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MAGNETOSTRICTION NEAR THE MAGNETIC-FIELD-INDUCED PHASE TRANSITIONS OF CrzO3

R.D. YACOVITCH and Y. SHAPIRA

Francis Bitter National Magnet Laboratory,* Massachusetts Institute of Technology, Cambridge, Mass. 02139, USA

An abrupt length-change was observed at the spin-flop transition of Cr20~. The thermal expansion coefficient exhibited lambda anomalies at both the paramagnetic-to-antiferromagnetic and paramagnetic-to-spin-flop transitions. The phase diagram in fields up to 175 kOe (including the region near the bicritical point) was determined.

Recently, the investigation of multicritical points has led to a renewed interest in phase diagrams of antiferromagnets [1]. Here we dis- cuss the phase diagram of Cr203 which has a rhombohedral (trigonal) structure and is a uni- axial ant iferromagnet with the easy axis along the trigonal direction (c-axis). When the mag- netic field H is parallel to the easy axis, the phase diagram in the temperature-field ( T - H ) plane consists of three phases: paramagnetic (P), antiferromagnetic (AF) and spin-flop (SF), as discussed in [1, 2]. The A F - S F transition at Ha(T) , known as the spin-flop transition, is of first order, whereas the P - A F and P - S F tran- sitions are of second order. The boundaries between the three phases meet at the bicritical point (Tb, Hb). Previously, the temperature dependence of Hs~ in Cr203 was measured by several techniques [3, 4], and the magnetostric- tion at the spin-flop transition for T < Tb was measured by Dudko et al. [5]. In the present work we have observed anomalies in the mag- netostriction or in the thermal expansion at all three phase boundaries, and have determined the phase diagram for fields up to 175 kOe.

Variations in the sample's length l(H, T) with H (magnetostriction) or with T (thermal ex- pansion) were measured using a capacitance technique. Two single crystals were used. The results for both crystals were very similar, except that: a) the N6el temperature TN in crystal No. 1 was 307.5 K compared to 307.3 K for No. 2, b) Hsf was ~ 2% higher in crystal No. 1, and c) the transitions in crystal No. 2 were sharper. All data were taken with H parallel to the c-axis to within 2 degrees.

The insert in fig. 1 shows the H-dependence of Al/l = [ / ( H ) - I(O)]/l(O) at 77.8 K. H e r e l is the length along the c-axis. At H,f there is a

*Supported by the National Science Foundation.

~ Cr203 3~ H 11 ~ II c - a x i s

45 65 8 H (kOe) 0 I _ I I . . . . •

0 I 0 0 2 0 0 3 0 0 T ( K )

Fig. 1. T-dependence of the jump in length, 81, at the spin-flop transition. The insert shows the H-dependence of Al/l = I/(H) - l(O)]/l(O) at 77.8 K, where l is the length of the sample along the c-axis.

jump 81 in I. This behavior is similar to that reported in [5], but our value for 8l/l is 25% higher. The temperature dependence of ~l[l is shown in fig. 1. At 4.2 K, 8Ill = (3.5 -+ 0.4) x 10 -5, compared to ~l/l = 3.0 z 10 -5 calculated from the dependence of Hsf on uniaxial pressure [6] using the magnetic analog of the Clapeyron-Clausius equation [7].

The variation of Hsf with T is shown in the insert of fig. 2. These results were obtained by averaging the data for the two crystals. The demagnetizing field was less than 0.1% of H, and was ignored. The solid curve in the insert of fig. 2 was calculated from the theoretical ex- pression

Hsf = [2HEHA/(1 - a)] I/z, (1)

where HE, HA are the exchange and anisotropy fields, respectively, and a = Xtl/XI is the ratio of the parallel and perpendicular susceptibilities. Values for (2HEHA) and a were taken from [8]. Our data are in excellent agreement with eq. (1),

Physica 86-88B (1977) 1126--1127 © North-Holland

T I o • - - V T - - Y-

160 7 0r203 SF /.O HIIc-oxis

120 ~ TN= 507"3 K

~ 80 ~2o

\ 40 60

0 100200 300 T{K}

0 I I ~ ] I [ -0.6 -0 .4 -0 .2 0

T-T~ (K}

Fig. 2. P -AF and P -SF phase boundaries of Cr203 for Hllc-axis, as determined from anomalies in the thermal expansion coefficient. The insert shows the T-dependence of Hsr. The solid curve in the insert was calculated from eq. (1).

and are also in agreement with previous results [3, 4]. At 4.2 K, Hsf = (59.3 --- 1.0) kOe. The bi- critical field is Hb = (121 -+- 1.5) kOe.

The thermal expansion coefficient, at a fixed H, was measured as a funct ion of T near the P - A F and P - S F phase boundaries. At H = 0 the expansion coefficient along the binary direction (two-fold axis) showed a lambda-type peak at TN, whereas the expansion coefficient along the trigonal direction showed a lambda- type dip. These observations are consistent with X-ray data for the lattice parameters [9]. No discontinuous change in the lattice parameter was observed in either direction. Such a dis- continuous change is expected if the transition at TN is of first o r d e r - a possibility which was suggested recently [10].

The P - A F and P - S F phase boundaries were determined from the lambda anomalies of the thermal expansion coefficient along the c-axis. Results for crystal No. 2 are shown in fig. 2. The

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data for crystal No. 1 are similar. The bicritical temperature Tb is 0.5 K below TN. For the P - A F boundary,

(d T/dH2)u=o = - (2 .9 + 0.3) x 10 -II K/Oe 2.

The qualitative features of the phase diagram in fig. 2 are in agreement with recent predictions by Fisher and coworkers [1]. Specifically, for H just above Hb the P - S F transition temperature increases with increasing H. More detailed and more precise data for these phase boundaries were obtained from ultrasonic attenuation measurements in which H was parallel to the c-axis to within 0.05 degrees [11]. These data and a detailed comparison with the theoretical predictions in [1] will be presented elsewhere. Here we note only that if the parameters 4~, Q and q in [1] are taken from theory, then a much bet ter fit of the data to the theory is obtained assuming that there are preferred directions for the spins in the c-plane (n = 2 case, in notation of [1]) rather than a zero anisotropy in the c-plane (n = 3 case).

References

[1] M.E. Fisher and D.R. Nelson, Phys. Rev. Letters 32 (1974) 1350. M. Fisher, AIP Conf. Proc. 24 (1975) 273; Phys. Rev. Letters 34 (1975) 1634.

[2] Y. Shapira, J. Appl. Phys. 42 (1971) 1588. [3] S. Foner and S.L. Hou, J. Appl. Phys. Suppl. 33

(1962) 1289. [4] Y. Shapira, Phys. Rev. 187 (1969) 734. [5l K.L. Dudko, V.V. Eremenko and L.M. Semenenko,

Phys. Stat. Sol. (b) 43 (1971) 471. [6] K.L. Dudko, V.V. Eremenko and L.M. Semenenko,

Phys. Lett. 30A (1969) 459. [7] A.I. Mitsek, Fiz. Metal. Metalloved. 16 (1963) 168. [8] S. Foner, Phys. Rev. 130 (1963) 183. [9] S. Greenwald, Nature 177 (1956) 286.

[10] R.H. Bruce and D.S. Cannell, Bull. Am. Phys. Soc. 21 (1976) 231.

[11] Y. Shapira and C.C. Becerra, Phys. Lett. 59A (1976) 75.