru capping layer was deposited after the annealing.
Measurements of the temperature dependence of magnetic properties were carried out by using a vibrating sample magnetometer in fields up to 9T over a temperature range from 4K to about 400K. The uniaxial magnetic anisotropy constant K u was estimated by torque magnetometer for the out-of-plane mode in fields up to 9T over the temperature range mentioned above. The K u values were obtained by extrapolating the amplitude of the two and four fold symmetry components to an infinite field strength, defining K u as (K u1 + K u2 ), where K u1 and K u2 are the first and second magnetic anisotropy constant in the hexagonal formula, respectively.
The crystal structure of the films thus fabricated was characterized by X-ray diffraction (XRD) with Cu (Kα) and Co (Kα) radiation, by transmission electron microscopy (TEM), and by scanning electron microscopy (SEM), together with energy-dispersive X-ray spectroscopy (EDX).   Figure 1(a), 1(b) and 1(c) show the XRD patterns for the {Mn(2nm)/Bi(3.2nm)x10 }films fabricated (T a and t a were 450 • C and 0.5hr, respectively ) onto MgO (100), (110) and (111) substrates, respectively, together with the result for the silica glass substrates for which T a and t a were 550 • C and 0.5hr, respectively. 7 It is clearly seen that all the samples are of the low temperature phase with the c-axis orientation along the film normal. The lattice constant c for those films is shown in Fig. 1(e). The values of c are 6.073, 6.083, 6.071 and 6.09 A for MgO (100), (110), (111) and fused silica substrate, respectively, which are all smaller than the bulk value (=6.125A) by about 1 %. 8 Figure 2(a) shows the SEM image of the sample-surface of the sample fabricated onto the MgO (100) substrate. The image clearly shows the island structure of the LTP MnBi. Such island structure is also found for other cases of MgO (110) and (111). It is further noted that when the annealing condition changed to T a and t a were 450 • C and 0.5hr for silica glass substrates, a similar island structure was also formed. The size of those islands varies from place to place, but averagely ranges from a sub-micron to several microns. Fig. 2(b) reveals that the islands are of a mountain-like shape with a height of approximately 1 µm, much larger than the nominal thickness for the present multilayer, which is 52 nm.  and O. It is shown that the island has the uniform distribution of Mn and Bi elements, forming the LTP. The atomic contents of Mn and Bi at different positions within the island vary from position to position, but averagely 52.5 and 47.6 at%, respectively, as shown in Fig. 2(d) and 2(e). The result indicates that the LTP phase of MnBi island is of Mn rich phase. It is noted that this morphology is much different from the case for the LTP films deposited onto fused glass substrates at T a = 550 • C for 0.5 hr, where such island structure was not formed, but instead the film structure consisting of both the regions of LTP MnBi and Bi was formed. 6 Figure 2  plane, but the diffraction pattern of MnBi island shows very little evidence for the coherence in orientation. The same phenomenon was observed for the cases of MgO (110) and (111). It is also noted that there is a few nm thick interfacial region between the substrate and MnBi. While the XRD patterns for all the samples exhibit the c-axis orientation along the film normal, those TEM results are at variance with the XRD result. However, this discrepancy between the TEM and XRD analyses is not unusual if there be a dispersion in the c-axis orientation. To clarify the reason for this discrepancy, a more detailed analysis of the c-axis dispersion is in progress. Such an island growth is known as Volmer-Weber growth-model, where a 3D islands formation takes place through a stronger binding of film-atoms to each other than to substrate and/or slow diffusion. 9 In this case, one would not expect any close correlation in crystallographic orientation between the film and the substrate. High resolution images for all the cases of the MgO orientations shows little evidence to support an epitaxial growth in all the cases.

III. RESULTS AND DISCUSSIONS
Surface energy is an important quantity in considering the evolution of microstructure in small-scale material system. One may estimate the surface energy Υ MnBi of the LTP MnBi island by using Young's equation for the wetting angle which is about 40∼60 degree in the present case. By using the surface energy Υ MgO of MgO(100) to be 1.2 J/m 2 and that for the interface surface energy Υ MnBi/MgO between MnBi and MgO(100) to be 0.8 J/m 2 , one obtains Υ MnBi to be 0.5∼0.8 J/m 2 , where the surface energy Υ Bi of Bi is assumed to be 0.4 J/m 2 . 10 Therefore, a so-called spreading parameter S, which is defined as (Υ MgO -Υ MnBi -Υ MnBi/MgO ), is negative (-0.1∼-0.4 J/m 2 ), meaning the island structure is preferable for MnBi onto MgO substrates. Figure 3(a) and 3(b) shows the out-of plane M-H curves at different temperatures from 50 to 400K for the MgO (100) and (110) cases, respectively. All the curves shows a high squareness, except for that measured at 50K for both MgO (100) and (110). Fig. 4 shows the temperature dependence of coercivity H c for both MgO (100) and (110), together with the data for fused silica glass substrate. 6 It is of interest to note that all the films exhibit a very similar dependence of H c on T, drastically increasing for T beyond 150 K and reaching to about 18 kOe at 350 K.   for both the MgO (100) and (110) cases are nearly the same, which are higher than that for the fused silica case by about 30%, but smaller than that for bulk by about 20%. The reason for this smaller M s values than the bulk values are presumably due to the presence of other phases than the LTP, such as Bi, as revealed in the XRD pattern given in Fig. 1(a). Figure 5(b) shows the temperature dependence of magnetic anisotropy constant K u for both the cases of MgO (100) and (110), together with the data for the bulk and the fused silica substrates. The K u values increase almost linearly with T beyond 150 K, reaching to about K u =1.5 x 10 7 erg/cc at about 400 K for the MgO (100) case. It is pointed out that there remains the positive K u values of order of 10 6 erg/cc for T even below 100K for the case of fused silica glass substrate, for which temperatures, the easy axis for magnetization for bulk is in the c-plane. 2 In the inserted figure in Fig. 5, the correlation between K u and lattice constant c at 300K is plotted. As mentioned above, the c values for all the present thin films are smaller by about 1% than that bulk value. It seems there is a trend for K u with lattice constant c, but a further detailed study must be made for better understanding.
As discussed by theories, the magnetic anisotropy constant is more sensitive to lattice constant a than c. 4,6 Since the lattice constant a is not known for those films deposited onto MgO substrates in the present study because of the c-axis orientation along the film normal, one cannot discuss the validity of the theoretical prediction. However, as far as its dependence on lattice constant c goes, the present result seems to suggest the correlation between K u and c, as shown in Fig. 5.
The magnetic anisotropy mechanism has been discussed in terms of the correlation between magnetic anisotropy and saturation magnetization over a wide temperature range. [11][12][13] This information is useful to identify either single ion-model or two ions model predominant, as demonstrated elsewhere. 6,13,14 Figure 6 shows the correlation between K u and M s for the cases of MgO (100) and (110), together with the result for the fused silica substrate 6 and for bulk. 2 It is interesting to note that the correlation is nearly the same for both MgO (100) and (110), inversely proportional to M s 5 . On the other hand, the correlation for the fused silica and bulk cases is inversely proportional to M s 8 , and M s 11 , respectively. 2,6 No theoretical prediction on LTP MnBi has been put forward to account for this correlation as yet.
FIG. 6. The correlation between the magnetic anisotropy constant K u and the saturation magnetization M s for Mg(100), and (110), together with the data for the fused silica glass 6 and bulk. 2 Note that the temperature ranges for MgO, fused silica and bulk are about 100 ∼400K, 150∼400K and 150∼370K, respectively.

IV. SUMMARY
The island-structured LTP MnBi was, for the first time to the authors' knowledge, found to form onto MgO single crystal substrates. From the wetting angle of those island, the surface energy of LTP MnBi is estimated to be 0.5∼0.8 J/m 2 .
The MnBi islands possesses the easy axis for magnetization perpendicular to the substrate plane with the magnetic anisotropy constant K u and saturation magnetization M s close to those for bulk. There seems to be a correlation between K u and lattice constant, c, measured at 300K. The K u is found to be inversely proportional to M s 5 over the temperature range from 5 K to 400 K, as compared to M s 8 dependence for those fabricated onto fused silica glass.