Supplementary Information

Electronic structure and magnetic anisotropy of L10-FePt thin film studied by hard

x-ray photoemission spectroscopy and first-principles calculations

S. Ueda, M. Mizuguchi, Y. Miura, J. G. Kang, M. Shirai, K. Takanashi

In this supplementary section, we would like to show the orbital projected density of

states (PDOS) and total DOS for L10-FePt obtained from the first-principles

generalized-gradient approximation (GGA) calculations and the effect of the Fe 3d

electron correlation in L10-FePt to the PDOS, total DOS, and cross-section weighted

DOS (CSW-DOS) obtained from the GGA+U calculations. We also show the

contribution to the perpendicular magneto-crystalline anisotropy (MCA) in L10-FePt

from the nonvanishing matrix elements of angular momentum operator for the Pt 5d

orbitals.

First-principles calculations for L10 ordered FePt

Figure S1 shows a schematic diagram of the atomic arrangement in L10-FePt. The red

and blue circles correspond to the Fe and Pt atoms, respectively. The primitive

tetragonal cell indicated by the solid lines was adapted in the first-principles GGA

calculations. Solid arrows in the figure indicate the definition of the x, y, and z-axes in

the calculations. In ordered to obtain the density of states (DOS) and magneto-

crystalline energy of L10-FePt, we have performed the first-principles calculations using

Vienna ab initio simulation package (VASP) [S1, S2]. The nuclei and core electrons are

described by the projector augmented plane-wave potential [S3, S4], and the wave

functions are expanded in a plane-waves basis set with a cutoff energy of 337.3eV. In

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the calculations, we have adopted the primitive tetragonal structures as the unit cell of

L10-FePt as shown in Fig. S1 and the experimental lattice parameters of L10-FePt, which

are a = 3.864 Å and c/a = 0.965. The Brillouinzone integration has been done with a

modified tetrahedron method with Blöchl corrections [S5] on the uniform 30 × 30 × 22

mesh. For the exchange and correlation energy, we have adopted the spin-polarized

GGA with the Perdew-Becke-Ernzerhof parameterization [S6].

Fig. S1: Schematic diagram of the atomic arrangement in L10-FePt.

Projected, total and cross-section weighted DOSs for L10-FePt obtained from the

first-principles GGA calculation

Fig. S2 shows the spin-resolved PDOSs for the Fe and Pt atoms and total DOS for

L10-FePt obtained from the first-principles GGA calculation. For comparison, cross-

section weighted DOS (CSW-DOS) for 6 keV is also shown to simulate the valence

band (VB) hard X-ray photoemission spectrum for the L10 ordered FePt film. In the

figure, CSW-DOS was broadened by a Lorentian function (FWHM varying ~ 0.2

(EEF) eV), then multiplied by the Fermi-Dirac function at 300K, and finally convoluted

by a Gaussian function (FWHM = 0.15 eV). We note that the experimental geometry

and X-ray polarization are taken into account to estimate the per electron cross-section

according to the Refs. [S7, S8]. As expected from the symmetry of the L10 ordered

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structure, the lifting of degeneracy in the Fe 3d orbitals is clearly seen in Fig. S2 as well

as the Pt 5d orbitals, while the dyz and dzx orbitals are degenerated.

Fig. S2: Spin-resolved PDOSs and total DOS for L10-FePt obtained form the GGA calculation. CSW-

DOS is also shown in order to compare with the experimental VB spectrum for the L10 ordered FePt thin

film.

Effect of the Fe 3d electron correlation in L10-FePt to the projected, total, and

cross-section weighted DOSs obtained from the GGA+U calculations

In order to qualitatively understand the electron correlation effect in the Fe 3d states in

the VB region, the spin-polarized GGA +U method [S9] has been used to account for

on-site correlation at the transition-metal sites. This method accounts for orbital

dependence of the Coulomb and exchange interaction, which is absent in the GGA

method. Figures. S3 and S4 show the results of the GGA+U calculations with U = 1

and 2 eV. For comparison, CSW-DOSs, which were broadened in the same sequence as

mentioned above, for 6 keV are also shown. In the CSW-DOS profiles, the structure

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located at around 1 eV shifts to the higher binding energy (EB) side with increasing U.

The Fe 3d states shift to the higher EB side due to the larger exchange splitting of the Fe

3d states under the presence of U in the GGA+U calculations. Therefore the Pt 5dyz and

5dzx states, which strongly hybridize with the Fe 3dyz and 3dzx states, also shift to the

higher EB side and contribute to the structure located at around 2 eV. One may think

that the use of larger U in the GGA+U calculations gives better CSW-DOS profile for

reproducing the experimental VB spectrum. However, the introducing of U in the

calculations gives the unreasonable enhancement of the Fe 3d magnetic moment in L10-

FePt. Thus we used the results of the GGA+U calculations as a guide to qualitatively

understand the electronic structure of L10-FePt with the electron correlation in the Fe 3d

states.

Fig. S3: Spin-resolved PDOSs and total DOS for L10 ordered FePt obtained form the GGA+U (U=1 eV)

calculation. CSW-DOS is also shown in order to compare with the experimental VB HAXPES spectrum

for the L10 ordered FePt thin film.

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Fig. S4: Spin-resolved PDOSs and total DOS for L10 ordered FePt obtained form the GGA+U (U=2 eV)

calculation. CSW-DOS is also shown in order to compare with the experimental VB HAXPES spectrum

for the L10 ordered FePt thin film.

Contribution to the perpendicular MCA in L10-FePt obtained from the non-

vanishing angular momentum matrix elements connecting the Pt 5d orbitals

Figure S5 shows the second-order perturbative contribution to the total energy of

nonvanishing angular momentum matrix elements connecting Pt 5d states to obtain

further understanding of the origin of the perpendicular MCA. For example, red (blue)

bar-graph of <x2-y2↑|Lx|xy> indicates that the matrix elements of Lx between the

occupied minority-spin (majority-spin) Pt 5dxy state and the unoccupied majority-spin Pt

5dx2-y

2 state. We found that the large matrix elements, which are the main contributing

factor for the perpendicular MCA, of the spin conservation (flip) term connecting Pt

5dxy (Pt 5d3z2-r

2 and Pt 5dyz) in L10-FePt. Details of the calculation were described in Ref.

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[S10].

Fig. S5: Non-vanishing matrix elements of angular momentum operators Lx and Lz between the occupied

and unoccupied states of the Pt 5d orbitals in L10-FePt. The positive (negative) value indicates the

perpendicular (in-plane) contribution to the MCA.

References

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Furthmüller, Phys. Rev. B 54, 11169 (1996).

[S3] P. E. Blöchl, Phys. Rev. B 50, 17953 (1994).

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[S5] P. E. Blöchl, O. Jepson, and O. K. Andersen, Phys. Rev. B 49, 16223 (1994).

[S6] J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996).[S7] J. H. Scofield, Lawrence Livemore Laboratory, Tech. Rep. UCRL -51326 (1973).[S8] M.B. Trazhaskovskkaya, V.I. Nefedov, and V.G. Yarzhemsky, Atomic Data Nucl.

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[S10] Y. Miura, S. Ozaki, Y. Kuwahara, M. Tsujikawa, K. Abe, and M. Shirai, J. Phys.:

Condens. Matter 25, 106005 (2013).

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