Linear optical anisotropy and domain structures at two successive antiferromagnetic phase transitions in α-MnS

Journal of Magnetism and Magnetic Materials 25 (1982) 317-334 North-Holland Publishing Company

317

LINEAR OPTICAL A N I S O T R O P Y AND DOMAIN S T R U C T U R E S AT T W O SUCCESSIVE A N T I F E R R O M A G N E T I C P H A S E T R A N S I T I O N S IN a - M n S W. K L E E M A N N , F.J. SCH,AFER Fachbereich 6 (Physik), Universitiit GH Paderborn, Postfach 1621, D 4790 Paderborn, Fed. Rep. GermalO,

and H. van der H E I D E Laboratoo' of hlorganic Chemist~., Material Science Center of the Universi(v, Nyenhorg 16, NL 9747 AG Groningen, The Netherlands Received 5 October 1981

Two successive antiferromagnetic phase transitions of a-MnS are confirmed to occur at Tc~ = 152.7 K and Tcz = 129.5 K, respectively, by microscopic observations of T domain formation and rearrangement, linear birefringence (LB), optical absorption and linear dichroism (LD) measurements. Stress experiments and X-ray data reveal a rhombohedral lattice contraction below Tcl, which switches into a trigonal elongation below Tc2. The second-order transition a! Tcl (fl=0.40) is proposed to yield the familiar fcc type-2 single axis spin order of NiO and MnO, whereas a multispin axis structure seems to be achieved via a first-order transition below Tc2. Model calculations of the exchange striction essentially agree with the observed lattice distortions, whereas neutron diffraction data are less conclusive with respect to the proposed spin structure transformation. The interdependence of LB and LD is shown via dispersion relations and a Kramers-Kronig analysis involving the d - d transitions of Mn2+ in the visible region.

1. Introduction

Based on neutron powder diffraction measurements [1] and on exchange striction data [2] the nature of the antiferromagnetic phase transition of cubic a-MnS has been discussed [3] to be in complete analogy with that of other transition metal oxides and chalcogenides as e.g. MnO and NiO. The low temperature spin structure below Tcl 152 K was identified to be of the well-known fcc type-2 [1], which is coupled with a trigonal lattice contraction and an isotropic volume contraction [2]. The situation, however, has turned to be more complicated after the detection of a second phase transition at Tc2 ~ 130 K [4]. This transition is accompanied by sudden changes of the magnetic susceptibility and seems to be characterized by a sign reversal of the rhombohedral distortion. This is measured by the cube comer angle ~L/2--+A,

with A going from +0.04 ° at Tc~ to - 0 . 0 2 ° at Tc~ [4]. Anomalies n e a r Tc2 were also found in the early measurements of the specific heat by Anderson [5], but they seemed to be disproved in a revised cp experiment of Huffman and Wild [6]. In order to clarify the situation and to confirm or to disprove the very existence of the second phase transition new experimental data are presented in this paper. They are mainly connected with the linear optical anisotropy occurring in the trigonal phases along with visual observations of magnetic domain structures. These techniques were successful in the investigation of NiO [7], where domain formation and rearrangement processes cause anomalies of the susceptibility at about T N - - 50 K [8]. At the first sight these effects seemed to indicate another phase transition, although they are merely connected with an excessive growth of the domain wall volume. By use of stress induced

0304-8853/82/0000-0000/$02.75 © 1982 North-Holland

318

W. Kleemann et al. / Properties of a-MnS at two successive phase transitions

reorientation of T domains, a well-known technique also applied to NiO [9,10], we have also tried to confirm the reported [4] sign reversal of the distortion angle A at Tc2. The linear optical anisotropies, i.e. the linear birefringence (LB) and the linear dichroism (LD), which are expected to be proportional to A similar as in NiO [7] and in MnO [11], are measured on microscopically selected single T domains [9]. This proves to be extremely essential in order to achieve unambiguous results, which are scarcely available from multidomain data [4]. A further confirmation of the second phase transition at Tc2 is deduced from the blue shift of the absorption edge in the near UV, which has proven to be a measure of the magnetic energy in a-MnS [12]. Finally, newly performed powder X-ray and neutron diffraction measurements are analyzed with the aim to achieve more informations on the spin structures above and below Tc2. Based on the new experimental data and in order to explain all of the observed anomalies, tentative spin structure models are proposed in the discussion. We assume that the spin structure is of the familiar fcc type-2 at temperatures between TCl and Tc2, whereas a multispin axis structure [13] becomes stable below Tc2. Our arguments are based on the theory of Lines and Jones [3], who predict spin wave instabilities due to additional biquadratic exchange under certain circumstances. Another point of interest lies in the temperature dependence of the order parameters of both phases, which vanish continuously at Tc~ and discontinuously at Tc2, respectively. According to renormalization group predictions [14] the transition at Tct is expected to exhibit a slight first-order character, at least in stress-free samples as evidenced for NiO [7]. The transition at Tc2, on the other hand, should rather obey an appropriate mean field theory of the Landau type. Another detailed study contained in this paper is devoted to the spectral dependences of the LB and of the LD, respectively, and to their relations among one another. These are tested by appropriate LB dispersion relations and by a Kramers-Kronig analysis involving the d - d transitions of Mn 2+.

2. Experimental procedure Thin transparent single crystals of a-MnS with an average size of 1.5 × 1.5 mm 2 and a thickness of 10 to 30 ~m were grown by chemical transport with iodine [ 15]. Their surfaces lie parallel to (111). Very often they are rhomb-shaped with edges parallel to [110], [011] and [10T], respectively, as indicated schematically in fig. 1. Thicker samples casually show growth edges on the surface, which exactly reproduce the directions of the sample edges. This is seen for instance at the left-hand sides of the figs l d - f . At room temperature the samples are optically isotropic (NaCl-type lattice structure, henceforth called phase I) and nearly strainfree. Only some stress induced birefringent stars with threefold symmetry are detected. They are virtually temperature independent and resemble punch patterns on octahedron faces of cubic crystals [16]. Obviously they evidence growth imperfections and may be due to small angle grain boundaries. In order to reduce internal strain leading to uncontrollable domain patterns in as-grown samples some of them were annealed for 24 h at 650°C in an atmosphere of 150 mbar Ar mixed with 150 mbar HzS. The LB is measured with an accuracy of about -+ 10 - 6 using a computer controlled modulation method described previously [17]. Prior to and during the experiment the sample can be oriented in situ and observed microscopically when placed onto the sample holder of a horizontal He gas flow cryostat. The temperature resolution is 0.01 K at an absolute accuracy of better than 0.1K. Some of the experiments were carried out under about 10 bar [111]-stress placing the sample between two clamped glass plates. The magnetic field dependence of the LB in transverse fields up to 3 T was measured in preliminary experiments, which, however, did not allow for a simultaneous observation of the domain structure. Optical absorption, k, and linear dichroism (LD), Ak = l k . ko 1, of selected suitably oriented single domains are measured by using the same microscopical setup as used for the LB. For measuring k the elasto-optical modulator serves as a 2 f = 100 kHz light chopper, whereas it switches the light from ~r to o polarization at the same frequency in the LD -

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W. Kleemann et al. / Properties of a-MnS at two successive phase transitions

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experiments. The resolution obtained on 50 ~m large domains is 8 k ~ 4 0 cm -I and 8 ( A k ) ~ 4 c m - I , respectively, referring to absorption coefficients being as high as k ~ 5000 c m - i . The spectral resolution using the light of a 150 W Xe lamp dispersed by a 0.25 m double monochromator was 8X ~ 1 nm in dispersion experiments and 8X ~ 0.4 nm when measuring blue shifts of absorption edges, respectively. X-ray diffraction on powdered samples of aMnS in order to confirm earlier studies of the lattice distortion in both phases [4] have been performed at temperatures between 50 and 160 K. Preliminary neutron diffraction measurements have been carried out on powdered samples at temperatures between 4.2 and 170 K at the high flux reactor of E.C.N. (Petten, The Netherlands).

3. Experimental results 3.1. Domain observations

Fig. 1 shows the antiferromagnetic domain structure of two different as-grown (111) platelets of a-MnS observed between crossed polarizers using white light. The series of photographs a - c and g-i were taken on a 22 ~m thick sample in the intermediate phase II ( T = 139.0 K) and in the low temperature phase III (T---- 115.0 K), respectively, whereas the series d - f refers to a sample of 25/.tm thickness, which displays a particularly welldefined domain stru.cture in the low temperature phase (T---74 K). As indicated at the left-hand side of fig. 1 we have chosen the direction of the polarizer (P) to be parallel to [211], [121] and [112], respectively. It is seen that in any of these orientations, which correspond to the projections of [111 ], [111] and [liT] onto (111), respectively, distinct groups of domains are optically neutral. They are dark for the respective direction of P and brighten up in the two others. Some of these domains, which we call T2, T 3 and T4, respectively, a r e indicated at the edge of that photo, where they appear dark. The corresponding bright patterns are easily found in the two other photos of the same series. These observations strongly suggest that we

probe the uniaxial birefringence of T domains, which seem to resemble those found in NiO by the same optical technique [ 18]. The projections of the optical axes of T2, T3 and T4 onto the (111) plane form angles of -+ 60 ° with one another. The fourth type of T domains, which we call T~ henceforth, is seen in fig. lg-i, where large portions of the area under inspection remain dark for whatever direction of P. Evidently in these domains the optical axis lies parallel to [111] and thus perpendicular to the (111) habit plane. Hence, in agreement with the expected spin structure of a-MnS we have identified all possible T domains referring to the rhombohedral distortions of the crystal along the four (111) directions. A very remarkable feature of the three domain configurations shown in fig. 1 is their different outward shape. Whereas welldefined domain walls with linear contours are observed in the series of fig. l d - f , they are less distinct, but still linear in fig. la-c, but still more washed out with curvilinear shapes in fig. lg-i. It has been observed that the quality of the domain structure depends strongly on the internal stress of a given sample. Even the mounting procedure prior to the cooling down of the cry'ostat has proved to yield unpredictable changes of the domain structure in one and the same sample. The situation becomes more distinct for samples being annealed as described in section 2. We obtain nearly exclusively T~ domains in phase II, whereas only T 2, T 3 and T4 domains arise in phase III. The conversion of T I into T,_.3.4 domains and vice versa at Tc2 is reproducible and can be traced back to the sign reversal of the trigonal distortion angle A at Tc2 as will be discussed in section 4. Fig. 2a and b shows the temperature dependence of given domain configurations in phase III referring to fig. I f and i, respectively, when passing into phase II at Tc2 -~ 130 K. Note that the direction of the polarizer is [112] throughout. It is seen that the domain transformation takes place in the temperature range of Tc2 -+ 3 K. It must be remarked, however, that in the backward direction when passing from phase II into phase III the domain rearrangement generally takes a considerably larger temperature range, depending on the annealing state of the sample. As-grown samples (fig. l d - f ) need temperatures as

14/. Kleemano et al. / Properties of a - M n S at two su~x~essive phase transitions

321

Fig. 2. Transformation of T domain structures at the III-II transition observed on heating at two different samples (a) and (b), corresponding to fig. If and i, respectively, with PII[I12] throughout.

low as Tc2 --50 K for complete domain stabilization, whereas the phase III domain structure in annealed samples is fully stabilized at Tc2 - 10 K. Two features are extracted from fig. 2 and seem to be fairly general for both, as-grown and annealed (111) platelets of a-MnS at the III-II phase transition: (i) Sharply contoured domain structures transform into smoothly contoured ones (fig. 2a), and vice versa (fig. 2b), (ii) Domain structures containing TI type domains at an appreciable amount transform preferably into configurations with exclusively T2, T3 and T4 type domains (fig. 2b), and vice versa (fig. 2a) as can easily be confirmed by rotating the analyzer. Only the latter situation, similar as shown in fig. 2a, is realized in annealed samples. Domain rearrangements under [ 111 ] stress induced by clamped glass plates have been observed in both phases. Enhanced TI domain formation is

found in phase II, whereas T2,3, 4 domain patterns become stabilized in phase III. This is consistent with a compressed trigonal axis in phase II (A > 0) and an elongated configuration (A < 0) in phase III, respectively, as found by Heikens et al. [4]. In annealed samples evidently the free (111) surface exerts a [111] stress onto the interior of the sample thus favoring T~ domain formation in phase II. Similar surface tension effects have been observed in improper ferroelastic perovskites like SrTiO 3 and RbCaF3, where free (110) surfaces tend to form crystallographic single domains with [001] orientation in the elongated tetragonal low temperature phase [ 19]. We have also tried to find S domains within given large T domains, which should show a slight biaxial LB with a secondary optical axis perpendicularly to the direction of the rhombohedral distortion [18,7]. The search for S domains should be particularly successful for T I domains, the primary LB of which is invisible. Careful inspections, however, of large homogeneously dark T I

322

W. Kh, emann et aL / Properties +3"a - M n S at two m~'Ucce.~sit;ephase tramitmns

domains in both phases did not reveal unambiguous S domain ~ontrasts on rotating P within the (111) plane. O n the other hand the appearance of faint stripe-like LB contrasts within Tj domains ( j = 1-4) in phase II might give a hint at a possible S-domain structure in that phase. However, superpositions of different T domain cannot be excluded to explain this observation. Hence, we are left solely with the unambiguous identification of (111) distorted T domains in both antiferromagnetic phases. An interesting point is the identification of twin domain walls, which are particularly well-defined in fig. l d - f . Following the symmetry arguments of Slack [10] we expect domain walls of the (100} and the (110} type, which exclusively satisfy the condition that they bisect the angles between the cube diagonals. Among these planes only the walls parallel to (110), (10T) and (011) are perpendicular to the (111) habit plane. Their intersecting lines lie parallel to [112], [121] and [211], respectively. On the other hand, the planes (110), (101) and (011) intersect the (111) plane along [110], [10]] and [011], respectively, at a tilt angle of 45 °. The same intersecting lines are found for (111) and the domain walls parallel to (001), (010) and (100), respectively. Their tilt angle is 54.7 ° . Hence only the domain walls containing the ~112) directions are expected to be sharply bordered, whereas those containing (T10) directions must appear broadened and washed out owing to their acute tilt angles with the sample surface. This is excellently confirmed by fig. l d - f , where e.g. all horizontal domain edges (i.e. parallel to [110]) form washed out rims or broad dark stripes between brightened domains, whereas those parallel to e.g. [121] and [211] yield extremely sharp contrasts or narrow dark lines when adjoining two bright domains. These lines and the dark stripes along (110), as well, are due to the rotation of the axis of deformation from one (111) direction to another in the twin domain wall, thus passing an optically neutral direction, the projection of which onto (111) is parallel to the axis of one of the polarizers. To conclude this section we shall briefly consider another quite different interpretation of the domain structures shown in figs. 1 and 2, which

cannot be ruled out a priori. The domain contrasts observed in phase III might also be due to three different types of S domains, which develop below Tc2 within a single Tj domain. The mechanism of formation might be connected with thermally activated domain wall migration as was observed in NiO [8]. This interpretation would be more consistent with the neutron data available at present (cf. section 3.3) and might explain some of the susceptibility data under [111] stress [4] in a less constrained way than within the framework of the above discussed T domain model. However, since several other important features are not consistent at all with the S domain model (the sign of the rhombohedral distortion should not change at Tc2; the order of magnitude of the LB (cf. section 3.2) is about 103 times larger than expected and found in the S domain LB in NiO [18]; considering a thermally activated process the III-II transition would be unusually steep (fig. 5); oblique walls as those containing (110) directions (fig. l d - f ) are unlikely to appear between S domains as verified on (111) platelets of NiO [18,20]), we shall not pursue this model in the following. However, a final decision against or in favor of it needs more experimental data, which are not available at present. 3.2. Linear birefringence and X-ray diffraction measurements

Fig. 3 shows the temperature dependence of the trigonal LB measured between 5 and 160 K at 560 nm wavelength. The curves 2 and 1 refer to single T domains, which have been selected in phase III in an annealed sample and in phase II in an as-grown sample, respectively. The latter choice was necessary owing to the absence of all but T~ domains in annealed samples in phase II. Although our experiments do not yield the sign of the LB, we tentatively correlate the LB curves with the distortion angle A, being positive in phase II and negative in phase III [4]. For comparison two sets of A values are plotted in fig. 3, the absolute values of which are fitted to the LB at low temperatures. The first set (circles) was obtained by Heikens et al. [4] from the splitting of the (420) reflection of a polycrystalline sample, using CrK,,

W. Kleemann et al. / Properties of a - M n S at two successive phase transitions

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of A is not visible in this experiment. It becomes relevant, however, in the case of curve 1, which exhibits a decrease by about 2 / 3 at the I I - I I I phase transition. A simple calculation shows that indeed an average LB of + 1/3 of the initial single domain LB should emerge provided that (i) a statistical domain mixture of all types of domains except the initial one appears below Tc2, and (ii) the LB as measured with respect to the trigonal axis merely changes its sign at Tc2. In the calculation it has to be taken into account that 1/3 of the orignal LB gets lost due to the appearance of optically inactive T I domains and that the projections of the trigonal axes of the two optically active domains onto (111) lie under angles --+~r/3 with respect to the projection of the original domain axis. Within phase II the LB decreases continuously and becomes zero at Tcl =.152.7 K. This critical temperature agrees well with that obtained from specific heat measurements [6]. It has been calculated from a best-fit of the experimental data points within the temprature range 5 × 10-3 < tl = 1 - T/Tcn ~ 2 X 10 -2 to the power law (cf. section 4.2)

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where fl is th~ critical exponent of the order parameter. As can be seen in fig. 4, the fit is excellent yielding fl = 0.40(1) and An o = 5.47 × 10 -2 It may be noted that in contrast to the corresponding LB curve of well-annealed NiO [7] no discontinuity or kink is detectable near Tc~. Bearing in mind that LB experiments on (111) samples of a - M n S necessitate internal strain to stabilize a ( j = 2, 3 or 4) domain, the smoothness of the LB curve at Tel does not disprove a possible first-order discontinuity in well-annealed samples. Adequate measurement should be possible on (100) samples, which were not available in the present investigation. It may be noted that 13 = 0.40 is very near to the value found for N i O [7] at very low internal stress. This might indicate that we are indeed rather near to a tricritical point. The phase transition at Tcz being first-order, although somewhat smeared out by domain effects (fig. 5), can be fitted to the well-known Landau expression [ 17]

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Fig. 5. Temperature dependence of the LB at 560 nm (full circles) near the III-II transition, compared with the LD of t h e 4Tig band at 607 nm (open circles) and fitted to the expression (7) (solid line) by use of the experimental data in the range 0.02~t~0.1 as indicated by vertical dashed lines. Residual signals between 130 and 150 K are due to incomplete transformation of the sample into a single TRdomain.

Magnetic field effects on the LB have not yet been performed in great detail. Contrary to NiO [18,20] no S domain contrast has been achieved or changed by application of transverse magnetic fields up to 0.3 T in both phases. Preliminary LB measurements on multidomain samples reveal significant changes, starting at about 0.5T and saturating at about 2.8 T in phase II and 2.3 T in phase III, respectively. Presumably these effects are d u e to T domain reorientation as observed in NiO at very similar field strengths [10]. Microscopic investigations of these effects at high magnetic fields will be performed in near future. The spectral dispersion of the LB measured at 12.2 K is shown for the visible range (14.3-24.1 × 103 cm - I ) in fig. 6a. Obviously the curve is dominantly determined by the strong band-gap absorption in the near UV [21]. A similar result was recently [12] deduced for the room temperature refractive index, which was shown to follow the dispersion law n 2 = 1 +A/(f

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In this expression n is a mean refractive index ( n > A n ) and fd is a mean oscillator frequency, which should lie near to fo. Dichroic contributions from high frequency transitions ( f > f d ) are taken into account by the constant B, whereas ihe anisotropy of the oscillator strengths and of the resonance frequencies around f([ are contained in the constants C and D, respectively. Negleting the D term in eq. (4) in our frequency range we have fitted all of our data points displayed in fig. 6a, while inserting n according to eq. (3) into eq. (4). We obtain very reasonable agre ement with the best-fit curve (solid line in fig. 6a) using the parameters B = -0.047, C = 4.51 × 107 cm -2 and f~ = 2.62 × 104 cm - t , which indeed lies near to f0. Hence, both, An and n, are pre-

326

IV. Kleemann et al. / Properties of a - M n S at two successive phase transitions

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ponderantly due to the same optical transition, which was shown to correspond to the magnetic exciton involving a hole in the 3d orbitals and an electron in the 4p orbitals of l~In2+ ions [12]. f0 and f~ agree rather e~/actly with the average peak energy of the band-gap absorption bands D (24691 cm - l ) and E (27397 cm - I ) reported by Komura [21]. At a closer inspection of the LB dispersion curve in fig. 6a slight anomalies are found, which unambiguously can be attributed to d - d transitions of the Mn 2+ ions (cf. section 3.3). Two prominent transitions (6A]g "-'*4TIg at 16.7× 10 3 cm -1 and 6Al~--,4A~g +4Eg at 22.3 X 10 3 c m -1,

cf. fig. 7) are dearly resolved in the LB spectrum, although much less distinct than in MnO [11]. The third crystal field transition (6Alg ---*4T2g at 19.8 × 103 c m - J, cf. fig. 7) gives rise to a nearly negligible S-shaped anomaly in the LB spectrum. The correlation of these LB anomalies with the corresponding anomalies of the linear dichroism will be discussed in section 4.2.

3.3. Optical absorption, absorption edge shifts and neutron powder diffraction The optical absorption obtained at different temperatures between 6.5 and 211 K on a 15 # m

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Fig. 7. Unpolarized optical absorption of ~-MnS taken at 6.5, 65.2, 139.0 and 211.0 K (curves I-4), uncorrected for reflection losses and measured at muttidomain samples in the antiferromagnetic phases. Insert: absorption edge blue shift for 88.7, 100.2, 110.3, 121.5, 130.5, 151.9, 161.0, 171.6 and 180.2 K (curves I-9). The arrows refer to the constant absorption curves displayed in fig. 8.

thick sample in the visible region is shown in fig. 7. It contains three crystal field absorption bands (6mlg-~4Tig, 4T2g and 4Aig+4E g, referring to Mn 2+ in octahedral site symmetry, neglecting spin -orbit interaction) and ends at the edge due to the magnetic exciton at about 24 × 103 cm -1. The peak positions and their heights agree well with the values reported by Komura [21]. The fine structure of the 4Aig +4Eg band [21] is not completely resolved in our LHeT spectrum. With regard to the magnetic ordering two other obvious features are of major interest: (i) the surprisingly large oscillator strength of the d - d transitions and their peculiar temperature dependence [22], (ii) the marked blue shift of 0.22 eV of the absorption band edge between LHeT and RT [12]. Both effects are considered to be proportional to the magnetic energy, i.e. proportional to shortrange spin order. In view of the novel detection of two successive antiferromagnetic phase transitions in a-MnS,

which were not yet considered by Terasawa et al. [12], we have measured the blue shift phenomenon with a better temperature resolution at temperatures around Tel and Tc2. Some of the corresponding absorption spectra are shown in detail in the insert of fig. 7. Without correcting for the overlap with the adjacent 4Ais +4Eg band we have continuously recorded the photon energy corresponding to optical densities of D = 2.7, 3.0 and 3.3, respectively, as indicated by horizontal arrows in the insert of fig. 7 and as displayed as a function of the temperature in fig. 8. Clearly both phase transitions at Tel and Tc2 become visible by giving rise to different slopes of the constant D curves in the phases I, II and III, respectively. This is best seen in the D = 3.3 curve, which is least perturbed by the overlapping 4Alg +4E~ band at high temperatures (cf. insert of fig. 7). The change of the slope on going from phase I to phase II is continuous and starts at about Tel + 10 K. This indicates the influence of magnetic short-range order, which in the fee type-2 antiferromagnet is mainly due to correlations be-

328

W. KleemaJm et aL / Properties of a-MnS at two successive phase transitmns

tween next-nearest neighbor (nnn) spins [3]. This is also consistent with the model of the exchange split magnetic exciton being responsible for the absorption edge, which involves not only nn, but also very essentially the nnn spins [12]. The change of the slope at Tc2 is rather sharply defined. Some scatter of the data points is very likely due to domain effects (wall scattering and dichroism of differently oriented transient domains, cf. fig. 2). The considerable decrease of the slope from 19 c m I / K in phase II to l l c m - I / K in phase III seems to indicate that the development of magnetic order in phase III becomes hampered, possibly due to the onset of a multispin axis structure with a reduced sublattice magnetization as discussed below. Similar anomalies, although less pronounced than in the absorption edge are also found in the temperature dependence of the d - d absorption band broadening. This is shown in fig. 8 for the constant D curves recorded at D =- 0.8, 0.6 and 0.4,

2/..0 ..

TIT

•

I

n"

"e. %° %~ -.%

respectively, at the low energy slope of t h e 4Tig band as marked by arrows in fig. 7. The most significant effect is detected in the D = 0.4 curve with a slope of 9 c m I / K in phase II, which decreases to 6 c m - I / K in phase III. Taking these shifts as a measure of the temperature dependence of the oscillator strength, which varies like the magnetic energy [22], we thus have another hint at a reduction of the antiferromagnetic moment in phase III. The assumptions made above do not seem, at first sight, to be confirmed by preliminary neutron diffraction experiments. A profile analysis of the pattern obtained at 4.2 K, in which the single axis A(11 l) model (spins confined parallel to the (11 l) plane [13]) was taken as a basis for the refinement procedure, fitted fairly well. The magnetic moment was determined to be 4.42~B/Mn + +. The analysis is in agreement with earlier reported data for a-MnS [l]. Following the (l l l) magnetic reflection intensity as a function of temperature (fig. 9) an interesting feature is observed in the vicinity of Tc2. This is best seen in the derivative curve IdI/dTI, showing two peaks near Tel and Tc2, respectively. The former is related to the onset of magnetic ordering ( I - I I transition), while the latter points to a discontinuous change of (111) magnetic reflection, unacounted for in a Brillouin type behavior of the sublattice magnetization. The tern-

5-

E tJ

1.0

23.0

:

¢-i

E D tO

>

-~~'~'~'~!C~

I i I "I,-.,,, I

- D=08 ~

160 2,. -

"----,,,

", I"'-.. "-..0=3.3 .... I" ". °"-'. I "-. 0=2.7 ".~.

~ . ,

f

D=O.~ " . ~ . _ J 15.5

--

".L.__. i~.,~,,.

i

"'~---~.._

0.8

s

0.6

E

0.t. 0.2

100

I

i

""-~L I

rt

I

//!

pot,-

I

I

120 1/.0 160 Temperoture / K

i

180

Fig. 8. Constant optical density D vs. temperature curves referring to the absorption edge and to the 4Tig band, respectively, as indicated by arrows in fig. 7.

I ,...,

S.N"

dI

so

o

V

./

I "~.1

00 [

rrr

"~..

~ Temperoture/ K

Fig. 9. Temperature dependence of powder neutron diffraction of the ( I I I) reflection (intensity I) and its temperature derivative (Idl/dT]), interpolated by eye-guiding lines. The intraplanar spin order patterns proposed for phase II and III, respectively, are schematically sketched after ref. [I 3].

IV. Kleemamt et a L / Properties of a - M n S at two sutz'essive phase transitions

perature region for the occurrence of this effect coincides with that for the observation of the domain rearrangement by the optical measurements (cf. section 3). Roth [13] has argued that neutron scattering from powder specimens cannot lead to an unambiguous solution of the spin arrangement. Dropping the restriction of a single magnetic axis in a domain, a variety of nmltiaxis structures was found to be consistent with data obtainable from powder specimens. The optical measurements indicating that the development of the magnetic order is hampered at Tc2, we suggest that this might be connected with a magnetic phase transition. As will be discussed more in detail in section 4.1 we propose Roth's spin structures A ( l l l ) and F in phase II and III, respectively. Structure F may be' described as a system with four ferromagnetic or two antiferromagnetic sublattices, respectively, and has a reduced intraplanar moment. Both spin structures are schematically sketched in fig. 9. At T--- 0 the (l I l) reflection intensity, I I11, of structure F should be about 25% smaller than that of A ( l l l ) [13]. A similar jump is expected at the

329

actual transition point, Tc2. In view of the drastic domain rearrangements around Tc2 (fig. 2) the discontinuity of It~ t could be smeared out by domain wall effects.

3.4. Linear dichroism LD spectra obtained in the visible region on selected single domains are presented in fig. 10, chosing the same temperatures as for the absorption spectra in fig. 7. Very significant LD is observed in the 4Tlg band with A k / k = 0.22 at 6.5 K. This explains the particularly well resolved LB anomaly as shown in fig. 6. On the other hand, similar to the LD of MnO [Ill only small effects are found in the other d - d bands. Strong LD, however, arises in the near UV in agreement with the analysis of the LB dispersion (cf. section 3.2 and further discussion in section 4.2). Both, LD and LB, are intimately coupled with the rhombohedral lattice distortion and, hence, vanish at temperatures above Tc~. The figs. 4 and 5 show the nearly perfect proportionality between both linear anisotropies in the critical temperature

400

/%.

E 300

,.'

".'.I

N ~

,i

g, Eg

-i 100 i

. . . .

i

'

I

16

"

"-,.

'

I

J

"~

I

18 20 22 Wovenumber / 103cm-1

"

i l

I

24

Fig. 10. Linear dichroism obtained on single T domains of a-MnS at 6.5, 65.2, 139.0 and 211.0 K (curves I - 4 ) in the visible range. I n t e r f e r e n c e fringes d u e to d i c h r o i c s u r f a c e reflection are s h o w n in the 65.2 K s p e c t r u m (see text).

330

W. Kleemann et al. / Properties of a-MnS at two successive phase transitions

ranges of phase II and III, respectively. The LD was measured at the maximum of the 4T~g band at 607 nm. Obviously the scatter of the LD data is much larger than that of the LB. This is a consequence of the different measurement methods involved. Although both experiments, LB and LD, are performed in principle on identical single domains, their signal-to-noise ratio is quite different. The LB profits of the large light flux in the transparent region and uses a sensitive null-method, whereas the LD measures small absolute intensities in a range of high absorption (ILD ~ ILB/10) • In fig. 4 it is noted that the LD curve ceases to be proportional to the LB above about 147 K. Its steeper dropping to zero demonstrates the influence of misoriented twin domains, which casually develop near Tcl despite the careful selection of a single domain at a somewhat lower temperature. Another typical complication of our measurements is demonstrated in fig. 5, where the LD transition temperature appears to be about 1 K higher than the LB transition temperature (Tc2 = 129.5 K). This is due to the fact that the LB was measured on a virgin annealed sample, whereas the LD curve refers to the same sample after about 25 cycles across both phase transitions. The displacement of Tc2 demonstrates the susceptibility of the spin ordering to internal strain via magneto -elastic coupling. It explains also some of the scatter of the Tcl and Tc2 data given in the literature. In the transparent region of the LD spectra one often observes periodic interference fringes superimposed by longer period beats. This is shown for the 65.2 K LD curve in fig. 10 around 14.5 × 103 cm - t . The short period is due to the ordinary periodicity of the reflectivity of a transparent thin film with the light wavelength depending on the mean refractive index n and the sample thickness d. The beat period, on the other hand, measures An, since the LB gives rise to slightly different periods of the reflectivity of ~r and o light, respectively. This interference phenomenon can be used to determine roughly n and An or d, respectively.

4. Discussion

4.1. Multispin axis structure in phase 111 of a-MnS? In previous discussions of the antiferromagnetic order of a-MnS [3] the fce type-2 spin structure was assumed to be valid at low temperatures. This structure involves 6 parallel and 6 antiparallel nearest neighbors (pnn and ann, respectively) and 6 antiparallel next-nearest neighbors (nnn). Assuming antiferromagnetic exchange between nn (J1 > 0) and nnn (J2 > 0), the structure becomes stabilized by a contraction along the trigonal axis (A > 0), thus leading to enhanced ann, but to lowered pnn exchange interactions .(Jr + >J1 and J i - < J1, respectively). This model was successfully applied to NiO and MnO [23,24] and seemed also to be confirmed by Morosin's exchange striction data of a-MnS [2], yielding A > 0 in the whole temperature range from L H e T to 150 K. After the advent of the new A data of Heikens et al. [4], which are confirmed in this paper, a revised discussion is necessary. A < 0 in phase III rules out the possibility of the fcc type-2 spin order at low temperatures. This could only be stabilized via anisotropic exchange [25] as observed in FeO [26], which, however, is negligible in a-MnS because of the S ground state of the Mn 2÷ ion. Moreover, the elongated trigonal structure due to anisotropy magnetostriction requires [25] perpendicular sublattice magnetization, S I1[111], which is absent in a-MnS [1]. Hence, another interaction competing with the isotropic exchange has to be taken into account. Following Lines and Jones [3], we consider the biquadratic exchange interaction originating from indirect quadrupolequadrupole interaction due to virtual exchange of optical phonons [28]. This effect is generally very small, but should be particularly well observable in a-MnS [3] because of its very small exchange striction (about one order of magnitude smaller than in MnO [2]) and because of the virtually vanishing magnetic anisotropy. The spin Hamiltonian including bilinear and biquadratic exchange and the exchange striction is given by [3]

W. Kleemann et al. / Properties of a-MnS at two successive phase transitions ~3~--= ~ [gl+ S i ' S j - - j l ( S i ' S j )

2]

ann

+ ~ [Jl-S,'Sj-j,(Si'Sj) 2] pnn

+ ~, [Jz+S,.Sj-j2(S,.Sj)2],

(5)

nnn

where J,-+ = J, [1 -+ c , a / 2 - ,l(,~ala)],

(6)

J2+ : J 2 1 1 - , 2 ( 8 , , / a ) 1 , with c i = - 0 ( l n J / ) / O ( l n r ) > 0 (i=1,2), A= trigonal distortion angle, c$a/a : isotropic contraction of all cube edges. The biquadratic exchange interaction constants Jl and J2 are assumed to be insensitive to the interspin distance r, at least in comparison with the distance dependence of Jl + and ,/2+ . In spin-wave approximation.the biquadratic spin operators ( S i • Sj) 2 may be replaced by bilinear spin operators. For S = 5 / 2 due to Mn 2+ ions one eventually obtains the reduced Hamiltonian

[3]: %=

J V S , .sj + ann

J*;S .sj + pnn

J S, .sj,, nnn

(7) where J*l+ = J i l l + , 1 A / 2 - - ¢ , ( 8 a / a ) ]

+ ( 1 7 / 2 ) j 1, (8)

J * ? = J l [ 1 - - , I A / 2 -- ¢1(8a/a)] -- ( 1 5 / 2 ) j I, (9) Jff --" J2[1 --¢205ala)] + (17/2)j2,

(10)

with the equilibrium distortions

A = NJ1¢1S'2/C44,

(11)

(Sa/a) = --NJ2,2S'2/(C,1 + 2C12 ),

(12)

involving N spins of the system and the elastic constants CII, CI2 and Co of the cubic phase. It has been stressed by Lines and Jones [3] that the stability of the single spin axis order requires AJ~' = J * l + - - J * ~ =JIetA + 16j, > 0 .

(13)

In the case AJ~' ~ 0 spin wave instabilities occur. Hence, the system should be instable for AJ~ < 0. In order to explain the specific heat anomalies of

331

a-MnS found by Anderson [5] at 139 and 147 K, Lines and Jones [3] considered the possibility that Jl < 0 , but [j~ [ < J l c l A / 1 6 at low temperatures. In that case AJ~' would be positive at LHeT, but might become negative at some intermediate temperature Tc with 0 < T¢ < TN. This is possible, since both, A and jl, are expected to vary roughly as g2, but should not have exactly the same temperature dependence. Thus, the possible transformation of the fcc type-2 spin order into a multispin axis structure just below T N (T~ = 139 K after ref. [5]) was already taken into account in the early discussion of Lines and Jones [3]. Using the same arguments, but taking into account that A < 0 at low temperatures, we now propose just the contrary, namely a multispin axis order for T < Tc2 = 129.5 K, where A J ~ < 0, and a single axis order for Tc2 < T < Tcl = 152.7 K, where A J? > 0. Some arguments towards such an interpretation have already been given in section 3. Here we like to add a tentative explanation of the negative sign of A in phase III. In multiaxis structures like those proposed by Roth [13] the intraplanar ferromagnetic moment is generally reduced or even quenched. This holds e.g. for the structure F, which is sketched in fig. 9 as a possible structure model of phase III. In this special case nn spin pairs are either perpendicular or antiparallel. Hence, the magnetic energy is evidently lowered when compressing the (111) plane as a consequence of a trigonal elongation (A < 0). For other structures like Roth's models G, AA or AC [13] this effect will be smaller due to the small residual ferromagnetic moment. These structures seem to be in better agreement with our neutron data of I~,~/111~ than the model F. For convenience, however, and awaiting more reliable neutron data, we shall confine our detailed discussion in section 4.2 to the relatively simple F structure. On the other hand, the probability of having ferromagnetic nearest neighbors between adjacent (111) planes is larger in multiaxis structures than in the A ( l l l ) structure, which has an unambiguous antiparallel interlayer spin order. Without knowing exact details of the interlayer stacking sequence of spins in multiaxis structures we can presume that an elongation along [ 111] will at least be energetically more favorable than for the single

332

W. Kleemann et al.

/

Properties of a - M n S at two suc('essit:e pha~e transttion.~

axis A ( l l l ) structure. After all, both, the intraand the interlayer spin order of multiaxis systems should favor an elongated equilibrium configuration. The nature of the order parameters in the phases II and III depends largely on the actual spin configurations. For the spin orders discussed here the adequate order parameters seem to be the sublattice magnetizations S referring to the ferromagnetic intraplanar order of A(I 11) and to the antiferromagnetic intraplanar sublattice order of structure F, respectively. Both order parameters are virtually independent from one another. Hence, within the framework of the Landau theory, which does not account for the microscopic origin of the phase transitions, coupling between both order parameters can be neglected. This justifies the separate analysis of their temperature dependences by use of the formulae (1) and (2), respectively. It is clear that further experiments are highly desirable in order to confirm our spin structure models. E.g. neutron single crystal diffraction in the vicinity of Tc2 performed on well-defined domain structures should reveal more details of the spin structures in both phases. At least some reduction of Iii t at Tc2 when passing from A(111) to F [13] should be visible. Smearing-out effects by domain walls need special consideration. Similar ideas apply to susceptibility measurements. One should e.g. obtain a clearcut spin-flop transition in phase II on application of the magnetic field parallel to the easy plane of T~ domains in well-annealed samples. The influence of domain walls on going from a single axis T~ domain into a multi axis T2,3, 4 domain mixture has explicitly to be taken into account.

4.2. Linear optical anisotropy It is well-known that the linear optical anisotropy at magnetic phase transitions may be connected with the spin dependent electronic polarizability a n d / o r with magnetostrictive lattice distortions. The latter mechanism, which involves a magneto-elastical and an elasto-optical part, has been found to be dominant in NiO [27] and in MnO [11], the crystallographic and magnetic structures of which are very similar to those of a-MnS.

Hence, it seems to be appropriate to apply the same ideas discussed in refs. [ 11,27] to a-MnS and to adopt the results

dik ~ AnocSxt~l/Xjl I oc A cc ff 2.

(14)

In this expression 8x~1 j / x ~ signifies the trigonal lattice distortion being proportional to the distortion angle A. ~ i s the sublattice magnetization. The original deduction of the relations (14) explicitly accounts for the fcc type-2 antiferromagnetic order and yields the relation (11) instead of the mere proportionality di ~ ~-2. On the other hand, the proportionality constants between 8 x ~ i / x ~ and An and Ak, respectively, are independent from the spin structure and are solely determined by the elasto-optical constants of a-MnS. This is also evident from fig. 3. Hence, in the present context we can confine our discussion to the modification of eq. (11) when passing into the phase III spin order. Assuming the structure F and neglecting biquadratic' exchange we obtain a modified Hamiltonian, here given for N Mn 2+ ions:

J, S , ' ~ + t=l

ann intraplanar

+

Y.

J,+S,.Sj + 2J2+Si.S~}, pnn

J,+S,.~

ann intcrplanar

(15)

nnn

interplanar

where Ji- and ~+ are given by the relations (6). In (15) all perpendicular nn spin pairs have been omitted, since they do not contribute to the magnetic energy. From the F structure model (fig. 9) it is seen that only two intraplanar ann spin pairs are contained in the first sum of (15). On the other hand the contributions of ann and pnn interplanar spin pairs depend on the stacking sequence of adjacent F type (111) planes. Maintaining the directions of the spin axes in all (1Jl) sheets (e.g. [110] and [112] as depicted in fig. 9) and chosing a periodic ABCABC... sequence (in agreement with the observed size of the magnetic unit cell) one easily distinguishes 16 different spin configurations belonging to five different energy states. Ignoring all intraplanar and perpendicular

W. Kleemann et aL / Properties of a-MnS at two successive phase transitions

spin pairs and those ann and pnn contributions, which cancel out, these states are given by t h e following effective interactions: (i) 2 pnn + 6 annn, (ii) 1 pnn + 3 annn, (iii) 0 p n n / a n n + 0 a n n n / pnnn, (iv) 1 ann + 3 pnnn, (v) 2 ann + 6 pnnn. Considering only the energetically most favorable case (i) with respect to an elongated rhombohedral distortion, and introducing the elastic energy [24] Fe, = 3C44A2/2 + 3(C1, +

2C,2)(Sa/a)2/2, (16)

we readily obtain from the minimum conditions

and (a~C/a[Sa/a]),

a F e , / a A : (a'X/aA)

OF~tla[Salal

=

(17)

the equilibrium distortions

At: = -NJ,,,ff2/3C~,

(18)

(Sa/a)v: -NJ2¢2ff2/(Ci. + 2C12 ).

(19)

Compared with the result for the A ( l l l ) spin order, eq. (11), the sign of A v is negative as expected. Its absolute value is reduced by a factor of 3 in good agreement with the observed reduction of Ianl at T ¢ 2 : I a n ( T ~ ) / a n ( T ~ ) l = 2 . 8 (figs. 3 and 5), the slight deviation from the value 3 being possibly due to different values of ~ at Tc~ and Tc~, respectively. On the other hand, eq. (19) happens to be identical with eq. (12), in agreement with the observed continuity at Tc2 [2,4]. Hence both, eqs. (18) and (19), fit well in the experimental results, which thus can be taken as a confirmation of our model calculation. To some extent, eq. (18) explains also the relatively small lattice distortion in comparison with that of MnO, being about 6.4 times larger at T = 0 [2]. Moreover, using Morosin's data [2] Jn(MnO)/ J l ( a - M n S ) = 1.43, c l ( M n O ) = 23 a n d C44(MnO)/C,~(a-MnS)= 1.52, we obtain a revised value of cl(a-MnS) = 10.1, which is substantially larger than Morosin's value, c n = 5.5 [2]. Note that the J~ values used are high temperature data [3], which are not in conflict with the actual low temperature spin order in a-MnS. Returning to the linear optical anisotropy as a consequence of the trigonal lattice distortion, it seems to be remarkable that a-MnS exhibits a very

333

large LB despite its relatively small A values. The elasto-optical response as defined by An/A is by a factor of about 30 larger than for MnO. Qualitatively this may be traced back to the larger polarizability of the S 2- ion compared with 0 2- . Quantitatively as described by eq. (4) the absolute value of the LB in the visible region depends essentially on the dichroism of the near UV absorption bands. Indeed, the nature of the transitions located in the near UV is fundamentally different in both compounds. Whereas relatively weak d - d absorption bands arise in MnO (4T2s(II) at 25.7 X 103 cm-1 [29]), the dipole allowed band gap absorption [21] with its large LD (fig. 10) is dominant in a-MnS and replaces the intraionic d - d transitions. Lacking exact data of the near UV absorption we confine our quantitative discussion of the relation between LB and LD to the contributions of the d - d absorption bands in the visible region. The corresponding LB anomalies are displayed for T= 12.2K in fig. 6b by taking the difference between the measured and the calculated excitonic LB according to eq. (4). Starting from the wellknown Kxamers-Kronig relation

,,(.,)-1=7

(20)

between the refractive index n and the absorption index K, we deduce a corresponding relation between An and Ak, where k = 4~r~f and f = w/2~rc: An ( f ) = ~-~--/~ 1 2 f0 °°

d f ' A k ( f ' ) / (/,2 _ f 2 ) .

(21)

Restricting the integration to the range of the d - d bands (14.3-24.1 × 103 cm -~) in the LD spectrum (fig. 10, curve 1) we calculate an LB curve, which agrees reasonably well with the experimental one (fig. 6b). The order of magnitude and the essential fine .structure features are well reproduced without using any fitting parameter. Slight distortions and shifts of the LB peaks and points of inflexion, however, prevent both curves in fig. 6b from agreeing completely. Probably the misfits are due to errors in the subtracted baseline according to eq. (4). As explained above this contains the dispersion law (3) of the refractive index [12], which in

334

W. Kleemann et al. / Properties of a - M n S at two su('ce.~,~it;e phase transition.s

our opinion is oversimplified and deviates significantly from the experimental n data (cf. fig. 2 of ref. [12]). A modified relation n 2 = 1 +a

+A/(fo

2

_f2)

(22)

probably would have been more appropriate, where a v~ 0 globally accounts for dispersion oscillators with frequencies lying beyond f0. The B term in the LB dispersion law (4) results from similar correction terms. Further spectroscopic details of the LD spectra, which merit an ample discussion, will be considered in a future paper. 5. Conclusion T domain observations, stress experiments and new X-ray diffraction data confirm that a-MnS undergoes a trigonal contraction of the cubic unit cell on cooling below Tct = 152.7 K, but switches into an elongated trigonal structure at Tc2 = 129.5 K. The phase transitions are second-order at Tel and first-order at T¢2, respectively, as revealed by linear birefringence and linear dichroism data on selected single T domains. All of these observations strongly suggest that the magnetic ordering of a-MnS cannot be understood on the base of simple exchange perturbation arguments as proposed by Jansen et al. [30]. In addition biquadratic exchange and exchange striction [3] have explicitly to be taken into account. In particular these interactions seem to cause the system to change its magnetic order from a single axis type (Tc2 < T < T c l ) into a multiaxis type below Tc2. Spin structure models proposed for each of the two phases seem to be in favor with our experiments. The powder neutron diffraction data are, however, less conclusive. They only seem to hint at a smeared-out discontinuity at To2, but do not confirm the proposed F type multiaxis model at low temperatures. This seems to indicate that either another multiaxis structure (G, AA, AC .... ) or even the parent structure All 11) apply. In order to disprove or to confirm the latter possibility, being very unlikely as discussed in section 3.1, and to determine the actual spin structure, further clarifying experiments are necessary. Neutron diffraction and susceptibility measurements on well-defined annealed single domains are most promising.

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