~ i ~ Journal of

Journal of Magnetism and Magnetic Materials 177-181 (1998) 549 550

m:t neusm
magneticmaterials

ELSEVIER

Magnetic structure and dipolar interaction in antiferromagneticsuperconductor BCT-ErRh4B4
M. Ikebe a'*, H. Fujishiro a, H. I w a s a k i b
aFaculty of Engineering, lwate University, 4-3-5, Ueda, Morioka 020, JapanbSchool of Material Science, Japan Advanced Institute of Science and Technology, Tatsunokuchi-machi, Ishikawa 923'12, Japan

Abstract

Metamagnetic transitions in the antiferromagnetic superconductor BCT-ErRh4B4 have been analyzed on the basis of
the magnetic dipolar interaction by applying the group theoretical method of Luttinger and Tisza. The analyses allowed
us to uniquely determine the magnetic structures of the ground state and the intermediate states. © 1998 Elsevier ScienceB.V. All rights reserved.
Keywords. Dipolar interactions; Metamagnetism; Magnetic structure; Superconductivity - magnetic

It is well-known that the primitive tetragonal (PT)phase of ErRh4B4 is a typical ferromagnetic superconductor with Ts = 8.7 K, which shows re-entrant behavior
at Tc = 0.95 K [1]. Making a marked contrast, thebody-centered tetragonal (BCT) phase of ErRh4B4 is anantiferromagnetic superconductor with Ts = 7.8 K andTN = 0.65 K, and superconductivity and antiferromagnetism coexist below TN [2, 3]. We previously reported
peculiar metamagnetic transitions in the BCT-ErRhgB4
single crystal under four-fold anisotropy in the c-plane,
which is reproduced in Fig. 1. As can be seen in thefigure, the magnetization jumps on two steps with applied field in the [1 0 0] (and [0 1 0]) direction, whileit takes a one-step jump in the [1 1 0] direction. Themagnetization of the intermediate state is one half ofthe saturation moment M0 in the [1 0 0] direction andthat in the [1 1 0] direction is Mo/x/2. The easy magnetization axes are the [1 0 0] and [0 1 0] axes and the[0 0 1] axis is the very strong hard magnetization axis.
Since TN of BCT-ErRh4B~ is as low as 0.65 K and the magnetic moment # of Er 3 + ion is pretty large (F = 9.6 ~tB in
free-ion state), the magnetic dipolar interaction shouldplay a role of fundamental importance to determine themagnetic structure in this compound [-4, 5]. We analyze
the metamagnetic transitions in BCT-ErRh4B4 by*Corresponding author. Fax: +81 19 621 6373; e-mail:ikebe@msv.cc.iwate-u.ac.jp]

IlI

ErRh4B4 (bct)

I0.1K{:Z~lv_.
12HIII

345(kOe)

Fig. 1. Solid line represents magnetization with HI][1 0 0] anddashed line with HIll1 1 0] [2].

applying the method and results of Luttinger and Tisza(LT) [-6] for the dipolar energy of the cubic lattice.
If we direct our attention only to Er atoms in BCTErRhaB4, they are located almost on face-centeredcubic (FCC) lattice points. Let F be the group of cubictranslations, F = l l i + 12J + 13k. Here Ib 12, 13 are integers and i, j, k are cubic lattice vectors in the x, y, z
directions. We consider the general ordered arrays
which are invariant under translations of the form,/-2 = 11(2i) + 12(2J) + 13(2k)./.2 is the subgroup of F. Forsimple cubic (SC) lattice, any ordered array of the class
F 2 can be represented as a linear combination of the 24
basic arrays, Xi, Y, Zi, i = 1, 2..... 8 (see Fig. 2). The

0304-8853/98/$19.00 © 1998 Elsevier Science B.V. All rights reserved
PII S 0 3 0 4 - 8 8 5 3 ( 9 7 ) 0 0 5 4 2 - 8

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M. Ikebe et al./Journal of Magnetism and Magnetic Materials 177 181 (1998) 549 550~.~

XI

X2

X3

X4xs

X6

X7

Xezx

(a)

~---~ x(b)Fig. 2. The eight basic arrays for the x component of the magnetic moment. X~ and the similar basic arrays Y~and Z~ span theclass 1"z magnetic structures [6].

strength and the symmetry of the fields at the lattice
points and face-centers of a cube (ft - f s , ht - h4) aretabulated in Tables I and II of Ref. [6]. One F C C lattice
can be decomposed into four SC lattices and the dipolarenergy of various magnetic structures can readily becalculated because we know the fields of the lattice points
and face-centers. We now introduce the notation
I-P, Q, R, S] to denote the F C C magnetic structure with
P a basic array at lattice points, Q at X Y face-centers,R at Y Z face-centers and S at Z X face-centers. As LT
pointed out, the ground-state spin configuration (g-state)is [X8, Ys, - Xs, Ys], energy U s per spin being given by
Up = - hM~Z/2a 3 = -- 7.232/~2/a 3 = - 0.48 K,-(hi+h4)#2/4a 3 = - 4 . 6 9 9 # 2 / a 3 =-0.31K.

(2)
This I~-state is realized from g-state by changing thearray at Y Z and Z X face-centers to ferromagnetic basic
array X1.
The state with moment M o / x / 2 in the [1 1 0] direction(I2-state) is [X1, X1, Y1, Y1] and the dipolar energy is
given byUI2--

h t # 2 / 2 a 3 = -- 2.167kt2/a 3 -- -- 0.15 K.

(d)Fig. 3. Proposed magnetic structures, (a) the ground state, (b)the intermediate ferromagnetic state with Mo/2 for nil [1 0 03; (c)the canted ferromagnetic structure with Mo/x/2 for HII [-1 1 0],(d) the final ferromagnetic state for HII[1 0 03. Cubes (shadedand not shaded) represent Rh4B4 units.

(1)

where we used the measured value # = 5.3 lab for thesaturation m o m e n t [2], and a = 7.4 A for the F C C lattice
constant. The U s value seems to be consistent with
Tr~ = 0.65 K of this compound.
The lowest dipolar energy state with moment Mo/2 inthe [1 0 0] direction (ll-state) is [Xs, Ys, X~, X~] withthe dipolar energy
Uil=(c)(3)

If we assume a spherical sample, the metamagnetictransition between g-state and Ii-state should take placeat Hla = 1000Oe, between g-state and I2-state at
Hzd = 1300 Oe and between /t-state and the final fer-romagnetic state (UF = 0) at H3a = 1700 Oe, respectively. These values are favorably compared with the experimental values, H1 = 1120Oe, H2 = 1250Oe andH3 = 2770 Oe. The minor discrepancy can be remedied
by introducing very weak exchange interaction between
Er moments. The proposed magnetic structures are schematically presented in Fig. 3. Low-temperature neutron
diffraction studies to confirm these structures are highlydesirable.

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