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Ising-like magnetism in rare-earth cuprates
Physica C 235-240 (1994) 1549-1550 North-Holland
PHYSICA
Ising-like magnetism in rare-earth cuprates V. Nekvasil and I. Veltrnsk# Institute of Physics, Cukrovarniekll 10, 162 00 Prague 6, Czech Republic
We examine general conditions for an Ising-like behaviour of rare-earth subsystem in high-Tc cuprates and related compounds. We show that such behaviour might possibly occur in compounds containing Tb, Dy, and Ho due to the special nature of low-lying 4f states imprinted by the crystal-field interaction.
1. INTRODUCTION Rare-earth (RE) ions enter many high-To superconductors and related layered cuprates. They usually form a layer either sandwiched between two CuO2 layers or adjacent to one of these layers. The RE subsystem orders antiferromagnetically near I K. The two-dimensional(2D) magnetic order establishes in some cuprates [1] at finite Try. The 2D order is dictated by the crystallographic structure, the Tr~# 0 is due to an anisotropy within the spin system 121. This anisotropy can be strong: there art: cuprates in which the critical behaviour appears to approximate to an exactly soluble 2D Ising model [11. The aim of this communication is to examine conditions allowing to describe the pair interaction between RE moments in euprates by an Ising form:
perturbation of free-ion states of 4f electrons in cuprates. The over-all splitting of the J multiplets in cuprates is probably larger than in any other oxide and the local symmetry is usually tetragonai or orthorhombic. Consequently, the ground state is often a well isolated (quasi) doublet and the lowtemperature magnetic properties can be described introducing effective spin hamiltonian with s'= 1/2. The (quasi) doublet ground state implies Ising-like moments directly in the case of non-Kranaers ions as the Zeeman term has the form: = A¢'_.~+ ttBg~H~s~ ,
(2)
where J,j is an interaction strength and s' = 1/2 is the effective spin. First, we examine if very strongly anisotropic, or Ising-like RE moments can be found in cuprates. The Ising-like nature of magnetic moments is a necessary (but not sufficient) condition for an Ising-like behaviour in the critical region.
where A is the splitting of the (quasi) doublet. The crystal direction to which the magnetic moments are constrained is dictated by symmetry properties of wavefunctions of the ground-state (quasi) doublet. The Zeeman admixture of higher energy CF states is presumed to be small and is neglected in eq. (2). In the case of Kramers doublets the anisotropy of g-tensor is determined by the form of wavefunctions rather than by their symmetry properties. For an isolated Kramers doublet with gz~'gx, gy the spin hamiltonian takes the desired form. (2), A =0, teo.
2. ISING-LIKE MAGNETIC MOMENTS
3. COOPERATIVE INTERACTIONS
The coordination polyhedra of RE3+ ions in regular lattice sites in cuprates are typically formed by eight oxygen ligands situated at comers of slightly distorted cubes. These ligands give major contribution to the crystal field (CF) acting at the RE sites [31. The CF interaction is the strongest
A magnetic dipole-dipole coupling is the dominant long-range interaction in cuprates. Presuming that non-Ising components of magnetic moment are negligible this coupling can be written directly in the form (1). The RKKY interaction probably plays a negligible role. We only note that
~l~= X Jijs~s~j,
(1)
0921-4534/941S07.00 © 1994 - Elsevier Scmnce B.V. All nghts reserved SSDI 0921-4534(94)01341-1
1550
V. Neb~astL L Veltrus~/Phvswa C 235-240 (1994) 1549-1550
its projected form would be again (1). Short-range interactions including anisotropic exchange, electric multipole coupling, and virmalphonon coupling can be described by the same hamiltonian spanning the lowest J-mnltiplet I41 ~exeh = ~Jna'Ttm ram' (n)(Jt)T,~ (n') ' (J2).
(3)
There are 346 independent interaction strengths j,m~: in eq. (3) for nearest-neighbour pairs of RE ions in D21a and D41a symmetry compounds. Projection of the operator (3) onto the states s' = + 1/2 gives besides the Ising form (1) also non-Ising terms. Their smallness is not guaranteed ~ priori by a strongly anisotropic character of the magnetic moments. Magnitudes of the non-Ising terms depend on the form of the CF wavefunctions and have to be examined fol each compotmd separately [51. 4. ISING BEHAVIOUR IN CUPRATES A reliable set of the CF parameters is available only for a few RE cuprates, In remaining cuprates where RE ions reside in geometrically similar dodecahedral sites we approximate the 4th- and 6thorder CF parameters by our superposifion model values in REBa2Cu3OT.~ [31. That is possible as the electronic ground-state properties are only little sensitive to variations in values of the higher-order CF parameters associated with structural variations of the coordination polyhedra from one RE cupr~:~ to another (this is not entirely true for Tin). Ground state properties are thus governed by the 2nd--order parameters. As there is no theory allowing to relate these parameters to the cuprate structure we treat them as unknowns. Calculating the moments at 0 K we let the CF parameters B2o and B22 to vary in respective ranges -600 to 600 cm-~ and -500 to 500 cm-~ with higher-order parameters fixed to the REB:hCu307 values. In that way we believe to cover all Ising-like RE moments which might possibly occur in cuprates. As Ising-like we assign in the following those moments which can be treated as effective spins s' = 1/2, eq. (2), anfJ their dominant component at 0 K exceeds remaining components at least by factor 10 in magnetic fields of 1 T (-TN). Indeed moments of several RE ions are Ising-like in large areas in the (B2o, B22) plane with following lsing
directions. Sm: c; Dy: a, b, or c; Ho: a (groundstate quasidoublet F 2, 1"3); Tb: a (F1, I"4) or c (I',, I'2). Obviously, only c can become the Ising axis in tetragonal compounds. Remaining RE moments are either weakly anisotropic (Nd, Yb) or the Ising areas in the (132o, 1322) planes are very small. Different possible choices of the higher-order parameters can change the size or locations of the Ising areas somewhat but not influence their magnetic Ising-like magnetic features. Best candidates for Ising behaviour are Dy, Ho, and Tb compounds where the magnetic moments in Ising areas are close to gjJ and J > 4 . In such cases the non-Ising terms are expected to be small. Among the cuprates studied so far only Dy in 1-2-3, 2-4-7, and 2-4-8 compounds with the easy axis [I c can be seriously considered to approximate to the Ising mode~. [11 though not as close as some other compounds, e.g., Dy3AIsO~ [61. The resemblance to the Ising model revealed in, e.g., REBa2Cu3OT, RE=Nd [71, Er II1 appears fortuitous. The principal difference between the Ising-like cuprates and standard nearest-neighbour Ising model lies in the importance of contribution of the long-range magnetic dipole-dipole coupling. Consequently, critical exponents are expected to shift from lsing model values towards those predicted by the meanfield theory I81. This work was supported by the GA CR grant No. 202/93/1165. REFERENCES 1. J.W. Lynn, J. Alloys and Compounds, 181 (1992) 419. 2. A.P. Yang, Ordering in Strongly Fluctuating Condensed Matter Systems, ed. T. Riste, Plenum Press, New York, 1980, p. 11. 3. V. Nekvasil, P h ~ ca C, 170 (1990) 469. V. Nekvasil, Solid State Commun., 65 (1988) 1103. 4. W.P. Wolf, J. Phys. (Paris), 32 (1971) C1-26. 5. R.J. Anderson et al., J. Phys. C, 4 (1971) 1618. 6. W.P. Wolf et al., Phys. Rev. B, 5 (1972) 4472. 7. K.N. ~'ang et al.. Phys. Rev. B, 40 (1989) 10963. 8. H.E. Stanley, Phase Transitions and Critical Phenomena, Oxford U. Press, New York,1971; A. Aharony, Phvsica. 86-88B (1977) 545.
PHYSICA
Ising-like magnetism in rare-earth cuprates V. Nekvasil and I. Veltrnsk# Institute of Physics, Cukrovarniekll 10, 162 00 Prague 6, Czech Republic
We examine general conditions for an Ising-like behaviour of rare-earth subsystem in high-Tc cuprates and related compounds. We show that such behaviour might possibly occur in compounds containing Tb, Dy, and Ho due to the special nature of low-lying 4f states imprinted by the crystal-field interaction.
1. INTRODUCTION Rare-earth (RE) ions enter many high-To superconductors and related layered cuprates. They usually form a layer either sandwiched between two CuO2 layers or adjacent to one of these layers. The RE subsystem orders antiferromagnetically near I K. The two-dimensional(2D) magnetic order establishes in some cuprates [1] at finite Try. The 2D order is dictated by the crystallographic structure, the Tr~# 0 is due to an anisotropy within the spin system 121. This anisotropy can be strong: there art: cuprates in which the critical behaviour appears to approximate to an exactly soluble 2D Ising model [11. The aim of this communication is to examine conditions allowing to describe the pair interaction between RE moments in euprates by an Ising form:
perturbation of free-ion states of 4f electrons in cuprates. The over-all splitting of the J multiplets in cuprates is probably larger than in any other oxide and the local symmetry is usually tetragonai or orthorhombic. Consequently, the ground state is often a well isolated (quasi) doublet and the lowtemperature magnetic properties can be described introducing effective spin hamiltonian with s'= 1/2. The (quasi) doublet ground state implies Ising-like moments directly in the case of non-Kranaers ions as the Zeeman term has the form: = A¢'_.~+ ttBg~H~s~ ,
(2)
where J,j is an interaction strength and s' = 1/2 is the effective spin. First, we examine if very strongly anisotropic, or Ising-like RE moments can be found in cuprates. The Ising-like nature of magnetic moments is a necessary (but not sufficient) condition for an Ising-like behaviour in the critical region.
where A is the splitting of the (quasi) doublet. The crystal direction to which the magnetic moments are constrained is dictated by symmetry properties of wavefunctions of the ground-state (quasi) doublet. The Zeeman admixture of higher energy CF states is presumed to be small and is neglected in eq. (2). In the case of Kramers doublets the anisotropy of g-tensor is determined by the form of wavefunctions rather than by their symmetry properties. For an isolated Kramers doublet with gz~'gx, gy the spin hamiltonian takes the desired form. (2), A =0, teo.
2. ISING-LIKE MAGNETIC MOMENTS
3. COOPERATIVE INTERACTIONS
The coordination polyhedra of RE3+ ions in regular lattice sites in cuprates are typically formed by eight oxygen ligands situated at comers of slightly distorted cubes. These ligands give major contribution to the crystal field (CF) acting at the RE sites [31. The CF interaction is the strongest
A magnetic dipole-dipole coupling is the dominant long-range interaction in cuprates. Presuming that non-Ising components of magnetic moment are negligible this coupling can be written directly in the form (1). The RKKY interaction probably plays a negligible role. We only note that
~l~= X Jijs~s~j,
(1)
0921-4534/941S07.00 © 1994 - Elsevier Scmnce B.V. All nghts reserved SSDI 0921-4534(94)01341-1
1550
V. Neb~astL L Veltrus~/Phvswa C 235-240 (1994) 1549-1550
its projected form would be again (1). Short-range interactions including anisotropic exchange, electric multipole coupling, and virmalphonon coupling can be described by the same hamiltonian spanning the lowest J-mnltiplet I41 ~exeh = ~Jna'Ttm ram' (n)(Jt)T,~ (n') ' (J2).
(3)
There are 346 independent interaction strengths j,m~: in eq. (3) for nearest-neighbour pairs of RE ions in D21a and D41a symmetry compounds. Projection of the operator (3) onto the states s' = + 1/2 gives besides the Ising form (1) also non-Ising terms. Their smallness is not guaranteed ~ priori by a strongly anisotropic character of the magnetic moments. Magnitudes of the non-Ising terms depend on the form of the CF wavefunctions and have to be examined fol each compotmd separately [51. 4. ISING BEHAVIOUR IN CUPRATES A reliable set of the CF parameters is available only for a few RE cuprates, In remaining cuprates where RE ions reside in geometrically similar dodecahedral sites we approximate the 4th- and 6thorder CF parameters by our superposifion model values in REBa2Cu3OT.~ [31. That is possible as the electronic ground-state properties are only little sensitive to variations in values of the higher-order CF parameters associated with structural variations of the coordination polyhedra from one RE cupr~:~ to another (this is not entirely true for Tin). Ground state properties are thus governed by the 2nd--order parameters. As there is no theory allowing to relate these parameters to the cuprate structure we treat them as unknowns. Calculating the moments at 0 K we let the CF parameters B2o and B22 to vary in respective ranges -600 to 600 cm-~ and -500 to 500 cm-~ with higher-order parameters fixed to the REB:hCu307 values. In that way we believe to cover all Ising-like RE moments which might possibly occur in cuprates. As Ising-like we assign in the following those moments which can be treated as effective spins s' = 1/2, eq. (2), anfJ their dominant component at 0 K exceeds remaining components at least by factor 10 in magnetic fields of 1 T (-TN). Indeed moments of several RE ions are Ising-like in large areas in the (B2o, B22) plane with following lsing
directions. Sm: c; Dy: a, b, or c; Ho: a (groundstate quasidoublet F 2, 1"3); Tb: a (F1, I"4) or c (I',, I'2). Obviously, only c can become the Ising axis in tetragonal compounds. Remaining RE moments are either weakly anisotropic (Nd, Yb) or the Ising areas in the (132o, 1322) planes are very small. Different possible choices of the higher-order parameters can change the size or locations of the Ising areas somewhat but not influence their magnetic Ising-like magnetic features. Best candidates for Ising behaviour are Dy, Ho, and Tb compounds where the magnetic moments in Ising areas are close to gjJ and J > 4 . In such cases the non-Ising terms are expected to be small. Among the cuprates studied so far only Dy in 1-2-3, 2-4-7, and 2-4-8 compounds with the easy axis [I c can be seriously considered to approximate to the Ising mode~. [11 though not as close as some other compounds, e.g., Dy3AIsO~ [61. The resemblance to the Ising model revealed in, e.g., REBa2Cu3OT, RE=Nd [71, Er II1 appears fortuitous. The principal difference between the Ising-like cuprates and standard nearest-neighbour Ising model lies in the importance of contribution of the long-range magnetic dipole-dipole coupling. Consequently, critical exponents are expected to shift from lsing model values towards those predicted by the meanfield theory I81. This work was supported by the GA CR grant No. 202/93/1165. REFERENCES 1. J.W. Lynn, J. Alloys and Compounds, 181 (1992) 419. 2. A.P. Yang, Ordering in Strongly Fluctuating Condensed Matter Systems, ed. T. Riste, Plenum Press, New York, 1980, p. 11. 3. V. Nekvasil, P h ~ ca C, 170 (1990) 469. V. Nekvasil, Solid State Commun., 65 (1988) 1103. 4. W.P. Wolf, J. Phys. (Paris), 32 (1971) C1-26. 5. R.J. Anderson et al., J. Phys. C, 4 (1971) 1618. 6. W.P. Wolf et al., Phys. Rev. B, 5 (1972) 4472. 7. K.N. ~'ang et al.. Phys. Rev. B, 40 (1989) 10963. 8. H.E. Stanley, Phase Transitions and Critical Phenomena, Oxford U. Press, New York,1971; A. Aharony, Phvsica. 86-88B (1977) 545.