arXiv:cond-mat/0511180v1 [cond-mat.str-el] 8 Nov 2005
Comment on ”Strong dependence of the interlayer coupling on
the hole mobility in antiferromagnetic La2−xSrxCuO4(x < 0.02)”
I. Ya. Korenblita, A. Aharonya,b, and O. Entin-Wohlmana,b
aSchool of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences,
Tel Aviv University, Tel Aviv 69978, Israel
bDepartment of Physics, Ben Gurion University, Beer Sheva 84105, Israel
(February 2, 2008)
Using the experimental data given in the above paper, we show that – unlike
the effective coupling discussed in this paper – the net average antiferromag-
netic interlayer coupling in doped lanthanum cuprates depends only weakly
on the doping or on the temperature. We argue that the effective coupling
is proportional to the square of the staggered magnetization, and does not
supply new information about the origin of the suppression of the magnetic
order in doped samples. Our analysis is based on a modified version of the
equation describing the spin-flip transition, which takes into account the de-
crease of the staggered moment with temperature and doping.
xxxxxx PACS numbers: 74.25.Ha, 74.72.Dn, 75.30.Hx, 75.40.Cx
The prototype high-temperature superconductor is La2−xSrxCuO4, which is antiferro-
magnetic, with the N´ eel temperature TN strongly decreasing with increasing doping for
∼0.02, and superconducting at x > 0.05. Stoichiometric La2CuO4has alternate weak
ferromagnetic moments in the c-direction (perpendicular to each CuO2plane), due to the
Dzyaloshinsky-Moriya (DM) interaction, allowed by its orthorhombic structure. These mo-
ments flip into the same direction (together with a flip of the in-plane staggered moments),
generating a net ferromagnetic moment, at a temperature-dependent spin-flip (SF) magnetic
field Hc(T) along the c direction.1
In a recent paper,2H¨ ucker et al. studied the temperature and field dependent spin-flip
transition in La2−xSrxCu1−zZnzO4. In a separate paper3they also studied this transition in
La2−x−yEuySrxCuO4. For each sample, they also measured the ferromagnetic moment at the
SF transition, MF(T). The aim of the study was, according to the authors, “to find out the
primary controlling parameter for the suppression of the 3D AF order in La2−xSrxCuO4”.
To this end, they “have studied the magnetic interlayer coupling J⊥ as a function of Sr
and/or Zn doping” (see p. 1 of their paper). Actually, however, H¨ ucker et al. calculated
∆E(T) = MF(T)Hc(T),(1)
and defined an “effective interplanar coupling”, J⊥(T) = ∆E(T)/S2. It is from the doping
and temperature dependences of this quantity that they tried to find out the reason of the
suppression of the AF order in doped lanthanum cuprates.
In this Comment we show that for doped samples the “effective interlayer coupling” is
not related directly to J⊥even at T = 0. Then we use the experimental data by H¨ ucker et al.
to conclude that in fact J⊥depends only weakly on T and x. It is probably also independent
of z. Therefore, J⊥is not the primary controlling parameter for the suppression of the 3D
order. The decrease in J⊥(T) results from the decrease in the staggered moment, which is
probably caused by doping dependent changes in the intraplanar correlation length, due to
changes in the intraplanar interactions.
The energy ∆E(T) should balance the net interplanar antiferromagnetic exchange cou-
pling energy at the (first order) flip transition. Therefore, at T = 0 and x = z = 0, Thio
et al.1equated the energy ∆E(0) to J⊥S2, where S represents the ground state staggered
moment per Cu ion, to deduce the interlayer exchange energy J⊥. Since J⊥results from a
delicate balance between four bonds which couple each Cu ion to its neighbors in the next
plane, one might expect this energy to depend on doping even at T = 0.
Our main argument relates to the value of ∆E(T) at non-zero temperature and/or dop-
ing. As T increases from 0 to TN, the staggered moment per Cu ion, M†, decreases from
S to zero. A similar decrease may result from the doping, even at T = 0. Therefore, the
relation ∆E(0) = J⊥S2of Ref. 1, which was also used in Ref. 2, should be generalized into
the effective mean-field interlayer energy given by
∆E(T) = J⊥[M†]2.(2)
Thus, J⊥(T) = J⊥[M†/S]2, and the decrease in J⊥results mainly from the decrease in M†.
H¨ ucker et al. claimed that J⊥(0) = J⊥(see p. 3 of the paper), and derived from this relation
J⊥for doped samples. However, as argued above, this relation holds only for pure samples,
when M†= S. Therefore, the values of J⊥reported in Table 1 of Ref. 2 do not represent
the interlayer coupling J⊥.
Note that because of the in-plane and out-of-plane spin exchange anisotropy, the stag-
gered moment in lanthanum cuprates is finite at finite T even at vanishing interlayer cou-
pling, and hence it need not be very sensitive to the interlayer coupling. Its decrease with
the increase of T is due to thermal fluctuations. At relatively high doping, this decrease
may also be due to stripe formation.5However, the possibility of stripe formation in the
(low doping) AF ordered region of lanthanum cuprates is still controversial: The recent ex-
perimental results by Gozar et al.6exclude the phase separation scenario suggested in Ref.
5 for Sr doping in the relevant range x ≤ 0.02. At these concentrations, the strong decrease
of M†with localized hole doping is most probably due to frustration in the planes.7
Given the mean field DM free energy per site, −4DM†MF, where D is the DM interaction
energy,4the ferromagnetic moment is given by
MF(T) = χ⊥4DM†,(3)
where χ⊥ is the transverse ferromagnetic susceptibility. For the undoped system below
TN, χ⊥≈ 1/(8J), where J is the intralayer exchange energy. Therefore, equating the two
expressions for ∆E(T) yields
Using the data from Fig. 3 and Table 1 of Ref. 2, we plot in Fig. 1 the ratio α versus
T/TN for different samples, doped with Sr and Zn. We also calculated α for Eu doped
samples, using the data from Fig. 24 of Ref. 3. Roughly, α is seen to be essentially the same
for all temperatures and Sr (holes) or single crystal Eu doping (data for Eu doping are shown
only at temperatures where the crystal remains orthorhombic). The overall slow increase
of α with T can be explained by the decrease of D, see Eq. (4), because of the decrease
of the orthorhombic distortion with increasing temperature.4This latter decrease may also
cause a small decrease in J⊥, which is apparently compensated by the larger decrease in D.
In any case, these changes are all small. In contrast, substitution of Cu by Zn apparently
yields somewhat smaller values of α. However, this could still be consistent with no change
in J⊥. It is known8that in vacancy doped planar isotropic AF systems the susceptibility
χ⊥diverges at any doping concentration. Magnetic anisotropy removes the divergency, but
the susceptibility may still be large, since the anisotropy in lanthanum cuprates is small.
This increase may also account for the increase of MF observed in Ref. 2, see our Eq. (3),
and the decrease of α in Fig. 1. An alternative source for the decrease of α would involve a
doping-dependent octahedral tilt angle, which would lead to the increase of D.2The same
mechanism can explain the decrease of α in polycrystaline Eu doped samples.
Thus, the values which we deduce for α are consistent with a scenario in which J⊥
essentially does not depend on T or on doping. Since J⊥represents a net superexchange
energy, which is an average local quantity, this result implies that fluctuations due to doping
average out and have no strong effect on the measured J⊥; the local J⊥increases or decreases
depending on which sub-lattice is doped. Given that the average J⊥is constant, the “effective
interlayer coupling” J⊥(T) does not give more information than the staggered magnetization
M†. The approach of J⊥(T) to zero when T approaches TNdoes not imply that the interlayer
coupling diminishes. Thus, the statement in the abstract of Ref. 2, that the “interlayer
coupling plays a key role in the suppression of the AF phase”, is unjustified.
The title of Ref. 2, which states that the interlayer coupling (i.e., J⊥rather than J⊥)
depends strongly on the hole mobility, is also misleading. First, as shown above, the change,
if any, of J⊥due to doping is small. Secondly, the paper presents no direct evidence that
the hole mobility has any direct effect on the magnetic properties of lanthanum cuprates. In
contrast, it was shown that the strong suppression of the AF order by Sr (hole) doping – in
variance with Zn (vacancy) doping – can be explained by the long-range dipole-type mag-
netic distortion introduced by localized holes.9–11The theory based on this model describes
quantitatively the phase diagrams of Sr doped as well as of Sr and Zn doped lanthanum
cuprates.10,12Hence the attempt of the authors to explain this difference by the effect of
hole mobility is only a suggestion, which has no quantitative support. The idea of dynamic
magnetic antiphase boundaries evoked by the authors to support their statements is, as
noted above, still controversial.
In conclusion, we have shown that all the available data are consistent with a constant
J⊥, essentially independent of T, x, y and possibly also z. Therefore, it is not necessarily
the interlayer coupling which controls the AF order in Sr doped lanthanum cuprates. In
fact, the suppression of the AF order can be fully explained by the reduction of the in-plane
correlation length with Sr doping, due to frustration.10,11
We acknowledge useful discussions with B. B¨ uchner and with M. H¨ ucker, and support
from the US-Israel Binational Science Foundation (BSF).
1T. Thio, T. R. Thurston, N. W. Preyer, P. J. Picone, M. A. Kastner, H. P. Jenssen, D.
R. Gabbe, C. Y. Chen, R. J. Birgeneau, and A. Aharony, Phys. Rev. B 38, R905 (1988).
2M. H¨ ucker, H.-H. Klauss and B. B¨ uchner, Phys. Rev. B 70, R220507 (2004).
3M. H¨ ucker, V. Kataev, J. Pommer, U. Ammerahl, A. Revcolevschi, J. M. Tranquada and
B. B¨ uchner, Phys. Rev. B 70, 214515 (2004).
4T. Thio and A. Aharony, Phys. Rev. Lett. 73, 894 (1994).
5M. Matsuda, M. Fujita, K. Yamada, R.J.Birgeneau, Y. Endoh, and G. Shirane. Phys.
Rev. B 65, 134515 (2002).
6A. Gozar, B.S. Dennis, G. Blumberg, S. Komiya, and Y. Ando, Phys. Rev. Lett. 93,
7A. Aharony, R. J. Birgeneau, A. Coniglio, M. A. Kastner, and H. E. Stanley, Phys. Rev.
Lett. 60, 1330 (1988).
8A. B. Harris and S. Kirkpatrick, Phys. Rev. B 16, 542 (1977).
9L. I. Glazman and A. S. Ioselevich, Z. Phys. B 80, 133 (1990).
10V. Cherepanov, I. Ya. Korenblit, A. Aharony, and O. Entin-Wohlman, Eur. Phys. J. B 8,
11O. P. Sushkov and V. N. Kotov, Phys. Rev. Lett. 94, 097005 (2005).
12I. Ya. Korenblit, A. Aharony, and O. Entin-Wohlman, Phys. Rev. B 60, R15017 (1999).
FIGURES Download full-text
00.2 0.40.6 0.81
T / TN
× x=0.017, z=0.10
• x=0, z=0.15
* x=0, y=0.2, s
∆ x=0, y=0.2, p
FIG. 1. The ratio α = Hc/MF versus temperature for lanthanum cuprate doped with Sr
(concentration x), Zn (z) and Eu (y). The experimental data are taken from Refs.  and .
The typical error bars are from Table 1 in Ref. . “s” and “p” stand for single and polycrystal