Dysprosium

2.1.3 Figures .1 Cerium

2.1.3.8 Dysprosium

Intensity (relative)Intensity (relative) Intensity (relative)

Wavevector [Å ]q ⁻¹

Wavevector [Å ]q ⁻¹

Dy

H= 0 H= 3 kOe

H= 8 kOe 1200

1000

1000

1000

800

800

800

600

600

600

400

400

400

200

200

200

0

0 6.62 0

6.62

6.64

6.64

6.66

6.66

6.68

6.68

6.70

6.70 spiral

Wavevector [Å ]q ⁻¹

6.62 6.64 6.66 6.68 6.70

ferro

ferro

spiral

a b

c

Fig. 147. Magnetic field dependence of the X-ray dif- fraction pattern of Dy at T = 95 K where the phase tran- sition induced by magnetic field takes place. The (006) diffraction pattern along the c*-direction. (a) H = 0 (virgin state). Only a single hexagonal phase appears.

Two peaks are caused by Kα¹ and Kα² lines of Cu target. The arrow indicates the position of hexagonal phase reflected by Kα¹ line. (b) H = 3 kOe. The diffraction profile for the coexistence of hexagonal and

orthorhombic phases. Two arrows correspond to the hexagonal and orthorhombic phase reflected by Kα¹ line. (c)H = 8 kOe. The diffraction pattern corresponds to a single orthorhombic phase. The arrow corresponds to the orthorhombic phase reflected by Kα1 line. The coexistence of the spiral and ferromagnetic phase is a typical case of the first order phase transition from spiral to ferromagnetic structure [95S].

Temperature [K]T Temperature [K]T

Dy

5

5 4

4 3

3 2

2 1

1 0

0 176

176

178

182

180

188

182 184

194

186

200 β

β

= 0.33

= 0.39 2D - model

Int.intensity [10counts]4 Int.intensity [10counts]3

a

b

γ- power law 2D - power law

Magnetization [G cmg]31− σ

Temperature [K]T

Dy

Critical field[kOe]Hcr

H aII 400

300

200

100

0

12

8

4

100 140 180 2200

60

1 2 3 4

5 6

Fig. 148. Integrated intensity for the (0,0,2–δ) neutron reflection vs. tem- perature for Dy. In (a) fits to (t−)^2β dependence of the spontaneous mag- netization in the ordered region and to a 2D-planar spin model in the paramag- netic region. In (b) fits to the persistent intensity observed in the paramagnetic region are indicated [95dP].

Fig. 149. Temperature dependencies of the specific magnetization and critical field H^cr for a Dy single crystal at H||a (the easy magnetization direction) and for various pressures; (1):H = 12 kOe, p = 10⁶ dyn cm^–2; (2):H = 12 kOe, p = 10¹⁰ dyn cm^–2; (3):H = 5 kOe, p = 10⁶ dyn cm^–2; (4):H = 5 kOe, p = 10¹⁰ dyn cm^–2; critical fields: (5)p = 10¹⁰ dyn cm^–2, (6)p = 10⁶ dyn cm^–2. The magnetic field shifts the temperature Θ1 towards higher and the pressure towards lower temperature [91N].

Magnetization [G cmg]31− σ

Magnetic field [kOe]H

Dy

360

240

120

0 5 10 15

78 K

128.5 K 1

2 3

H aII H bII 1,3 2,4 4

Fig. 150. Dependence of specific magnetization σ^{on the} field under atmospheric pressure for a Dy single crystal.

The sharp increase of σ at the critical value Hcris caused by the destruction of helicoidal antiferromagnetism (see curves 3 and 4) [91N].

Magnetization [G cmg]31− σ [G cmg]31−σ

Temperature [K]T

[K]

T

300

200

100

080 120 160 200 240 280

H= 0.75 kOe

15

10

5

0170 180 190 200 210 220 230

H aII

Dy

H= 1.6 kOe

H= 0.75 kOe

Fig. 151. Temperature dependence of the magnetization of Dy monocrystal in the case a fixed magnetic field of 0.75 kOe (H||a). Inset: H = 1.6 kOe and 0.75 kOe [96D].

Magnetization [G cmg]31− σ

Temperature [K]T

[K]

T

Dy

2.0

1.5

1.0

0.5

0

40 60 80 100 120 140 160 180 200 220 240 260

µ₀H= 0.01 T IIb

0.02 0.01 0

−0.01

−0.02

150 170 190 210

Magnetization slope

Fig. 152. Magnetization of Dy as a function of temperature at 0.01 T along the b axis, arrows indicate magnetic transitions. The inset is the slope of magnetization, the arrow shows the vortex transition [97A].

Magnetizationσ

Temperature [K]T

Dy

40 60 80 100 120 140 160 180 200 220 240 260

µ₀H= 0.3 T 2.1 T 1.5 T

0.9 T

H bII

Magnetization [G cmg]31− σ

Magnetic field [kOe]H

Dy

180 150 120 90 60 30

0 10 20 30 40 50

T= 100 K 120 140 165 K

Fig. 153. Magnetization of Dy as a function of temperatures at µ0H = 0.3, 0.9, 1.5, and 2.1 T along the b axis, arrows indicate magnetic transitions {97A].

Fig. 154. Magnetization of Dy as a function of field along the b axis at T = 100, 120, 140, and 165 K, arrows indicate magnetic transitions [97A].

Temperature [K]T Temperature [K]T

Susceptibility[relative]acχ Susceptibility[relative]acχ

Dy

H bII

H cII

1.0 1.0

0 0

0.2 0.2

0.4 0.4

0.6 0.6

0.8 0.8

0 40 80 120 160 200 0 40 80 120 160 200

a b

160 165 170 160 170

Fig. 155. Alternate-current susceptibility (χac arbitrary units) of single-crystal Dy along the b (a) and c axis (b).

TC,TN and the anomalies near 6.5 and 167 K are shown by arrows. The insets show the anomalies near 167 K.

The anomaly is most likely due to the so-called "vortex state" of Dy what means that the long-range order associated with the antiferromagnetic state has not fully developed [91W2].

Temperature [K]T Temperature [K]T

Dy

H bII

H cII

a b

Magnetization [G cmg]31− σ Magnetization [10G cmg]−−431 σ

0.12

0.10

0.08

0.06

0.042 3 4 5 2 3 4 5

10.0

9.8

9.6

9.4

Fig. 157. Magnetization as a function of temperature along the b (a) and c axis (b) of single crystal Dy in an applied field (0.002 T). The anomalies in the magnet-

ization at T = 4.3 K and ac susceptibility at T = 6.5 K are due to a lifting of a component of the magnetic moment of Dy onto the c axis [91W2].

T= 95 K

Dy

T= 100 K

T= 110 K T= 120 K

Volume fraction

1.0

0.8

0.6

0.4

0.2

0

Volume fraction

1.0

0.8

0.6

0.4

0.2

0

Magnetic field [kOe]H

0 2 4 6 8 10

Magnetic field [kOe]H

0 2 4 6 8 10

a b

c d

Fig. 156. Magnetic field dependence of the volume fraction of the orthorhombic (ferromagnet) phase. The abscissa is the external field. The hysteresis becomes small as the temperature is increased. (a)T = 95 K. Most

of the crystal structure remains at orthorhombic in the remanent state. (b), (c), (d) are the results for T = 100 K, 110 K, and 120 K, respectively [95S].

Temperature [K]T

Dy

Magnetostriction[10]−4ω

H aII 8

6

4

2

0

−2

80 100 120 140 160 180 200

H= 11 kOe 5 kOe

1 kOe

Fig. 158. Temperature dependence of the volume mag- netostrictionω of a Dy single crystal at H||a:H = 11, 5 and 1 kOe [91N].

Dy

Magnetostriction[10]−4 ω

Magnetic field [kOe]H 7

6 5 4 3 2 1 0

−1

0 2 4 6 8 10 12

H aII T= 100 K 110120

130 140

145 150

155 160

170 K

Velocity[m s]v331−

Dy

Peak intensity [10counts]3 Attenuation[10dB m]3321−α

Temperature [K]T T_N

T_N T_N 6

4

2

0 2925

2910

2895

2880 20

15

10

5 0

179 180 181 182 183

Fig. 159. Dependencies of volume magnetostriction ω ^on the magnetic field for a Dy single crystal at H||a [91N].

Fig. 160. Helical-paramagnetic phase tran- sition in Dy. Simultaneously measured ultrasonic velocity v33and attenuation α33, and peak scattered neutron intensity vs.

temperature for single-crystal Dy. The longitudinal ultrasonic wave was propa- gated along the c axis and neutrons probed the (0, 0.2 – δ) satellite. Open symbols indicate measurements taken during the cooling and closed symbols refer to the subsequent heating run [95dP].

Temperature [K]T

Temperature [K]T

Temperature [K]T

Dy

Thermoelectric power change d/d[mW mol]Qt−1 Thermoelectric power change d/d[mW mol]Qt−1 Thermoelectric power change d/d[mW mol]Qt−1

10

5

0179 180 181 182

7.5 J mol⁻¹

0.2 J mol⁻¹ 36.6 J mol⁻¹ 200

150

100

50

090 91 92

1.0

0.5

0165 166 167 168 171 172 173 174

a b

c

0.2 J mol⁻¹

Fig. 161. Investigation of the nature of the magnetic transitions in high-purity Dy with a high-resolution microcalorimeter. Change in energy content of Dy as a function of temperature (a) at the antiferromagnetic

transition, (b) at the ferromagnetic transition, (c) in the helical regime. The splitting of the curve T^C into number of smaller peaks can arise from domain-related effects [88Å].

Temperature [K]T

Energy change [K]

Dy

6

4

2

0 100 120 140 160

1

2

3

4

Fig. 162. Temperature dependencies of the change of (1) exchange energy ∆Eexch, (2) magnetoelastic energy ∆Eme, (3) energy of magnetic anisotropy

∆EA

b, and (4) elastic energy ∆Eme

b in Dy during magnetic phase transition of the first type helicoidal antiferromagnetism-ferromagnetism [91N].

Temperature [K]T Entropy[J molK]Stot11−−

65

60

55

50

45140 160 180 200

H a

Dy

II

H= 0 60 kOe

Fig. 163. Temperature dependence of the total entropy of Dy single crystal at H = 0 and 60 kOe (H||a) [91N].

Temperature [K]T

Entropy[J molK]Sm11−−

Dy

H aII

Entropy change[J molK]−∆Sm11−−

2.5

2.0

1.5

1.0

0.5

−0.5 0

100 125 150 175 200

75

20

15

10

5 0 25 H= 0

10 kOe 60 kOe

Fig. 164. Temperature dependence of the change in the magnetic part of the entropy in a Dy single crystal in the field applied along the a axis: H = 10 kOe, 60 kOe, and temperature dependence of the magnetic part of Dy in a zero field [91N].

Magnetic field [kOe]H Entropy[J molK]Sm11−−

Dy

30

20

10

0 2 4 6 8

T= 200 K 175 160 130 100 K

Temperature [K]T Temperature [K]T

Temperature shift[K]∆T Temperature shift[K]∆T

Dy

H aII H bII

8

6

4

2

0

40 100 160 220 280

1

1

2 2

3 3

4 5 4

6 5

6 a

7

5

3

1

100

50 150 200 250

b Fig. 166. Temperature dependencies of the magneto- caloric effect in a Dy single crystal in fields applied (a) along the a axis and (b) along the b axis : H = 60 kOe

(1), 50 kOe (2), 40 kOe (3), 30 kOe (4), 20 kOe (5), 10 kOe (6) [91N].

Fig. 165. Dependence of the magnetic part of the entropy Sm (H, T) of a Dy single crystal on the field applied along the a axis [91N].

Energy [keV]E IIntensity[10counts]6

Dy L

_III

T= 105 K 5

4

3

2

1

07.77 7.78 7.79 7.80 7.81 7.82

4000

2000

0 −1Absorption coefficient [cm]

σ σ

σ π

WavevectorQ_z [Å ]^-1

Intensity [10counts]2

1.80 1.90 2.00 2.10 2.20 2.30 2.40 2.50 2.60

[Dy /Y ]

_{16 20 89}

320 280 240 200 160 120 80 40 0

T T< _c

T T> _c

magnetic order peaks (0002) structure

peaks

Y

Dy SDW

no 4f magn.

moment

Fig. 168. Scattered neutron intensity for a scan along the c* direction (Qz) in a [Dy16/Y20]89 multilayer above and below the helimagnetic ordering temperature 167 K (shown as T^C). For T > T^C the small peak to the right of (0002) is a bilayer harmonic. Below TC the fundamental and two bilayer harmonics are shown for both Q^–

(≈ 2.02 Å^–1) and for Q⁺(≈ 2.42 Å^–1) magnetic satellites.

For the multilayer structure see Fig. B. The right inset schematically depicts the Dy 4f local moment configuration and the long-range conduction electron spin density wave in both Dy and Y [89R1].

Fig. 167. Resonance enhancement of the magnetic scattering about the L_»»» absorption edge of Dy at the first-harmonic (0, 0.2+τ) with a total intensity that was 3⋅10^–5 weaker than the charge peak at the (0, 0.2). Upper curve shows the absorption profile for a Dy foil taken with a singly bent, asymmetrically cut Ge(111) mono- chromator. Lower curves show the integrated intensity of the (0, 0, 2+τ) magnetic satellite for both scattered polarisation: σ to π and σ to σ. The intensity of the magnetic satellite drops by a factor of 90 when the incident X-ray energy is tuned below the absorption edge to E = 7.668 keV [89I].

Intensity [relative]

[Dy /Y ]

_{16 20 89}

250

200

150

100

50 0

1.80 2.00 2.20 2.40 2.60

T= 165 K

160 150

130

110

80

6 K

WavevectorQ_z [Å ]^-1

Fig. 169. Neutron diffraction scans around the (0002) principal Bragg peak which is also the propagation’s direction (K) for the incommensurate helical magnetic order for the [Dy16/Y20]89 multistructure for several temperature below TC = 167 K. Note the temperature independence of the (0002) peak at Q2= 2.215 Å^–1. The small peak to the right of the (0002) is a bilayer harmonic. The fundamental and two bilayer harmonics

are shown for both Q^–1(≈2.02 Å^–1) and for Q⁺(≈2.42 Å^–1) magnetic satellites and are observed to be temperature dependent. The presence of the fully resolved Q^–1 satellites makes it immediately obvious that the magnetism is coherent over many multilayer periods.

The coherence range can be calculated from the width of the magnetic peaks [87R].

Intensity (relative) Intensity (relative) T= 150 K

1.8 2.0 2.2 2.4 2.6 1.8 2.0 2.2 2.4 2.6

WavevectorQ_z[Å ]⁻¹ WavevectorQ_z[Å ]⁻¹

T= 160 K

[Dy / Y ]

_{15 14 64}

[Dy /(Dy Y) ]

_{9 8 90}

130

110

80

10 K

40 40

32 32

24 24

16 16

8 8

0 0

155

150

140 130

80

40 10 K

a b

Fig. 170. The (000l) scans in the neutron diffraction experiments for:

(a) [Dy₁₅/Y₁₄]₁₄ and (b) [Dy₉/(DyY)₈]₉₀ made up of about 15 growth planes of Dy atoms followed by 14 planes o Y atoms. The second sample has 90 layers, each layer consisting of 90 Dy atomic planes and 8 Dy_0.5Y_0.5 alloy planes. As the temperature is lowered additional peaks of magnetic origin appear on either side

ofτ⁰. In sample (b) only two additional peaks are found in the zone about the primary nuclear peak and the scattering pattern is identical to that found in the conventional helimagnetic phase such as bulk Dy. In sample (a), by contrast, a triad of magnetic peaks appear on either side of τ⁰ below 175 K [87E].

Intensity (relative)

[Dy / Y ]

_{15 14 64}

T= 10 K 80

70

60

50

40

30

20

10

01.8 1.9 2.0 2.1 2.2

WavevectorQ_z[Å ]⁻¹ WavevectorQ_z[Å ]⁻¹

(0002- )

(0002- )

H= 0 H= 0

1.5 kOe 1.5 kOe

10 10

25 25

Hreduced to 0

H= 0 warmed to 60 K

[Dy / Y ]

_{15 14 64}

T= 130 K

1.80 1.90 2.00 2.10 2.20

,

Fig. 171. Field dependence of the helimagnetic state is shown for sample Dy₁₅/Y₁₄]₆₄ at temperatures of 10 and 130 K with the field along the easy direction. At low temperature the magnetic satellite intensity decreases for fields above about 1.5 kOe with complete ferromagnetic saturation by 25 kOe. Very little broadening of the magnetic satellites is observed at 10 K. However, at

130 K the first effect of the applied field is to broaden the magnetic satellites, and a field of 10 kOe is sufficient to limit the helimagnetic coherence to a single bilayer.

The helimagnetic state is not reformed at low tem- perature, but can be regained upon warming, although with a shorter coherence length than the zero-field cooled state [87E].

Intensity (relative)

[Dy /Y ]

_{16 9 100}

WavevectorQ_Z[Å ]⁻¹ 240

180

120

60

2.100 2.20 2.30 2.40

H= 0

1 kOe

3

5

10

18 kOe

a

Intensity (relative)

WavevectorQ_Z[Å ]⁻¹ 240

180

120

60

2.100 2.20 2.30 2.40

H= 0

T= 130 K T= 40 K

kOe3

5

10

18

25

kOe40

b

Fig. 172. (a) Nuclear peak intensity for a [Dy16/Y9]100

multilayer at 40 K as a function of applied field showing the added ferromagnetic component arising from the gradual elimination of the helical incommen-surate phase order. (b) Similar nuclear peak scans as a function of field at 130 K [89R].

Intensity (relative)

[Dy /Y ]

_{16 9 100}

WavevectorQ_Z[Å ]⁻¹ 240

180

120

60

2.100 2.20 2.30 2.40 H= 0

kOe 3

10

18 kOe

a

Intensity (relative)

WavevectorQ_Z[Å ]⁻¹ 0

1.90 2.00 2.10 H= 0 T= 10 K

3 kOe

10

18 kOe

b 36

30

24

18

12

6

Fig. 173. (a) Excess ferromagnetic intensity remains on the (0002) nuclear peaks following application of the field which indicates the strong metastability of the induced ferromagnetic state at 10 K for the multilayer with only 9 Y planes. (b) Residual intensity for H = 0 at theQ^– satellite positions in the [Dy16/Y9]100 multilayer after applying each of the fields shown [89R].

Binding energy [eV]E Binding energy [eV]E

Dy /W

T= 55 K hν= 100 eV

Intensity

I K

L

D F

5 5

5

5 7

0 10 0

10 15

15

a b

MCD spectrum

theory

5 5

Fig. 174. (a) Dy 4f photoemission (PE) spectra (hν ⁼ 100 eV) of a remanently magnetized Dy(0001)/W(110) film (150 Å thick; T = 55 K). Open (solid) dots are for nearly parallel (antiparallel) orientation of photon spin

and sample magnetization. (b) Solid squares: Intensity difference of the experimental magnetic circular di- chroism spectra in (a), the solid curve at the bottom of (b) represents the theoretical MCD spectrum [95A].

Magnetization [G cmg]31− σ

Magnetic field [kOe]H

Dy/Lu

H aII

H_f T= 5 K

H_cr 400

300

200

100

0 5 10 15 20

120

160

200 K 6040

80 100

140

Fig. 175. Field dependent magnetization curves for the field-cooled (Y_0.45Lu_0.55)_1500Å/Dy_50Å/(Y_0.45Lu_0.55)_100Å superstructure grown along the [0001] direction at various temperatures. The magnetic field was applied along one of the a axis in the growth plane. Note that aboveTC = 90 K the magnetization exhibits a low field anomaly at Hcr before its rapid rise to saturation. The critical fields Hcr and Hf are indicated by dashed lines [93T].

Layer thicknessd_Y[Å]

Dy/Y

30 40 50 60

20

d

c

b

a 6.8

6.4 6.0 200 100 0.5 0 140 120 Θ[K]σσrem/(45 kOe)∆[K]D[meV Å]2

Fig. 176. (a) Curie temperature Θ obtained from a Curie-Weiss law fit above the paramagnetic transition at 2 kOe, (b) the fractional remanence magnetization, σ^rem at 10 K after saturation in a field of 45 kOe, and (c) the spin-wave anisotropy gap and (d) the spin-wave stiffness D obtained from fits of the saturation magnetization to spin-wave dispersion relations, all as functions of Y layer thickness in single-crystal superlattice of Dy and Y [87B].

Magnetic field [kOe]H Magnetic moment[]pµBMagnetic moment[]pµBMagnetic moment[]pµBMagnetic moment[]pµB

12 12 12 12

10 10 10 10

8 8 8 8

6 6 6 6

4 4 4 4

2 2 2 2

0 0 0 0

0 20 40 0 20 40 0 20 40 60

easy

hard

bulk Dy

4 K 80 K

130 K easy

hard easy

hard

d

easy easy

easy (1120)

hard

hard

hard (1010)hard

hard (1010)

T= 10 K

[Dy /Y ]_{15 14 64}

[Dy /Y ]_{15 14 64}

[Dy /(Dy Y) ]_{9 8 90}

80 K

80 K

80 K

130 K

140 K a

b

easy

easy easy

T= 10 K

T= 10 K

c Fig. 178. (a) Magnetization of

[D15/Y14]64 sample from neutron experiment for fields applied along the easy and hard directions in the basal plane. (b) Magnetometer measure- ments on the same sample. (c) [Dy₉/(DyY)]₉₀ multilayer. The basal- plane anisotropy is observed to be similar to that of bulk Dy shown in (d).

At low temperatures the slope of the curves is clearly not demagnetization limited, and the first-order transition from the helimagnetic to ferromagnetic states in bulk Dy is not as sharp in the superlattice [87E].

Temperature [K]T Layer moment[]pDyBµ

12 10 8 6 4 2

0 30 60 90 120 150 180

Brillouin function ( =15/2)J

[Dy / Y ] total integrated intensity_{15 14 64} [Dy /Y ]_{16 20 89}

[Dy /Y ]15 14 64

Fig. 177. Temperature dependence of the coherent Dy layer moment in [Dy₁₆/Y₂₀]₈₉ and [Dy₁₅/Y₁₄]₆₄compared to a Brillouin function. Also shown is the total integrated magnetic intensity for [Dy₁₅/Y₁₄]₆₄ [87R].

Magnetization / (45 kOe)σσ

Magnetic field [kOe]H

0 5 10 15 20 25 30 35 40 45

[Dy / Y ]_{16 9 100} [Dy / Y_{16 12.5 62}] [Dy / Y ]_{16 20 89} 1.0

0.8

0.6

0.4

0.2

Fig. 179. Field-cooled magnetization σ as a function of applied field at 10 K for the three superlattices as indicated. All results have been scaled by the value of the magnetization at 45 kOe unlike pure Dy, the initial susceptibility shows metamagnetic behavior at low fields [87B].

Magnetization [G cmg]31− σ Magnetization [G cmg]31− σ

Magnetic field [kOe]H Magnetic field [kOe]H

0 50 0 50

−50 −50

3.5ÅDy / 6ÅY

3.5ÅDy / 6ÅTa 5.25ÅDy / 6ÅY

5.25ÅDy / 6ÅTa 7ÅDy / 6ÅY

7ÅDy / 6ÅTa

14ÅDy / 6ÅY 14ÅDy / 6ÅTa

II II

T

T II

II

T

T II

II T

T

II

II T

102 T

83.9 121 98.1 151 116 188 146

26.9 25.1 39.3 36.1 51.0 44.3 79.7 73.8

a b

Fig. 180. (a) Layers-thickness dependence of hysteresis loops for Dy/6ÅTa and (b) for Dy/6ÅY superstructure at

5 K. Figure shows that all Dy/Y samples have σ¸¸>σŏ, i.e., in-plane anisotropy [91S1].

Temperature [K]T Magnetic moment[]pµB

0 60 120 180

16

12

8

4

[Dy / Y ]_{16 9 100}

[Dy / Y ]_{16 20 89}

[Dy / Y ]_{15 14 64}

Fig. 181. Uncompensated net layer moment resulting from incomplete helices in Dy layers. In an applied field this net moment is a pseudo-random order parameter coupled to the external field which is suggested to destroy the long-range coherence for T approaching TN [89R].

Magnetization [G cmg]31− σ

Temperature [K]T 120

80

40

0 100 200 300

NM = Y NM = Ta

5.25 ÅDy / 6 ÅNM

Fig. 182. Temperature dependence of magnetization at H = 55 kOe for 5.25ÅDy/6ÅTa and 5.25ÅDy/6ÅY multilayer superstructure. All the magnetization comes from Dy but is strongly effected by the Ta and Y atoms [91S1].

Magnetic fieldµ₀H[T]

Dy /Y

_{25 15}

0.20 0.15 0.10 0.05 0

0.1 0

−0.1

−0.2

−0.3

12010 160180

180 140

8060 2010K T= 60K

80 100

140

160

100 40 120 Magnetoelastic stress[GPa]aσ~Magnetoelastic stress[GPa] bσ~

0 2 4 6 8 10 12 14

0.2 a

b

Fig. 183. Magnetoelastic stress isotherms for SL (Dy₂₅/Y₁₅)×50 superlattices. σ^~_a ^{(a) and} σ^~b ^(b)

correspond to SL clamping along the a and baxes [97dM].

Temperature [K]T

Turn angleω

50°

40°

30°

20°

10°

00 25 50 75 100 125 150 175

[Dy / Y ]_{9 17 30} [Dy / Y ]_{21 20 34} [Dy / Y ]_{30 13 30} [Dy / Y ]_{38 20 35} 200 nm Dy

Fig. 184. Temperature dependence of interplane turn angles of the helimagnetic spiral for Dy/Y superlattices and 200 nm thick Dy film. The values are weighted averages of the turn angles of the Dy and the Y layers [97T-B].

Temperature [K]T 1.00

0.75

0.50

0.25

0

−0.25

0 50 100 150 200 250 300

helimagnetic

ferromagnetic

[Dy / Y ]

_{30 13 30}

Peak intensities√() /−NN(0002) III

Fig. 185. Dy/Y superlattices. Temperature dependencies of the magnetic peak relative intensities. The solid circles represent the ferromagnetic moment component derived from the square root of the excess integrated intensities of the (0002) peak at different temperatures normalized by its average value above T^N. The open circles represent the helimagnetic component derived from the square root of the integrated intensity of the (0002)^– and the (0002)⁺ helimagnetic satellites normalized to the (0002) nuclear peak intensity [97T-B].

Temperature [K]T Magnetization /sσσ

0.008 0.007 0.006 0.005 0.004 0.003 0.002 0.001

0 50 100 150 200 250 300

H= 100 Oe (ZFC)

[Dy /Y ]

_{21 20 34}

Fig. 186. Zero field cooled SQUID magnetization measurement for the superlattice [Dy21/Y20]34. The measurement was performed with increasing temper- ature from 10 K at a magnetic field of 100 Oe [96T-B].

Temper atureT[K]

Critical field[kOe]Hcr

10

5

0

2 1 0

−1 −2 0

50 100

150 T_cr

Strain [%]ε

Fig. 187. Magnetic phase diagram for epitaxial Dy thin films grown along the c axis. The phase boundary corresponds to the locus of critical field Hcr. Tcr is defined where the phase boundary intersects the T-ε plane at zero field. The open circles are data points for (YxLu1–x)1500Å/Dy50Å/(YxLu1–x)100Å sandwich films. The dashed line through the nearly linear part of the Tcr curve indicates the equivalent bulk uniaxial behavior [93T].

Temperature [K]T

Turn angle〈〉ω

2.836

2.835

2.834

2.833

2.832

2.831

0 100 200 0 100 200 300

2.86

2.85

2.84

2.83

bulk 2.82 Dy

Y [Dy / Y ]_{15 14 64}

[Dy /(Dy Y) ]_{9 6 90}

superlattice

Interplanar spacing/2 [Å]〈〉c

a

55°

45°

35°

25°

Y

Dy

0 0.5 1.0

Temperature /T T_N b

[Dy / Y ]_{15 14 64}

[Dy /(Dy Y) ]_{9 6 90}

Fig. 188. (a) Average interplanar spacing along the c axis obtained from the position of the primary nuclear Bragg peak. The temperature dependence in the Dy/Y superlattice is a weighted average of the behavior in the

constituent materials. Note the change of scale when comparing to the bulk materials. (b) shows the average turn angle in the superlattices as well as in the bulk materials [87E].

600 600

500 500

400 400

300 300

200 200

100 100

0 5 10 15 20 25 30 35 0

Number of Y layers

Coherence length [Å]ξ Coherence length [Å]ξ8

6 4

2 0

Number of bilayers

0.01 0.02 0.03 0.04

Inverse Y thickness− r⁻¹[Å ]⁻¹

200 100 50 30 25

Y thickness [Å]− r

single Dy layer

≈140 Å [Dy / Y ]_{15 14 64}

[Dy / Y ]_{16 20 89} T_c= 169 K

T_c= 171 K

T_c= 171 K T_c= 171 K [Dy / Y ]_{16 9 100}

[Dy / Y ]_{14 34 74}

Fig. 189. (Left) Magnetic coherence length ξ (in both Å and number of complete bilayers) obtained from the intrinsic Q width of the magnetic satellite peaks as a function of Y thickness for the four samples. (Right)

Linear inverse dependence of the coherence length on the Y interlayer thickness. The extrapolated ξ drops to a single Dy layer at 140 Å. In the figures Tc denotes the helical ordering temperature [89R].

Intensity (relative)

WavevectorQ [Å ]^-1

Dy/Lu

z

1.8 2.0 2.2 2.4 2.6

T= 150 K 170 K

170 K 150 K 10

8

6

4

2

0

Fig. 190. Diffraction scans for a Dy/Lu superlattice [94R].

300 250 200 150 100 50

0 5 10 15 20 25 30

Number of Lu interlayers

Coherence length [Å]ξ

bilayer thickness

Dy/Lu

Fig. 191. Magnetic coherence length vs. number of Lu interlayers for spiral (triangles), aligned ferromagnetic layers (open circles), and antialigned layers (solid circles). The actual spacing is 2.77Å/Lu layer [93B].

Temperature [K]T Magnetic moment[]pDyBµ

Dy/Lu

5

4

3

2

1

0 50 100 150 200

40 Å Dy

145 Å Dy

H= 200 Oe

Fig. 193. Magnetic moment of Lu(500Å)/

(145Å)Dy/Lu(500Å) (solid circles) and Lu/40ÅDy/Lu (open circles) trilayers as a function of temperature.

Both field-cooled (200 Oe) and zero-field-cooled data are shown. Arrows indicate whether the temperature was being raised or lowered. The thermal hysteresis in the FM transition of the 145 Å film is probably connected to structural distortion occurring at Tc. The Dy helical magnetic order yields to ferromagnetism (FM) at temperatures almost double Tc = 85 K of the bulk element [93B1].

Temperature [K]T

Dy/Lu

Magnetizationσσ/s

0.8

0.6

0.4

0.2

0 50 100 150 200 250

H= 1 kOe 200 Oe 50 Oe

200 Oe (ZFC)

Fig. 192. FC magnetization vs. temperature for the 40 Å Dy layer (sandwich between 500 Å slabs of Lu (Lu/40Å - Dy/Lu ) in the fields of 50 Oe, 200 Oe (FC and ZFC ) and 1 kOe [93B].

Magnetic moment[]pDyBµ

Dy/Lu

40 Å Dy 145 Å Dy

Magnetic field [kOe]H 10

8

6

4

2

0 2 4 6 8 10

Fig. 194. Zero-field-cooled magnetization (at T = 10 K) vs. field for the 40ÅLu- and 145ÅDy/Lu films. The field required to saturate the magnetization is large for thinner films, exceeding 10 kOe for the 40 Å sample.

The saturation moment psfor the 40 Å sample is 65 % ofps bulk Dy [93B1].

Magnetization [G cmg]31− σ

Temperature [K]T 70

60 50 40 30 20 10

0 50 100 150 200 250 300

Dy/Zr

HII plane

Fig. 196. Temperature dependence of the magnetization for zero-field-cooled, field-cooled Zr(200Å)/Dy(600Å) (solid circles) and Zr(200Å)/Dy(100Å) (open circles) samples. The applied field (500 Oe) was in film plane.

The sense of variation of temperature is indicated by arrows [95L].

Temperature [K]T Temperature [K]T

[K]

T T[K]

χ−1 (relative) χ−1 (relative)

Dy/Cu

MagnetizationM[10G cm]−43 MagnetizationM[10G cm]−43

8

4 6

2

0 50 100 150 200

1.80

1.30

0.80 0.30

30 70 110 150

FC

FC

ZFC

ZFC 0.04

0.02

0 10 20 30 40

0.03

0.01

2.00

1.20

0.405 14 23 32

a b

Fig. 195. (a) Low field M(T) data for Dy/Cu multilayers deposited on to crystalline Cu(111) with the composition [Cu(100Å)/Dy(20Å)]_30.Inset: χ^{–1 vs.} T. (b) Low field

M(T) data for [Cu(100Å)/Dy(40Å)]₂₀ sample. Inset: χ^–1 vs.T [94T2].

Magnetization [G cmg]31− σ Magnetization [G cmg]31−σ

Temperature [K]T Temperature [K]T

60 50 40 30 20 10

0 50 100 150 200 250 300 0 50 100 150 200 250 300

T_Cb

T_Cb T_Nb

T_Nb HII plane

Zr 200 Å/Dy 600 Å

a b

140 120 100 80 60 40 20

Dy 20 Å/Zr 30 Å]₄₀ [

Fig. 197. (a) Temperature dependence of magnetization measured in the bilayer Zr(200Å)/Dy(600Å) and (b) [Dy(20Å)/Zr(30Å)]40 grown on Si(111) after previous

depositions of a 600Å-thick Zr buffer layer. Both samples were field-cooled. The magnetic field (500 Oe) was applied parallel to the layer plane [93L].

Magnetization [G cmg]31− σ

HII plane Dy 30 Å/Zr 30 Å]₁₀₀

[

Dy 15 Å/Zr 30 Å]₅₀ [

Dy 8 Å/Zr 30 Å]80

[

Magnetic field [kOe]H

HII

HII 300

150 200

100 100

50 0

0

−100

−50

−200

−100

−300

−150 200 150 100 50 0

−50

−100

−150−200

−50 −25 0 25 50

H T plane

H T

H T

Fig. 198. Hysteresis loops measured at 10 K in multi- layers [Dy(xÅ)/Zr(30Å)]_n (x = 30, 15 and 8), for applied fields parallel and perpendicular to the layer plane [93L].

Dy/Sc Sc Nb Al O_{2 3}

Dy Dy - Sc Sc Dy - Sc Dy

Fig. 199. Sketch of the Dy/Sc superlattice (SL) with the enlarged section to the right indicating the Dy-Sc alloyed layers on both sides of each Sc layers [94T1].

Intensity (relative)

WavevectorQ_c*[Å ]⁻¹

Dy/Sc

a b c 8000

4000

0 2000 6000

2.0 2.3 2.6

Fig. 200. Neutron diffraction from c-[Dy25Å/Sc40Å]66for scans along the [0002] diffraction (a) nuclear intensity at 160 K showing five structural superlattice sidebands and (0002) Sc reflection from the buffer layer; (b) zero- field scan at 10 K showing the short-ranged ferromag- netic order along the growth direction that is indicated by the thick line underneath the unchanged structural superlattice peaks; and (c) zero-field-cooled scan at 10 K, and at 60 kOe field applied along the a axis showing the magnetic superlattice intensities on top of structural peaks, indicating a coherent ferromagnetic order with vanishing short-ranged order [93T2].

Magnetization [G cmg]31− σ

Temperature [K]T

Dy/Sc

H =10 Oe T c

H =100 Oe IIc a

b 10

5

0 1.0

0.5

00 50 100 150 200 250

Fig. 201. Temperature dependence of the field-cooled (open circles) and zero-field-cooled (solid circles) magnetizations for c-[Dy25Å/Sc40Å]66: (a) 10 Oe field applied perpendicular to the c axis, and (b) 100 Oe field applied along the c axis [93T2].