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Domain Wall Spin Dynamics in Kagome Antiferromagnets E. Lhotel,1,∗ V. Simonet,1 J. Ortloff,1,2 B. Canals,1 C. Paulsen,1 E. Suard,3 T. Hansen,3 D. J. Price,4 P. T. Wood,5 A. K. Powell,6,7 and R. Ballou1 1Institut Néel, CNRS & Université Joseph Fourier, BP 166, 38042 Grenoble Cedex 9, France 2Institute for Theoretical Physics, University of Wu¨rzburg, Germany 3Institut Laue Langevin, BP 156, 38042 Grenoble Cedex 9, France 4Univ Glasgow, School of Chemistry, WestCHEM, Glasgow G12 8QQ, Scotland 5Univ Cambridge, Chem Lab, Cambridge CB2 1EW, England 6Institute of Inorganic Chemistry, Karlsruhe Institute of Technology, Engesserstrasse 15, D-76131 Karlsruhe, Germany. 2 7Institute for Nanotechnologie, Karlsruhe Institute of Technology, Postfach 3640, D-76021 Karlsruhe, Germany 1 (Dated: January 4, 2012) 0 2 We report magnetization and neutron scattering measurements down to 60 mK on a new family of Fe based kagome antiferromagnets, in which a strong local spin anisotropy combined with a low n exchange path network connectivity lead to domain walls intersecting the kagome planes through a strings of free spins. These produce unfamiliar slow spin dynamics in the ordered phase, evolving J from exchange-released spin-flips towards a cooperative behavior on decreasing the temperature, 3 probably due to the onset of long-range dipolar interaction. A domain structure of independent magnetic grains is obtained that could be generic to other frustrated magnets. ] l e PACSnumbers: 75.60.Ch,75.40.Gb,75.25.-j,75.50.Ee - r t s . Ordered magnets ordinarily display fragmentations Moriya(DM)interaction,non-stoichiometry...) mayalso t a into magnetic domains, interrelated to each other by release the frustration usually leading to complex mag- m the symmetries lost at the ordering. Such domains have netic orderings [4, 7]. In the kagome antiferromagnet - mostlybeenstudiedinferromagneticmaterials[1]. Inves- for instance, a multiaxial anisotropy characterized by a d tigations of antiferromagnetic domains are more elusive three-fold direction of the spins in a triangle will grad- n duetotheabsenceofaspontaneousmagnetizationandto ually fix the spin orientation in the whole lattice. This o c ultra-fast spin dynamics [2]. In all instances the domain lifts the massive ground state degeneracy leading to a [ walls might exhibit cooperative slow dynamics, but in- non-collinear magnetic order. 2 dividual spins are never free. A paradigm for protected We have investigated such a model system with v spins might emerge from topological frustration, which new metallo-organic compounds, built from FeII 0 hasprovidedanincrediblereservoirinthesearchofnovel and bridged by C O2− oxalate ligands. Two new 2 4 4 magnetic phases [3, 4]. An untackled question though is isostructural series were synthesized using hy- 5 the influence of the lattice topology on the domain wall drothermal methods: series I with the composi- 5 . spin dynamics. We reporthere on the importance of the tion Na2Ba3[FeI3I(C2O4)6][AIV(C2O4)3] where AIV 8 lowconnectivityoffrustratedlatticessuchasthecorner- = SnIV, ZrIV; and series II with the composition 0 1 sharing-triangle kagome one, which allows spins inside a Na2Ba3[FeI3I(C2O4)6][AIII(C2O4)3]0.5[AIII(C2O4)2(H2O)2]0.5, 1 domain-wall to be free from exchange interactions. where AIII = FeIII, AlIII. In the following, these quin- : Topologically frustrated lattices may produce in ex- ternary oxalate compounds will be abbreviated QO-FeA v treme cases highly degenerate ground states, which in- referring to the common divalent FeII and the cation i X hibit magnetic ordering and lead to disordered phases A=SnIV,ZrIV,FeIII (QO-FeAlwasnotconsideredinthe r with short-range spin-spin correlations and remarkable present study). They crystallize in the chiral trigonal a excitations[3,4]. IntheclassicalHeisenbergkagomelat- P321 space group. The only magnetic ions are the tice with antiferromagneticnearest-neighbor(NN) inter- FeII except in QO-FeFe where paramagnetic FeIII in actions, a strongly correlated paramagnetic state (spin the low spin state (S=1/2) are present between the ◦ liquid) with 120 spin arrangements on each triangle is kagome planes, without significant interactions down expected down to the lowest temperature [5]. Another to the lowest temperature. The magnetic FeII network example is the disordered spin ice ground state discov- forms, in the (a, b) plane, a distorted kagome lattice eredinsomepyrochlorematerials,wheretwospinspoint stacked along the c axis, topologically equivalent to into and two out of each corner-sharing tetrahedron [6]. the kagome one if NN interactions only are considered This was shown to result from exchange and dipolar in- (See Fig. 1). All QO-FeA compounds present the same teractionsassociatedwithastrongmultiaxialanisotropy. magnetic properties driven in particular by a strong Additional parameters in the Hamiltonian beyond the single-ion anisotropy and weaker exchange interactions. NN interactions (next neighbors exchange interaction, These parameters explain the magnetic structure de- single-ionanisotropy,dipolarinteraction,Dzyaloshinskii- termined by neutron diffraction and the magnetization 2 neutrondiffraction(See Fig. 3). The magnetic structure refinementindicates anantiferromagneticstackingalong the c axis and the so-called q=0 in-plane arrangement ◦ consisting of magnetic moments at 120 from each other andlyingalongthe a, b and−a−b axes,withthe same spin chirality for all the triangles (see Fig. 1(a)) [8]. The energy scale of the main interactions can be estimated from the Curie-Weiss temperature θ. The lin- ear susceptibility χ = M/H was fitted in the range [50-300 K] using a Curie-Weiss model C/(T − θ) with C =NAµ2eff/3kB. Thisyieldsµeff =6.4µB (S=2,L≈2) NN andθ =−5 K,giving3 K for the exchangeenergyE exch due to the antiferromagnetic NN J exchange interac- 1 tions. This value is consistent with those reported in other compounds where the superexchange interactions are mediated by C O2− oxalate ligands [9–11]. J is ex- 2 4 1 FIG. 1. (Color online) (a): Projected structure of QO-FeZr pected to be much strongerthan the next nearestneigh- on the (a,b) plane (right) and the (b,c) plane (left) with a= bor(NNN)J (in-plane)andJ (inter-plane)interactions b=10.45 ˚A,c=7.54 ˚A.There are threeFeII per unit cell at 2 3 sincetheJ andJ exchangepathsarelongerandinvolve 2 3 positions(0,0.6145,0),(0.6145,0,0)and(0.3854,0.3854, 0). The black lines materialize theFeII NN exchange interaction two C atoms (see Fig. 1(a)) [12, 13]. ThelowdegreeofmagneticfrustrationintheQO-FeA, lattice. TheNNNJ2 andJ3 exchangeinteractionsareshown by the green and dashed pink arrows respectively. The blue estimated from TN/|θ| ≈ 1, is due to the large multi- arrows represent the ordered magnetic moments. The 180◦ axial magnetocrystalline anisotropy. The Fe octahedral antiferromagnetic domains (red and blue) are shown in the symmetries can favor a moment orientation along the triangular lattice (b) and in the QO-FeA distorted kagome structural twofold axis, resulting in a different axis for lattice (c),with a string of exchange-released spins along the ◦ each spin of the triangle at 120 from each other, as ob- domain wall. served. The 3-dimensional ordering is ultimately stabi- lized via antiferromagnetic interplane interactions, that can be much weaker than TN. An anisotropy energy measurements, as briefly reported hereafter. Although of 10 K is inferred from the energy barrier determined the frustration is actually released by the anisotropy, by AC susceptibility in the single spin-flip regime as ex- the lattice topology maintains spin degrees of freedom plainedbelow,whichagreeswiththeanisotropyreported associated with defects inherent to the magnetic struc- in other FeII oxalate compounds [9, 14–16]. ture. The signature of these quasi-Ising free spins in the TheHamiltonianoftheQO-FeAwasvalidatedbycom- ordered state is subsequently described in this letter. paringitsexactgroundstatesatzeroKelvintomeasure- We measuredthemagnetizationandACsusceptibility ments,asfollows. Themodelincludingantiferromagnetic ofpowdersamplesofthethreecompoundsbytheextrac- NN and inter-plane exchange interactions corresponding tion method, using a purpose-built magnetometer and a to energies ENN =3 K and Einter=0.3 K, and a multi- exch exch QuantumDesignMPMSmagnetometerfortemperatures axial anisotropy term Eanis=10 K, yields the observed above 2 K, and a superconducting quantum interference magnetic structure. The powder averaged magnetiza- devicemagnetometerequippedwithaminiaturedilution tion vs magnetic field, assuming a magnetic cell doubled refrigerator developed at the Institut Néel for tempera- along the c axis, was also computed [17]. Some features tures down to 65 mK. Measurements were carried out in the magnetization curves below TN are reproduced: forfrequenciesbetween1.1mHz and5.7kHz(morethan a metamagnetic process at ≈ 1 T and a non saturated six decades), with an applied AC field of 0.5 Oe. Pow- magnetization at 8 T (see Fig. 4(a)). derneutrondiffractionmeasurementswereperformedon Whereas neutron diffraction in zero field has proven the two two-axis diffractometers D20 and D2B with a that there is no change of the magnetic structure itself wavelengthequal to 2.4 ˚A at the Institut Laue-Langevin down to 60 mK (See Fig. 3), additional features ap- high-fluxreactor,Grenoble,France. Diffractogramswere pear in the magnetization on lowering the temperature, recorded down to 2 K on the three compounds (deuter- associatedwithslowspindynamicsasprobedbyACsus- ated for series II), and down to 60 mK on the QO-FeZr ceptibility. Below 2 K, there is a frequency dependence compound. of the real partχ′ andimaginary part χ′′ of the AC sus- Inthe QO-FeA,the transitionto anantiferromagnetic ceptibility (See Fig. 2). This is intrinsic to the system, order is evidenced by a cusp in the magnetizationat the sincethesamebehaviorwasobservedinseveralQO-FeZr Néel temperature TN = 3.2 K (See Fig. 2) and the rise samplesfromdifferentbatchesaswellasinQO-FeSnand below TN of magnetic Bragg peaks, as seen in powder QO-FeFe compounds. Measurements of magnetization 3 FIG. 3. (Color online) Magnetic diffraction pattern of QO- FeZrobtainedfromthedifferencebetweenthediffractograms measuredat1.5and10KonD2B.Theredlineisafitwitha propagationvector(0,0,1/2)andrefinedmagneticmomentof FIG. 2. (Color online) AC and DC susceptibility vs temper- 5.2(2) µB. The absence of magnetic rearrangement is shown ature: M/H in an applied field HDC=500 Oe (red circles), from the flat difference between the 0.06 and 1.3 K diffrac- ′ real part χ and imaginary part χ” of the AC susceptibility tograms. with HAC=1 Oe and 0.21 Hz<f <211 Hz. The inset shows τ vs 1/Tmax in a semi-logarithmic plot. The error bars indi- ′′ catetheuncertaintyinthedeterminationoftheχ maximum. spinsisthereforethesameineitherofitstwopossibleori- aTnhdeElin1e=s1a0reKfit(sfutloltlihnee)Aarrnhdenτ0iu2s=la1w.1w×it1h0τ−031s=a2n.d1×E210=−28.8s entations and this spin is free to flip over the anisotropy barrier. This is illustrated in Fig. 1 where antiferro- K (dashed line). magneticdomainsareschematizedintheQO-FeAlattice (Fig. 1(c)) and in a triangular lattice (Fig. 1(b)) with a larger connectivity inhibiting the presence of the free relaxation vs time show that most of the magnetization spins. In the QO-FeA compounds, the single spin-flips goestozeroinaveryshorttime(<10s)at65mK.These are incoherent and should not result in a global motion observationsprove that there is no strong pinning in the ofthe string-likedomainwalls. The size ofthe antiferro- system and that only a small fraction of the quasi-Ising magnetic domains could be roughly estimated from the spins, estimated ≈ 5%, is concerned with the dynam- neutrondiffractograms. The broadeningof the magnetic ics. Assuming that the dynamics is governedby a single Braggpeaks with respect to the nuclear ones (resolution relaxationtimeτ, χ”(T)ismaximumwhenthemeasure- limited)yields,usingtheSherrerequation[19,20],anav- ment time (= 1/2πf) is equal to τ. In a usual thermal erage domain diameter of ≈500 ˚A. This is in agreement activated process over an energy barrier E, τ follows an with the domain size computed for 5% of spins within Arrhenius law τ =τ0exp(E/kBT), where τ0 is the char- the domain walls. acteristicrelaxationtime. Here,theplotofτ vs. 1/Tmax Below 0.8 K, the thermal single spin flip mechanism (see inset of Figure 2) reflects the need to consider two becomes too slow and a crossover is observed towards a distinct temperature regimes. moreefficientprocess. Thelattercanbedescribedbelow The ”high” temperature regime (T > 0.8 K) can be ≈500mKbyanArrheniuslaw(dashedlineintheinsetof fitted by an Arrhenius law with τ ≈ 2×10−8 s and Fig. 2)withanabnormallyhighcharacteristicrelaxation 01 E = 10 K (full line in the inset of Fig. 2). This is con- time τ ≈10−3 sanda reducedenergybarrierE =2.8 1 02 2 sistent with single spin flips over the anisotropy barrier. K. The dipolar energy was estimated to be ≈ 0.2 K, of Thatsuchspinscanfreelyflipina3-dimensionalordered the proper orderof magnitude to explainthis dynamical antiferromagnetis unusual. The key to this behavior re- cross-over. Long-range dipolar interactions could start sides in the influence of the lattice topology on the spins coupling the free spins along the domain walls whereas atthe boundarybetweenantiferromagneticdomains. As the anisotropyenergybarriermay be partially erasedby a result of the symmetry lowering at the phase transi- quantum tunneling. The full understanding of this dy- ◦ tion, two 180 domains, where all the spins are reversed, namicsisnotachievedyetbutitisinterestingtonoteits coexist in the kagome planes. The single atomic dis- similaritywithwhatisreportedinthepyrochlorespinice tance width of the domain walls is caused by the strong materials[21–23]. Thespin-icedynamicsischaracterized anisotropy. Duetothelowconnectivity,aboundaryspin by a high temperature regime of single spin-flips above isonlysharedbytwotrianglesbelongingtoeachdomain an anisotropy barrier [24]. Then, below 10 K, quantum and is blind to its neighbors along the domain wall [18]. tunnelinginitiatesanotherregimewithalargerτ ,where 0 The energy resulting from its interaction with the other spin-flipscanbedescribedasdeconfinedmagneticexcita- 4 attheboundarybetweentheantiferromagneticdomains, before they become correlated through dipolar interactions. An assembly of magnetic nanocrystals, related to eachotherbythe time-reversalsymmetryoperation,but magnetically decoupled due to interstitial paramagnetic spins, is thus achieved, providing an example of a clas- sical protectorate of free spins [26]. The observed dy- namicscouldbegenerictogeometricallyfrustratedmag- nets, where residual spin fluctuations often are observed in the ordered phase [27]. These results could also be relevantforapplicationsutilizingfrustratedmagnetslike multiferroics where the magnetoelectric manipulation of magnetic/ferroelectric domains is foreseen [28]. We would like to thank D. Givord, P. Molho, J-.J. FIG. 4. (Color online) (a) Measured magnetization M vs H PréjeanandC.Trainforfruitfuldiscussions,andP.Con- in QO-FeZrat 400 mK (red circles), 2 K (blacksquares) and 5K(bluetriangles). Inset: inblack,calculatedT=0Kpow- vert for his help during the first neutron experiment on dermagnetization with EeNxNch=3K, Eeinxctehr=0.3 K,Eanis=10 D20. DJP,PTWandAKParegratefulforfinancialsup- K and a magnetic cell doubled along c. Calculations includ- port from the EPSRC. ingdipolarinteractionsarenotsignificantly different. Inred, same calculation but with the exact powder average contri- butionof5%oftheparamagneticquasi-Isingspinsbelonging tothedomain walls computed at400 mK.(b)Zoom of M vs H at low field: 2 K (black squares), 400 mK (red circles), 70 ∗ [email protected] mK (green squares). [1] Jubileum issue, J. Magn. Magn. Mater. 200, 1-789 (1999). [2] A. V.Kimel et al.,Nature429, 850 (2004). [3] R. Moessner and A. P. Ramirez, Physics Today 59, 24 tions called monopoles, which become frozen by dipolar (2006). interactions [22, 23] at the lowest temperatures. [4] Introduction to Frustrated Magnetism, edited by C. IntheQO-FeA,the presenceofthefluctuatingbound- Lacroix, P. Mendels, and F. Mila (Springer-Verlag, ary spins is further evidenced in the magnetizationmea- Berlin, 2011). surements. 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