Journal of Magnetism and Magnetic Materials 123 (1993) 141-146 North-Holland Ad/

An improved detection coil system for a biaxial vibrating sample magnetometer

J.P.C. Bernards, G.J.P. van Enge l en and H.A.J . C r a m e r

Philips Research Laboratories, P.O. Box 80.000, 5600 JA Eindhoven, The Netherlands

Received 29 September 1992

A detection coil system, consisting of 12 coils, for use in a biaxial vibrating sample magnetometer is described. For such a coil system the dependence of the sensitivity on the position of the sample is much smaller than for other systems, not only for the detection of the magnetisation component in the direction of the applied field, but also for the detection of the magnetisation component perpendicular to the applied field.

1. Introduction

The measurement of the magnetisation vector with a vibrating sample magnetometer (VSM) is very useful for magnetic anisotropy measure- ments with a VSM [1,2], for recording simulation experiments [3,4], for measuring intrinsic hystere- sis curves [5-7] and for determining the easy magnetisation direction [8]. A coil configuration suitable for measuring the magnetisation vector has to meet the following requirements:

• it must be biaxial, i.e. it must be possible to measure the magnetic moment in the direction of the applied field (x direction) and perpen- dicular to the applied field (y direction; the sample is assumed to be vibrating in the z direction);

• there must be enough space for the sample between the coils;

• the sensitivities for both measuring directions must be sufficient and the noise must be low;

Correspondence to: Dr. J.P.C. Bernards, Philips Research Laboratories, P.O. Box 80.000, 5600 JA Eindhoven, The Netherlands. Tel.: +31-40-742351; telefax: +31-40-744282; e-mail: BERNARDS@PRL.PHILIPS.NL.

• the dependence of the sensitivities on the posi- tion of the sample must be small;

• the effect of a magnetic moment perpendicular to the measuring direction on the measured signal (cross talk) must be small. Note that this also depends on the position of the sample; for an infinitely small sample in the centre of the detection coil system the cross talk is zero for symmetry reasons.

The last two requirements are especially impor- tant when large samples are used or when angle- dependent measurements are performed. In all the applications of a biaxial VSM mentioned above the sample is rotated in the xy plane during the measurements. The position depend- ences of the sensitivities result in a change in the detected signal for two reasons. Firstly, in most cases a thin sample is used without cylindrical symmetry in the plane of rotation. Secondly, it is very difficult to keep the sample exactly in the centre of the detection coil system during rota- tion. Therefore, the position dependences in the xy plane have to be small.

The most common coil configuration for a uniaxial VSM is a configuration with 4 coils which have their axes parallel to the x direction [9] (fig. 1). The position dependence of the sensitivity and

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142 J .P .C . B e r n a r d s et al. / De t ec t i on coi l s y s t e m f o r a V S M

~ H Fig. 1. Coil configuration for a uniaxial VSM.

the cross talk are quite large for such a configura- tion. To improve this, a configuration with 8 coils, which have their axes perpendicular to the x direction, has been proposed [10] (fig. 2a). Such a configuration has a very small position depen- dence of the sensitivity in the x direction and also the cross talk is small. However, the noise induced by small rotational vibrations of the coils in the applied field is large [11]. This noise is proportional to a, the amplitude of the rotation. If the axes of the coils are parallel to the applied field, the noise is proportional to a 2, which is much smaller for small a.

For a biaxial VSM four coil systems are men- tioned in the literature:

al b)

C Dz

)v

c) d)

Fig. 2. Coil configurations for a biaxial VSM.

• the same 8 coil configuration mentioned above [12] (fig. 2a)

• a 4 coil configuration with the axes of the coils parallel to the z direction [13] (fig. 2b);

• two independent sets of 4 coils, one for detec- tion in the x direction and the other for detec- tion in the y direction [14] (fig. 2c);

• a configuration with 8 coils with their axes parallel to the applied field [3] (fig. 2d).

Table 1 shows the way in which the signals from the different coils have to be added for the four configurations to measure the two magnetisation components.

The noise generated by small rotational vibra- tions of the coils is smallest when the coil axes are parallel to the applied field (fig. 2d), as ex- plained above. In addition to this, the position dependences and the cross talk are also smallest for the fourth configuration. This configuration is the best compromise between the requirements in both measuring directions and combines suffi- cient sensitivity in both directions with position dependences and cross talk which are reasonable, but still substantial. Some examples of such a configuration, their calculated sensitivities and their position dependences are shown in table 2. Because we use in our VSM an electromagnet to apply fields, the presence of images, due to the soft-magnetic properties of the pole shoes of the electromagnet, was included in the calculations as it has been shown [15] that they contribute signifi- cantly to the measured signal. Further details on the calculations can be found elsewhere [11,16].

Table 1

The way in which the signals from the coils have to be added

to measure the magnetisation components M x and My for the coil configurations in fig. 2

Coil no. 1 2 3 4 5

a M x - + + +

a M y - + + -

b M~ + + -

b M y + +

c M~ - - + +

c M y

d M~ - + + -

d M y - + + - +

6 7 8

- +

+ +

+ + + +

+

J.P.C. Bernards et al. / Detection coil system for a VSM 143

.el

<1

<1

<1

o)

e~

k~

x~

e~

I I I I I I I I

I I I I I P I

I I

I n I ~ ~ I I

¢Q o0 ,~- ¢ q ~ - t 'q

• , .

ca

144 ZP.C. Bernards et al. / Detection coil system for a VSM

In our calculations we restricted ourselves to the sensitivities and their position dependences; con- siderations about the noise of such-coil systems are published by Richter [17].

The problems caused by the substantial posi- tion dependences and cross talk can be reduced by using a very small sample and a high precision rotation system, or constructing a coil system with smaller position dependences and smaller cross talk. In this paper we will show that the latter solution can be achieved with a coil system con- sisting of 12 detection coils.

2. Calculations

As mentioned above, the coil configuration of fig. 2a can be constructed in such a way that it has a very small position dependence of the sensi- tivity (S~) for the magnetisation in the x direction (M~) [10] and little cross talk. The basis of our 12 coil configuration is such an 8 coil configuration, but the coil system is rotated over 90 ° . This results in a configuration with a very small posi- tion dependence of the sensitivity (Sy) for the magnetisation in the y direction (My). In addi- tion to this, the noise induced by vibration of the coils in the applied field is low because now the coils have their axes parallel to the applied field. An example of such a configuration is shown in

z

Fig. 3.12 coil configuration for a biaxial VSM.

table 2. To this set of 8 coils, which are used for measuring M X and M v, 4 coils are added which are used for measuring Mx only. This 12 coil configuration is shown schematically in fig. 3. The sizes and positions of the 4 coils are optimised to minimise the position dependence of S x. At the same time, the cross talk between both compo- nents is greatly reduced too.

An example of such a 12 coil configuration is shown in table 2. The sensitivity, the position dependences and the cross talk are compared with the 8 coil configurations. The sensitivities are comparable to the sensitivities of the first 8 coil configuration, but the position dependences and cross talk are much smaller. The space for the sample is less than for the 8 coil configura- tion, but it is still sufficient (17 mm; the sample size rarely exceeds 10 ram).

3. Experimental results

The 12 coil configuration of table 2 has been constructed and the position dependences of the sensitivities have been determined experimentally by using a sample with a size of less than 1 mm in the direction of displacement. In addition to this, the position dependences of S x of both coil sub- sets (8 and 4 coils) have been measured sepa- rately. All measured curves have been compared with the calculations.

Figs. 4a and b show the results for the 8 and 4 coil subsets, respectively. When the sample is displaced in x or y direction, S x changes very rapidly for both subsets, but in opposite direc- tions. When the two subsets are combined to a 12 coil configuration, these changes compensate each other. This results in an S x which hardly changes when the sample is displaced from the centre, as is shown in fig. 5 (note the different scales in figs. 4 and 5).

Fig. 6 shows the dependence of Sy of the 12 coil configuration on displacement of the sample (which is the same as for the 8 coil subset since only 8 coils are used for measuring My). Again a small position dependence is measured. In all cases the measured curves agree very well with the calculated ones.

J.P.C. Bernards et al. / Detection coil system for a VSM 145

aSx [%]

t

50 50

25

-25

-50

Y •

5 10 position [ram]

aSx [%]

25

-25

-50 0

Y •

5 10 ~- position [mm]

Fig. 4. Measured (symbols) and calculated (lines) position dependences of the x sensitivity (S x) for the 8 coil subset (a) and for the 4 coil subset (b) for a displacement in x, y and z direction.

The cross talk has also been measured. In both cases the cross talk was too small to be measured accurately.

4. Remarks

The configuration built by us is just an exam- ple of a 12 coil configuration suitable for vector

20

ZlSx [%] 10 o ~ l • Y

x • • o

0 , - - - -

-10

-20 5 10 position [mm]

Fig. 5. Measured (symbols) and calculated (lines) position dependence of the x sensitivity (S x) for the 12 coil configura-

tion for a displacement in x, y and z direction.

magnetisation measurements. Other combina- tions of 8 and 4 coil subsets might be appropriate too. The choice of coil distances and sizes will depend on the particular requirements and limi- tations of each VSM, such as sensitivity needed, allowable sample size, distance between pole shoes (50 mm in our case) and type of measure- ments to be carried out.

20

~s~ [%]

10

-10 x ~

-20 5 10 position [mm]

Fig. 6. Measured (symbols) and calculated (lines) position dependence of the y sensitivity (Sy) for the 12 coil configura- tion for a displacement in x, y and z direction. The calcu-

lated curves for y and z displacements coincide.

146 J.P.C. Bernards et al. / Detection coil system for a VSM

5. Conclusions

The proposed 12 coil configuration for a biax- ial VSM is much better than the configurations available at the moment. It is even better than the available uniaxial VSMs. A small position dependence is obtained for measuring the mag- netisation component in the x direction as well as for measuring the magnetisation component in the y direction. The cross talk is small too.

An example shows that the average position dependences in the xy plane can be 5 times better compared to a typical 8 coil configuration with comparable sensitivities. The measurements with the realised system agree well with the calcu- lations.

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