Apr. 5, 2013 /34 Y. Gohda

temperature dependence

4

Fe B Nd Dy

κ(Nd2Fe14B) < κ(Dy2Fe14B)�

D. Hirai1, Y. Tatetsu1, H. Misawa1, Y. Gohda1, S. Tsuneyuki1,2, T. Ozaki3 1Department of Physics, The University of Tokyo 2The Institute for Solid State Physics 3Japan Advanced Institute of Science and Technology

Introduction

Simulation Methods

Numerical Results

SummaryElectronic states in Nd2Fe14B/Nd4O • After the structure optimization, the fcc structure of Nd4O is kept • The interface electronic states and spin moment of Fe are totally

different from those in the bulk

・Grain boundary is important for enhancing coercivity

・Nd2Fe14B/Nd4O (VASP simulation)

This work was supported by the Elements Strategy Initiative Center for Magnetic Materials under the outsourcing project of MEXT. Calculations were partly performed on the K-computer (Grant No. hp120086) and the supercomputers at the Institute for Solid States Physics.

Acknowledgements

First-Principles Simulation of Nd2Fe14B/Nd-Rich Phases

H. S.-Amin et al., Acta Materialia 60, 819 (2012).

・Critical problem of Nd-Fe-B sintered magnet

By K. Hono

Very small coercivity: Hc ～ 1.2T

The ideal coercivity ～ 7.7T

Dy doping → Hc～ 3 T

• Elements strategy: Dy should not be used • Physics: Why Hc is so small and what determines Hc ?

as-sintered sample. On the other hand, the greylycontrasted Nd-rich phase shows a uniform contrast in theannealed sample. These differences will be explained inthe following section based on the 3DAP results.

3.2. Atom probe analysis results of grain boundaries

Fig. 3 shows the 3DAP result from a GB in the as-sintered sample. Fig. 3a shows the RE = (Nd + Pr) atom

Fig. 1. SEM BSE images of (a and c) as-sintered sample, (b and d) annealed sample. (e) Intensity profile from the selected boxes in (c and d). The peakintensity of the two curves was normalized with the intensity from the brightly imaged Nd-rich phase grains.

Fig. 2. High-magnification SEM BSE images from Nd-rich phases in (a) as-sintered and (b) annealed sample. Two types of contrasts are observed fromthe Nd-rich phase grains at the triple junctions.

H. Sepehri-Amin et al. / Acta Materialia 60 (2012) 819–830 821

as-sintered sample. On the other hand, the greylycontrasted Nd-rich phase shows a uniform contrast in theannealed sample. These differences will be explained inthe following section based on the 3DAP results.

3.2. Atom probe analysis results of grain boundaries

Fig. 3 shows the 3DAP result from a GB in the as-sintered sample. Fig. 3a shows the RE = (Nd + Pr) atom

Fig. 1. SEM BSE images of (a and c) as-sintered sample, (b and d) annealed sample. (e) Intensity profile from the selected boxes in (c and d). The peakintensity of the two curves was normalized with the intensity from the brightly imaged Nd-rich phase grains.

Fig. 2. High-magnification SEM BSE images from Nd-rich phases in (a) as-sintered and (b) annealed sample. Two types of contrasts are observed fromthe Nd-rich phase grains at the triple junctions.

H. Sepehri-Amin et al. / Acta Materialia 60 (2012) 819–830 821

Hc = 0.8T Hc = 1.2T

Clear Nd-rich grain boundary is made by annealing

Coercivity Hc becomes higher

ObjectiveUnderstanding of coercivity microscopically: to clarify the electronic

structures in grain/GB interface

Problems in terms of elements strategy and physics

・Electronic structure calculation: density functional theoryVASP code: • Plane wave basis

• PAW method • GGA-PBE exchange correlation functional • GGA+U method for 4f orbitals in Nd (U = 6eV) • 4f orbitals of Nd in the core for structure optimization

・Large scale simulationOpenMX code: • Optimized pseudo-atomic orbital basis

• Pseudopotential method • GGA-PBE exchange correlation functional • GGA+U method for 4f orbitals in Nd (U = 6eV) • Krylov-subspace order-N method

Original space

Krylov subspace

Abundant Nd

|W0) = (|i1�, |i2�, · · · , |iMi�)basis:

UK = {|W0), A|W0), A2|W0), · · · , Aq|W0)}A = (S(i))�1H(i)

basis:

Before structure optimization

After structure optimization

・Order-N simulation of Nd2Fe14B (OpenMX simulation)

•Nd2Fe14B: √2×√2; Nd4O: √5×√5 •Lattice mismatch: 1.2%

1000 1200 1400 1600 1800 2000

0.01

0.1

223302398

1000 1200 1400 1600 1800 20000.00001

0.0001

0.001

0.01

223302398

UK UK

�E

(har

tree

/ato

m)

�µ

s(µ

B/a

tom

)

Confirmation of accuracy of O(N) calculation

-10 -5 0 5 10

DO

S(a

rb.un

it)

Energy (eV)

Density of states: band calculation vs. O(N) calculation

fcc is kept

-8 -6 -4 -2 0 2 4 6 8

-8 -6 -4 -2 0 2 4 6 8

DO

S(a

rb.un

it)

Energy (eV)

0

DO

S(a

rb.un

it)

0

bulk

interface

Density of states for d-orbital of Fe

2.44μB

2.64μB

• The chemical accuracy is accomplished even for small UK. • When the number of atoms in a cluster is small, the accuracy widely fluctuates

with increasing UK.

• The electronic states in the bulk and at the interface are drastically different

• Spin moment is large at the interface

The density of states is reproduced using the information in O(N) simulation0

band O(N)

Application to large-scale systems: Nd2Fe14B/Nd-rich phase

Order-N calculation on Nd2Fe14B • The Krylov-subspace method can reach the chemical accuracy by

significantly smaller computational cost than conventional divided-conquer methods

• We determined appropriate parameters such as the cluster size and the Krylov dimension, for Nd2Fe14B/Nd-rich phase simulations

c axis

average # of atoms in a cluster

chemical accuracy

Future

400 420 440 460 480 500 520 540 560

4

6

8

10

12

14BandKrylov

Number of atoms in the supercell

Mem

ory

size

(GB

)

512 nodes (MPI+OpenMP)@京