Magnetic Behaviour of RM 5 Intermetallic Compounds where R is a Rare- - PowerPoint PPT Presentation

Magnetic Behaviour of RM 5 Intermetallic Compounds where R is a Rare- Earth and M=Ni or Co E.Burzo Faculty of Physics, Babes-Bolyai University Cluj-Napoca, Romania 1. Technical Applications RNi 5 – hydrogen storage RCo 5 – permanent magnets 2. Crystal structure 3. Magnetic properties RNi 5-x Cu x (R = La, Nd) RNi 5-x Al x (R = La,Dy) Gd x La 1-x Ni 5 4. Band structure calculations 5. R5d, Y4d band polarizations 6. Critical field for appearance of Ni ordered moment

Band structures NdNi 5 M Ni (3g)=0.24 µ B , M Ni (2c)=0.17 µ B Different local environments Ni(2c):6Ni(3g); 3Ni(2c); 3Nd Ni(3g):4Ni(3g); 4Ni(2c); 4Nd Ni moments induced by the presence of Nd Magnetic moments of Nd and Ni parallely oriented M Nd M Ni NdNi 5-x Cu x x ≥ 1 M Ni decrease with Cu content M Ni (3g)=0.006 µ B ; M Ni (2c)=0.06 x = 1 x = 2 M Ni (3g)=0.04 µ B ; M Ni (2c)=0.03 µ B High delocalized Ni states

Gd 3 Ni 15 Gd 2 LaNi 15 GdLa 2 Ni 15

Gd x La 1-x Ni 5 •Magnetic data general information on induced moments M Ni =0 LaNi 5 at 1.7 K M s =6.2 µ B /f.u. GdNi 5 at 1.7 K M Gd =7.0 µ B ; M Ni ≅ 0.17 µ B •Band structure calculations - gradual shift of Ni(2c), Ni(3g) spin up and down bands (exchange splitting) - induced moments: Gd(5d); La(5d); Ni(2c); Ni(3g) M Ni (3g)>M Ni (2c) - mean Ni moments depend on E exch : E exch,cr ≅ 0.03 eV - magnetic moments per formula unit agree with experimental data

Brilouin zone for RNi 5 -structure

Band structure and bonding LaNi 5 , GdNi 5 Analysis method •in terms of projections of the bands onto orthogonal orbitals •“fat” band representation: each band is given a width proportional to the (sum of the) weight(s) of corresponding orthonormal orbital(s) •local coordinate system: Ni(2c), Ni(3g), R=La,Gd(1a) z -axis || c -axis for all sites Ni(2c) x-axis along shortest Ni(2c)-Ni(2c) distance Ni(3g) y-axis || a -axis La site d dominant 5d-5d interactions between orbitals with lobs − 3 z 1 2 pointed along c → decorated (fat) bands . The bands strongly dispersed in K- Γ , Γ -A directions

LaNi 5 La La 5d xy 5 d − 3 z 1 2 La La 5d xz 5d yz

Ni2c site LaNi 5 d xy orbitals create “fat” bands at -1eV GdNi 5 d xy ( ↓ ) orbitals create “fat” bands near E F d xy ( ↑ ) orbitals create “fat” bands at ≅ 0.4 eV above E F Ni3g site LaNi 5 d “fat” bands in particular are formed at the Fermi level for − 3 z 1 2 d orbitals along A-L direction and orbitals along Γ -A direction − x 2 y 2 GdNi 5 d “fat” bands are created at the Fermi level for ( ↓ ) orbitals along A-L − 3 z 1 2 d direction and at 0.4 eV above E F for ( ↑ ) orbitals along A-L − 3 z 1 2 direction. For ( ↓ ) orbitals “fat” bands are formed at E F along Γ -A direction d − x y 2 2 and at 0.4 eV above E F for ( ↑ ) orbitals along Γ -A direction d − x y 2 2 Important interactions are between almost all projected orbitals of nickel

LaNi 5 Ni(2c) Ni(2c) 3d xz 3d xy Ni(2c) Ni(3g) 3 d − x y 2 2 3d yz

GdNi 5 Ni(2c) Ni(2c) ( ↓ ) 3 d − 3 z 1 2 ( ↑ ) 3 d − 3 z 1 2 Ni(2c) Ni(2c) 3d xz ( ↑ ) 3d xz ( ↓ )

LaNi 5 Ni(3g) Ni(3g) 3 d − 3 z 1 2 3 d − x y 2 2 Ni(3g) 3d xz

GdNi 5 Ni(3g) Ni(3g) 3 d ( ↓ ) ( ↑ ) 3 d − 3 z 1 2 − 3 z 1 2 Ni(3g) Ni(3g) 3d xz ( ↓ ) 3d xz ( ↑ )

GdNi 5 Ni(2c) Ni(3g) 3 d ( ↓ ) ( ↑ ) 3 d − x 2 y 2 − x y 2 2

The exchange interactions between nickel atoms were also computed by using the LDA+U approach. Using the Green function method to calculate the effective exchange interaction parameter, J ij , as second derivative of the ground state energy with respect to the magnetic rotation angle, was shown that the exchange interactions between i and j atoms may be described by: = J I i χ ij I j ∑ ij mm' mm' m" m" ' m" m" ' (2) {m} where the spin dependent potentials, I i , are expressed in terms of the single ↑ − = ↓ V : I i V i V i particle potential , while the effective inter-sublattice mm' mm' mm' mm' susceptibilities, χ ij , where defined in terms of the LDA+U eigen functions Ψ as: − n n = ij ↑ ↓ ilm * ilm" ilm' jlm"'* χ ψ ψ ψ ψ nk n' k ∑ (3) − mm' m" m"' ↑ ↑ ↓ ↓ nk nk n' k nk ε ε knn' ↑ ↓ nk n' k We denoted by n i the orbital occupancy of d electrons, l the orbital quantum number and m the magnetic quantum number.

GdNi 5 GdLa 2 Ni 15

YCo 4-x Ni x B

RA 5 A=Co, Ni α ’=1.4·10 -2 µ B M 5d =M 5d (0)+ α ’G M 5d (0) =0.32 Co =0.08 Ni β ’=1·10 -2 µ B Co M 3d =M 3d (0)+ β ’G =1.6·10 -2 µ B Ni M 5d (0)/M 3d (0)=0.045 RCo 4 B, RA 5 2 2 = + H J S ( 0 ) S J S S ∑ ∑ ∑ − − 3 d 5 d 5 d 5 d 5 d 5 d 5 d = = i 1 n 3 d , n i 1 i i i ⇓ ∆ ∝ ∝ M ( 0 ) H n M ∑ 5 d exch i i i c

Critical field for appearance an ordered Ni moment: • magnetic measurements Hc=35 T • band structures Hc=48 T

Thank you very much for your attentions.