Anomalous spin lattice relaxation in some cobalt salts at liquid helium temperatures

Van den Broek, J. Van der Marel, L.C. Gorter, C. J. 1959

Physica 25 371-390

ANOMALOUS SPIN LATTICE RELAXATION IN SOME COBALT SALTS AT LIQUID H E L I U M T E M P E R A T U R E S b y J. VAN D E N B R O E K , L. C. VAN D E R MAREL- and C. J. G O R T E R Communication No. 314c from the Kamerlingh Onnes Laboratorium, Leiden, Nederland

Synopsis Paramagnetic relaxation experiments have been made on powders and single crystals of some cobalt salts by means of a Hartshorn bridge. A new method of measuring long relaxation times is described. A deviation parameter is introduced to describe the difference between the experimental dispersion and absorption curves and Casimirdu Pr6 theory. In cobalt ammonium sulphate the relaxation parameters depend on the parallel magnetic field in a remarkable way. Double relaxations and an anomalous dependence of the high frequency susceptibility on the magnetic field are found. The crystalline anisotropy of these phenomena is studied. In some cases a very strong dependence of the relaxation parameters on temperature (T-q) is observed.

1. Introduction. Previously paramagnetic dispersion and paramagnetic absorption have been studied in a rather large number of salts at liquid helium temperatures. A satisfactory general interpretation of the results has not yet been proposed and it m a y be said that even a coherent phenomenological description of the data is still lacking. Nevertheless some general statements m a y be made. In all substances at high frequencies a frequency independent susceptibility, %~o= (1 --F);~0, is found which decreases when the external parallel magnetic field He increases. For substances which obey Curie's law reasonably well, Casimir and Du Pr6's relation 1

--

F = Zao/7~0 = b/(b + CHe 2)

(1)

applies, where %0 is the static susceptibility, Zad is the so-called adiabatic susceptibility and C is Curie's constant ; b is the coefficient in the expression for the specific heat of the spin system at He -----0

Cs = b/T 2.

(2)

It m a y be mentioned that even if C is strongly anisotropic -- such as is the case in the salts studied in the present paper -- the deviations from (l) in a powder will remain quite small. The transition of ;( between %o and Zoo occurs in a region of frequencies --

371

--

372

j.

VAN D E N BROEK, L. C. VAN D E R MAREL AND C. J. GORTER

near the inverse of the average relaxation parameter pay. In the frequency region of this dispersion a maximum of the absorption coefficient ;~" is also found. In some cases the magnetic behaviour in the dispersion and absorption region m a y be described well b y a Debije function: Z'/X,o = F/(1 + p2v2) + 1 - - F

x"lxo = Fpv/(1 +

p2v2).

(3) (4)

This is, for instance, the case in the magnetically dilute Fe- and Cralums. In these substances the relaxation constant p is of the order of 10-1 to 1 second. This constant varies with a low negative power of T (between --1 and --2) and decreases rapidly in high parallel fields He. In the non diluted alums, however, (3) and (4) are not obeyed. It is usual to describe the deviations of the dispersion and absorption curves from the Debije curves b y shape parameters, differing from 1 (see figure 2). The average relaxation parameters pay are considerably shorter and vary more rapidly with T (powers between -- 3 and -- 6). They increase with increasing Hc though there are indications of a maximum in high fields. In the diluted and non diluted Tutton salts of Mn and Cu the results are not quite similar. In the Cu case diluting with non magnetic material even has an opposite effect, it leads to shorter average relaxation parameters and to a more rapid variation with T. Our investigations on cobalt salts have been induced b y an investigation of H a s e d a and K a n d a 1), according to which pay in powdered cobalt ammonium Tutton salt decreases with increasing He. It was soon discovered that the decrease acquires an anomalous character in powders of diluted cobalt Tutton salt and the anomaly was then also studied in single crystals. In cobalt silico fluoride no similar anomaly was observed. 2. S a m p l e s and methods. In the present investigation we have mainly

concerned ourselves with cobalt ammonium Tutton salt diluted with the isomorphous zinc compound according to the formula Col/(n+l) Znn/(n+l) (NH4),.(SO4)s.6H20. Also a corresponding cobalt potassium salt was investigated. These substances form monoclinic crystals (space group C2h). There are two molecules per unit cell; the tetragonal symmetry axes of the crystalline electric fields acting on the cobalt ions lie in a plane through the b-axis, and make angles cc of about 34 ° with the ac-plane upward and downward, respectivily. Each ion has in the highly diluted salts g / / = 6.45, g± -- 3.06 parallel and perpendicular to its tetragonal axis, respectively. The resulting g values along the principal susceptibi]ity axes are then gl = 5.70, g2 =-- 3.06, g3 = 4.36 2).

373

SPIN LATTICE RELAXATION IN SOME COBALT SALTS

The relative positions of crystallographic, magnetic and tetragonal axes are shown in fig. 1 (c/. 2) s) *)). ¢

b=K~ o

/ oc - p l o n ¢

f'--.

f / ~ a;34 °

~

bK1- plane

Fig. 1. Positions of magnetic susceptibility axes (K) a n d tetragonal field axes (T) with respect to the crystallographic axes in cobalt a m m o n i u m sulphate.

Cobalt silico fluoride Col/(n+l)Znn/(n+l)SiF6.6H20 was also investigated. It forms trigonal crystals having only one kind of cobalt position. The g values have axial symmetry about the trigonal axis; in diluted salts g//= 5.82, g± ---- 3.44 2). The samples were prepared b y normal methods. Powders were recrystallized from warm saturated solutions. Particles of 1-2 mm size were used, contained in an open glass tube. Single crystals were grown by slow evaporation of saturated solutions at about 30°C. Regular and transparent single crystals of about 10 g were obtained in a few weeks. They were ground to cylindrical shape and mounted on the open end of a glass tube using parafin wax and scotch tape. A relatively large filling factor can be obtained with a given crystal by this w a y of mounting; the crystals can be oriented with accuracy of a few degrees. The degree of dilution 1 : n of powder specimens was, as usual, determined b y comparing the measured Curie constant per mole (in units of the bridge) with that of pure cobalt ammonium Tutton salt. These determinations were in good agreement with the ratios Co : Zn in the aqueous solution. The same procedure can also be applied to the single crystals, using the known g values. However, owing to the different filling factor these results are less reliable than those on the powders. Nevertheless, for the cobalt ammonium sulphate single crystals the dilutions obtained from the Curie constant, which we have used, were in satisfactory agreement with the known concentration of the solutions. For the silico fluoride the dilution in the aqueous solution has been given. *) These positions are apparently not in agreement with those given by several other authors 4)s) 6)

374

j. VAN DEN BROEK, L. C. VAN DER MAREL AND C. ]. GORTER

The dispersion and absorption measurements have been carried out by means of the Hartshorn bridge with extended frequency range described in a previous paper 7). Measurements of relaxation parameters up to about 1 second can be made. In order to measure longer relaxation parameters a new method was developed. At a constant magnetic field He the bridge is compensated. This is done at a frequency v where pv >~ 1 (227 Hz is used). Then the field is changed by an additional A H e . After re-establishing of equilibrium in th'e sample this auxiliary field is switched off. After this adiabatic demagnetization the bridge signal does not instantly return to zero, but O.5 O.4 1

".,. 11p'qb,

0,3

0.2 ! /

I

XI

i

//

\

~. x

i i

~\\Xa

O.8

i F

~tt[pditp 0.6

t , -iF -- ~ ~"-~ -~-F""~~

0.4

~

I'F 0

1o9 v

I

I

2

Fig. 2. Example of theoretical double relaxation curves (sum of two Debije curves) defining the various parameters.

decreases to zero as a function of time. It is a fortunate circumstance that in the substances studied so far by this method the decrease has an exponential character. From photographic recording of this phenomenon the relaxation time ~ is easily determined. Values of T varying from 1/6 to 16 seconds (p = 2 ~ from 1 to 100 s) have been obtained. They are in satisfactory agreement with the p-values obtained from the extrapolation of the dispersion and absorption measurements. The auxiliary field is produced by a

SPIN LATTICE RELAXATION IN SOME COBALT SALTS

375

direct current in a separate solenoid placed inside the coil magnet. Its magnitude is usually of the order of 50 Oe. As already mentioned in the introduction, deviations between the measured dispersion and absorption curves and the theoretical Debije function given in relations (3) and (4) are often found. In order to describe these deviations we introduced in a previous paper 7) two relaxation parameters (pdisp and pabs) and four shape parameters: namely, the slope S of the dispersion curve at half height, the height h of the absorption carve, and the left- and right-hand halves 6(1) and 6(r) of its half width, each parameter divided b y its theoretical value. For the double relaxations found in this investigation two sets of analogous parameters can be introduced as shown in fig. 2. To reduce the number of data to be tabulated we make use of the experimental relations between the various parameters of a single relaxation. Within the experimental error proportionality is found between the deviation from 1 of the reduced slope S/1.1513F and the deviation of the reduced height 2h/F: 1

--

S/1.1513F =

1.7(1 --

(5)

2h/F).

1.0

T-2'4 0.5

log

f~ -C

I O Lo9T O.2

I OA

I 0.6

0 tog T C).2

0.4

0.6

3.0

I O Io(jT O.2

r 0.4

i 0.6

~'~~

i

O togTO.2

0

0 00

4kC)eO.2

I I 0.4 H m|

i

1

0.4

O~

2.O

if I 0.4

P H ~1

I 2

4kO¢O.2

I 0.4

H |

I

I 2

4kOeCL2

I 0.4

I H ),|

i 2

I 2

4kO¢

Fig. 3. pdlsp/[(T) VS He and /(T)~s T for powdered cobalt ammonium and cobalt

potassium sulphates. In the upper diagrams solid symbols give /(T) at low magnetic fields, open symbols represent /(T) at high fields.

376

J. VAN D E N B R O E K , L. C. VAN D E R M A R E L A N D C. J. G O R T E R

A similar relation was found to apply between the reduced total width ½(6(1) + ~(r))/1.1438 of the absorption curve and its height: {½(~(1) + ~(r))/1.1438}

-

1 = 2.3(1 -- 2 h / F ) .

-

(6)

Both of these relations appear to be valid even for deviations from 1 of the order of 0.5. Finally there should be a relation between the asymmetry of the absorption curve ~(1)--~(r) and the difference log paisp--logpabs. This relation cannot be accurately established from the available experimental data. Thus we will confine ourselves to stating paisp and pabs, and one deviation parameter d defined as the average of 1 - - 2 h / F and (1 - - S / 1 . 1 5 1 3 F ) / 1 . 7 ; the half widths are not used, as in m a n y cases only one could be determined. In all cases a mean value of this deviation parameter over all available temperatures is given. 3. Results. a. P o w d e r s . Five powdered samples have been investigated.

Four of them were cobalt ammonium sulphates, undiluted (1:0) and diluted 1:5.45, 1:12.2 and 1:21. The fifth sample was a 1:14.5 cobalt potassium sulphate. The relaxation parameters obtained are given in table I and summarized in fig. 3. A notable difference in the behaviour of p(H) at high and at low magnetic fields is found, especially in the highly diluted samples. At high fields the relaxation parameters follow approximately a T -2 law, those at low fields depend only weakly on temperature between 1.3 and 3°K and much more strongly at 4°K. This difference in temperature dependence is not so 1 : 3 7 K:I

1:14.5 K

I : 10

&

O.I

Xz

0.2

0.2

0.2

0,1 Q

O

~ i

i

i

0.2 O.I O 0.2 O.I

i

O

i

0.2

0.2

0.1

0.1

0 :9.5~

0.1

0.2

O.I

O.I

i

l

I

i

f

i

i

®

0

i

i

i

i

i I

i 2

4kO¢

0,2

0

0.2

0

i

X//

0.3

0.2

i

i

t:10

1237Kt

i

i

i

0

1:21

I

:9.5~

0 I 0.4

0

I:0 0.2

0.2

O.2

.

O.I

O

O.I

O 02

i O.4

H

i 1

i 2

, O 4kO¢ Q2

^ ,° ~ 0.4

_j~9"

O.I

l H

I

O 2

4kO¢

02

-0.4

H

Fig. 4. Deviation parameter d as a function of the magnetic field. Diagrams on the left: powders, middle diagrams: cobalt ammonium sulphate single crystals, ~liagrams on the right: cobalt silico fluoride single crystals.

i

,

- -o ~o oo ~o

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oo oo, oo, ooo oo o

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:378

J. VAN D E N B R O E K , L. C. V A N D E R M A R E L A N D C. J. G O R T E R

pronounced for the l :12.2 a n d l :14.5 salts; for each of the two salts a m e a n t e m p e r a t u r e function can be given. The deviation parameters given in fig. 4 indicate t h a t deviations from the behaviour defined by relations (3) and (4) occur especially at higher fields. •Generally deviations decrease at higher dilutions. It is clearly seen t h a t in the diluted salts the deviations increase suddenly at the high fields where the s h o r t e r relaxation parameters occur. The high frequency susceptibility Zoo --: (l -- F)Z0 differs from the expression (1) for the adiabatic susceptibility Zao as d e m o n s t r a t e d in fig. 5. F o r the undiluted salt these deviations decrease at lower temperatures. A t low fields a normal decrease of Zoo with H is always observed; from this LO

0.5 I : 14.5 K

~--'-0 0,5

I

3 1:21

0.5

3

I : 12.2

O.S 1:5.5

0,!

3

T

1-F

'-

- 222 I

O

H

!

2

3

F i g . 5. T h e r e d u c e d h i g h f r e q u e n c y s u s c e p t i b i l i t y Zoo/Z0 =

4kO¢

1 - - F as a f u n c t i o n of

He in cobalt ammonium sulphate and cobalt potassium sulphate powders.

Fully drawn lines give the theoretical curves 1 -- F = b/(b + CH2).

379

S P I N L A T T I C E R E L A X A T I O N IN SOME COBALT SALTS T A B L E II Values of measured b/C, calculated C/R and b/R Substance cobalt a m m o n i u m sulphate (CAS) powders

cobalt silico fluoride single crystals

(ROe 2)

:0 : 5.45 : 12.2 :21 : 9.51 : 9.5 II : 9.5 III : 37 K1 : 14.5 : /1 :0 .L : 1 0 1/ :lOJ_

CAS single crystals CKS powder

b/C

dilution, orientation

l

0

0.183 0.088 0.084 0.078 0.056 0.114 0.093 0.050 0.125 0.45 1.74

0.043 0.121

Ccalc/R g

= 11.27 x 10-1°g2 ( 10-8 deg ~ 0e -z)

b/R ( I 0-Sdeg21 4.19 2.01

2.29 2.29 2.29 2.29 3.66

1.92 1.79

1.68

5.70 3.86 4.36 5.70

2.14 3.66 2.29 (4.11) (1.o6) 3.82

(6.04) (3.07) 5.82 3.44

2.05 1.92 1.98

1.82 2.86 (18.5) (18.5)

1.33

1.66 1.62

(deg)'

2

t

0

I

c

50

F i g . 6. T h e s p e c i f i c h e a t c o n s t a n t

c= A ~" (D • (~

ot°/o

Co

100

b a s a f u n c t i o n of t h e c o b a l t c o n c e n t r a t i o n

1/(n+l).

Malaker 5) ] cobalt ammonium sulphate Benzie, C o o k e a n d V ~ r h i t l e y 8) This investigation cobalt potassium sulphate Benzie, Cooke and \Vhitley 8) This investigation

380

J. VAN DEN BROEK, L. C. VAN DER MAREL AND C. J. GORTER

it is possible to determine b/C in the usual way (c/. rel. (I), (2)). With the aid of the known g values 2) we find C1 ---- 5.70, C~. = 0.876, C3 = 1.78 cgs per mole Co. Using these we computed the values of b/R given in table II. These values are compared with those obtained by B e n z i e , C o o k e and W h i t l e y 8) and by M a l a k e r 5) in fig. 6. 2.0

1.5

1.0

0.5

0.0

-0.5

109 fit l 1 - '00

I 0.21o 9 T ~ 4

0.6

3.s

.

I •

.

I m-

3.0

2.5

2.0

1.5

A

1.0

o.~.2~

I 0.4

I H i~,1

I 2

I 4 kO¢ 0.2

I 0.4

I H 1

I 2

I 4kOt 0.2

I 0.4

H I

I

I 2

I 4k0¢

Fig. 7. poispl/(T) vs He a n d ](T) vs T for 1 : 9.5 diluted cobalt a m m o n i u m sulphate single crystals. (D pdisp/](T) (single relaxations) , & [(T) at low magnetic fields ~ p ' disp//( T ) ~ (double relaxations) ~7 [(T) at high m a g n e t i c fields • ~ p t t otsp//( T )

b. S i n g l e c r y s t a l s . Three rather large single crystals of diluted cobalt ammonium sulphate obtained from a 1"10 solution were ground to cylindrical shape in the following orientations:

SPIN LATTICE R E L A X A T I O N IN SOME COBALT SALTS

381

crystal I parallel to the Kl-axis, crystal III parallel to the Ks-'axis, and crystal II parallel to a direction in the ac-plane making 24 ° with the K2-axis and 34 ° with the a-axis. De corresponding g values are : gI = 5.70, glI =3.86, glII = 4.36. Using these we obtain from the susceptibilities a dilution 1:9.5. The relaxation parameters measured are given in tables III and IV and in fig. 7. 1.Oi 0.8-

r

0.6)

0.4 ~ 0.2

N

I

,

°0 ,o9,2~ Fig. 8. D o u b l e

relaxations Q

,:o

i:~

-~.~-

in 1 : 9.5 d i l u t e d c o b a l t crystal II at T = 3.503°K. H e = 2025 0 e ~7 H e He = 21370e ~ He He = 2250Oe [] H e

2'.s

3.0

ammonium

sulphate

= 2362 Oe = 2475Oe = 25870e

The general behaviour of the crystals is the same as that found for the powders. In addition a few new details are observed. The p(H) curves show a remarkable structure in the high field region. In a restricted part of that region double relaxations are found (fig. 8). Their relaxation parameters are given separately in table IV. The dependence of p on temperature is again different in the low and high field regions. All high field relaxation parameters vary approximately with T -2, just as in the powders. The low field

J. V A N D E N B R O E K , L. C. V A N D E R M A R E L A N D C. J, G O R T E R

382

TABLE

III

Relaxation parameters (in ms) of diluted cobalt ammonium Tutton salt single crystals He(Oe)

0

225

450

675

900

1012

I 1 2 5 1350

1575

1687 1800 191~

151 153

108 136 I12 i I17 92 97,

T(°K) I : 9.5 crystal I

1.33 {

pdlsp

288oo

22ooo

2o5oo

1.65 2.036 {

pdlap

z~6oo 7800

2oooo 8800

266oo 8800

1230

1380

3.005 {

pabs

pabs pdlsp

I

paba

3.497 {

palap

4.005 (

pdlsp paba

!

1050 (1050) 490 380

p~bs

1260

500 470

890

i 350 (1200) (810) 430

210 215

300 280 245 255

225 205 172

510

420

215 210 I57

370!

370

162 !182

1 : 9.5 crystal II 1.23

2.087 3.004 {

3.505 { 3.998 {

4.461 {

282oo : 9500

238oo

273oo zo5oo

pdlsp pabs

pdlap pabs

234oo zz4oo

(5ooo)! (6500)

6000

Pdlsp Oab8

~63oo 223oo

450!

460

420

420

(510) 186 186

520

(450) 200 179

pdtap

I !

400

pab,

' zz9oo

430 340 (430) (390) 172 168

260 210

81[ 79

1 : 9.5 crystal I I I 1.30

1.816 2.082 {

2.498 3.005

{

3.503 { 4.002 {

pdl~p

Oabs

pdl,p paba

47000 38000 17ooo

5zooo 3zooo 20000

44000[25000 25000 226oo 22000 z38oo

8200 6300

92oo 35oo

zI4oo 3500

io9oo i 8800 (4000) 4900

7500

I

e9oo

I

250 255

500 280 1 9 8 ( 4 4 0 ) 246 215

I

380

(370)

i

I 176 180

Oal~p pabs

480

palsp

560

(510) (590)

pabs

590

(600)

6OO

580

(580)

--

275

]

157

235

(230) 145

215

I : 37 K,-axis 1.22 1.720 2.087 {

2.492

palsp p~ba

3.310 3.598 3.998 {

44ooo (44ooo)

27000

2Iooo

7800

patsp pabs

5ooo

iSzoo

(1000) --

(225)

(3000)

680 --

184 200

l

z48oo

2.778 3.001 {

82000 38000

I

275

i 3500

3zoo 2400

630

P dlsp

620 (600)

(630)

pabs

I 490

138 135

I (510)

I : 37 Ks-axis 1.789 1.951 2.127 2.484 2.998 4.137 {

pdlsp pdtap psbs

3zooo 282oo z76oo 3000

"35000 3zooo 28000 25000 27600 ze6oo

400

320

28000 z88oo zzoool zz3oo i

310

280 L

'

383

SPIN LATTICE RELAXATION IN SOME COBALT SALTS

TABLE

III

(Continued)

Functions of H c a n d T ( N u m b e r s i n italics h a v e b e e n m e a s u r e d p h o t o g r a p h i c a l l y )

2025

22501247512700

281212925

303713150[3375

3600

3825

3960

4050

4275

4500

I : 9.5 c r y s t a l 141 145

480 43O

82 91 34 32 35 33 22.0 21.0

285 25O 120

92 93

(120) 115 105 72 73

1 : 9.5 crystal II

430 400 360 340

186

255

220

(225)

260 25O 230 20O 137

(1oo) 1o5 105 I : 9.5 c r y s t a l I I I

330 290

159 155

300 (235)

200 --

250

192

89

250

205 133

(80)

150

142 115 116

152

141 153

38 36 23.5 22.0

65 57

1 : 37 K , - a x m

205

360

490

(340) 143 182

255 234

250 234

225 (225)

240

143 182

145 182

-

220 186

-

114 138 74 71

92 87

162 155

1 : 37 K 2 - a x i s

(lOOO) 270

245

340

50 3l 29.0

41

138 92 90

225

200

155 85 81

384

j. V A N D E N B R O E K , L. C. V A N D E R M A R E L A N D C. ]'. GORTER TABLE

IV

Double relaxation parameters (in ms) of 1 : 9.5 cobalt ammonium Tutton salt single crystals as functions of He and T 1575

1687

1800

T (°K)

I

1 9 1 2 2025

2137

2250

I

2362

2475

2587

I

2700

2812

2923

crystal I )t~lip )'=b, )udisp )~alos )t(yJap

4.3O (22o) 52

2.03(

fsbs ~#d.lip 3x&bl :f(tlip

3.00' "

)'~b, :)~dlsp )~abs )'¢Lisp )'=l), )#dJllp 2"=b| 3"dlip

(180) 42 4O 215 175

1.33

3.49~

4.00~

620 I

(360) I

36o

330

(135) (125)

143

~.6

137

~'=b, ~#dlsp

I 15.5

~)'abl

(11.2

1% I

17o .I

14.2 225 210 16.0

i

20.0

152

I

112

I

93 91 (12.6)

,_,.8[I

134

(213) 25.0

tlO7 I •

10.2

(12.61

crystal II

f~,o [ P'." p amp II

3,004

P;'" p .lip I

171 243 10.4

O'&bJ ~);=,p p abs p'dlip pS,.~, p dlip p~abs

3,505

3.998

•

380

I(31o Jo

10.9

290 32 32

1;;

(33)

200

2OO

(°21 (300!6 (i~'i i~

(243) 9.8 (15.81

2801 I0.7

p~=,,, ! P.=,,, p ¢u,p [

4.461

550) 380) 10.7 (11.2 26O 280

62

(80) 8.8

109

18.o

17.1 18.2

pSabs crystal I I I fl p'tuep 2.090 Jl p~.,.b,

II P ='° t l p"=bt fl P ,,li.

1(5oo)

(243)

(62--)

36O

912 ~

99

43O 370}

g;

430 (3701

(100) 73

N18.2

(86)

3.005 ~l p~,b,

/I p.(u,p ~,1 P/")" /I P ~"

/I 4.o02 .~1 /I tj

P'~"°

P>" P '~p /=-

(16) 215

{126) 20

3.5o3 ,~1 p',b, /I~,I Pp',,t,. ='~

123 1 .

.5

108 (801 13.2 (161

205) 42

360 320

35

135 101 12.6

I~ 118 --

(161

values however have a very strong temperature dependence ( ~ T -7) down to rather low temperatures now. The high frequency susceptibility Zoo = ( 1 - _F)Z0 has an abnormal behaviour in the field region where the double relaxations occur, as demonstrated in fig. 9. The b/C and b/R values obtained from the normal parts .of the 1 -- F curves are given in table n and ill fig. 6.

SPIN LATTICE RELAXATION IN SOME qOBALT SALTS

385

In fig. 9 we also give the intermediate 1 -- F ' values corresponding to the double relaxations (c/. fig. 2). T h e y v a r y rapidly with v a r y i n g field. 1.0

1.O

O.S

0,5

1

H

t

1

1=. 2

3

4 kO¢

Qeeoo~ O.5

I

H

~

2

4 kOe

~ o.sL

~

i

1

H

Ib

mmm~m

2

3

4 kOe

2

3

4 kO¢

I-F

0

H

1

Fig. 9. The reduced high frequency susceptibility Xoo/X0---- 1-F and the quantity l-F" (cf. fig. 2) in the 1 : 9.5 diluted single crystals. + x A Physica

25

T=4.0°K T=3.5°K T ----3.0°K

(9 []

T=2.1°K T= 1.3°K-

386

J. VAN DEN BROEK, L. C. VAN DER MAREL AND C. J. GORTER

All anomalous effects found have a strong crystalline anisotropy. To characterize this we give the values of the magnetic field where the first minimum of p(H) occurs: H I = 1160 Oe, HII = 1690 Oe, Hi11 == 1490 Oe. Within the limits of accuracy these values are found to be inversely proportional to the g-values for the three directions. 1=;

x,

X2

10

Q~

0

-O.5 log t~ -t.~

I

4

O to9 o2T==

I

04

0

0.6

I

IogT

02

0,6

Q4

4D X2 35

3D

1°9 f ~ i t~

I

0.2 0.4

I

I

I

.2

I

I

4 kO¢ 02. 0:4.

I I

I 2

I

kOt

Fig. 10. pdisp//(T) vs He a n d /(T) vs T for the 1 : 37 diluted cobalt a m m o n i u m sulphate single crystals. A /(T) at low magnetic fields V /(T) at high magnetic fields

The deviation parameters given in fig. 4 are smallest at low magnetic fields in agreement with the powder results. Generally the deviation parameters are Smaller for the crystals than for the powders. L~ke most of the differences between powder and single crystal results, this m a y be a consequence of the fact that in the powder all orientations are present and so all anisotropic phenomena are mixed up. This results in a broadening of dispersion, absorption, p(H) and 1 -- F curves as found experimentally.

SPIN L A T T I C E R E L A X A T I O N

IN S O M E ,COBALT S A L T S

387

Two diluted single crystals obtained from a l: 40 solution have beei~ investigated. They were ground parallel to their K1- and K2-axes, respectively. With gl = 5.70 and g2 = 3.06 we obtain from the measured Curie constants a dilution 1:37. The measured p values are given in table I I I and fig. 10, the deviation parameters in fig. 4. The main difference with the 1:9.5 crystals is the absence of double relaxations and anomalies in the high frequency susceptibility. The b/C value obtained from the 1 -- F curve for the Ks-axis crystal is given in table II; for the K2-axis the accuracy was not sufficient to state more than t h a t b/C was between 0.1 and 0.2 kOe 2. At low fields and in the higher temperature region the dependence of p on temperature is about a s T -7.

At the first minimum of p(H) we find Hmin = 1930 Oe and 3510 Oe, respectively, which values are considerably larger than those found in the 1:9.5 crystals but which again are inversely proportional with the corresponding g values. c. C o b a l t s i l i c o f l u o r i d e . Undiluted and 1:10 diluted crystals of cobalt silicofluoride were investigated in the ;g// and ~¢± directions. As demonstrated in tables V and VI and in fig. 11, these measurements did not reveal any abnormal behaviour such as found in the Tutton salts. Writing p = 2:~CI-I/~ = 2_,~(b + CH2)/~T 2 we find that in the undiluted salt the heat transmission coefficient a is isotropic except perhaps at the highest fields, while in the I:10 salt the anisotropy ~///~± increases gradually from 1 to about 2 with increasing field. The 1 -- F curves are normal. The b/C values are given in table II. Those found in the undiluted salt can be brought into agreement with B e n z i e , C o o k e and W h i t l e y ' s value b/R = 18.5 × I0 -a for the powder 8) by taking g//---- 6.04 and g± = 3.07. These values do not agree very well with B l e a n e y and I n g r a m ' s g values for very dilute samples (g/!-- 5.82, g± =: 3.44 2)). The deviations from Casimir-du Prd behaviour (rel. (3) and (4)) (see fig. 4) are very large in the undiluted samples, as is usual in large samples of nondiluted salts; deviations in the diluted crystals are smaller, increasing slightly at the highest fields in one case.

4. Discussion. We regret that we are unable at this, moment to propose an explanation of the marked anomalies observed in the cobalt Tutton salts. It is striking that the field at which, in the single crystals, the first sharp minimum of pay occurs is apparently inversely proportional to the g value in the direction of the field. This suggests that the absolute value of the magnetic splitting in the salt is of importance. This direction independent splitting is about 0.31 cm -1 in the 1:9.5 crystal and 0.51 cm -1 in the 1:37 crystal. When this splitting is introduced by the external field, apparently a

388

J. V A N

DEN

BROEK,

L. C. V A N

DER

TABLE

MAREL

AND

C. J. G O R T E R

V

Relaxation parameters (in ms) of undiluted cobalt silicofluoride single crystals as functions of He and T

~ e )

1 225 I

450

Odlsp

3.006

pabs pdlsp !

3.993 {

1.80 1.02 0.57 (0.56) 6.3

,f t

1.43 1.812

{

(7.6) 4.7 3.2 2.25 2.10

Odtsp pabs

2.104 {

pdlSPpabs

2.995

pdlsp

1350

1800

2250

2812

1.33 0.94

1.29

(1500)

illl 98

1.38

1.36

0.88

0.95

0.62 (0.63) X.L-crystal 6.6 5.0 (8.8) (I0) 4.7 3.2 2.65 4.4 2.15 1.76 1.91 1.70 1.52 1.66 0.94 0.89 0.76 0.66 TABLE

3375 I

I

3.6 2.8 1.86 2.95

l

(0.77)

p.,bs i pdisp ! (o.4) pabs i --

pdlsp pabs ~" pdlsp I. pabs

1.30

i125

Zii-crystal 27.5 28.0 2.95 2.45

20.5 I 20.0 2.55

2.071 {

t

900 i

~" pdiap t p~bs

1.27

675

i

1.16 1.48 0.75 1.00 (0.68) (0.83)

i 5.5 2.20 1.45 1.07

II.I 7.8 I0.3 4.2

2.05

I(o.74)

4.3

3.8

3.3

3.1

3.3 3.8 1.53 1.48 1.46 0.81 0.6

3.1 4.4 1.37 1.36 1.43 1.00 0.67

3.4 4.7 1.31 1.15 1.56 1.20 0.75

3.7 6.0 1.23

1.01 1.68 1.25 0.83

VI

Relaxation parameters (in ms) of I : I0 diluted cobalt silicofluoride single crystals as functions of He and T

/-/c(Oe) l,

T ( OI ' ~) ~

!

[i

1.27 1.740

{

pdisp pabs

2.097

{

pdlsp

3.010

{

4.001

{

3.015 { 3.972 {

z5oo

x35o

133 135 29.0

(195) 50

55 3.0 3.1 0.6 (0.6)

225

450

pdlsp pabs pdisp p.bs

17.5 18.6

23.5 1.66 1.86

[

675

'

900

(0.6)

85 23.0

99 102

0.96 1.0

I

pabs

I

72 72

330 (340) 90 93 5.8 5.6

I

84

1800 2700 3375 4500

z/l-crystal x85o (r9oo)

Z j_-crystal 126 129 31 38 29.5 36 2.75 3.2 0.5

pdlsp pdlsp p,b,

iI 9 0 0 ' 1i 1 2 5

675

220

(0.3) (0.3)

.o,oe)

2.124 {

450

28.0

pabs pdisp pabg pdlsp pabs

T (°K)~

1.793 {

225

220 (2O0) 97 96 9.2 8.9

94

89 10.7

1.53

1.48 1575

159 • 159

56 58 4.8 5.4 0.8 1.0

143 129 71 68 11.9 10.3

9.6 2.05 2.20

] 2250I

3150

4500

157 145 65 72 6.4 6.3 I.I, 1.3

146 141 69 76 8.3 8..~ I.~3 1.74

70 74 II.I I0.0 2.25 ! [# 2.20

SPIN L A T T I C E R E L A X A T I O N

IN S O M E

COBALT

389

SALTS

new and very effective relaxation mechanism has started which depends relatively weakly on T and therefore is more striking at lower temperatures. It may be remarked that the total hyperfine splitting is 0.09 cm-1 and thus is much smaller than the magnetic splitting found, while both the electric splittings and the Debije cut-off frequency are much larger. 3.O

2.~

Xll

I:0,

1 : 0 t X2.

: tO,

Xll

t:lO,

Xa.

2O

15

.

&

ID

-05 + log liT) -I.(

0

I

I

0.2

I

0,4

laqT •

0.6

I 0 iogTQ2=

I 0.4

I O.6

I 0 i0 g TO.2

I 0.4

to,x

.¢

ID

Q5

,o0 -0.5

02

9 I 04

H

I |

I 0 IogT02=

I 0.4

/

/ • /

I : O,X//

I 06

I:10,

/

~-0.6

/ ,o×+

X//

/

• ' o:/

/ /

/

/

I 2

4k0¢0.2

I I 0.4 H ==1

I 2

L 4k0¢0.2

I I 0.4 H ==1

I 2

¢

4kOtO.2

0.4

l

I

H =!

2

4k0¢

Fig. 11. pdlsp//(_F) VS H c a n d / ( T )

v s T f o r the u n d i l u t e d and 1 : lO diluted single crystals of cobalt silico fluoride.

The situation is particularly complicated at the intermediate concentration 1:9.5 w h e r e w e find double relaxation times and anomalously high 1 -- F values indicating the existence of a still shorter spin-lattice relaxation time. This complicated behaviour may be connected with the fact that some

390

SPIN L A T T I C E R E L A X A T I O N IN SOME C O B A L T SALTS

of the cobalt ions have no other cobalt ions as nearest neighbours while, on the other hand, large fractions have one or two cobalt ions as nearest neighbours. But again we cannot propose a satisfactory explanation. We finally wish to stress that the coupling between the cobalt ions and the lattice is known to be very much stronger than in the case of ferric, chromic and manganous ions. In the latter ions the magnetic and mechanical moments are almost exclusively due to electronic spins, but for the cobalt ions the orbital contribution to the moment in the ground state is higher b y a factor of the order 102. Another indication of this is a spin-lattice relaxation time which is at least 103 times shorter at liquid air temperatures. It m a y therefore well be that the non-elastic scattering of phonons -- sometimes called the quasi-Raman effect -- which should be negligible at liquid helium temperatures in other salts, plays an important r61e in the relaxation of cobalt salts at these temperatures. The strong temperature dependence (T -7) of this process at temperatures small compared with the Debije temperature m a y be responsible for the relaxation both in the diluted Tutton salts at low fields and in the fluoro silicates. At still lower temperatures a mechanism which is less strongly dependent oll temperature must be expected to take over and this is, in fact, indicated b y the data. The authors wish to express their thanks to Mr. B. U. F e l d e r h o f , nat.phil.cand., to Mr. S. L. Th. v a n Agt, nat.phil.cand., to Dr. J. P a ~ e s (Praha), to Dr. F. G o m e z B e l t r a n (Zaragoza) and to Dr. M. A. L a s h e e n .(Alexandria), who cooperated with them during experiments and calculations. They are very indebted to several members of *.he technical staff of this laboratory for valuable advice and help. Received 1-2-59

REFERENCES 1) H a s e d a , T. and K a n d a , E., Physica 22 (1956) 647; Physica 24 (1958) p. S 166. 2) B l e a n e y , B. and I n g r a m , D. J. E., Proc. roy. Soc. A 208 (1951) 143. 3) K r i s h n a n , K. S., C h a k r a v o r t y , N. C. and B a n e r j e e , S., Phil. Trans. roy. Soc. London A 232 (1933) 99.

4) 5) 6) 7)

t

B a r t l e t t , B. W., Phys. Rev. 41 (1932) 818. M a l a k e r , S. F., Phys. Rev. 84 (1951) 133. G a r r e t t , C. G. B., Proc. roy. Soc. A 2@6 (1951) 242. V a n d e r M a r e l , L. C., V a n d e n B r o e k , J. a n d G o r t e r , C. J., Commun. Kamerlingh Onnes Lab., Leiden No. 306a; Physica 23 (1957) 361. 8) B e n z i e , R. J., C o o k e , A. H. and W h i t l e y , S., Proc. roy. Soc. A 23"2 (1955) 277.