Gadolinium

POH-

2.1.3.7 Gadolinium

lb 1 2.0

6

1.6 5

4 1.2 I

3 9

0.8 Q a= 2

0.6 1

0 0

-1

0 0.2 04 0.6 0.8 1.0 1.2 A-’ 1.c sir&M -

Fig. 140. Neutron magnetic scattering amplitudes of raoGd at 96K, normalized to give the magnetic form factor p/b (on right-hand scale) relative to the nuclear scattering amplitude, or directly the 4f magnetic moment (on left-hand scale). The experimental points are deter- mined either from (hk0) reflexions or from (Okl) reflexions.

The full line corresponds to the theoretical curve of Blume- Freeman-Watson [62Bl] fitted to have for sinO/A=O the experimental 4f magnetic moment paf=6.42pB [71 K 31.

150 Gcm3 9 120

-

I 90 b

60

30 +

0 150 300 650 600 750 Oe 900

H-

Fig. 142. Magnetic field dependence of the magnetic mo- ment of Gd single crystals, along the a axis at 269.8 K, the b axis at 270.1 K and the c axis at 270.4K showing that the c axis is the easy axis of magnetization just below Tc [63N 1-j.

300 Gcm3

9 250 I-

I 200 I- b 1st I -

lO[ I-

5[ I-

1 I

Gd

15 30 45 60 75 kOe

H-

O Fig. 141. Curves of the magnetization, e, vs. a magnetic field, H, applied along the b axis at different temperatures in Gd single crystal. The saturation value at 4.2K is obtained for a field of 12 kOe [69 F 11.

280 Gcm3

r

9 260

I 240

6 220

2oc

180

161:

l=SOK I

I ol

8

16 2L 32d02 K3” LO

73/2- 270

. 80K 0 w

250.

0 2 4 6 .103K2 8

12 -

Fig. 143. Saturation magnetic moment of Gd single crystals as a function of T3j2 or T2 with magnetic field applied either along the n axis or along the c axis [63 N 11.

H. Drulis, M. Drulis

Landolt-BGmstein New Series 111/19dl

Ref.

p.

1831 2.1.3.7 Gd: figures 99

300

Gcm3 I Gr-i I _“V R

L_. I I i03

I 200 6 I

g 150 100

600 K 700 T-

Fig. 144. Temperature dependence of the spontaneous magnetic moment and reciprocal magnetic susceptibility in Gd. T,=293 K, 0 =317 K. The solid curve is the S=7/2 Brillouin function. Departures from the Curie- Weiss susceptibility near 0 result from short-range ordering [63 N 1, 65 B I].

60”

f 45”

a 30”

15"

0"

0 50 100 150 200 K k0

T-

Fig. 145. Temperature dependence of the angle between the easy magnetization direction and the c axis in Gd.

Open and closed circles represent the neutron diffraction results of Cable and Wollan [68 C 21 as determined from different reflections. Open triangles denote the torque results of [76 C 23 at 0.85 T: full triangles show their H = 0 extrapolated values. Immediately below Tc the easy axis is the c direction, with decreasing temperature the easy axis begins to tilt away from [OOOI], reaching a maximum cone angle of 60” at 180K and about 30” at 4.2K [81 L2].

1.2 106 - erg cm3

0” 15” 30” &So 60” 75” 90”

Y-

Fig. 146. Magnetic torque curves of Gd in a plane containing the c axis; w is the angle between the direc- tion of the applied magnetic field and the c axis;

H = 10 kOe; p = 1 bar. From the magnetic torque curves the position of the easy magnetization axis as a function of temperature was determined, cf. Fig. 147 [77 F 33.

Land&B6mstein

New Series 111/19dl

H. Drulis, M. Drub

100 2.1.3.7 Gd: figures [Ref. p. 183

m

30" - I

I k

0"

L-

o

50 100 150 200 250 K 300

I-

Fig. 147. Angle between the easy direction of magnetiza- tion and the c axis in Gd as a function of temperature, full curve: p= 1 bar; broken curve; 3 kbar, determined from the magnetic torque curves given in Fig. 146. The easy axis is sytuated in the basal plane in temperature interval 100 and 250 K [77 F 31.

251 I I , I I I

PI I I I I a

2”r

5, J

J

0 w 1000 1250 K 1500

I- ,- -

,_.--- -;

30 - I

201 I I I I

283 286 289 292 295 K

T-

I8 Fig. 148. Temperature dependence of the reciprocal mag- Fig. 149. Pressure dependence of the relative initial sus- netic susceptibility, x, ofGd in the high-temperature range ceptibility of single crystal Gd along c and b axes in the between 330 and 1500 K. Full line is a theoretical lit (Van vicinity of the Curie temperature. The general features of Vleck equation) including exchange interaction between the results show that transition temperature T, increases magnetic moments with 0 = 310 K (64 A 1-J. in a completely linear fashion with pressure [68 B 11.

H. Drulis, M. Drub

Landok-B6mstein New Series III/1961

Ref.

p.

1831 2.1.3.7 Gd: figures

25 me\i

20

Gd

i;

/

b direction I-L

0 T= 78K A 232 K

1 A;ect ion,

di rection ol$ ,013 012 ol,

. . 0 0.2 0.4 0.6 0.8 1

K l- A

Fig. 150. Magnon dispersion relations for Gd at 78 K along a, b, and c directions [70K2]. Since the magnon anisotropy in Gd is neglected, the curves are directly proportional to the values of the interplanar exchange integrals Jzbvc.

1

0.2 THz I 3.3

Y-

Fig. 151. Temperature dependence of the magnetic excita- tion spectrum of Gd at 4 =0.15.2n/c in the [OOOl] c direction, obtained from inelastic neutron scattering studies. The peaks symmetrically displaced about the central peak correspond to spin waves propagating along the c axis direction [81 C I].

15 CO1 mol K 12

I 9 z

6

60 120 180 240 300 K :

T-

O

Fig. 152. Temperature dependence of the specific heat of Gd between 4 and 360 K. The anomaly at 291.8 K shows the transition from the paramagnetic state to ferromag- netic state [54 G I].

Land&-Bknstein

New Series III/l9dl

H. Drulis, M. Drulis

102 2.1.3.7 Gd: figures [Ref. p. 183

30

2GI 280 320 K 360

I-

Fig. 153. Specific heat of Gd single crystal as a function . 01 temperature, showing a maximum value of 66 J mol - I K - r at T,,, = 293.55 K. The symbols indicate results of different authors [SO L 23.

251 I I I

0 10

A-.-

30 K2 VI

I I I I,, I I

10 12 14 16 18 20 25 30 K I-

Fig. 155. C,/T vs. T* for the temperature interval from 1.5 to 5 K of Gd. The solid line is the curve calculated as

Fig. 156. Magnetic specific heat of Gd metal plotted as a sum of the electronic, magnetic (Cmag = BT”) and lattice

Cmag vs. Ton logarithmic scales (bottom and right-hand

contributions using the

side) and C,,$T3/* vs. T on logarithmic (left-hand side) parameters

y=3.7mJmol-‘K-‘, B=1.94mJmol-‘K-(“+I),

and l/T (top) scales. The straight lines correspond to the n=1.75 and 8,=187K [74Wl].

relations (1) C=24 T3/’ exp( -26/T) mJ/mol K and (2) C,,,=O.19 T*.’ mJ/mol K, with T in K [66 L 11.

1.8 I molK

1.5

1 1.2

e 0.9

0.6

Fig. 154. Heat capacity of Gd between 1.5 and 14K [74W 1-J.

T-

10 12 14 16 18 20 K 25

!OOO mJ nol K IO00 800 600

H. Drulis, M. Drulis

Landok-BBmstein New Series 111/19dl

Ref.

p.

1831 2.1.3.7 Gd: figures 103

900

*ICI3 e's cm3

300

I 0 k

-300

-6OC

-9oc I

I

I

I -1200

0 40 80 120 160 G&/g 240

Fig. 157. Anisotropy constants

K,

and

K,

of Gd plotted as a function of the magnetic moment of the sample. The parameters indicate the temperature the magnetization corresponds to. The anisotropy constants were strongly field-dependent, particularly near the Curie temperature [63Gl, 62G1, 67Gl].

.,of - erg cm3

-2

I -3

- -0.016

0 40 80 120 K 160

T

Fig. 158. Experimental points and theoretical plot of the planar anisotropy constant

Kg

vs. temperature in Gd.

The full line and the open circles represent the data of Graham [67 G I], while the full circles represent the data of Darby and Taylor [64D I]. The dashed line is a theoretical curve given by

Kg = Kim",

where

K:(O) =

- 6.4. IO3 erg/cm3 and m is the magnetization relative to the zero-temperature value [67 G 11.

“U

0.6

I I I I I

^{1 K/at}

0.4

0.2 t 0 * 3

406 erg 3

I 1

* 0

-21 i-o.4

0 50 100 150 200 250 300 K 350

T-

Fig. 159. Experimental values of the anisotropy con- stants

K2, K,,

and

K6

vs. temperature in Gd. The circles represent the data of [69 F I], the triangles the data of [63 G 11. The dashed line gives the data of [62 C I] for KS.

Land&-BBmstein

New Series III/19dl

H. Drulis, M. Drulis

104 2.1.3.7 Gd: figures [Ref. p. 183

-253 91

0 50 100 150 200 250 300 K 350

-253

0 50 100 150 200 250 300 K 350

Fig. 160. Saturation magnetostriction constants of Gd as a function of temperature. l.,,,,cn denotes A//l measured along the a, b, c, d direction, shown in the inset [64A 23.

163 pRcr:

Gd

120

I 80 e clr

IC

/’

/ 1’

0 a

0 200 300 K LOO

l-

100 150 200 250 K 300

Fig. 161. Spontaneous magnetostrictions, sbr,, and E,, along the b and c axis of Gd as a function of temperature.

The full lines are the experimental data of [63 B l] after correction for the thermal dilatation of the nonmagnetic lattice. Dashed lines are the theoretical determination of [71 B 1-J.

136 JlQcn

t 132

&

&128

126 2 b

7

300 320 3LO 360 380 K LOO

I- 120

pQcm

t -\

/II c 118

e

“116 -

280 300 320 3&O 360 380 K 400

c I-

Fig. 162. (a) Temperature dependence of the electrical resistivity of Gd single crystals along the b and c axes.

The residual resistivity is substracted. (b) and (c) show e-e, vs. T on an enlarged scale near 300 K for electrical currents along the b and c directions, respectively [63 N 1-J.

H. Drulis, M. Drulis

Ref.

p.

1831 2.1.3.7 Gd: figures 105

0.4

I

I I

Gd

^{T= 4.2 K}

^(ioio)

H=92.5 kOe I I

0.1

0.2 I

I I

Hllc HII a

0.1 0.:

a

a I

(OOOll

0 0 c 0 000 oooooco 0 D c Do 0

150

~ODOOO

200 250 300 K 350

T- 0.3

Fig. 163. Temperature derivative of the electrical resistiv- ity of a polycrystalline Gd sample in a temperature range encompassing the spin reorientation temperature T, and I

the Curie temperature, Tc [79 S I]. F 0.2

B

rllr t