2.1.3 Figures .1 Cerium
2.1.3.3 Neodymium
1 (8+1/3)×
7 1×
A sites B sites C sites
a a
a
a*
a*
a*
3 2
1
2
3 1
Nd
Nd
a b
Fig. 8. Single layer moment patterns of double-q structure of dhcp Nd: (a) from q1 and q2; (b) from q3 and q4 .The moments associated with q1 and q2 are on
"hexagonal" layer and those with q3 and q4 are on the cubic layer, respectively of the dhcp lattice [89F].
Fig. 7. Projection of all atoms in the dhcp lattice on a single hexagonal plane. Cubic A sites and hexagonal B and C sites are shown. The hold parallelograms indicate the 7x1 and 1x(8+1/3) commensurate magnetic unit cells, respectively. Also shown are the real (ai, i = 1, 2, 3) and the reciprocal lattice unit vectors (ai*, i = 1, 2, 3). If the crystal structure dominates the formation of the incipient magnetic order a commensurate modulated magnetic structure would be described by vector that connects hexagonal sites only. This is illustrated by the 7x1 magnetic unit cell. As the temperature is lowered the order on the hexagonal sites induces a moment on the cubic sites. The magnetic structure to be commensurate would be as is illustrated in figure where the 1x(8+1/3) magnetic unit cell corresponds to (qx,qy) = (3/25,0) [94L].
∗
∗
Nd
q2
q1
q2 q3
q1
q4
µ
µ µ1
µ1
µ2 µ2
3
4
a
b
Fig. 9. Basal plane projections of modulation vectors, moment amplitudes, and the corresponding diffraction pattern around a nuclear Bragg point (*) in Nd. (a) for the 2-q structure and (b) for the 4-q structure. Full circles result from the arrows shown, and solid circles arise from domain averaging [97G].
q2 q2
q1 q1
q1
q1
q2 q2
q3
q3
q3 q3
q3 q1
q1 q4
Nd
µ0H= 0 µ0H= 0.8 T
µ0H= 2.5 T
µ0H= 3.6 T µ0H= 4.7 T µ0H= 3.0 T
Fig. 10. Schematic representation of the wave vectors associated with the various magnetic phases of Nd at T ≈ 1.8 K. The arrow indi- cates the direction of the applied magnetic field [91Z].
Nd
TN= 19.95 K T2= 19.1 K
T5= 6.3 K T3= 8.2 K
Fig. 11. Schematic representation of the magnetic satellite reflections observed around (100) at various temperatures and zero applied magnetic field in Nd metal. The solid and open circles denote the hexagonal and cubic satellites, respectively [91Z].
Wavevector / *q ay
Wavevector / *q ay
Neutron intensity [counts/min] Neutron intensity [counts/min]
Nd
70
50
30
T= 18.27 K T= 18.27 K
18.62
18.62 1- 1-
, , ,0) ,0) q q
0 q
x x
( x
(
50
30
30
30 40
40
40 50
50 40
18.82 18.82
19.10 19.10
19.33 K
19.33
−0.010
−0.010 0
0 0.010
0.010 a
b 1500 1000
1000
1000 500
500
500
500
500
500
500 0
0
0
0
0
0
0 0 200
19.70
19.90 20.05 K
18.0
18.5
19.0
19.5
20.0
Temperature[K]T
30
1000
Fig. 13. Temperature evolution of the magnetic satellites near the (100) reciprocal lattice point measured on heating in Nd. The data show the transition from the
single-q state near TN to the two-q state appearing below TN≈ 9.1 K [94L].
Wavevector/*qa1yWavevector/*qa1y
Wavevectorq a1x/ * 0.010
0.010 0.008
0.008 0.006
0.006 0.004
0.004 0.002
0.002 0
0
T5
T5 T5
T5 T4
T4 T3
T3
T2
T2 heating
cooling
Nd
a
b
3/283/28 3/263/26 3/253/25 1/81/8 1/71/7
Temperature[K]T
Pressure [kbar]p 25
20
15
10
5
0 2 4 6 8 10 12 14 16
P
cubic site F
Nd
hex.site 1- AFq
hex.site 2- AFq
hex.and cubic site AF,3- and 4-q q
hex.site
2- AFq cubic site F, hex.site
2- AFq
cubic site F, hex.site 1- AFq
Fig. 12. Basal plane components of the modulation vector describing the magnetic structure in pure Nd metal. The q1y component is shown as function of the q1x component in Nd metal. The temperature is an implicit parameter for both axes and T2 corresponds to (q1x, q1y) = (1/7, 0). The numbers against the dashed lines indicate the commensurate values of q1x. The tran- sition temperatures TN and T2 - T5 correspond approxi- mately to 19.3, 17.9, 10.5, 7.7, and 6.3 K on heating and to 19.1, 17.9, 8.7, 6.8, and 5.2 K on cooling. (a) and (b) correspond to heating and cooling, respectively. The stars correspond to (qx, qy) calculated for the higher- order commensurate structures [94L].
Fig. 14. Magnetic phase diagram of Nd under pressure.
Where hexagonal or cubic sites are not mentioned they are disordered [96W2].
Temperature [K]T Magnetic field[T]µ0HMagnetic field[T]µ0H
12
12 10
10 8
8 6
6 4
4 2
2 0
00 2 4 6 8 10 12 14 16 18 20
Nd
H aIIH bII
P
P multi - domain double -q
multi - domain double -q single -q
single -q quadruple -q
quadruple -q
single - domain double -q
single - domain double -q a
b
Squared magnetic field (µ0H) [ T ]2 2 Néel temperature[K]TN
0 40 80 120 140
20 19 18 17 16 15 14
Nd
H aII
H bII
Fig. 15. (a) Magnetic phase diagram of Nd, measured with the magnetic field along the a axis, (b) with the magnetic field along the b axis. Data are taken from thermal expansion (solid circles) and magnetostriction (open circles) ex- periments, respectively [91Z].
Fig. 16.TN vs. H2 for magnetic fields along the a and b axes of Nd [91Z].
Temperature [K]T
Thermal expansion/[10]∆ll−5
80
60
40
20
0
−2
−4
4 6 8 10
Nd
H aII µ0H= 3.5 T2.5 T
1.43 T 0.23 T
0 T3
T3
T5 T4 T3
T3 T6 T5 T4
Fig. 17. Thermal expansion of Nd, measured along thea axis, at H = 0.0, 0.23, 1.43, 2.5, and 3.5 T. Note the change of scale for H > 0 [91Z].
Temperature [K]T
Thermal expansion/[10]∆ll−5
80
60
40
20
0
−2
−4
4 6 8 10
Nd
H bII2.5 T
1.43 T
0.23 T
0 T3
T3
T5
T6 T3
T3
T3 T6 T5 T4 T3
0.66 T µ0H= 3.5 T
T4
Fig. 18. Thermal expansion of Nd, measured along theb axis, at H= 0, 0.23, 0.66, 1.43, 2.5, and 3.5 T.
Note the change of scale for H > 0.23 T [91Z].
Nd
H aII
Magnetic fieldµ0H[T]
Magnetostriction/[10]∆ll−4
32
24
16
8
0 1 2 3 4 5
1 3
1’ 2 1’
1’
1’
1’
1’
1
1
1 2
3 2
2
2 2
3 3 3 2
T= 8.5 K 7.5 6.5 6.0
5.0 4.2
1.1 K 1
1 1
3
3
5.5 1 2
Fig. 19. Magnetostriction of Nd, measured in increasing field along the a axis, for various temperatures. Average values of the magnetic fields indicated by arrows are
(1) 1.15 T; (2) 2.2 T; (3) 3.2 T; (4) 4.4 T [91Z].
Nd
H bII
Magnetic fieldµ0H[T]
Magnetostriction/[10]∆ll−4
32
24
16
8
0 1 2 3 4 5
1
3
2’
1’
1’
1’
1’ 1
1
1 1
2
3 2
2
2’
3 3 3
3
2’
T= 9.2 K 7.6 6.5 6.0 5.0 4.2
1.0 K 1
3 2’
4 4
4 4
4 2.5 1
2
3 1’
1
Fig. 20. Magnetostriction of Nd, measured in increasing field along the b axis, for various temperatures. Average values of the magnetic fields indicated by arrows are
(1) 1.15 T; (2) 2.2 T; (3) 3.2 T; (4) 4.4 T [91Z].
Intensity (relative)
Photon energy [keV]E 102
10
1
10−1
10−2
6.19 6.20 6.21 6.22 6.23
Nd
Fig. 21. High resolution magnetic X-ray diffraction of antiferromagnetic ordering in the neodymium metal, near the LII and LIII absorption edges. The vertical line indicates the positions of the absorption edges in zero magnetic field [96W].
Temperature [K]T Magnetic moment[]pNdBµ
0.04
0.03
0.02
0.01
0 10 20 30 40 50
Nd
H= 500 Oe200 Oe 100 Oe
Fig. 22. Zero-field cooled magnetization of the 582 nm Nd film with the field along the (100) easy axis. The anomaly near 27 K is associated with the Néel point, which is significantly higher than in bulk Nd; the peak near 8 K arises from cubic-site ordering [97E].
Temperature [K]T Magnetic moment[]pNdBµ
0.24 0.20 0.16 0.12 0.08 0.04 0
−0.04
0 10 20 30 40 50 60 70 80
FC
ZFC
Nd
TN= 32 K
H= 500 Oe 200 Oe 100 Oe
Fig. 23. Field-cooled and zero-field cooled data on a [Nd (3.2 nm)/Y (2 nm)]120 superlattice. The Néel tem- perature extrapolated to a zero-field has 32 K, much above the bulk value of 19.9 K [97E].
Magnetic moment[]pNd,hexBµ
Nd concentration 2.5
2.0
1.5
1.0
0.5
00.4 0.5 0.6 0.7 0.8 0.9
Nd/Y
helical order bulk-like orderFig. 25. Magnetic moment per hexagonal site associated with helimagnetic order and the moment per atom associated with bulk-like order of hexagonal sites vs. the Nd concentration in the Nd/Y superlattices. The Nd atoms are in the dhcp structure in all samples [97E].
Temperature [K]T Magnetic moment[]pNdBµMagnetic moment[]pNdBµ
0.8
0.6
0.4
0.2
0 2.0
1.6
1.2
0.8
0.4
0 10 20 30 40 50
[Nd (3.9 nm) / Y (3.9 nm)]109 [Nd (8.7 nm) / Y (2.4 nm)]80
[Nd (4.2 nm) / Y (12 nm)]90 [Nd (3.2 nm) / Y (2 nm)]120 Nd0.62 0.38Y alloy
Fig. 24. Temperature dependence of the magnetic moment per Nd atom (hexagonal and cubic sites) that orders in the helimagnetic structure for several Nd/Y superlattices and the alloy sample. The temperatures at which this component vanishes agree semiquantita- tively with the Néel temperatures from the magnet- ization data [97E].