Page 71 - ILLS Annual Report 2018

SCIENTIFIC HIGHLIGHTS
68-69
Figure 2
Top) Main super-exchange path for the magnetically
frustrated J interaction. 3
Bottom) Atomic displacements releasing the J3 (left part) and J6 (right part) frustrations.
polarisation.
In the Pbam non-polar group, J3 does not contribute to the
each unit cell one is located between atoms FM-ordered, the other between atoms AFM-ordered (figure 1). It is thus the symmetry breaking from Pbam to Pm that allows the two J3 interactions to be non-equivalent and that is responsible for the observed polarisation. From the picture of the main super-exchange path involved in J3 (figure 2), it is easy to see that the main way to reach this goal is to change the angles α and β so that the increase/decrease of the Mn3+(t2g)-04(2p)-Mn4+(t2g) orbitals’ overlap
will increase/decrease the AFM character of J3. As a consequence, the Mn3+ ions will shift alternatively along the ±a direction and the Mn4+ along the ±a + εb, while the 04 oxygen bridging the Mn3+ and Mn4+ ions will move alternatively along the ±a − ηb direction (figure 2). Within the entire unit cell, these shifts result in a global relative displacement of the negative charges along −b, and of the positive ones along the +b direction, i.e. in a macroscopic electric polarisation along b and breaking the inversion symmetry.
Let us now analyse the Gd–Mn interactions. One must first remember that the Gd3+ ion is in a 4f7,S = 7/2,L = 0 configuration. As a result, in a first approximation
→→→ →→
Let us analyse the mechanism at the origin of the electric
thathyaietlydield
magnetic energy as its two cotnhtraibtuytioenlds cancel out: in that yield
that yield
(spherical, atomic), the spin-orbit interaction on the Gd3+ ground-state and thus the Gd3+ magnetic anisotropy is nil. The super-exchange paths depend on the square of the transfer integrals between the set of 4f orbitals of the Gd ion and the 2p orbitals of the bridging oxygen, times the square of the hopping between these oxygen 2p orbitals and the Mn 3d ones. Another consequence of the equal occupation of all 4f orbitals is thus a distance- only dependence of the super-exchange paths involved in the J6s. As a result, the strongest J6 interaction should be the one bridged by the oxygen closest to the Gd. At low temperature this is the 01 oxygen. As 01 mediates the interaction J5 between the Mn3+ dimer and J6 between the two Mn and the two Gd ions, (Gd2 and Gd3 in figure 2), there is a strong magnetic frustration. Within a simple mean-field approximation, the associated magnetic energy is
E
s
In aInPabaPmbagmrougproEup=E0=as0 as
In a P bam group E = 0 as In a P bam group E = 0 a
→ → → → 3+ → → → →
=E J= J〈S〈S〉〈· S〉〈· S3+〉 〉J+ J〈S〈S〉〈· S〉〈· S3+〉 〉
6,2a6,2aGd2 Gd2 MnaMna 6,2b6,2Gbd2 Gd2 Mn Mn 3+
+J+J〈S〈S〉〈· S〉〈· S3+
bb
E=J 〈S 〉〈·S 3+〉+J 〈S 〉〈·S 3+〉 6,2a Gd2 6,2b Gd2
→→ →→ →→ →→
E = J 〈S 〉〈·MSna 3+
2 In a Pbam g6r,o2aup EGd=
ab
〉+ J 〈S 〉〈·MSn 3+ 0 Mn 6,2b Gd 2 bMn
〉 〈→ 〉〈→ 〉 〈→ 〉〈→ 〉
→→→→ →→
3+ Mn aMn a Mn bMn b
S =S −=〈S−〈S〉=〈〉S=〈S〉 〉 Gd2 Gd2 Gd3 Gd3
3=+
〉−〈=S−〈S3+
〉
J=J=J=J=J 6,2a 6,3a 6,2b 6,3b
In order to lift =the〈mSagn =〈MSna 3+
→
〉=−〈MSn 3+ M→n a →bMn
〉
〉J+J〈S〈S〉〈· S〉〈· S3+ 〉
〉+3+
6,3a6,3aGd 3 Gd 3 Mn aMn a 6,3b6,3bGd 3 Gd 3 Mn bMn b
〉
→→→→ →→→→
3+
+J S ·S 3+ +J S ·S 3+
J =J+6,3JJa= 〈JGSd=3 J= JMSn= J=3+ J+6=,3JbJ= JGSd3 66,3,2aa6,2Gad 36〉,3〈·a6,3aa 6,〉2b6,2b6,63,b3〈b6,3Gbd 3
Mn 〉 〈· S b
J=J=J=J=J 6,2a 6,3a 6,2b 6,3b
3+
3+ e〉tic=fru−〈stSration
〉one needs both
→→→b
different Gd moments (〈S 〉 ≠ −〈S 〉 as found
→ →Gd2→Gd3 S=−〈S 〉=〈S 〉
Gd2 Gd3 S=−〈S 〉=〈S 〉
magnetic energy. In other words
Ja
andanSd S< S< S 2 23 3
Gd2 Gd3
in the magnetic structure (see figure 1), and atomic displacements such that the amplitudes of the J interactions
J=JJ=J=J=J ≠≠J=JJ=J=J=J andand|J6||J<||J<||J|
a
a 6,2a6,2a 6,3a6,3a b
b 6,2b6,2b 6,3b6,3b a
a b b
→cou→plin→g t→he larges→t AF→M Gd − Mn interaction lower the
S =S〈S=〈S〉 ≠〉 ≠S =S −= −
2 2 Gd2Gd2 3 3 Gd3Gd3
= J = J ≠ J = J = J and |J | < |J | 6,2a 6,3a b 6,2b 6,3b a b
J = J = J ≠ J = J = J and |J | < |J | a 6,2a 6,3a b 6,2b 6,3b a b
SE=〈=ES(=J(〉−JJ≠−)J(S)(=−SS−−)S·)· an0d0S <S 2 Gda2 abb3332G2d3 2 3
→→ →→→→→ →→→→→
S=〈S 〉≠S=− andS<S 2Gd2 3Gd3 23
→→ →→
E = ( J − J ) (S − S ) · → 0
E = ( J − J ) (S − S ) · → aabb3322
0
As the Mn-Gd magnetic exchanges are mediated by the oxygens, a displacement of the Gd ions will result in an equal modification of J and J (similarly J
6,2b 6,3b 6,2a and J6,3a), and thus will not lift the frustration. That means
that one must shorten the 01-Mn3+ bond and lengthen 3+ b
the 01-Mna bond, as pictured in figure 2. These displacements do not interfere with the original exchange striction issued from the release of the J3 frustration. They result in a further increase in the polarisation along b, which is responsible for the very large value of the GdMn205 polarisation within the RMn205 family.
3b
At 12 K the structural data exhibit a crossover between the Gd–01 and Gd–02 distances, the Gd–02 becoming the shortest. In contrast to the 01 oxygen the 02 ions do not mediate any magnetic frustration, and thus at T > 12 K the frustration weakens (as observed experimentally), as do the extra polar displacements.
〉 〉
→→ →→
3+
= 〈=S〈S3+ →→→→→→
〉
Mn a
Mn b
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〈S〈S〉 〉
→→
〈S 〉 〈S 〉
→
→