Spin canting and lattice symmetry in La 2CuO 4 Xiao Hu1A. Sapkota2 1V. O. Garlea3G. D. Gu1I. A. Zaliznyak1and J. M. Tranquada1 1Condensed Matter Physics and Materials Science Division

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Spin canting and lattice symmetry in La2CuO4

Xiao Hu,1A. Sapkota,2, 1 V. O. Garlea,3G. D. Gu,1I. A. Zaliznyak,1and J. M. Tranquada1, ∗

1Condensed Matter Physics and Materials Science Division,

Brookhaven National Laboratory, Upton, New York 11973-5000, USA

2Ames Laboratory, Iowa State University, Ames, IA 50011, USA.

3Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA

(Dated: March 17, 2023)

While the dominant magnetic interaction in La2CuO4is superexchange between nearest-neighbor

Cu moments, the pinning of the spin direction depends on weak anisotropic eﬀects associated with

spin-orbit coupling. The symmetry of the octahedral tilt pattern allows an out-of-plane canting of

the Cu spins, which is compensated by an opposite canting in nearest-neighbor layers. A strong

magnetic ﬁeld applied perpendicular to the planes can alter the spin canting pattern to induce a weak

ferromagnetic phase. In light of recent evidence that the lattice symmetry is lower than originally

assumed, we take a new look at the nature of the ﬁeld-induced spin-rotation transition. Comparing

low-temperature neutron diﬀraction intensities for several magnetic Bragg peaks measured in ﬁelds

of 0 and 14 T, we ﬁnd that a better ﬁt is provided by a model in which spins rotate within both

neighboring planes but by diﬀerent amounts, resulting in a noncollinear conﬁguration. This model

allows a more consistent relationship between lattice symmetry and spin orientation at all Cu sites.

I. INTRODUCTION

Interest in La2CuO4, the parent compound of the orig-

inal high-temperature superconductor family [1, 2], was

renewed recently with the discovery by Taillefer and

coworkers that, at low temperature, it exhibits an un-

usually large thermal Hall conductivity [3]. The origi-

nal measurements were performed in a c-axis magnetic

ﬁeld of 15 T, which puts the system into the weak ferro-

magnetic phase, associated with a ﬁeld-induced in-phase

alignment of the small out-of-plane canting of the Cu

spins [4, 5]. Further studies have provided evidence that

the thermal Hall conductivity is due to phonons [6] and

that a sizable response can also be found in nonmag-

netic compounds such as SrTiO3[7]. While a number of

possible explanations based on intrinsic eﬀects have been

proposed [8–10], extrinsic eﬀects involving skew scatter-

ing oﬀ of defects might be the dominant eﬀect [11, 12].

Nevertheless, experimentalists have discussed the eﬀect

in terms of chiral phonons [6, 13].

Following on work by Reehuis et al. [5], we re-

cently demonstrated [14] that the structural symmetry

of La2CuO4is lower than originally determined [15, 16].

In particular, the ordered rotation of the CuO6octahe-

dra includes a small component rotated around the Cu-O

bond axis, with associated anomalous soft phonons. A

complete softening of such phonons occurs in the related

compound La1.8Eu0.2CuO4below 133 K [17]. Similari-

ties between the magnetization of that low-temperature

phase and the ﬁeld-induced weak-ferromagnetic phase of

La2CuO4led us to wonder whether the soft phonons

might couple to the canted spins in an interesting way

(despite the fact that measurements on other cuprates

indicate that canted moments are not essential for obser-

vation of a large thermal Hall conductivity [13]).

∗jtran@bnl.gov

We have used neutron scattering to study the impact

of a 14-T magnetic ﬁeld applied along the c-axis of a

crystal of La2CuO4. We ﬁnd that the crystal structure

is quite stable to the ﬁeld, and no signiﬁcant change to

phonons was detected. The measurements did, however,

provide an opportunity to reconsider the proposed model

for the weak ferromagnetic phase. We propose a new

model involving a noncollinear arrangement of spins in

neighboring planes and show that it gives a better ﬁt to

our measured magnetic peak intensities.

To provide context, we note that, as La2CuO4is a

charge-transfer correlated insulator [18, 19], it exhibits

strong antiferromagnetic correlations within the CuO2

planes from high temperatures [20–22] driven by a large

nearest-neighbor superexchange energy [23, 24]. Antifer-

romagnetic order [25, 26] develops below a N´eel temper-

ature of TN∼325 K [27], which is sensitive to oxygen

stoichiometry [28]. While the ordered Cu moments lie

largely within the CuO2planes [see Fig. 1(a)] [25], there

is a small canting perpendicular to the planes that is ap-

parent as a rise in the magnetization (measured with a

ﬁeld perpendicular to the planes) on cooling toward TN,

where the magnetic layers are decoupled; below TN, the

canting in neighboring layers cancels out, resulting in a

decrease in the magnetization [29, 30]. The approximate

magnetic structure and its relation to the octahedral tilt

pattern are illustrated in Fig. 1(a).

The spin canting has been explained [29] as a con-

sequence of exchange terms resulting from the eﬀects of

spin-orbit coupling as originally identiﬁed by Dzyaloshin-

sky [31] and Moriya [32] (DM). The evaluation of the DM

interaction for cuprates with particular lattice symme-

tries is not trivial, and it received considerable attention

in the decade following the discovery of cuprate super-

conductivity [33–40].

Empirically, the moment direction and canting in zero

ﬁeld are found to be orthogonal to the octahedral rota-

tion axis [17, 41]; this comes from studies of Nd- and Eu-

arXiv:2210.01156v3 [cond-mat.str-el] 16 Mar 2023

z = 0.5

z = 0

(a) (b) (c) (d)

FIG. 1. Schematics of possible spin conﬁgurations in CuO2layers, where each arrow represents a Cu spin, circles indicate

oxygen atoms (white/gray indicates displacement above/below plane; size indicates relative displacement), dashed line indicates

octahedral tilt axis, and lower/upper panel corresponds to the plane displaced along the cby z= 0/z= 0.5. The orientations of

the aand baxes are indicated at the lower left; the deﬁnition of the spin rotation angle θis indicated in red. (a) Conventional

model of antiferromagnetic order in zero ﬁeld. (b) Conventional model of order in the weak ferromagnetic phase, with spins

in the z= 0.5 layer rotated by 180◦. (c) Zero-ﬁeld model allowing for in-plane canting of spins, following the octahedral

tilt direction in the revised structure, plotted here with α= 5◦. (d) Spin and tilt pattern in low-temperature phase of

La1.8Eu0.2CuO4exhibiting weak ferromagnetism [17].

doped La2CuO4, in which the low-temperature phase has

a modiﬁed octahedral tilt pattern and a noncollinear spin

order, as shown in Fig. 1(d). In fact, the Eu-doped com-

pound exhibits weak ferromagnetism in the noncollinear

phase at low ﬁeld, with a magnetization very similar to

that of the high-ﬁeld magnetization of La2CuO4[17].

This makes it tempting to associate the canting of the

moments with the octahedral tilts. There are two prob-

lems with such an association: 1) The size of the canted

moment estimated from the high-ﬁeld magnetization is

much smaller than one would expect from the measured

moments and tilt angles. 2) The relationship between the

spin direction and the octahedral tilt direction reverses

from one layer to the next in the zero-ﬁeld phase, as can

be seen in Fig. 1(a). One might try to explain the lat-

ter point in terms of the impact of interlayer exchange;

however, that energy is quite small and nearly frustrated

[42]. We note that one feature not considered in the pre-

vious analyses is the shear distortion of the octahedra

associated with the monoclinic symmetry [5, 14]. That

distortion has the same orientation for Cu sites in neigh-

boring planes with the same zero-ﬁeld spin direction, in

contrast to the opposite signs of the tilt directions.

If the spin structure of La2CuO4were collinear, with

the spin direction determined by the interlayer coupling

[42], then it would be reasonable that a high magnetic

ﬁeld could ﬂip the spin in every other layer, as originally

proposed [29] and as shown in Fig. 1(b). A challenge,

however, is that we now know [14] that the octahedral

tilts are rotated slightly away from the baxis, as indicated

in Fig. 1(c), and we expect a corresponding noncollinear

rotation of the spins. In fact, we will show that a ﬁt to

our neutron diﬀraction intensities in zero ﬁeld indicates

a ﬁnite in-plane rotation angle for the spins.

The noncollinear structure suggests that anisotropies

due to DM interactions plus Coulomb exchange inter-

actions determine the directions of the ordered spins

[17, 37, 39]. In such a case, it seems more reasonable

that a large applied ﬁeld will cause spins in both layers

to rotate in some fashion. Indeed, we ﬁnd that such a

ﬁeld-induced spin rotation model gives a better ﬁt to our

high-ﬁeld neutron diﬀraction data than does the collinear

spin-ﬂip model.

The rest of the paper is organized as follows. After a

description of the experimental methods, the results are

presented in Sec. III and analyzed in Sec. IV. We end

with a summary and discussion in Sec. V.

II. EXPERIMENTAL METHODS

The La2CuO4sample studied here is the same 11-g

vacuum-annealed crystal used previously in [14]. Based

on the temperature dependent peak in the magnetic sus-

ceptibility, TNis equal to 327 K. The lattice parame-

ters of La2CuO4at low temperature are a= 5.335 ˚

b= 5.415 ˚

A, and c= 13.12 ˚

A [43]. We will express the

momentum transfer Q= (H, K, L) in reciprocal-lattice

units (r.l.u.) given by (2π/a, 2π/b, 2π/c).

The present neutron scattering experiment was per-

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SpincantingandlatticesymmetryinLa2CuO4XiaoHu,1A.Sapkota,2,1V.O.Garlea,3G.D.Gu,1I.A.Zaliznyak,1andJ.M.Tranquada1,1CondensedMatterPhysicsandMaterialsScienceDivision,BrookhavenNationalLaboratory,Upton,NewYork11973-5000,USA2AmesLaboratory,IowaStateUniversity,Ames,IA50011,USA.3NeutronScatteringDivision,...

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Spin canting and lattice symmetry in La 2CuO 4 Xiao Hu1A. Sapkota2 1V. O. Garlea3G. D. Gu1I. A. Zaliznyak1and J. M. Tranquada1 1Condensed Matter Physics and Materials Science Division.pdf

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Spin canting and lattice symmetry in La 2CuO 4 Xiao Hu1A. Sapkota2 1V. O. Garlea3G. D. Gu1I. A. Zaliznyak1and J. M. Tranquada1 1Condensed Matter Physics and Materials Science Division

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