First-Principles Simulation of Nd2Fe14B/Nd-Rich Phases
D. Hirai1, Y. Tatetsu1, H. Misawa1, Y. Gohda1, S. Tsuneyuki1,2, T. Ozaki3
1

Department of Physics, The University of Tokyo
The Institute for Solid State Physics
3
Japan Advanced Institute of Science and Technology
2emperature dependence
Introduction

Numerical Results

・Nd2Fe14B/Nd4O (VASP simulation) • Nd2Fe14B: √2×√2; Nd4O: √5×√5• Lattice mismatch: 1.2%

The ideal coercivity 〜 7.7T

Before structure optimization

Density of states for d-orbital of Fe
DOS (arb. unit)

・Critical problem of Nd-Fe-B sintered magnet

Very small coercivity: Hc 〜 1.2T

Dy doping → Hc〜 3 T
After structureoptimization
821

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

FeB

0-8

Problems in terms of elements
strategy and physics

Dyfcc is keptc axis

• Elements strategy: Dy should not be used
• Physics: Why Hc is so small and what determines Hc ?
Sepehri-Amin et al. / Acta Materialia 60 (2012) 819–830
・Grain H.boundaryis important for enhancing coercivity

821

Abundant NdDOS (arb. unit)By K. Hono

Ndbulk
2.44μB

-6-4-202468interface
2.64μB0• The electronic states in the bulk andat the interface are drasticallydifferent• Spin moment is large at the interface-8-6-4-202

Energy (eV)468・Order-N simulation of Nd2Fe14B (OpenMX simulation)
Confirmation of accuracy of O(N) calculation

κ(Nd Fe B) < κ(Dy Fe B)
214Hc = 1.2T
H. S.-Amin et al., Acta Materialia 60, 819 (2012).

chemical accuracyµs (µB /atom)

14E (hartree/atom)

2Hc = 0.8T

0.01

0.001

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.

Clear Nd-rich grain boundary is made by annealing

Coercivity Hc becomes higher

0.0001223302398

0.000011000 1200 1400 1600 1800 2000

4 /34

0.1

0.01

223302398

average # ofatoms in acluster

1000 1200 1400 1600 1800 2000
Y. Gohda
UUKKObjective• The chemical accuracy is accomplished even for small UK.
Understanding of coercivity
microscopically: to clarify the electronicFig. 2. High-magnification SEM BSE images from Nd-rich phases in (a) as-sintered and (b) annealed sample. Two types
contrasts areobserved
from• ofWhenthenumberof atoms in a cluster is small, the accuracy widely fluctuates
the Nd-rich phase grains at the triple junctions.
structures in grain/GB interface
with increasing UK.

Simulation Methods

3.2. Atom probe analysis results of grain boundaries

・Electronic structure calculation: density functional theory

ages of (a and c) as-sintered sample, (b and d) annealed sample. (e) Intensity profile from the selected boxes in (c and d). The peakurves was normalized with the intensity• from the brightly imaged Nd-rich phase grains.

VASP code:

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

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

Plane wave basis• PAW method• GGA-PBE exchange correlation functionalDOS (arb. unit)

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

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

0• GGA+U method for 4f orbitals in Nd (U = 6eV)

• 4f orbitals of Nd in the core for structure optimization
・Large scale simulation
OpenMX code: • Optimized pseudo-atomic orbital basis• Pseudopotential method• GGA-PBE exchange correlation functional• GGA+U method for 4f orbitals in Nd (U = 6eV)
• Krylov-subspacecation SEM BSE images from Nd-rich phasesin (a) as-sintered and (b) annealed
sample. Twotypes of contrasts are observed fromorder-N
methodOriginal spaceple. On the other hand, the greyly
ch phase shows a uniform contrast in the. These diﬀerences will be explained intion 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 assintered sample. Fig. 3a shows the RE = (Nd + Pr) atombasis: |W0 ) = (|i1 , |i2 , · · · , |iMi )Krylov subspacebasis: UK = {|W0 ), A|W0 ), A2 |W0 ), · · · , Aq |W0 )}A = (S (i) ) 1 H (i)14Memory size (GB)ains at the triple junctions.

12BandKrylovFutureApplication to large-scale systems:
Nd2Fe14B/Nd-rich phase

bandO(N)-10-50

Energy (eV)510Summary
Electronic 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 totallydifferent from those in the bulk
Order-N calculation on Nd2Fe14B• The Krylov-subspace method can reach the chemical accuracy bysignificantly smaller computational cost than conventional dividedconquer methods• We determined appropriate parameters such as the cluster size and theKrylov dimension, for Nd2Fe14B/Nd-rich phase simulations

1086512 nodes (MPI+OpenMP)@京4400 420 440 460 480 500 520 540 560

Number of atoms in the supercell

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