Observation of a level crossing in a molecular nanomagnet using implanted muons
T. Lancaster, J.S. Moeller, S.J. Blundell, F.L. Pratt, P.J. Baker, T. Guidi, G.A. Timco, R.E.P. Winpenny
aa r X i v : . [ c ond - m a t . s t r- e l ] A p r Observation of a level crossing in a molecularnanomagnet using implanted muons
T. Lancaster , J.S. Moeller , S.J. Blundell , F.L. Pratt , P.J.Baker , T. Guidi , G.A. Timco and R.E.P. Winpenny E-mail: [email protected] Oxford University Department of Physics, Clarendon Laboratory, Parks Road,Oxford, OX1 3PU, UK ISIS Facility, Rutherford Appleton Laboratory, Chilton, Oxfordshire OX11 0QX, UK School of Chemistry and Photon Science Institute, University of Manchester, OxfordRoad, Manchester M13 9PL, UK
Abstract.
We have observed an electronic energy level crossing in a molecularnanomagnet (MNM) using muon-spin relaxation. This effect, not observed previouslydespite several muon studies of MNM systems, provides further evidence that the spinrelaxation of the implanted muon is sensistive to the dynamics of the electronic spin.Our measurements on a broken ring MNM [H N t Bu is Pr][Cr CdF (O CC(CH ) ) ](hereafter Cr Cd), which contains eight Cr ions, show clear evidence for the S =0 → S = 1 transition that takes place at B c = 2 . S = 1 regime.PACS numbers: 75.50.Xx, 76.75.+i bservation of a level crossing in a molecular nanomagnet using implanted muons S . Excitedstates will possess other values of S and the splitting of these levels in an appliedmagnetic field often leads to level crossings in which an excited spin state in zero fieldbecomes the new ground state at fields above the field at which a crossing occurs.MNMs have been widely studied in recent years, most recently in anticipation of theirpossible deployment as elements of quantum computers [2], although much interest alsocentres on the quantum tunnelling of the magnetization (QTM) which can take placewhen the magnetic energy levels are at resonance [1]. When implanted muons werefirst used to probe the spin dynamics in these systems, it was hoped that they would besensitive to level crossings. However, early studies failed to observe any signature of suchcrossings [3] and, despite the possible observation of effects ascribed to a matching of theMNM electronic energy level splitting with that of the muon hyperfine levels [4] and theobservation of crossings in broadly related systems [5], the observation of a crossing ina MNM has remained elusive until now. Here we demonstrate that muons are sensitiveto the electronic energy level crossings in MNMs. Our measurements on a broken ringsystem, made using the new HiFi spectrometer at the ISIS facility, demonstrate theeffect of the level crossing on the integrated positron asymmetry and on the muon-spinrelaxation rate.The material measured in this study is related to the octonuclear system[Cr F (O CC(CH ) ) ] [6]. That material has a S = 0 ground state due toantiferromagnetic coupling ( J Cr − Cr ≈ . ( s = 3 /
2) spins. In contrast, the broken ring system Cr Cd [7] (full formula[H N t Bu is Pr] [Cr CdF (O CC(CH ) ) ], shown in figure 1(a)) has one s = 0 Cd ionadded to the ring which interrupts the strong intraring exchange interactions, effectivelydisconnecting two Cr spins and changing the topology of the magnetic interactions [8].This has the effect of significantly altering the bulk magnetic behaviour of the system,whose first level crossing ( S = 0 → S = 1) occurs at a magnetic field of B c = 2 . ).In a muon-spin relaxation ( µ + SR) experiment [9], spin-polarized positive muonsare stopped in a target sample. The time evolution of the muon spin polarization isprobed via the positron decay asymmetry function A ( t ) to which it is proportional.Our µ + SR measurements were made on the new HIFI spectrometer [10, 11] at the ISISfacility, Rutherford Appleton Laboratory, UK. This instrument allows the applicationof magnetic fields of up to B = 5 T, longitudinal to the initial muon spin direction andis optimised for time-differential muon spin relaxation studies at a pulsed muon source.For the measurements, six crystallites of Cr Cd, prepared as reported previously [7],were arranged on a silver plate attached to the cold-finger of a dilution refrigerator.The crystallites were aligned such that their a -axes were directed perpendicular to thedirection of the applied field.Example data measured at T = 70 mK are shown in figure 1(b) for two values bservation of a level crossing in a molecular nanomagnet using implanted muons P z t ) t ( s)3.1 T2.5 T (a) (b) Figure 1. (a) The Cr Cd molecule. (b) Example muon-spin relaxation spectrameasured at 70 mK in applied longitudinal magnetic field. of applied magnetic field. The muon polarization P z ( t ) (which is proportional to thepositron asymmetry) is seen to decrease monotonically and is well described by anexponential relaxation function. This is typical behaviour for these MNM systems [12],and can be attributed to dynamic fluctuations of the local magnetic field distribution atthe muon sites in the material [13]. In order to follow the behaviour probed by the muonacross the level crossing in Cr Cd we plot the time-averaged asymmetry in figure 1(b)for scans in applied field at temperatures of 70 mK and 20 K. Resonance-like minimaare clearly observable, which may be identified with the electronic energy level crossingbetween S = 0 and S = 1 ground states. At 70 mK the minimum occurs at B = 2 .
29 Twith a FWHM of approximately 0 . A ( t ) = A rel e − λt + A bg , (1)where A rel is the relaxing amplitude and A bg is the background contribution, whichwe expect to be highly field-dependent due to the effect of the magnetic field on theincoming muons and outgoing positrons due to the Lorentz force. The amplitude A rel was held fixed throughout the fitting procedure and the extracted relaxation rate λ ,measured at 70 mK is shown in figure 2(b). The relaxation rate is seen to increasesharply around B c and peak at B = 2 .
54 T. Note that the peak is observed well withinthe S = 1 regime. (The origin of the apparent broad, low-amplitude peak in the low-field region is unclear, although this most-likely represents a background contributionto the relaxation.) bservation of a level crossing in a molecular nanomagnet using implanted muons -4-3-2-101 C o rr ec t e d a s y mm e t r y ( % )
70 mK20 K ( M H z ) B (T) Figure 2. (a) Average asymmetry (corrected for background) as a function of appliedmagnetic field measured at 70 mK and 20 K. Resonance-like minima are observed atthe level crossing. (b) Relaxation rate λ at 70 mK resulting from fitting the measuredspectra to equation (1). The peak is displaced to slightly higher fields than the levelcrossing. Our previous study of MNM systems[12] identified the mechanism through whichthe muon spin is relaxed in these materials. Specifically, measurements on Cr and onthe related S = 1 MNM system Cr Mn showed that the muon spin ensemble is relaxedby static nuclear magnetism in S = 0 systems such as Cr and by the large electronicspin in S = 0 MNMs such as Cr Mn. Moreover, a large difference in relaxation ratesbetween protonated and deuterated samples demonstrates that the proton fluctuationsare largely responsible for the dephasing of the large MNM electronic spin that wedetect with muons at low temperatures. It is likely, therefore, that for our level crossingmeasurement of Cr Cd, the channels through which the muon spins are relaxed change bservation of a level crossing in a molecular nanomagnet using implanted muons S = 0 regime to strong electronicrelaxation upon traversing the level crossing to the S = 1 regime above B c . Although itis probable that the fluctuation rate of the net moment of a molecule is symmetricallypeaked about the crossing, the effective coupling of the muon to the electronic spins onthe molecule is likely to be smoothly turned on upon crossing into the S = 1 regimeand this may cause the peak in the muon response to be shifted to slightly higher fields,as we observe. Another possibility for the shift is that the electronic fluctuation ratelies outside the muon time window close to the transition, but slows above the crossingcausing the maximum in λ as it decends into the regime in which the muon is sensitive.In conclusion, muon-spin relaxation has been shown to be sensitive to the levelcrossing in the molecular nanomagnet Cr Cd. This opens up possibilities for its usein probing such crossings in other systems. Future work will involve examining thecrossings between two S = 0 states in order to further examine the nature of thecoupling of the muon to the molecules.Part of this work was carried out at the ISIS facility, Rutherford AppletonLaboratory, UK and is supported by a beamtime award from STFC (UK). This work issupported by the EPSRC (UK) and the EU (MolSpinQIP). References [1] Gatteschi D, Sessoli R and Villain J 2006
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Phys. Rev. B , 092402[9] Blundell S J 1999 Contemp. Phys. Physica B in preparation .[12] Lancaster T, Blundell S J, Pratt F L, Franke I, Steele A J, Baker P J, Salman Z, Baines C,Watanabe I, Carretta S, Timco G A and Winpenny R E P 2010
Phys. Rev. B Phys. Rev. B20