Journal of Magnetism and Magnetic Materials 9 (1978) 273-275 0 North-Holla.nd Publishing Company
MAGNETIC PHASE TRANSITIONS
R. HERZ and H. KRONMULLER Max-Planck-Institut fiir Metallforschung, Institut fiir Physik, and Institut fiir Theoretische Universitlit Stuttgart, Stuttgart, Fed. Rep. Germany
Received 19 April 1978
By measuring isothermal magnetization curves in the temperature range between 4.2 K and 190 K we were able to establish a H-T-phase diagram of the spin structures of Dysprosium. The phase boundaries for the phase transitions helicalfan, helical-ferromagnetic and fan-ferromagnetic were determined in dependence of the temperature and the applied field.
and furthermore to determine the temperature dependence of the critical field HQ). The final aim of these investigations was the construction of a H-Tphase diagram for the ordered spin structures of Dy.
1. Introduction Wilkinson et al. [l] found by neutron diffraction experiments, that the HCP Dy orders ferromagnetitally for temperatures T < T, = 85 K, where the spin moments are lying parallel to one of the easy a-axes ((1120)-directions). In zero applied magnetic field, at T, = 85. K, a phase transition from the ferromagnetic spin structure to the helical phase takes place, which exists up to TN = 179 K, where the magnetic phase changes to the paramagnetic state. The temperature range between T, and TN is of special interest, because here magnetic phase transitions can be induced by means of a magnetic field. Theoretical investigations of Enz , Herpin and MCriel , Nagamiya , and Kitano and Nagamiya [ 51 predict critical fields H,(T) and Hr(T), where phase transitions from the helical to the ferromagnetic and to the fan state, respectively from the fan to the ferromagnetic state should take place. Measurements of the magnetization curves of Behrendt et al. , magneto-resistance measurements of Akhavan et al. , and recent ultrasonic measurements of Isci and Palmer  confirm the existence of critical fields. But only the last two works give values for Hf, whereas so far from magnetization measurements the existence of the critical field Hf could not be derived. With the present measurements we intended to accomplish the H,(T)-measurements
In the temperature range between 4.2 K and 190 K measurements of the isothermal magnetization curves parallel to an easy n-axis were performed with a Foner vibrating sample magnetometer. With a superconducting coil external fields up to 4 X lo6 A/m could be produced. Because of the spherical specimen and its demagnetizing field of Hd = -NM, where N = l/3 and M means the magnetization, the maximum value of the internal magnetic field H = Hext -NM amounted to about 3 X IO6 A/m for Dy. In fig. 1 the magnetization curves of Dy are represented. For the temperature range T < Tc we found magnetization curves as expected for ferromagnetic materials. Between T, and TN and for low fields H < Hc the magnetization curves increase linearly with the increasing field. At a temperature dependent critical field H,, the magnetization increases discontinuously by a strong magnetization jump for T < 168 K. For T > 168 K only a continuous change of the magnetization is observed. For magnetic fields H > H, and 213
a b :
z t 2.0
Fig. 1. tization,
Isothermal magnetization curves of Dysprosium in the temperature range between 4.2 K and 178 K. M denotes the magneand H the internal magnetic field, which lies parallel to one of the easy (1 l?O)-directions.
temperatures T > 13.5 K we can distinguish in addition two different characteristic regions of the magnetization curves (see curve 1 of fig. l), called in the following the “low-field” and the “high-field” regions. In the temperature range T > TN = 178 K, we found the expected paramagnetic behaviour for Dy.
3. Discussion of results To investigate the influence of a magnetic field on the helical spin structure, one has to consider the
total energy as a sum of exchange energy, @ex,magnetostatic energy, @H,in the applied field, magnetostrictive energy, @,, , magneto-crystalline energy, &f, and stray-field energy, $,. By differentiating the total energy the stable spin configuration may be derived in dependence of the magnetic field . In the following we will shortly describe the theoretical results and compare them with the experimental values. Small magnetic fields applied parallel to one of the (l l jO)-directions cause a slight distortion of the helix, a linear dependence between the resulting magnetization and the magnetic field is expected [lo]. By neglecting magnetostriction and
R. Herz and H. Kronmiiller f Magnetic phase diagram of Dy
1 l.OC I
Fig. 2. Phase diagram of Dysprosium as derived from the magnetization curves of fig. 1. rc = 85 K, TN = 178 K, To = 168 K.
basal-plane anisotropy, at a critical field HL an abrupt transition of first order (for T < T,-,)respectively of second order (for T > To), where To is close to TN, to a fan-like spin structure should take place. With increasing field the opening angle of the fan decreases, and at another critical field Hi, a phase transition of second order to the ferromagnetic state is expected. Calculations show, that tif corresponds to approximately twice the critical field H’,. For temperatures not too high above T, the planar anisotropy and magneto-striction become so large, that they have to be taken into account. Under these conditions the critical fields, denoted now H, and Hf, are smaller in comparison to H’, and Hk. In particular it may occur that Hf becomes smaller than H,. In this case the helix will directly change into the ferromagnetic state.
If we compare these theoretical results with our experimental results, we find a good correspondence. We identify our “low-field” regions with the fan-state regions of the theoretical curves. The disappearing of the fan state for lower temperatures (T < 135 K) is also observed. The “high-field” regions are due to the ferromagnetic state. The order of the different phase transitions corresponds with the theoretical predictions. Furthermore the change of the order of the phase transitions at Hc for T close to TN is observed. By means of the temperature dependent critical fields H,(T) and Hf(T) the phase diagram of the Dy spin structures was constructed (see fig. 2). For the phase boundary to the paramagnetic state we have drawn in our H-T-phase diagram a vertical line at TN = 178 K, because no indication for a field dependence of the transition temperature TN could be measured.
References [l] M.K. Wilkinson, W.C. Koehler, E.O. Wollan and J.W. Cable, J. Appl. Phys. 32 (1961) 495. U. Enz, Physica 26 (1960) 698. A. Herpin and P. Mkriel, J. Phys. Rad. 22 (1961) 337. T. Nagqmiya, J. Appl. Phys. 33 (1962) 1092% Y. Kitano and T. Nagamiya, Progr. Theoret. Phys. Kyoto 31 (1964) 1.  D.R. Behrendt, S. Legvold and F.H. Spedding, Phys. Rev. 109 (1958) 1544..  M. Akhavan, H.A. Blackstead and P.L. Donoho, Phys. Rev. B8 (1973) 4258.  C. Isci and S.B. Palmer, J. Phys. F. 8 (1978) 247. 191 H. Kronmi.ilIer and W. Schmidt, Physica 80B (1975) 330. [lo] T. Nagamiya, Solid State Physics, Vol. 20 (Academic Press, New York, 1967) p. 305ff.    [S]