Giant spin canting in the S = 1/2 antiferromagnetic chain [CuPM(NO3)2(H2O)2]n observed by 13C-NMR

0.21 MB·English

by  A. U. B. Wolter

Giant spin canting in the S = 1/2 antiferromagnetic chain [CuPM(NO3)2(H2O)2]n
observed by 13C-NMR
A.U.B.Wolter,1 P.Wzietek,2 S.Su¨llow,1 F.J.Litterst,1 A.Honecker,3 W.Brenig,3 R.Feyerherm,4 andH.-H.Klauss1
1Institut fu¨r Metallphysik und Nukleare Festk¨orperphysik,
TU Braunschweig, 38106 Braunschweig, Germany
2Laboratoire de Physique des Solides, Universit´e Paris-Sud, 91405 Orsay
5
3Institut fu¨r Theoretische Physik, TU Braunschweig, 38106 Braunschweig, Germany
0
0 4Hahn–Meitner–Institut GmbH, 14109 Berlin, Germany
2 (Dated: February 2, 2008)

n We present a combined experimental and theoretical study on copper pyrimidine dinitrate
a [CuPM(NO3)2(H2O)2]n, a one-dimensional S = 1/2 antiferromagnet with alternating local sym-
J metry. From the local susceptibility measured by NMR at the three inequivalent carbon sites in

4 thepyrimidinemoleculewededuceagiantspincanting,i.e.,anadditionalstaggered magnetization
perpendicular to the applied external field at low temperatures. The magnitude of the transverse

] magnetization, thespin canting of (52±4)◦ at 10 K and 9.3 T and its temperature dependenceare
i
c in excellent agreement with exact diagonalization calculations.
s
- PACSnumbers: 75.50.Ee,76.60.Cq,75.10.Jm,75.50.Xx
l
r
t
m
One-dimensional quantum magnets show a rich vari- and direction of a transverse staggered magnetization
.
t ety of magnetic ground states, such as spin liquids with m andits temperature dependence have notbeen ver-
a s⊥
m quantum critical behavior or gaps in the spin excitation ified experimentally by now.
spectrum [1, 2, 3]. The ideal S = 1/2antiferromagnetic In this Letter we report the first direct observation of
-
d Heisenbergchain(S =1/2AFHC)withuniformnearest- the staggered magnetization m in a S = 1/2 linear
s⊥
n neighborexchangecouplingisofparticularinterest,since chain, i.e. CuPM, via a detailed 13C-NMR study. We
o
it is exactly solvable using the Bethe ansatz equations compareourdatawithexactdiagonalizationcalculations
c
[ [4, 5, 6]. Its ground state is a spin singlet with gapless based upon the staggered S = 1/2 AFHC model. At 10
excitations in contrast to S = 1 Haldane-gap systems. K and 9.3 T the transversemagnetization gives rise to a
2
The ground state properties of the S = 1/2 AFHC giantspincantingof(52±4)◦withrespecttotheexternal
v
7 are highly sensitive to even small modifications, which field. This observation manifests the strong influence of
4 often result in real spin chain systems from a low lattice spin orbit coupling in this system.
1 symmetry. The case of an alternating local environment
We measured the local susceptibility via the NMR
5 of the magnetic ion can be treated theoretically includ-
frequency shift δ at three inequivalent carbon sites in
0
ing the Dzyaloshinskii-Moriya (DM) interaction and/or
4 the pyrimidine molecule as a function of temperature
astaggeredg tensor,bothasconsequenceofthe residual
0 andmagnetic fieldorientation. Thetransversestaggered
/ spin-orbitcoupling [7,8,9]. WhereastheHeisenbergex- magnetizationm isidentifiedboth(i)asalowtemper-
at change JSiSi+1 prefers collinear spin arrangements, the ature deviation frso⊥mthe linear correlationbetween local
m DM interaction D(Si ×Si+1) prefers canted ones. This and macroscopic susceptibility and (ii) from the orien-
- can be described by the Hamiltonian [7] tation dependence of δ at a fixed temperature. The ob-
d
n servedmagnitude (ms⊥ ≈ 0.13µB at10Kin9.3T)and
o its temperature (T) dependence are in excellent agree-
c Hˆ =JX[SiSi+1−huSiz−(−1)ihsSix], (1) ment with the staggeredS = 1/2 AFHC model.
: i
v SinglecrystalsofCuPMhavebeengrownasdescribed
Xi which includes the effective uniform field hu = gµBH/J previously [14]. The Cu ions form uniformly spaced
and the induced staggered field h ∝ H perpendicular chains parallel to the short ac diagonal of the mono-
r s
a to the applied magnetic field H. We refer to this as the clinic crystal structure. The intrachain magnetic ex-
staggered S = 1/2 AFHC model. An essential result is changepathwayisprovidedbythepyrimidinering(Figs.
the opening of a spin excitation gap in external fields, 1 and 2). From a single crystal study of CuPM an ex-
with the excitation spectrum consisting of solitons, anti- change parameter J/k = 36.3(5) K is derived [10, 11].
B
solitons and their bound states called breathers [8, 9]. An additional Curie-like contribution to the magnetic
This model has been used to describe several1-Dspin susceptibility at low temperatures is observed. It varies
chain systems, that is, copper benzoate [2, 9], copper strongly with magnitude and direction of the external
pyrimidine dinitrate [CuPM(NO3)2(H2O)2]n (CuPM) fieldandis identifiedasthe longitudinalcomponentms||
[10, 11,12]andCuCl2 ·2(dimethylsulfoxide) [13]. How- ofthetotalstaggeredmagnetizationms. FollowingRefs.
ever, generic features of this model, i.e., the magnitude [10, 11] we denote with m the magnetization induced
s
2
H 70 C3 Cu H Cu
u.) 60 N N
hs a. C1
y ( 50 C3 C2 C3
sit 40 H H
Cu Cu Cu Cu nten 30 H
o i C2C1
mu mu ch 20
e
n 10
pi
ms⊥ ms ms ms⊥ S 0
-3000 --1000 1000 3000 5000
ms|| ms|| shift δ (ppm)
FIG. 2: A typical 13C-NMR spectrum of CuPM at 15 K in
an external field of 9.3 T applied along the chain direction.
FIG. 1: A chain segment of [CuPM(NO3)2(H2O)2]n viewed The site assignment of theobserved signals has been derived
along the b-direction. For clarity, only the Cu ions and
from the angular dependentNMR shift δ at 200 K [15].
the pyrimidine molecules are shown. The directions of the
different components to the magnetization, i.e., mu, ms =
ms||+ms⊥,areillustratedonthemiddlechainsegment. Note
that the different staggered components are not to scale.
3000 δ⊥ chain 7e) 9 e)
ol ol
δ ||chain 6m 8 m
abnydthaeusntaifgogremre(dmfiel)dcwohmicphonheanst.boItnhCausPtaMggmeredi(smosn⊥ly) pm) 2500 χχ ⊥|| cchhaaiinn 5emu/ 7 emu/
≤tiniod0nu.s1c1teodotfbhymetsmhaaengednxeatste|di|rzdnasatitloofinetihlndedHuunc.eifdTorbhmye edmiitffahgeernreentthtizesca||oetxniottnerribmnuau-l shift (pδ 12500000 34-3(10 ain 456-3 (10ain
h h
or staggeredfield are illustrated in Fig. 1. 1000 site C2 2 cχ || 3 χ c⊥
We have performed NMR experiments between 5-200 1 2
0 20 40 60 80 100
K in a magnetic field of 9.3 T. The single crystal was
T (K)
oriented with the ac-plane parallel to the external field.
The NMR spectra of 13C have been recorded using a
progressive saturation sequence with constant delay and
FIG. 3: The temperature dependence of the NMR shift δ of
Hahnspin-echodetection. TheNMRshiftδ isdefinedas
CuPMforH ||and⊥chainforcarbonsiteC2. Thesolidand
thenormalizeddifferencebetweentheobservedresonance dashed lines represent the corresponding experimental bulk
frequency ωres and the calculated value for the bare nu- susceptibility χ. The proportionality constants between the
nclueculse,uδs,=H0ωrweγsaµ−s0γHdµe00tHe0rm. γiniesdtfhreomgytrhoem1aHg-nNetMicRrarteisoonofanthcee sacnadleAs⊥forfoδr Hand|| χangdiv⊥ecthhaeinh,yrpeesrpfiencetivcoeluyp.ling constants A||
frequency of water at room temperature. In CuPM, the
threeinequivalentcarbonsitesC1,C2andC3withaddi-
deviations are present for lower temperatures.
tionalhyperfinecouplingtothenearestproton(I =1/2)
result in three pairs of resonance lines (Fig. 2) [15]. AfurthercomparisonoftheNMRshiftδ(T)withχ(T)
Fig. 3showstheTdependentshiftδ ofCuPMforH || for all three carbon sites is shown in Fig. 4. Here,
and⊥tothecopperchainsforcarbonsiteC2 [15]. Each the solid lines represent linear fits of the form δ(T) =
set of hyperfine doublets is represented by its average σ0+A·χ(T) for T ≥ 30 K. Whereas for H ⊥ chain this
shift. δ can be described by the sum of the chemical linearrelationisobeyedinthefulltemperaturerange(5-
shift σ0 and the Knight shift K. While σ0 represents 120 K), a large deviation is observed below 30 K for H
the T independent orbital shift due to closed electronic || chain. In this geometry the transverse component of
shells, K = A·χ(T) describes the hyperfine coupling to thestaggeredmagnetizationms⊥ resultsinanadditional
the paramagneticelectronicmoments mainly residingon Knight shift Ks [16].
the Cu sites. Here, A is the hyperfine coupling constant, Ks is extracted from the data via Ks(T) = δ(T)-σ0-
whichcaneitherhavepositiveornegativesign,andχ(T) A·χ(T) and is shown in Fig. 5 (a) for sites C1, C2 and
isthemagneticsusceptibility. Thesolidanddashedlines C3,respectively. ThesolidlinesrepresentfitstoK (T)=
s
inFig. 3representtheexperimentalbulksusceptibilityχ A ·C /T+K . The hyperfine coupling constant
dip,↑↓ s s,corr
of CuPM for H || and ⊥ chains. Clearly, χ(T) is similar for a staggered magnetization along the b-axis, A ,
dip,↑↓
to δ(T) for T > 30 K. However, for H || chain distinct is calculated in localized dipole approximation within a
3
4000
H || chain 2500
3000 C1
2000 C2
2000 m) C3
1500
1000 pp
120 K (
30 K K s1000
m) -10000 5 K shift 500
p
p
(δ H ⊥ chain 0 (a)
shift 32000000 CCC123 30 K 0,4 eexxppeerriimmeennttaall aavveerraaggee m(_ms⊥+m ) 0,4 m)
5 K m) u s|| 0,3 o
-110000000 120 K m ( / Cu atoµB 000,,,123 mmsu ((tthheeoorryy,, NN==1166)) 00 ,,__12 m ( / Cu atµs⊥B
0.000 0.002 0.004 0.006 0.008
(b)
χ (emu/mole) 0,0
0,0
0 5 10 15 20 25 30
T (K)
FIG. 4: NMR shifts δ vs experimental magnetic susceptibil-
ity χ for CuPM with the external field H || and ⊥ to the
chain in the ac-plane. The solid lines are fits of the form FIG. 5: (a) The T dependent transverse staggered contri-
δ(T)=σ0+A·χ(T) for T ≥ 30K. bution to the Knight shift, Ks, in CuPM with H || to the
Cu chains. The solid lines are a parametrization to Ks =
Adip,↑↓·Cs/T+Ks,corr. (b)ms⊥ and(mu+ms||),theexperi-
sphereof120˚Acenteredatthe respectivecarbonsite. A mentalaverageofthethreecarbon sitesofthestaggered and
total uniform components, respectively, in comparison with
smalloffset K ≈ -250ppm hadto be included since
s,corr exactdiagonalization calculations of alinear chain withN =
in this analysis the experimental value K (30K) is fixed
s 16 spins for both, the staggered magnetization ms and mu.
to zero. Fromthe fitted parametersCs forthe three car- Notethatthesmalloffset(-0.02µB/Cuatom)ofthemagne-
bonsiteswe deduce independentvalues forms⊥, namely tization scales between theexperimental ms⊥ and calculated
ms⊥(C1)=(0.07±0.01)µB,ms⊥(C2)=(0.16±0.01)µBand data results from the analysis which sets Ks(30 K) = 0.
ms⊥(C3)=(0.07±0.01)µB at 10 K and µ0H = 9.3 T.
InFig. 5(b)wecomparetheaverageoftheexperimen-
K [15], 30 K and 10 K (Fig. 6). We take into ac-
talresultsobtainedfromthethreecarbonsites,m and
s⊥
countanisotropicdipoleandisotropichyperfinecoupling
(m +m ), with results for the uniform z-component
u s||
to the longitudinal susceptibility χ +χ , anisotropic
mu and the staggered x-component ms of the magneti- u s||
zation obtained by full diagonalization of the S = 1/2 dipole coupling to the transverse susceptibility χ , and
s⊥
AFHC chain Hamiltonian (1) with N =16 sites and pe- the orbital shift σ:
riodic boundary conditions. Here, we have used J/k =
B
36.5 K, a ratio of the staggered and uniform field hs/hu 1
= 0.083and g = 2.117for H || chain [10, 11]. Compari- δ = H2H·(Adip,↑↑·(χu+χs||)+Aiso(χu+χs||)+
son with results for N <16 (not shown) and for N =20 +A ·χ +σ)·H. (2)
at T = 0 [11] indicates that the data for N = 16 yield dip,↑↓ s⊥
a goodapproximationto the thermodynamic limit at all Thedipolehyperfinetensorsforuniformandstaggered
temperatures. We find excellent agreement between ex- susceptibility,A andA ,areobtainedbydipole
dip,↑↑ dip,↑↓
perimentandtheoryinthewholetemperaturerange. At field calculations as described above. In order to ade-
10 K and 9.3 T || chain the ratio of the staggered mag- quately describe the data one needs to take into account
netization, ms⊥ = 0.13 µB, to the total uniform one, a finite moment transfer of 10% to the nitrogen atoms
(mu+ms||)=0.10µB,correspondstoagiantspincant- ofthe pyrimidine molecules inthe calculationof Adip,↑↑.
ing of (52±4)◦ with respect to the external field. With Themomenttransferisconsistentwithpreliminaryelec-
decreasing temperature the spin canting increases even tronic structure calculations [17] and it is close to the
further, extrapolating to ∼ 75◦. valueobservedinamolecularmagnetsystemwithMnCu
In an independent approach to extract m we mea- antiferromagneticchains [18]. Wealsoconsideredafinite
s⊥
suredthe angulardependence ofδ inthe ac-plane at200 momenttransfertothenitrogenatomsinthecalculations
4
of A . Here, a 100% transverse moment on the Cu
dip,↑↓ 4000
site yields the best description of our data and is used fit to Eq. (2)
throughoutthiswork. Theorbitalshifttensorσ wascal- 3000 C1 C2 C3
culatedfromσ0 measured||and⊥tothechain [19]. For
2000
30 K the contributions from the staggered susceptibili-
ties, χs|| and χs⊥, are nearly zero. Thus, to describe the 1000
experimentaldataat30K,A isthe onlyfitparameter
iso
0
and is determined to: Aiso,C1 = (0.05 ± 0.01)mole/emu, )
Aiso,C2 = (0.38 ± 0.01)mole/emu and Aiso,C3 = (-0.07 pm-1000 T = 30 K H || chain (a)
± 0.01)mole/emu. p
( fit to Eq. (2)
Using the isotropic constants Aiso determined at T hift δ 3000 modelfunction Eq. (2) without contribution s f r om χ_ s ⊥
= 30 K and the experimental values for χ from Ref. s
s|| 2000
[10], the remaining parameter to fit our NMR shift data
at 10 K is the transverse staggered susceptibility χ . 1000
s⊥
The solid lines in Fig. 6(b) represent the fits to Eq.
0
(2). We obtain m (C1) = (0.09±0.01)µ , m (C2) =
s⊥ B s⊥
(0.20±0.02)µ and m (C3) = (0.06±0.01)µ for H ||
chain. TheseBvalues arse⊥fully consistent with tBhe results -1000 T = 10 K H || chain (b)
of the analysis of the temperature dependence of Ks, as 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
presented above. If the transverse staggered component angle (rad)
H·A ·χ ·His omittedinourdescription(dashed
dip,↑↓ s⊥
curves in Fig. 6(b)), our data cannot be reproduced.
FIG. 6: The angular-dependent NMR shift δ of CuPM at T
We believe that the variance of the results of m for =30Kand10K,respectively,withtheexternalfieldaligned
s⊥
the three inequivalent carbon sites stems from the local- in the ac-plane. For furtherdetails see text.
izeddipoleapproximationwhichweusedtocalculatethe
dipole hyperfine coupling tensors A . This indicates
dip
that in order to improve the description of our data the
effect of delocalization of spin-density ought to be con-
sidered by means of extended electronic structure calcu- [1] F.D.M. Haldane, Phys. Rev.Lett. 50, 1153 (1983).
lations. [2] D.C. Dender et al.,Phys. Rev.Lett. 79, 1750 (1997).
[3] M.B. Stone et al.,Phys. Rev.Lett. 91, 037205 (2003).
In conclusion, we have performed 13C-NMR experi- [4] H.A. Bethe, Z. Phys.71, 205 (1931).
ments on [CuPM(NO3)2·(H2O)2]n as function of tem- [5] M. Takahashi, Thermodynamics of One-Dimensional
perature and magnetic field orientation. We extracted Solvable Models (Cambridge University Press, Cam-
bridge, 1999).
the transverse staggered magnetization as a low tem-
[6] A. Klu¨mper and D.C. Johnston, Phys. Rev. Lett. 84,
perature deviation from the linear correlation between
4701 (2000).
local and macroscopic susceptibility, and from the ori- [7] M. Oshikawa and I. Affleck, Phys. Rev. Lett. 79, 2883
entation dependence of the NMR frequency shift at 10 (1997); I. Affleck and M. Oshikawa, Phys. Rev. B 60,
K. The observed temperature dependence is in excellent 1038 (1999).
agreement with theoretical results for the staggered S [8] F.H.L. Esslerand A.M.Tsvelik,Phys.Rev.B 57,10592
= 1/2 AFHC model. The observed giant spin canting (1998); F.H.L. Essler, Phys. Rev.B 59, 14376 (1999).
[9] T. Asano et al.,Phys. Rev.Lett. 84, 5880 (2000).
highlightsthe stronginfluence ofonlyweakresidualspin
[10] R.Feyerhermet al.,J.Phys.: Condens.Matter 12,8495
orbit interactions in such systems. Our data also pro-
(2000).
vide detailed information on the hyperfine coupling in [11] A.U.B.Wolteretal.,Phys.Rev.B68,220406(R)(2003).
[CuPM(NO3)2(H2O)2]n as well as on the absolute value [12] S.A.Zvyaginet al.,Phys.Rev.Lett.93,027201 (2004) .
of the staggeredmagnetization. [13] M. Kenzelmann et al., Phys. Rev. Lett. 93, 017204
(2004).
This work has partially been supported by the DFG [14] T. Ishida et al.,Synth.Metals 85, 1655 (1997).
under Contract No. KL1086/4-2 and the European [15] A.U.B. Wolter et al.,Polyhedron 22, 2273 (2003).
Community Marie-Curie fellowship programme STRO- [16] Although for H ⊥ chain a small transverse staggered
COLODI. A.U.B. Wolter would like to thank the Lab- magnetization ms⊥ is also present [10], the dipole cou-
plingconstantforatransversespinpolarisation isnearly
oratoire de Physique des Solides for hospitality and D.
zero in this geometry and thusonecannot detect an ad-
J´erome for fruitful discussions. The numerical results
ditional Knight shift Ks.
presented in Fig. 4(b) were obtained on the compute- [17] K. Doll, privatecommunication.
server cfgauss of the TU Braunschweig. [18] B. Gillon, Mol. Cryst. and Liq. Cryst. 335, 53 (1999).
5
[19] Assuming the principal axes of the orbital shift tensor diagonalelementsofσ whicharenecessaryforarotation
σ to be the C-H bond axis, the perpendicular axis ly- of a magnetic field H in theac-plane.
ing in theplane of the pyrimidinemolecule and the axis
perpendicular to the pyrimidine ring, we obtain the two