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Vol. 124 (2013) ACTA PHYSICA POLONICA A No. 6 Study of Condensed Matter by Neutron Scattering and Complementary Methods AC Susceptibility Studies of Phase Transitions and Magnetic Relaxation: Conventional, Molecular and Low-Dimensional Magnets M. Baªanda∗ Institute of Nuclear Physics, Polish Academy of Sciences, Kraków, Poland Dedicated to the memory of Professor Jerzy Janik The paper presents the review of AC susceptibility measurements in study of magnetic phase transitions and spin dynamics. Examples of several types of phase transitions in conventional and molecular magnets are shown. The phenomenon of magnetic relaxation is briey ascribed and illustrated with results on relaxation in low-dimensional molecular magnets, such as single molecule magnets, single chain magnets and quasi 1-dimensional systems showing magnetic phase transition to the long-range ordered phase. The following experimental possibilities of the AC technique, which allow to get insight into properties of novel magnetic materials are mentioned: (i) change of the AC eld amplitude (in order to distinguish ferro-(ferri) and antiferromagnets); (ii) use of a static eld HDC (to conclude on the type of magnetic order and to study the phase diagram); (iii) measurement of nonlinear susceptibilities (to conclude on the type of phase transition); (iv) probing the dependence of both components of susceptibility on frequency of the AC eld (to study magnetic relaxation); (v) tests of the DC eld eect on the frequency dependence of χAC (to analyze the possibility of blocking or reentrant spin-glass transition). DOI: 10.12693/APhysPolA.124.964 PACS: 75.30.Cr, 75.30.Kz, 75.40.Gb, 75.50.−y 1. Introduction ies of paramagnetic salts [2], weak and low dimensional During last two decades of research on magnetism of magnets [3], spin glasses [4] and HTc superconductors [5]. condensed matter, many novel materials were obtained Besides investigation of the relaxation eects, measure- and new types of behaviour and magnetic order have been ments of AC magnetic susceptibility are used for studying found. Besides basic classes of magnetism i.e. diamag- phase transitions to the ordered state, spin reorientation netism, paramagnetism, ferromagnetism, antiferromag- or metamagnetic transitions. The method is also used to netism and ferrimagnetism, and those recognized later, analyse change in anisotropy energy. like metamagnetism, helimagnetism, spin glass, or super- AC susceptibility is a complex value and reads paramagnetism, nowadays one deals with various kinds 0 00 χAC = χ − iχ ; (1) of nanostructured or molecule-based magnetic materials. where the real component χ0, related to the reversible There are nanoparticles and ferrouids, nanowires, thin magnetization process, stays in-phase with the oscillat- lms or multilayers, molecular magnets and nanomag- ing eld nets, all of them showing new interesting properties. H(t) = H + h cos(2πft): (2) A sensitive and relatively less used tool for character- 0 The imaginary component 00 is related to losses due izing new materials is the dynamic magnetic susceptibil- χ to the irreversible magnetization process and energy ab- ity technique, also called AC susceptibility, . is χAC χAC sorbed from the eld, as the phase shift may occur in complementary to the measurements in the static (DC) θ magnetization in respect of given magnetic eld and becomes indispensable especially for M(t) H(t) investigations of phase transitions and magnetic relax- M(t) = M0 + m cos(2πft − θ): (3) ation. AC susceptibility is the dierential dM=dH re- In this way sponse of the magnetization (M) of the sample to an χ0 = m cos θ=h; (4) oscillating magnetic eld ( ). Operating frequencies H f 00 (5) vary most often from 1 Hz (to compare with static sus- χ = m sin θ=h: ceptibility) up to 10 kHz. The low amplitude of the driv- Components χ0 and χ00 of the susceptibility of a magnetic ing eld is used to probe the undisturbed ground state sample are functions of temperature and may depend on of the investigated system. Apart from oscillating mag- the frequency f and amplitude h of the driving eld, netic eld, the DC bias eld may be applied. Since the static bias eld H0, applied pressure and other external invention [1], the method was frequently used for stud- parameters. Irreversibility is a result of relaxation pro- cesses of various origin, like the irreversible movement of domain walls, small hysteresis loop in ferromagnets, spin lattice relaxation in paramagnets, relaxation of su- ∗e-mail: [email protected] perparamagnets or ux creep in superconductors. Re- laxation time, or its distribution, may be determined (964) AC Susceptibility Studies of Phase Transitions and Magnetic Relaxation . 965 from the relation between real and imaginary components the temperature of the long range magnetic ordering Tc. 0 0 of χAC (Argand plot). Dependence χ (2πf) is called mag- Tc may be determined from the dχ =dT minimum, the netic dispersion, χ00(2πf) is called magnetic absorption. χ00 onset or from the χ0 maximum. Usually the tem- Additional information on phase transition may be ob- peratures of dχ0=dT minimum and of χ00 onset coincide, tained from nonlinear susceptibilities, as in general case which is the case also here. 2 3 M(H) = M0 + χ1H + χ2H + χ3H + :::; (6) where χ1 linear (rst order), χ2 second order, χ3 third order susceptibilities. Nonlinear χ2 and χ3, de- termined from the signals detected at the frequency 2f and 3f, are called second (2hr) and third (3hr) harmon- ics and are expressed as 1 and 3 2, respectively. 2 χ2h 4 χ3h Nonlinear contribution to magnetization becomes usu- ally larger at temperatures close to the temperature of the long range magnetic ordering Tc. Peak in the third harmonic conrms the occurrence of the magnetic phase transition (e.g. paramagnetic to ferromagnetic, or para- magnetic to spin-glass state), while the second harmonic is observed only for samples with a spontaneous magne- tization. The paper presents the review on the representative AC susceptibility results obtained using the commercial LakeShore 7225 Susceptometer. The following experi- mental possibilities were used to get deeper insight into phase transitions and/or dynamics of the spin systems under study: (i) change of the AC eld amplitude (in or- Fig. 1. AC and DC magnetic susceptibility at the tran- der to distinguish ferro-(ferri) and antiferromagnets); (ii) sition from a ferromagnetic to the paramagnetic state II IV use of a static eld HDC (to conclude on the type of mag- for the molecular [Fe (H2O)2]2[Nb (CN)8]·4H2O 3D netic order and to study the phase diagram); (iii) mea- ferromagnet [6]. The related temperature derivatives 0 surement of nonlinear susceptibilities (to conclude on dχ =dT and dχDC=dT are depicted in the inset. the type of phase transition); (iv) probing the depen- dence of both components of susceptibility on frequency of the AC eld (to study magnetic relaxation); (v) tests 2.2. Unique phase transition in quasi two-dimensional system with XY anisotropy of the DC eld eect on the frequency dependence of χAC (to analyze the possibility of blocking or reentrant spin- Thanks to the modern synthetic chemistry molecu- -glass transition). Examples of several types of magnetic lar magnets of dierent dimensionality may be obtained: phase transitions in conventional and molecular magnets three-dimensional (3D) magnets, two-dimensional (2D) are shown. The phenomenon of magnetic relaxation is layered systems, one-dimensional molecular chains (1D) briey ascribed and illustrated with results on relaxation or high-spin molecules (0D). The two-dimensional molec- in molecular and low-dimensional magnets. A special ular networks are attractive due to their distinctive phase attention is paid to slow relaxation in single molecule diagram in the applied eld and as an alternative source magnets (SMM), single chain magnets (SCM) and also of technologically important magnetic multilayers. in quasi 1-dimensional systems showing magnetic phase Interesting behaviour was found by us [7, 8] for transition to the long-range ordered phase. the quasi-2D copper octacyano-tungsten compound (tetrenH5)0:8Cu4[W(CN)8]4·xH2O, where both Cu- and 2. Examples of magnetic phase transitions W-ions carry spin s = 1=2. The bilayered structure of as recorded by AC susceptibility the compound consists of anionic Cu4[W(CN)8]4 double- -layers aligned in the ac plane with tetren counterca- 2.1. Ferromagnetic to paramagnetic phase transition tions and water molecules located between the sheets. Figure 1 presents the temperature dependence of Unit cell is orthorhombic with approximate dimensions the AC magnetic susceptibility (measured with h = of a = 7:4 Å, c = 7 Å, b = 32 Å, and the distance between 3 Oe, f = 80 Hz) at the transition from a ferromag- the double-layers of ≈ 10 Å. netic to the paramagnetic state for the molecule-based As follows from the MerminWagner theorem [9], the II IV {[Fe (H2O)2]2[Nb (CN)8]·4H2O} magnet [6]. The DC 2D isotropic Heisenberg magnet can have the transition susceptibility measured at HDC = 2 kOe is shown for to the ordered state only at Tc = 0 K, while for the 2D comparison. The related temperature derivatives are de- system with XY anisotropy, the topological Kosterlitz picted in the inset. The substance is an example of the and Thouless transition [10], caused by the unbinding isotropic three-dimensional (3D) ferromagnet. As shown, of vortex-antivortex pairs, may take place at a critical the measurement of χAC assures precise determination of temperature TKT. 966 M. Baªanda Magnetic susceptibility χAC of the anomaly comes probably from the transformation from (tetrenH5)0:8Cu4[W(CN)8]4·xH2O powder sample the antiferromagnetic collinear to the sine-wave mod- and χDC of the single crystal (parallel and perpendicular ulated incommensurate structure. The anomalous be- 0 to the layers) measured in eld of 2 kOe are depicted haviour of dχ =dT starts at Tt = 42 K.
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