Successive phase transitions in the hexagonal-layered Heisenberg antiferromagnets MnX2 (X = Br, I)

PlW:A ELSEVIER

Physica B 213&214 (1995) 224 226

Successive phase transitions in the hexagonal-layered Heisenberg antiferromagnets M n X 2 (X -- Br, I) T. Sato a'*, H. K a d o w a k i b, K. lio a Department of Physics, Tokyo Institute of Technology, Tokyo 152, Japan b Institute for Solid State Physics, Universi~ of Tokyo, Tokyo 106, Japan

Abstract Successive magnetic phase transitions in the Heisenberg antiferromagnets MnX2 (X = Br, I) have been studied by neutron diffraction. Two (TN~ = 2.32 K and TN2 = 2.17 K) and three (TNt = 3.95 K, TN2 = 3.8 K and TN3 = 3.45 K) transitions were observed in the bromide and the iodide, respectively. In both compounds, transverse sinusoidally modulated structures occur in the intermediate phases (MnBr2:TN2 < T < TN~; MnI2:TN3 < T < TN~), whereas the T~,L~,(MnBr2) and helical (MnI2) structures occur through first-order transitions in the lowest-temperature phases. The successive transitions are brought about by several competing exchange interactions and the dipole interaction.

1. Introduction The manganese dihalides MnX2 (X = Br, I), which crystallize in the hexagonal-layered Cdl2 structure, are Heisenberg antiferromagnets. The magnetic ordering at the lowest temperatures (LT) has been investigated by neutron diffraction. In MnBrz, the magnetic moments order in q3~ sequence (TT~ structure) with the commensurate modulation vector qc = (¼0 ¼). The spin polarization is along the b-axis [1]. On the other hand, for Mnl2, a proper helical structure with q = (~60 ~ ) has been reported [2]. After these neutron diffraction studies, two successive phase transitions were found in both the compounds by optical studies [3,4]. The transition from the paramagnetic (P) to the intermediate temperature (IM) phase is second order, whereas that from the IM to the LT phase is first order. A first-order transition is puzzling for * Corresponding author. Present address: Institute for Solid State Physics, Universityof Tokyo, 7-22-1 Roppongi, Minato-ku, Tokyo 106, Japan.

a simple Heisenberg antiferromagnet with weak anisotropy, as is expected for MnX2, because it usually undergoes one or two second-order transitions, depending on the type of anisotropy [5]. To reveal the origin of the transitions, we performed neutron-diffraction experiments. Details will be reported elsewhere [6].

2. Experimental procedure and results Neutron-diffraction experiments were performed on the ISSP triple axis spectrometers ND1 (JRR-2), 4G-TAS and PONTA (JRR-3M) at JAERI (Tokai). Single crystals of MnX2 were prepared by the Bridgeman method. The crystals were mounted in a 3He cryostat. The temperature of the sample was controlled to within 0.01 K. In MnBrz, two successive phase transitions were observed at TN1 = 2.32 K and TNZ = 2.17 K. We searched for magnetic reflections in the IM phase (TN2 < T < TN~) using the single crystals. They were observed at Q = q + G, where G and q denote the reciprocal lattice vector and the modulation vector, respectively. In

0921-4526/95/$09.50 ,(" 1995 Elsevier Science B.V. All rights reserved SSDI 0 9 2 1 - 4 5 2 6 [ 9 5 ) 0 0 1 12-3

225

T. Sate et al./'Physica B 213&214 (1995) 224 226

MnBr2

(oo0

(00 I) qim:TN2
Mnl2

qim':TN3
(0021

o.~ - - -qim-

o~

°"*-.

I TN/ 1 (001) /e°/ "/ 0.361, , , , L . . . . I o . 3 ~ h o.22

! ,~•

°LII

" ~ " . . ~ ~/qim'~, [TNa / 8

o ~ooli/lg t * neatmg

I

TN2 TN1~

ok~

L,,'!

(000) ..,,o.,._l~.o~ 1

o~'~ ~001

ok*

I 0 ..... -'_:: --• / 3.4 3.6 3.8 4 fr • r~axls I Temperature (K) ~ 0.102S =(hh0)

~.,~ o

(~oo)

Fig. 1. Positions of nuclear and magnetic reflections in MnBr2. Squares, open circles and closed circles denote nuclear, magnetic (LT) and magnetic (IM) reflections, respectively. Inset: locus of modulation vector variation in IM phase.

15

'

°•

'

i

,

,

,

i

•

•

'

i

,

,

.

i

,

,

,

i

,

,

cooling

t-

~

2.12

heating

s 0 ~ ( 0 ' 2 0 7 0 0.387) 216

(h 0 0)

Fig. 3. Variation of modulation vector through three phase transitions in MnI2. Inset: variation along locus (~-axis)versus temperature.

(Si) = Scos(qicr i +

ciililng

,020 o K

0

k

which can be described as

•

~'~10 I

5

l

,

TN2

t-

Q18i"--,,..,,,,~.

MnBr z

heating

oo

(h -h 0)

2.2

2.24

2.28

Temperature (K)

2.32

2.36

Fig. 2. Temperature dependence of magnetic Bragg reflection intensity in MnBr:.

the LT phase q = qc. In the IM phase we found that q is incommensurate with qic "" (0.207, 0, 0.387). Thus the transition from the IM to the LT phase is characterized by the change in the modulation vector. These reflection positions are shown schematically in Fig. 1. The modulation q~ varies slightly as a function of temperature in the IM phase. The inset of Fig. 1 shows the locus of the variation of qic in Q-space. As temperature is decreased below TNt, q~¢ moves slightly toward q~. At T N 2 , the modulation vector jumps discontinuously to q,. The peak intensities of the magnetic reflections are shown in Fig. 2. The peak intensity continuously develops below TN~ through a second-order transition. The thermal hysteresis observed around TN2 shows that the lower transition is definitely first order. The magnetic structure of MnBr2 in the IM phase was determined by measuring the integrated intensities and performing polarization analysis. It is a transverse incommensurate sinusoidally modulated (TICS) structure,

~b},

(1)

where r~ stands for the Mn 2+ site and 0 is an arbitrary phase. The spin polarization vector S is parallel to the b-axis, which is perpendicular to q~c. The ~l,L structure in the LT phase can also expressed by Eq. (1) by replacing qic ---* qc and substituting q5 = ¼ft. We also confirmed this structure. For M n l : , we observed the three successive phase transitions at TNt = 3.95 K, TN2 = 3.8 K and TN3 = 3.45 K. These are characterized by a change in modulation vector as shown schematically in Fig. 3. As temperature is decreased, the Bragg reflection at qim = (0.1025,0.1025,½) appears at TN~. As temperature is further decreased, at TN2 the reflection position begins to move slightly out of the (hhl) plane towards the (hOl) plane, shown as q,,, in Fig. 3. Finally at TN3 it jumps to q~t ~ (0.181,0, 0.439). We note that the locus of the modulation-vector variation through qim, qim' and q=t is almost on one axis (i-axis) within the experimental error. The inset to Fig. 3 shows the temperature dependence of the variation along the locus. The transition at TN2 is clearly seen from the figure. Note that q~m' is plotted slightly below TN3. We confirmed that at this temperature q~m' and q=t coexist, suggesting that the transition is first order. The modulation vector q~t is close to the previously reported ( ~ 0 ~ ) , but is definitely incommensurate and depends on temperature. The temperature dependence of the intensity of the magnetic Bragg reflections is shown in Fig. 4. One can see that second- and first-order transitions take place at TN1 and T N 3 , respectively. The magnetic structures in the IM phases (TN3 < T < TNZ and TN2 < T < TN1) are expressed by Eq. (1). The spin polarization S is along the

226

"E Sato el al. /Ph.vsica B 213&214 (1995) 224-226 5

24 E 8 E,

Q~(0.182, O, 0.43a) .c~. \ TN D°" ~ l 3

Mnl2 • heating , cooling

3

2

"1

g •

heating

[ ~ ~,,~"

..... g 2.5

3

3.5

Temperature (K)

k.; 4

4.5

Fig. 4. Temperature dependence of magnetic Bragg reflection intensity in Mnl> [ i 10] direction, which is perpendicular to qim. For the LT phase, the previously-reported helical structure was confirmed.

decreased, the easy-axis component first orders with qic which maximizes J(q), the Fourier transform of the exchange interactions. At a lower temperature, the hardaxis component usually orders through a second-order transition to form an elliptical structure. However, if J(qic) ~ J(qc) and the anisotropy is sufficiently strong, the ~l~, structure can have lower energy than the elliptical structure. Along this line, we made a quantitative calculation using mean-field theory, and found that the first-order transition from the TICS to the ]j'~, structure can be reproduced [6]. It should be noticed that the successive transitions originate from the competition between several exchange interactions and the dipole interaction. Although the transitions in Mnl2 are rather complicated, we think that a similar mechanism gives rise to the three successive phase transitions. The authors would like to thank H. T a n a k a and N. Koido for their permission to use the single crystals of MnX2.

3. Discussion The appearance of linearly polarized structures in the IM phases apparently suggests the existence of weak |sing-type anisotropy. Because of the low temperatures and the large magnetic moment of M n 2+ {S = fi2J the dipole interaction is most likely the origin of the anisotropy. By evaluating the Fourier transform of the dipole interaction, we found that the easy axis of the dipole interaction gives the correct spin polarizations for both the compounds. Thus we think MnX 2 are well represented by a model Hamiltonian consisting of the exchange interactions and the dipole interaction [6]. Based on the model, the transitions in MnBr2 are interpreted qualitatively as follows. As temperature is

References [1] E.O. Wollan, W.C. Koehler and M.K. Wilkinson, Phys. Rev. 110 (1958) 638. [2] J.W. Cable, M.L. Wilkinson, E.O. Wollan and W.C. Koehler, Phys. Rev. 125 (1962) 1860. [3] Y. Farge, M. Regis and B.S.H. Royce, J. Phys. (Paris) 37 (1976) 637. [4] K. lio, H. Masuda, H. Tanaka and K. Nagata, J. Magn. Magn. Mater. 90 & 91 (1990) 265. [5] T, Nagamiya, Solid State Phys. 20 (1967) 305. [6] T. Sato, H. Kadowaki, H. Masuda and K. lio, J. Phys. Soc. Japan 63 (1994) 4583. (MnBr2); T. Sato et al., in preparation (Mnl2}.