Magnetic domain structures in CrBr3

Physica 80B (1975) 365-373 © North-Holland Publishing Company

M A G N E T I C D O M A I N S T R U C T U R E S IN CrBr 3 * B. KUHLOW and M. LAMBECK

Optisches Institut der Technischen Universitiit Berlin t, 1000 Berlin 12, Germany

Ferromagnetic domains in CrBr3 were made visible by means of the magneto-optic Faraday effect at 15 K. Meander, strip, and honeycomb domains could be produced at will by applying suitable fields during the cooling of the specimen. The influence of an increasing field normal to the specimen on these structures was studied. A honeycomb structure is transformed into a high-density state of bubbles. In a structure of wavy strip domains new coneshaped domains detach from the wavy peaks, thereby straightening the strips which finally contract to a low-density state of bubbles. The measured field dependences of domain sizes are in good agreement with theoretical calculations given in the literature.

1. I n t r o d u c t i o n CrBr 3 is f e r r o m a g n e t i c below 32.5 K 1,2) with a magnetic m o m e n t o f 3.0/.t B per Cr 3+ ion (Js = 0.34 Vs/m 2 at T = 03). T h e easy axis o f the mag n e t i z a t i o n is parallel t o the h e x a g o n a l c-axis which is the n o r m a l o f the graphite-like crystal platelets 4). Due to the high m a g n e t i c a n i s o t r o p y (KI = 9.3 × 104 J / m 3 at T = 0) the m a g n e t i z a t i o n lies in this easy axis w h e n n o external field is present s ). T h e high e n e r g y o f the demagnetiz a t i o n stray field leads to the f o r m a t i o n o f d o m a i n s with alternating antiparallel m a g n e t i z a t i o n . CrBr 3 is o n e o f the few f e r r o m a g n e t i c ion crystals which are transparent for visible light. T h e r e are t w o transmission bands, o n e for red light ( 6 0 0 to 7 0 0 nm), the o t h e r for green and blue light ( 4 7 0 to 5 5 0 nm). The F a r a d a y r o t a t i o n for green light is m u c h higher t h a n for red light, and the highest values are o b t a i n e d f o r blue light near the a b s o r p t i o n edge. F u r t h e r m o r e , the a b s o r p t i o n c o e f f i c i e n t s for right and left circularly polarized light d e p e n d o n the d i r e c t i o n o f the m a g n e t i z a t i o n . This circular dichroism is especially strong f o r blue light 6). C o n s e q u e n t l y , t h e r e * This work was supported by a grant of the ERP fund. t Ehemaliges I. Physikalisches Institut. 365

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B. K u h l o w and M. L a m b e e k / M a g n e t i c d o m a i n structures in CrBr a

are two possibilities to observe the magnetic domain structures in CrBr3 : 1) Using the rotation of the plane of polarization by the Faraday effect, the specimen is illuminated with linearly polarized light and observed through an analyzer which transforms the different states of polarization into image contrasts 7,8). This technique is employed for fig. 2; and 2) Using the circular dichroism, the specimen is illuminated with blue circularly polarized light so that differently magnetized domains appear as dark and bright areas, respectively, due to their different absorption coefficients. No analyzer is needed. This technique was employed for the figs. 1 and 5.

2. Experimental procedure The CrBr 3 crystals were cooled by means o f a liquid-helium cryostat between the poles of an electromagnet producing a field of up to 350 kA/m. The domains were observed with a microscope in the bore of the pole pieces using KiShler illumination and a high illumination aperture 9). The aperture o f the microscope was 0.85 so that a resolution o f 0.3/am could be obtained for blue light. The light source was a mercury high-pressure lamp HBO 200. Interference filters for 546 nm and 491 nm were used to select special bands.

3. Results and discussions The following domain structures were observed at a temperature of 15 K in a CrBr 3 single crystal with a thickness of (12 + 2)/am. When the crystal is cooled below the Curie temperature Tc, a domain structure is formed which is stable during further cooling. If there is no external field present when the specimen is cooled below Tc, the spontaneously growing structure consists of meander-like strip domains including some h o n e y c o m b domains 10-12 ). It is possible to produce different domain structures by applying relatively weak fields when the specimen is cooled below T c. If there is a field of 10 to 20 k A / m in the plane of the specimen, the strip domains are aligned nearly parallel to the field. If a field of 25 kA/m is applied normally to the specimen, a h o n e y c o m b structure shows up, the magnetization inside the hexagonal honeycombs being antiparallel to the field lO,~) (dark areas in fig. 5a). All the following experiments were performed at a temperature of 15 K. When these structures are exposed to an increasing external field nor-

B. K u h l o w and M. L a m b e c k / M a g n e t i c domain structures in CrBr 3

367

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Fig. 1. F o r m a t i o n of cone-shaped domains out of a meander-shaped d o m a i n structure under the influence of a field normal to the specimen. L o w e r part: domains in a CrBr 3 crystal ( 12 + 2/~m thick) at 15 K (the same for all following pictures), illuminated with blue circularly polarized light, a) H = 0 k A / m ; b) 33 k A / m ; c) 172 k A / m . U p p e r part: graphical interpretation of the d o m a i n structure.

real to the plane of the platelet, the domains magnetized in the direction of the field are energetically favored so that they grow at the expense o f the domains magnetized antiparallel to the field. Further increase o f the field finally leads to a uniform magnetization o f the whole specimen in the direction o f the field (saturation). When the field is decreased, a meander-like domain structure is formed which is independent o f the structure existing before saturation. The strip domains are significantly broader ( 3 0 - 5 0 % ) than the strip domains which are formed when the specimen is c.ooled below T c 13). The behavior o f the meander-like strip domains in an increasing field is demonstrated in detail in the lower part of fig. 1, while the upper part of fig. 1 contains graphical interpretations o f the corresponding domain structures ~4-16). Part " a " shows the demagnetized state without external field. The wavy structure of the domains is clearly visible, thus confirming the theory o f Goodenough predicting this structure as a means to reduce the stray field energy without closure domains 14). When the field is further increased, the disadvantageously oriented (dark) domains move apart from each other (part " b " o f fig. 1 ), coneshaped domains detach from the wavy domains, thereby straightening

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B. K u h l o w and M. Lambeck/Magnetic domain structures in CrBr 3

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the domains from which they emerged. These cone-like domains move half-way between the remaining domains so that the stray-field energy is further decreased b y this almost homogeneous distribution o f the domains. The cone shape o f these new domains as graphically shown in the upper part of fig. 1 is inferred from the fact that their Faraday rotation has less than half the value of the strip domains which extend from one surface of the crystal to the other. Further increase o f the field transforms all wavy peaks of the domains

B. K u h l o w and M. L a m b e c k / M a g n e t i c d o m a i n s t r u c t u r e s in CrBi" 3

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into cone-shaped domains positioned in the.middle between the remaining straight domains (part " c " o f fig. 1). At the surface o f the crystal the cone-shaped domains have a diameter o f about 0.4/am, which is just slightly above the limit of the optical resolution. The behaviour o f these domains in a further increasing field is shown in fig. 2 in the order a, b, c, d. The values o f the fields are given next to the pictures. The cone-shaped domains disappear before the saturation is reached. In a slightly higher field the remaining straight domains begin to reduce their length so that each straight domain contracts to a single cylinder-shaped domain 17). These domains are also called "bubble domains". These bubble domains are stable within a narrow interval o f the field. When the field exceeds this interval the bubbles collapse so that the specimen is saturated. When the field is decreased starting from the saturated state, first only strip domains appear ("f", "g" in fig. 2). The cones suddenly appear ( " h " in fig. 2) in a field which is m u c h lower than the field in which they

370

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vanished during the increase of the field. The cones arrange themselves regularly in the middle o f the strip domains ("i" in fig. 2). During further decrease of the field the cones attach to the strip domains so that the wavy domains are formed again when the field is switched off (fig. 1a). The widths of the strip domains in the increasing field are plotted in fig. 3. The width, d,, of the domains oriented disadvantageously with respect to the field decreases approximately linearly with the field. The width d 2 of the advantageously oriented domains increases slightly in low fields but strongly in high fields. The sum d, + d 2 is the period o f this domain structure. This period is plotted in fig. 4 as a function o f the field increasing to saturation and decreasing afterwards. The appearance o f the cone domains is marked by an increase o f d, + d 2 at 178 kA/m. During further decrease o f the field the curve is significantly higher than the curve in the increasing field. This is caused by the somewhat impeded rearrangement of the cones into the most favorable positions. The behavior o f the strip domains under the influence o f an external

B. Kuhlow and M. Lambeck/Magnetic domain structures in CrBr a

371

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Fig. 5. Honeycomb domains in an increasing field. The bright areas are energetically favored by the field (see text). Illuminated with blue circularly polarized light. field has been calculated for straight domains only 17,18). Therefore, only these structures appearing in the decreasing field up to the point o f renovation o f the cone-shaped domains could be compared with theoretical calculations. In agreement with Goodenough's theory ~a) the width of the wavy domains in zero field is considerably greater than the value calculated by Kittel 19) and M~ilek and Kambersk~ 23) for simple strip domains. The behavior o f h o n e y c o m b domains 20) under the influence of an increasing field is shown in fig, 5. Reverse domains (i.e., domains whose magnetization is antiparallel to the field) are shown as dark areas. Therefore, the pictures at the left side o f fig. 5 were taken with fight circularly

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B. Kuhlow and M. Lambeek/Magnetic domain structures in CrBr 3

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polarized light; the right pictures with left circularly polarized light. The field increases in the order a, b, c, d. The diameter of the honeycombs reduces while their distance increases. Thus the honeycombs continuously change into cylindrical domains (bubbles). This process leads to a much higher density of bubbles than the contraction of the strip domains (fig. 2d). Because the diameter of the bubbles is approximately 1 /am, they can be well detected optically. Their distances are so large that they are not coupled by their stray fields. When the field is parallel to the magnetization inside the honeycombs (right side of fig. 5), the honeycombs expand. At first there is only one cone shaped domain insideeach honeycomb ("a", "e" in fig. 5), which disappears when the honeycomb is transformed into a bubble in the opposite field. During further increase of the field parallel to the magnetization of the honeycomb, additional cone-shaped domains show up ("f" in fig. 5). They disappear during further increase of the field ("g"

B. Kuhlow and M. Lambeck/Magnetic d o m a i n s t r u c t u r e s in CrBr 3

373

in fig. 5). In a still higher field the net of the disadvantageously oriented strip domains surrounding the honeycombs breaks off. The strip domains become straight ("h" in fig. 5) and finally contract to one bubble each. This procedure results in a low-density state of bubbles. The measured diameters 2R of the domains and the lattice constants D (distances) of honeycomb domains are plotted in fig. 6. The data for the advantageous field (i. e., parallel to the magnetization inside the honeycombs) are shown on the left side, for the disadvantageous field on the right side of the diagram. It should be noted that the saturation is obtained at a lower field strength in the advantageous field than in the disadvantageous field. Calculations on the behavior of honeycomb domains and bubbles (apart from cone-shaped domains) in the field have been performed by Druyvesteyn and Dorleijn 21). The measured values for CrBr3 essentially agree with these calculations 22).

References 1) J.T. Ho and J.D. Litster, J. Appl. Phys. 40 (1969) 1270. 2) S.D. Senturia and G.B. Benedek, Phys. Rev. Letters 17 (1966) 475. 3) J.F. Dillon Jr., H. Kamimura and J.P. Remeika, J. Appl. Phys. 34 (1963) 1240. 4) I. Tsubokawa, J. Phys. Soc. Japan 15 (1960) 1664. 5) J.F. Dillon Jr., J. Appl. Phys. Suppl. 33 (1962) 1191. 6) J.F. Dillon Jr., H. Kamimura and J.P. Remeika, J. Phys. Chem. Solids 27 (1966) 1531. 7) M. Lambeck, Z. Phys. 179(1964) 161. 8) M. Lambeck, IEEE Trans. Magnetics MAG-4 (1968) 51. 9) M. Lambeck, Barkhausen-Effekt und Nachwirkung in Ferromagnetika (Walter de Gruyter, Berlin-New York, 1971). 10) B. Kuhlow and M. Lambeck, Intern. J. Magnetism 3 (1972) 47. 11) M. Griindler, B. Kuhlow and M. Lambeck, Phys. Letters 33A (1970) 285. 12) O. Bostanjoglo and W. Vieweger, Phys. Stat. Sol. 39 (1970) 471. 13) J.F. Dillon Jr. and J.P. Remeika, J. Appl. Phys. 34 (1963) 637. 14) J.B. Goodenough, Phys. Rev. 102 (1956) 356. 15) D.J. Craik and R.S. Tebble, Rept. Progr. Phys. 24 (1961) 116. 16) E.D. Isaac, Proc. Phys. Soc. 74 (1959) 786. 17) C. Kooy and U. Enz, Philips Res. Repts 15 (1960) 7. 18) V.A. Ignatchenko, I.F. Degtyarev and Yu.V. Zakharov, Bull. Acad. Sci_ USSR (Phys. Ser.) 25 (1961) 1452. 19) C. Kittel, Revs. Mod. Phys. 21 (1949) 541. 20) J. Kaczdr and R. Gemperle, Czech. J. Phys. B 11 ( 1961) 510. 21) W.F. Druyvesteyn and J.W.F. Dorleijn, Philips Res. Repts 26 (1971) 11. 22) F.A. De Jonge and W.F. Druyvesteyn, Magnetism and Magnetic Materials (conference) 1 (1971) 130. 23) Z. M~lek and V. Kambersk~, Czech. J. Phys. 8 (1958) 416.