Magnetostriction and magneto-structural domains in antiferromagnetic YBa$_{2}$Cu$_{3}$O$_{6}$

0.76 MB·

by  B. Nafradi

Magnetostriction and magneto-structural domains in antiferromagnetic YBa Cu O
2 3 6
B. N´afr´adi,1 T. Keller,1,2 F. Hardy,3 C. Meingast,3 A. Erb,4 and B. Keimer1
1Max-Planck-Institut fu¨r Festko¨rperforschung, Heisenbergstraße 1, D-70569 Stuttgart, Germany
2Max Planck Society Outstation at the Heinz Maier-Leibnitz Zentrum (MLZ), D-85748 Garching, Germany
3Institut fu¨r Festk¨orperphysik, Karlsruher Institut fu¨r Technlogie (KIT), D-76344 Eggenstein-Leopoldshafen, Germany
4Walter Meissner Institut fu¨r Tieftemperaturforschung D-85748 Garching, Germany
(Dated: January 7, 2016)
We have used high-resolution neutron Larmor diffraction and capacitative dilatometry to inves-
tigate spontaneous and forced magnetostriction in undoped, antiferromagnetic YBa Cu O , the
2 3 6.0
parentcompoundofaprominentfamilyofhigh-temperaturesuperconductors. Uponcoolingbelow
the N´eel temperature, T =420 K, Larmor diffraction reveals the formation of magneto-structural
N
6 domains of characteristic size ∼ 240 nm. In the antiferromagnetic state, dilatometry reveals a
1 minute (4×10−6) orthorhombic distortion of the crystal lattice in external magnetic fields. We
0 attributetheseobservationstoexchangestrictionandspin-orbitcouplinginducedmagnetostriction,
2 respectively, and show that they have an important influence on the thermal and charge transport
properties of undoped and lightly doped cuprates.
n
a
J
Correlated-electron systems exhibit multiple collective sistance in the CuO2-planes was found to exhibit a “d-
6
ordering phenomena whose interdependence and com- wave” symmetry upon rotation of the magnetic field in

petition are subjects of intense current research. The this plane, that is, the resistance increases (decreases)
]
l macroscopic properties of materials with strongly corre- when the magnetic field is parallel (perpendicular) to
e
- lated electrons are influenced not only by atomic-scale the current flow [12, 13]. This finding was unexpected,
r
t correlations, but also by emergent domain structures because at low doping levels the crystal lattice is be-
s
on nanoscopic and mesoscopic length scales [1]. Re- lieved to be tetragonal [16]. In this lattice structure,
.
t
a cent advances in research on some of the most promi- the two orthogonal a axes in the CuO2 planes are equiv-
m nent correlated-electron materials, the cuprate high- alent, and current flow along both axes should be iden-
- temperature superconductors, [2] have reinforced efforts tical. Ando et al. [12] attributed the anomalous magne-
d
to establish quantitative links between the doping de- toresistance to the magnetic-field-induced reorientation
n
pendent spin and charge correlations and the thermo- of charge stripes that locally break the tetragonal sym-
o
c dynamic and transport properties [3–5]. These efforts metry of the CuO2 planes. Related ideas have also been
[ are, however, complicated by the presence of defects and discussed for other families of cuprate superconductors

associated strains of the crystal lattice, which are invari- [2]. An alternative model [13, 17–20] invokes antifer-
1
v ablyassociatedwithdopingandstronglyaffectthemeso- romagnetic domains that are accompanied by a small
6 scopic organization of the electron system [6]. Recent orthorhombic lattice distortion due to magnetostriction
7 examples include magnetic hysteresis phenomena [7, 8] andarereorientedbythemagneticfield. Theorthorhom-
0 and charge density wave pinning [9–11] in moderately bicdistortionwasestimated[13]asa/b−1∼6×10−6,a
1
doped superconducting cuprates, whose origins have not value too small to be directly observed by x-ray or neu-
0
. yet been conclusively identified. tron diffraction techniques. Likewise, direct evidence of
1
the purported charge-stripe or magneto-elastic domains
0 To provide a solid basis for the investigation of doped
has thus far not been reported for undoped and lightly
6 high-temperature superconductors, it is important to es-
1 tablish a firm understanding of electronic correlations doped YBa2Cu3O6+δ.
:
v and their coupling to the crystal lattice in the undoped, In the present work, we used high-resolution neu-
Xi largelydefect-freeparentcompoundsthatexhibitantifer- tronLarmordiffractiontodirectlymeasurethemagneto-
romagnetic long-range order. Although the atomic-scale structural domain size, and capacitative dilatometry to
r
a spin correlations of undoped cuprates are well under- determine the minute orthorhombicity in the antiferro-
stood, there is little direct information on antiferromag- magnetic state by field-aligning the magnetic domains.
neticdomainstructuresandassociatedlatticestrains,de- Wediscussthesephenomenaintermsofdifferentmecha-
spite indications that they profoundly affect the charge nismsofmagnetostriction,andcomparetheresultsquan-
[12, 13] and heat [14, 15] transport properties and may titatively with heat and charge transport data on un-
act as seeds for mesoscopic inhomogeneities in doped doped and lightly doped cuprates. The methodology we
compounds [2, 6]. In particular, an anomalous mag- introduce provides interesting perspectives for the inves-
netoresistance has been reported for lightly doped, an- tigationofdomainstructuresassociatedwithchargeden-
tiferromagnetic YBa Cu O , [12, 13] a material that sity waves in more highly doped cuprates, and with elec-
2 3 6+δ
has served as a model compound for recent research on tronic ordering phenomena in other correlated-electron
high-temperaturesuperconductivity[2]. Themagnetore- materials such as the iron pnictides and chalcogenides.
2
spins precess with the Larmor frequency ω = 2πγH,
L
where γ is the neutron’s gyromagnetic ratio. The total
precessionangleisφ=ω t, wheret=2L/v isthetime
L ⊥
theneutronspendsinthefield. tonlydependsontheve-
locity component v = ((cid:126)/m)G /2, which is indepen-
⊥ hkl
dentoftheBraggangle(mistheneutronmass). Theto-
tal phase φ=2m/(π(cid:126))ω d is thus a measure for d .
L hkl hkl
A broadening of the Bragg reflection ∆G gives rise
hkl
to a linear variation of the Larmor phase ∆φ/φ = (cid:15) ,
hkl
with (cid:15) =∆G /G . The beam polarization P(φ) is
hkl hkl hkl
then the Fourier transform of the momentum-space pro-
file f((cid:15) ) of the Bragg reflection, so that the width of
hkl
P is the inverse of the width of f:
(cid:90)
P(φ)= f((cid:15) )cos(φ·(cid:15) )d(cid:15) (1)
hkl hkl hkl
Conventional diffractometers are based on measure-
FIG. 1. (color online) (a) Temperature dependence of the
ments of the Bragg angle, where the resolution is lim-
(1 1 5) antiferromagnetic Bragg peak intensity measured by
2 2 ited by the collimation and the monochromaticity of
neutron diffraction from YBa Cu O . The line is a guide
2 3 6.0
to the eye. Red and green symbols indicate temperatures the neutron beam. The resolution of LD, on the other
belowandaboveT =420K,respectively. (b)Neutronbeam hand, is limited by the relative error δφ/φ. The lead-
N
polarization P measured at the (200) Bragg reflection for ing contribution to δφ are fluctuations of H, which can
Larmor phase φ = 5000 rad (see Fig. 2). The reduction of be strongly reduced by replacing the static field by four
P below T indicates a reduction of the structural domain
N radio-frequency spin-flip coils C1-C4 (Fig. 1c). In this
size. (c) Sketch of the Larmor diffraction method. The radio
way, the momentum-space resolution can be enhanced
frequencycoils(C1-C4)actontheneutronspins(blue)inthe
by about two orders of magnitude [26].
same way as an effective static magnetic field H (green).
Figure 2 shows P(φ) profiles for several nuclear and
magnetic Bragg reflections. The instrumental resolu-
tion was taken into account by normalizing the profiles
The experiments were carried out on high-quality
to the one obtained from a perfect germanium crystal.
YBa Cu O singlecrystalsoftypicalsize1×1×0.1mm3
2 3 6.0 For clarity, the data are displayed after normalization to
andmosaicity≤0.1◦,whichweregrownbyafluxmethod
P(0) = 1. To extract the widths of Bragg reflections
[21]. For the dilatometry measurements, a single speci-
from the LD data, the P(φ) curves were fitted to Eq. 1
menwasmountedinacapacitancedilatometer[22],such
withGaussianpeakprofilesf((cid:15) )(linesinFig.2). The
hkl
that the expansion of the a-axis was measured. A small
widths of the (2 0 0) and (2 2 0) nuclear Bragg peaks
force of 20 N along the a-axis was applied to hold the
determined in this way are quite different (Fig. 2). For
crystal, resulting in a uniaxial pressure of (cid:39) 200 MPa. T >T ,thewidthofthe(200)reflection,(cid:15)=5.2×10−4,
N
The dilatometer was installed in three different orienta-
translates into a characteristic length L =370 nm, and
(cid:107)
tions in a 10 T magnet to apply the field along the crys-
theratioof1.4betweenthewidthsofthe(220)and(200)
tallographic a, b, or c-axes. For the neutron scattering
reflections matches the ratio of their respective recipro-
experiments, fifteen crystals of total mass 0.1 g were co-
callatticevectors. TheLDdataarethusconsistentwith
alignedwithcombinedmosaicity∼1◦. Thetemperature
square-shaped structural mosaic blocks of characteristic
dependenceofthemagnetic(0.50.55)Braggpeakinten-
sizeL alongtheCuO planes. Thedomainsizealongthe
(cid:107) 2
sity (Fig. 1a) shows a N´eel temperature of T = 420 K,
N c-axisextractedfromthe(006)reflection(insetinFig.2)
corresponding to full oxygen stoichiometry (6.0 oxygen
is L ∼ 390 nm. Possible origins of structural domain
⊥
atoms per formula unit) [23].
formation include a small number of residual impurities
TheneutronLarmordiffractionexperimentswerecon- (suchasinterstitialoxygen)andassociatedmicrostrains.
ducted at the TRISP spectrometer at the Heinz-Maier- A detailed analysis of the lattice defects in the param-
LeibnitzZentruminGarching[24]. Thebasicprincipleof agnetic state will require a survey of multiple Bragg re-
aLarmordiffractometry(LD)isshowninFig.1c. [25]. A flections and is beyond the scope of this paper, which
spin-polarized neutron beam crosses a uniform magnetic is focused on the influence of the electronically driven
field H twice, before and after being diffracted at lattice antiferromagnetic transition on the lattice structure.
planeswithspacingd =2π/G ,whereG isthere- Tothisend,wehavecarefullymonitoredtheevolution
hkl hkl hkl
ciprocal lattice vector. The boundaries of H are aligned of the P(φ) profiles across the antiferromagnetic phase
paralleltothelatticeplanes. Insidethefield,theneutron transition (Fig. 2). The width of the (200) reflection for
3
nian has the same (tetragonal) symmetry as the crystal
lattice (apart from the minute effect of the spin-orbit in-
teraction, to be discussed below). In the iron arsenides,
bycontrast,thesymmetryofthemagneticbondnetwork
differsfromtheoneofthecrystallatticeintheparamag-
neticstate,givingrisetoasequenceofdistinctstructural
and magnetic phase transitions.
The width of the LD profile of the antiferromagnetic
Bragg reflection (1 1 5) is comparable to, but somewhat
2 2
larger than those of the structural reflections (Fig. 2),
consistent with the expectation that structural domain
boundaries resulting from magnetostriction will usually
disruptmagneticorder[29]. Thespatiallyaveragedanti-
ferromagneticdomainsizeof240nmisquitecomparable
tothemagneticdomainsizemeasuredbyLDinclassical
antiferromagnets [30].
FIG. 2. (color online) Neutron beam polarization P versus
LarmorphaseφatT =300and500Kforthe(220)and(200) Since LD with radio-frequency coils is restricted to
nuclear Bragg peaks. P(φ=0) is normalized to 1. Lines are zero magnetic field, we used capacitative dilatometry as
the results of fits to Gaussian peak profiles (see text). Inset: a complementary tool to investigate manifestations of
P(φ) at T = 40 K for the (1 1 5) antiferromagnetic Bragg
2 2 forcedmagnetostrictionintheantiferromagneticstatefor
reflection (blue), compared to the (220) and (006) nuclear
T = 2 K. Figure 3 shows the relative expansion of the
Bragg reflections (red and green, respectively).
x-axis along the Cu-O-Cu bonds, with magnetic field B
along x, y (in the CuO planes), and z (perpendicular
2
to the planes). For B (cid:107) y (B (cid:107) x), ∆x/x is positive
T < TN translates into a characteristic domain size of (negative), corresponding to expansion and contraction,
L(cid:107) ∼ 340 nm, about 10% smaller than in the paramag- respectively. The resulting field-induced orthorhombic
netic state. The T-dependence of the profiles (Fig. 1b) distortionofthecrystalincreasesrapidlyforsmallB and
demonstrates that the broadening of P(φ) and the re- crosses over to a more gradual evolution for B ≥ 5 T
c
duction of L(cid:107) set in at T = TN. Within the experi- (definedastheinflectionpointinthe∆x/x-versus-B re-
mental error, the ratio of the (200) and (220) widths lation). TheexpansionforB (cid:107)z isclosetozero. Instark
is preserved upon cooling across TN (Fig. 2), indicat- contrasttoclassicalantiferromagnets[31,32],thereisno
ing shape-preserving shrinkage of the structural mosaic discerniblefieldhysteresisoftheforcedmagnetostriction
blocks as the spin fluctuations are arrested in the anti- which would indicate pinning of antiferromagnetic do-
ferromagnetic state. main walls.
The anomalous broadening of the P(φ) profiles is a The dilatometry data indicate that the lattice expan-
manifestation of coupling between the antiferromagnetic sion is coupled to the magnetic moment direction. Re-
order parameter and the crystal lattice. In rare-earth lated effects have been observed in other antiferromag-
antiferromagnets, magneto-structural interactions have nets including rare-earth magnets, where they can be
been detected through anomalies in the thermal expan- understood as consequences of the spin-orbit interaction
sion at the N´eel temperature, and were attributedto the [27]. Briefly, the spin-orbit interaction ties the spin di-
dependence of the exchange interactions on the distance rection to the orbital magnetization and hence to the
betweenthemagneticions(“exchangestriction”)[27]. In shape of the valence electron cloud around the magnetic
the cuprates, however, such anomalies are much harder ions, which in turn is coupled to the lattice structure via
torecognizebecauseofthequasi-two-dimensionalnature crystalline electric fields. The small magnitude of the
of the magnetism, which implies that the spin correla- forced magnetostriction, compared to the manifestations
tions in the CuO planes are already well developed for of isotropic exchange striction discussed above, can then
2
T =T . [28]OurdataestablishLarmordiffractionasan be attributed to the quenching of the spin-orbit interac-
N
alternative, highly sensitive probe of magnetostriction in tion in the cuprates, where the magnetic dipole moment
this situation. Following prior theoretical work [27], the arises almost exclusively from the spin-1/2 of the Cu2+
reduction of the structural domain size at T observed ions. Nonetheless,theobservedg-factoranisotropyofthe
N
in YBa Cu O can be understood as a consequence of Cu moments [33] indicates a small residual orbital mag-
2 3 6
exchange striction, which stiffens the crystal lattice so netization that can act as a source of magnetostriction.
thatitcanlesseasilyaccommodatestrainsfromresidual The inset in Figure 3 illustrates the spin-orbit medi-
impurities and defects. The fact that the shape of the ated magnetostriction. For B =0, both neutron diffrac-
mosaic blocks remains unchanged at the N´eel transition tion [34] and electron spin resonance [20] find an equal
agrees with the observation that the exchange Hamilto- population of domains with Cu spins oriented along the
4
hensive picture of the magneto-structural coupling we
haveobtainedtothetransportpropertiesofundopedand
lightly doped cuprates reported earlier. First, measure-
ments of the magnon-mediated thermal conductivity of
undoped, antiferromagnetic La CuO have yielded low-
2 4
temperaturemeanfreepathsintherange∼100−150nm,
[14, 15] somewhat lower than the magneto-structural
domain size of ∼ 240 nm inferred from our LD mea-
surements on YBa Cu O , where thermal conductivity
2 3 6.0
measurements have not yet been reported. Since both
experiments were carried out on different materials, we
regard the agreement as quite satisfactory. Our results
suggest that magneto-structural domains limit the low-
temperature heat conductivity mediated by magnons,
and they provide a motivation for more detailed model
calculations along these lines.
FIG. 3. (color online) Forced magnetostriction at T = 2 K
measuredbydilatometryparalleltotheCu-O-Cubonddirec- The spin-orbit mediated forced magnetostriction we
tion, x, in the CuO2 plane. The field-induced change of the identifiedintheantiferromagneticstatehasthesame“d-
sample length along x with magnetic field B applied parallel wave”symmetry(i.e.,positiveparallelandnegativeper-
tothex,y,z directionsisplottedinred,green,andblue,re-
pendicular to the B-field) and a similar crossover field
spectively. Inset: Illustration of spin-orbit coupling induced
(B ∼ 5 T) as the magnetoresistance in lightly doped
magnetostrictionforasinglemagneto-structuraldomainwith c
antiferromagnetic YBa Cu O [12, 13]. Our obser-
B (cid:107) b. Due to magnetostriction, the spin-flop transition in- 2 3 6+δ
duced by the field is associated with a realignment of the vations thus support models that ascribe the anoma-
crystallographic unit cell (dashed line for B = 0, solid line lous magnetoresistance to the magnetic field alignment
forB(cid:38)5T.)Theorthorhombicdistortionisexaggeratedfor oftheorthorhombicmagneticdomains. [13,17–20]. The
clarity. orthorhombicity a/b − 1 = 4 × 10−6 determined from
the forcedmagnetostriction (Fig.3) issomewhatsmaller
than the one estimated [13] on the basis of magnetore-
two orthogonal easy axes in the CuO2 plane. Within sistance data on YBa2Cu3O6.25, but since this estimate
each domain, the a and b axes are slightly different as is rather indirect, and both sets of measurements were
a consequence of the spin-orbit interaction, but domain taken on samples with different oxygen concentrations,
averaging results in a macroscopically tetragonal struc- the agreement is again quite satisfactory. There is thus
ture. For increasing B (cid:107) y, the Cu spins in the domain no need to invoke charge-stripe ordering in lightly doped
withspinspointingalongy flipby90◦ togainadvantage YBa Cu O to explain the magnetoresistance. This is
2 3 6+δ
of the Zeeman energy, whereas spins already along x do inaccordwithcurrentknowledgeofthephasediagramof
not flip. The observed macroscopic expansion, ∆x/x, is thiscompound,wherechargeorderonlysetsinathigher
duetotheslightorthorhombicdistortionofeachdomain doping levels (δ ≥0.5) [2].
that is tied to the spin direction. For the same reason, In summary, the complementary combination of neu-
∆x/x is opposite in sign for B (cid:107) x. (The slight dif- tronLarmordiffractionandcapacitativedilatometryhas
ference in the magnitudes of ∆x/x for B along x and provided direct insight into the mesoscopic structure of
y presumably arises from the uniaxial pressure along x the antiferromagnetic state in undoped YBa Cu O .
2 3 6.0
exerted by the sample holder, which increases the popu- Our data allowed us to elucidate the magneto-structural
lation of the domains with long axes ⊥x.) For B ≥Bc, couplingmechanismsandtheirinfluenceontheheatand
mostspinsareorientednearlyperpendiculartothemag- charge transport properties. Based on the solid foun-
netic field, and the crystal structure is macroscopically dation we have laid here, our experimental approach
orthorhombic. For larger fields, the gradual canting of can be straightforwardly applied to more highly doped
themagneticmomentstowardsB isanadditionalsource cuprates, where domain structures associated with spin
of magnetostriction, but this contribution is small be- densitywave, chargedensitywave, and“nematic”order-
cause it is opposed by the large in-plane exchange inter- ing phenomena and their influence on the macroscopic
action (J ∼ 100 meV). The remarkable absence of field properties are subjects of intense current research and
hysteresis may then be attributed to the approximate debate [2–11]. More generally, we have established neu-
coincidence of magnetic and structural domain bound- tron Larmor diffraction as a versatile probe of antifer-
aries noted above. Since most structural mosaic blocks romagnetic and magneto-structural domain structures
include a single magnetic domain, pinning of magnetic with sub-micrometer length scales, which opens up new
domain walls is largely suppressed. perspectives for the investigation of a large variety of
We now discuss the relationship between the compre- correlated-electron materials [1].
5
We are grateful to A. J´anossy, S.P. Bayrakci, and J. Rev. Lett. 90, 197002 (2003).
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