This is the submitted version of the article: Cuadrado R., Liu K., Klemmer T.J., Chantrell R.W.. In-plane/out-of-plane disorder influence on the magnetic anisotropy of Fe1- yMnyPt-L10 bulk alloy. Applied Physics Letters, (2016). 108. 123102: - . 10.1063/1.4944534. Available at: https://dx.doi.org/10.1063/1.4944534 In–plane/out–of–plane disorder influence on the magnetic anisotropy of Fe1−y Mny Pt–L10 bulk alloy R. Cuadrado,1,2 Kai Liu,3 Timothy J. Klemmer,4 and R. W. Chantrell1 1 Department of Physics, University of York, York YO10 5DD, United Kingdom 2 Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and The Barcelona Institute of Science and Technology, Campus UAB, Bellaterra, 08193 Barcelona, Spain 3 Physics Department, University of California, Davis, California 95616, USA 4 Seagate Technology, Fremont, California, 94538, USA (Dated: March 7, 2016) The random substitution of a non–magnetic species instead of Fe atoms in FePt–L10 bulk alloy will permit to tune the magnetic anisotropy energy of this material. We have performed by means of first principles calculations a study of Fe1−y Mny Pt–L10 (y=0.0, 0.08, 0.12, 0.17, 0.22 and 0.25) bulk alloy for a fixed Pt concentration when the Mn species have ferro–/antiferromagnetic (FM,AFM) alignment at the same(different) atomic plane(s). This substitution will promote several in–plane lattice values for a fixed amount of Mn. Charge hybridization will change compared to the FePt– L10 bulk due to this lattice variation leading to a site resolved magnetic moment modification. We demonstrate that this translates into a total magnetic anisotropy reduction for the AFM phase and an enhancement for the FM alignment. Several geometric configurations were taken into account for a fixed Mn concentration because of different possible Mn positions in the simulation cell. The FePt–L10 bulk alloy possesses a high value of mag- late the doping and MAE with the loss of the individual netocrystalline anisotropy energy (MAE) [1–3] and hence in–plane/out–of–plane value compared to the L10 struc- is a promising candidate for next generation ultrahigh ture. Cheng–Jun Sun et al, [15] through their proposed density magnetic recording media. The large MAE allows model based on directional short range order (DSRO) to overcome the superparamagnetic limit [4–6]. Given predicted the decrease of the ordering parameter with that high anisotropy media are likely to require Heat As- increasing Mn doping and hence the structural evolu- sisted Magnetic Recording to overcome the write field tion as a function of y concentration. To deal with this requirement, the low Curie temperature of FePt is a fur- complex system the ferromagnetic (FM) and antiferro- ther advantage. However, in the manufacturing process, magnetic (AFM) phases of FeMnPt–L10 between differ- the media must be annealed to transform a face–centered ent Mn planes have to be studied. We will present a cubic (f cc) A1 initial phase into an L10 highly chemically comprehensive analysis of the local range order (LRO) ordered alloy. As was pointed out in some recent experi- of Fe1−y Mny Pt–L10 (y=0.0, 0.08, 0.12, 0.17, 0.22 and mental and theoretical works, [7–12], introducing into the 0.25) bulk alloy having several different geometric con- FePt–L10 alloy magnetic or non–magnetic species such as figurations per fixed Mn:Fe ratio. In the present work, Ni, Mn or Cu, respectively, permits the reduction of TC the self–consistent ionic relaxation would not lead in an and control of the MAE values as the Fe concentration usual chemical disorder structure since the final geome- decreases. tries maintain the same atomic arrangement in space. Initial motivation for the experimental studies was pro- We note that in this case, the calculation of the chemical vided by model calculations of Sakuma [13] who inves- order parameter was not useful because of the bond dis- tigated the magnetic properties of FePt with different tances –key values that characterize S– are only slightly levels of band filling nef f using a fixed band structure different compared to the real disordered material, lead- model. However, experimental studies [8, 9, 11, 12, 14] ing to a S value of 1 for all the studied configurations. achieve variations in nef f using substitution of Fe sites We make a direct comparison with theoretical [7, 13] and with impurity atoms such as Ni, Mn, Co, Cr or Cu. experimental [8, 9, 15, 16] works on Mn doping, obtaining Recently [7] we showed that the alloying process itself good qualitative agreement after factoring in the temper- produces variations in atomic structure and consequent ature variation. changes in band structure which strongly affect the MAE We have performed density functional theory (DFT) and saturation magnetization leading to important differ- calculations of Fe1−y Mny Pt–L10 alloys with the SIESTA ences with the fixed band structure approach. package [17] using norm–conserving pseudopotentials Previously we studied the substitution of the Fe species for the core electrons and the generalized gradient ap- by Cr, Mn, Co, Ni, or Cu in FePt–L10 bulk alloys keep- proximation (GGA) for the exchange–correlation energy. ing the Pt concentration fixed [7]. Here we pursue the MAE is defined as the difference in the total energy be- effects of the magnetic ordering and also study the vari- tween hard and easy magnetization directions and it has ation of the anisotropy of bulk FePt–L10 via the substi- been obtained using a fully relativistic (FR) implementa- tution of Fe atoms by diluted Mn, with concentrations tion [20] in the GREEN [21] code employing the SIESTA much lower than in [7], while keeping Pt fixed. We corre- framework. 2 two mechanisms: the atomic rearrangement of the species after the ionic relaxation and the subsequent selfconsis- tent electronic configuration. The charge transferred be- tween different species will tend to fill the d states, mak- ing the structures more energetically stable. In our case, as the Mn concentration changes, the EF M -EAF M values are not constant, having two different ranges: ∼0.22 eV for y ≦ 0.12% and ∼0.5 eV when y ≧ 0.17%. The evolution of the lattice parameters a and c/a as a function of the Mn concentration is shown in Fig. 2 (right). Due to the Mn substitution, after relax- ation, the FePt–L10 stacking exhibited in–plane and out– of–plane distortions promoting a set of different in–plane lattice parameters for each geometric configuration and FIG. 1. (Left) Schematic picture of the FePt–L10 unit cell and its characteristic lattice values: a and c/a. Notice that one c/a value for each. In general, both FM and AFM–1 the in–plane diagonal of the unit cell phases follow the same trend as found in previous stud- √ corresponds to the lat- tice constant whilst the edge is a/ 2; (Right) Top view of ies [7, 16]: as the Mn concentration in FePt–L10 bulk FePt–L10 structure. A, B and C depict three different in– increases, a tends to increase and conversely the out–of– plane lattices with 8, 9 and 12 Fe atoms (z=0) and the same plane c/a decreases. There is however small discrepancies number of Pt atoms at z=cF eP t /2. The in–plane lattice vec- in a and c/a trends for larger concentrations between FM tors employed for each A, B and C supercell sizes are depicted and AFM–1 phases, mainly due to the rearrangement of by vi . the valence charge during the ionic optimizations process, leading to more energetically stable structures as well as different bonding distances. On the right side of the figure 1 is shown the schematic Site resolved magnetic moment (MM) values for in–plane view of three different supercell sizes with 8, 9 FM and AFM–1/–2 phase configurations exhibit dif- and 12 total number of Fe atoms, marked by A, B and ferent trends as the Mn y concentration changes in C, respectively. We replaced two or four Fe atoms on Fe1−y Mny Pt–L10 alloy, left and right columns in figure 3, these different supercells, depending on the desired level respectively. Pt MMs change significantly for the AFM of doping, by two or four Mn. Mn was randomly posi- phases, having constant values for FM coupling. This tioned locally within each of the Fe planes and we only is consistent with the origin of the Pt moment resulting applied the constraint that half of the Mn atoms were from the Weiss field from the magnetic sublattice [23], on each Fe plane. The number of possible different geo- which is clearly reduced by the AFM coupling of the Mn metric configurations for such systems is quite extensive. atoms. With increasing Mn concentration both types of However, due to the high symmetry of the simulation su- assumed magnetic order (FM and AFM) present differ- percell we took into account all the necessary geometric ent trends: when Mn atoms are FM aligned the MMMn configurations for each y in order to cover, locally, an increases, whereas if the Mn spins are AFM aligned the accurate prediction of their magnetic properties. MMMn reduce their net values. Consistent with the role We present a detailed study of the structural relax- of the Fe being to polarize the non-magnetic spins, it is ation and magnetic properties of Mn–doped FePt. As clear for the FM case that, Fe atoms polarize the non– demonstrated previously, the lowest energy configuration magnetic atoms whilst they do not do so for the AFM for Fe1−y Mny Pt–L10 alloys corresponds to an antiferro- case, as in bulk FePt–L10 alloy the Fe species do for Pt magnetic (AFM) alignment of the Mn atoms between atoms (at zero Mn concentration). different atomic planes [7, 22]. Consequently we carried Thus the proposal of Mryasov et. al. [23] that the out a survey of both FM and AFM phases, imposing the non–magnetic atoms are directly polarized by the Weiss magnetic constraint on the Mn species. However in the field from the Fe seems appropriate on introduction of present work and since the simulation supercell is bigger, the Mn impurity atoms. This also allows conjectures re- there is a possibility to have another AF aligment of the lating to the effects of the Mn doping on the MAE. Fol- Mn atoms at the same plane. From now on we will des- lowing Mryasov’s theory and the theoretical predictions ignate the antiparallel aligment with Mn out-of-plane as of Sawatzky et al [24], we are able to propose two mech- AFM–1 and that within the same plane AFM–2. anisms related to the polarization of the non–magnetic Figure 2 (middle) shows the average total energy values species in the MAE values, which will both affect the for a fixed Mn concentration (y) when its spins are FM, MAE. On the one hand, the MMP t reduction will pro- AFM–1 or AFM–2 coupled. It is clear that the AFM mote lower Fe–Pt–Fe indirect exchange between the out– phases have lower energy values than FM ones. This of–plane Fe species, and on the other the Mn concen- result agrees with previous theoretical works [22]. Phys- tration will induce similar behavior for the direct Fe–Fe ically, we can argue that the energy differences between exchange interaction, leading to a reduction of the total FM, AFM–1 and AFM–2 configurations is mainly due to magnetic anisotropy of the alloy as we will see in figure 4. 3 FIG. 2. (Left) Side view of the magnetic aligment between atoms. (Middle) Total energy comparison between ferromag- netic (filled green squares) and antiferromagnetic (empty turquoise squares and invested triangles) phases as the Mn concen- tration changes from 0.00% up to 0.25%. Each value has been calculated as an average value of several configurations for a fixed Mn concentration as it is shown in the text. The zero energy, E0i , has set to the minimum value of the energy between all the configurations. The straight lines are guide to the eye. (Right) In–plane lattice constant a (blue dots) and out–of–plane parameter c/a (red triangles) as a function of the y concentration in Fe1−y Mny Pt bulk phases. Blue and red dashed lines depict the experimental dependence of a and c/a as shown in the work of Meyer et al. [16]. The influence of the Fe substitution with non–magnetic tively. As pointed out in [7], each configuration pro- impurities in the FePt–L10 bulk alloy promotes changes duces a unique band structure, leading to variations in in its magnetization M and in the total magnetic the MAE as represented by the dispersion of the data anisotropy, increasing for the FM aligment and con- shown in Figure 4. It can be seen that there is a linear versely decreasing for the AFM phases, as shown in the increase (decrease) with the Mn concentration for the first and second rows in Figure 4 (left/central), respec- FM(AFM) configurations. However the decrease is more marked for the AFM configurations, for which there is also a rapid decrease of the magnetization values with y. The increase(decrease) of the MAE with the Mn con- centration in FM(AFM) structures is a consequence of the change in the electronic structure and hence in the magnetic interactions between different magnetic/non– magnetic atoms. As was pointed out earlier, the physical mechanism to explain the behavior of the MAE in L10 alloys is through direct and indirect exchange interac- tions between in–plane (Fe–Fe) and out-of-plane (Fe–Pt– Fe) neighbors, respectively. So in the AFM cases, there are two complementary ways to explain the reduction in MAE: 1) the reduction in the MMP t minimizing the out– of–plane indirect exchange interaction and 2) the reduc- tion of the in–plane magnetic interactions due to the fact that the Mn concentration acting as a“magnetic barrier” between Fe species. Specifically for a fixed amount of Mny in FePt, the dispersion in the MAE changes. Phys- ically, the Mn atoms are located at different Fe sites for each geometric configuration, this will imply the possi- bility to have not only one in–plane lattice parameter FIG. 3. Magnetic moment values per atom as a function of as in FePt–L10 but several ai depending on whether we the Mn concentration y. On the left column is depicted the have one or more Mn atoms at the same plane. In fig- FM configurations and on the right those AFM–1/–2. As ure 4 (right) is shown the in–plane lattice distribution explained along the text, the MM has been calculated as an function (LDF) that presents the localization of ai val- average of all the configurations for each concentration. From ues around the FePt bulk. For example, in FM/AFM– top to bottom is shown the non–magnetic species, Pt and Mn, Fe0.78 Mn0.22 Pt (blue dots) the dispersion in the values is red empty squares and green empty triangles, respectively. 30 meV and inspecting the solid blue line on the right The site resolved Fe MM values are presented in the last row by empty blue squares. Black dots present the Pt, Mn and the ai values are between 3.8Å and 4.1Å, conversely, for Fe MM values for AFM–2 configuration. y=0.12% (green triangles) the dispersion is smaller and 4 FIG. 4. (Left) Magnetization as a function of the Mn impurities concentration for the FM and AFM–1/–2 aligments. (Middle) Magnetic anisotropy energy (MAE) values as a function of the Mn concentration y for FM and AFM–1/–2 phases, top and bottom rows, respectively. Each set of the same symbols show different MAE values for a fixed amount of Mn. The addi- tional AFM–2 points are depicted inside black boxes besides their AFM–1 counterparts (Right) In–plane lattice distribution function (LDF) for FM and AFM–1 configurations. Same colors are used for each concentration–LDF. Vertical turquoise line depicts the FePt–L10 bulk lattice constant. The solid and dashed lines in the Magnetization and MAE graphs depict the experimental results obtained by Meyer et al. [16] and those from theory by Suzuki et al. [14], respectively. only three main ai peaks localized at 3.82Å, 3.94Å and tion with increasing Mn doping, albeit with an over– 4.05Å are depicted. estimated value. Again, this is most likely related to Finally in Fig. 4, we make a direct comparison with the effects of temperature, coupled with the reduction of the experimental data of Mn–doped FePt of Meyer et. Tc . Mryasov et. al. [23], using an atomistic model, show al. [16]. At the outset we note that the ab initio calcula- that thermal effects lower the MAE by approximately tions are zero K values, whereas the experimental values a factor of 2, which would bring the theoretical predic- are 300K measurements. This of course leads to a satura- tions reasonably close to the experimental values at low tion in the magnetization M and the MAE. In the latter Mn doping. However, the thermal reduction in the MAE case we note that the MAE as measured is a free energy value would be strongly exacerbated by the reduction in difference, the reduction with temperature arises from Tc with increasing Mn doping, consistent with the results spin fluctuations rather than a change in the MAE at shown in Fig. 4. the atomic level. Consider first the saturation magneti- We have carried out a DFT based study of zation. At low concentration the agreement is good, with Fe1−y Mny Pt–L10 bulk phase for y=0.08, 0.12, 0.17, 0.22 the ab initio calculations increasingly under–estimating and 0.25 in their FM and AFM phases. The calculations M under increasing Mn concentration. Here we propose were carried out by creating the specific alloy structures an explanation of this based on the temperature variation rather than relying on a fixed band structure model. Due of M . The pure FePt–L10 phase has a sufficently high to the Mn substitution, the FePt–L10 alloy exhibited a Curie temperature that the reduction in M from the zero set of different in–plane lattice parmeters and one out– K prediction is rather small, consistent with the results of–plane value for each configuration. These geometri- shown in Fig.4. It is likely that the discrepancy between cal changes promote electronic rearrangement and sig- the predicted and experimental M values arises because nificantly alter the magnetic behavior. From this point of a reduction of Tc with Mn doping. Although the calcu- of view, average Fe magnetic moments increase in a sim- lation of the temperature variation of M , requiring values ilar way for both FM and AFM configurations. However of the exchange constant J, is beyond the scope of the non–magnetic species exhibit different trends with the current work, Gilbert et. al. [9] demonstrate experimen- assumed Mn alignment. tally a rapid reduction of Tc with Cu doping, similarly A detailed comparison with the experiments of Meyer to the present work. Given that the measurements were et. al. [16] was also made. In general the calculated val- made at a constant temperature of 300K, the reduction ues showed qualitative agreement with the trend of the of Tc would result in a decrease of the measured M , con- experimental values with increasing Mn concentration. sistent with the increasing divergence, with increasing Even though the predictions over–estimated the exper- Mn doping, of the calculated and measured M values in imental values, it is clear that the AFM phase exhibits Fig. 4. fairly good agreements with experiments, while the FM Regarding the MAE, the calculated values for the AF phase shows the opposite trend. It was argued that this ordered phase correctly exhibit the experimental reduc- enhancement is a result of the temperature reduction of 5 the MAE. FEMTOSPIN is gratefully acknowledged. K.L. acknowl- The authors are grateful to Prof. Chih-Huang Lai for edges support from the US-NSF (DMR-1543582) and the helpful discussions. Financial support of the EU Sev- France–Berkeley Fund. enth Framework Programme under Grant No. 281043, [1] D. Weller and A. Moser, IEEE Trans. Magn., 36, 10 109, 07B739 (2011). (1999). [13] Akimasa Sakuma, J. Phys. Jap. 63, 3053 (1994) [2] C.J. Aas, P.J. Hasnip, R. Cuadrado, E.M. Plotnikova, [14] Takao Suzuki, Hiroshi Kanazawa, and Akimasa Sakuma, L. Szunyogh, L. Udvardi, R.W. Chantrell, Phys. Rev. B, IEEE Trans. Mag. 38, 0018 (2002) 88, 174409, (2013). [15] Cheng-Jun Sun, Dongbin Xu, Steve M. Heald, Jingsheng [3] R. Cuadrado and R.W. Chantrell, Phys. Rev. B, 89, Chen, and Gan-Moog Chow, Phys. Rev. B 84, 140408(R) 094407, (2014). (2011) [4] R. Cuadrado and R. W. Chantrell, Phys. Rev. B 86, [16] Gereon Meyer, and Jan–Ulrich Thiele, Phys. Rev. B 73, 224415 (2012). 214438 (2006). [5] P. Gambardella, S. Rusponi, M. Veronese, S. S. Dhesi, [17] J.M. Soler, E. Artacho, J.D. Gale, A. Garcı́a, J. Jun- C. Grazioli, A. Dallmeyer, I. Cabria, R. Zeller, P. H. quera, P. Ordejón and D. Sánchez-Portal, J. Phys.: Con- Dededrich, K. Kern, C. Carbone, and H. Brune, Science dens. Matter, 14, 2745, (2002). 300, 1130 (2003). [18] J. P. Perdew, K. Burke and M. Ernzerhof, Phys. Rev. [6] D. Weller, O. Mosendz, G. Parker, S. Pisana, and T. S. Lett., 77, 3865, (1996). Santos, Phys. Status Solidi A 210, 1245 (2013). [19] E. Artacho, D. Sánchez-Portal, P. Ordejón, A. Garcı́a, [7] R. Cuadrado, Timothy J. Klemmer, and R. W. Chantrell, and J. M. Soler, Phys. Status Solidi B 215, 809 (1999). Appl. Phys. Lett., 105, 152406, (2014). [20] R. Cuadrado and J. I. Cerdá, J. Phys.: Condens. Matter [8] D. B. Xu, J. S. Chen, T. J. Zhou, and G. M. Chow, Appl. 24, 086005 (2012). Phys. Lett. 109, 07B747 (2011). [21] J.I. Cerdá, M.A. Van Hove, P. Sautet, M. Salmerón, [9] Dustin A. Gilbert, Liang-Wei Wang, Timothy J. Klem- Phys. Rev. B, 56, 15885, (1997). mer, Jan-Ulrich Thiele, Chih-Huang Lai, and Kai Liu, [22] Zhihong Lu, Roman V. Chepulskii, and W. H. Butler, Appl. Phys. Lett. 102, 132406 (2013) Phys. Rev. B 81, 094437 (2010) [10] D. A. Gilbert, J. W. Liao, L. W. Wang, J. W. Lau, T. [23] O.N Mryasov, U. Nowak, K.Y. Guslienko and J. Klemmer, J. U. Thiele, C. H. Lai, and K. Liu, APL R.W. Chantrell, Europhysics Letters 69, 805 (2005). Mater. 2, 086106 (2014). [24] G.A., Sawatzky, W. Geertsma and C. Haas, J. Mag. Mag. [11] B. Wang, K. Barmak, and T. J. Klemmer, IEEE Trans. Mat. 3, 37 (1976). Magn. 46, 1773 (2010). [12] B.Wang, K. Barmak, and T. J. Klemmer, J. Appl. Phys.