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MAGNETIZATION PROCESSES IN HELICAL MnP
T. Nagamiya, S. Hiyamizu
To cite this version:
T. Nagamiya, S. Hiyamizu. MAGNETIZATION PROCESSES IN HELICAL MnP. Journal de
Physique Colloques, 1971, 32 (C1), pp.C1-972-C1-973. �10.1051/jphyscol:19711345�. �jpa-00214380�
NITRURES, PHOSPHURES ET CHALCOGENURES DE METAUX DE TRANSITION
MAGNETIZATION PROCESSES IN HELICAL MnP
T. NAGAMIYA and S. HIYAMIZU
Faculty of Engineering Science, Osaka University, Toyonaka, Japan
R&umg.
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On interprkte theoriquement les courbes d'aimantation et celles de couple ainsi que l'intensite des lignes de diffraction neutronique pour MnP a 4,2 OK par emploi de constantes approprikes &&change isotropique, d'echange anisotropique, et d'knergie d'anisotropie du modkle a un atome.Abstract.
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Observed peculier magnetization curves and torque curves, as well as neutron diffraction line intensities, for MnP at 4.2 OK are theoretically interpreted using approprlate constants of isotropic exchange, anisotropic exchange, and one-atom anisotropy energy.1. The orthorhombic crystal MnP (a > b > c) is ferromagnetic (Tc = 291.5 OK) down to 47 OK, below which it is helimagnetic. According to magnetic measurements [I], [2], [3], [4] the c axis is the easy axis, b the intermediate axis, and a is very hard. Neu- tron diffraction experiments [5], [6] show that in the helical state the spins of the Mn atoms rotate in the bc plane. On consecutive Mn layers of alternatingly a l l 0 apart and 4 a110 apart the moment turns by 200 and 00, respectively. The intensities of the diffraction lines at 4.2 OK can be understood by the assumption of an elliptical helix of axial lengths 1.73 pB and 1.41 pB per,{Mn atom. A t the same temperature the observed magnetization curves with magnetic field H in the bc plane are as shown in the upper part of figure 1 and the corresponding torque curves are as shown in the left part of figure 2 [2], 131, [4]. Theoretical interpretation
4 a M (Gauss )
FIG. 1. - Magnetization curvesin the bc plane, experimental (upper figure) and theoretically calculated (lower figure).
of these curves and neutron line intensities is the purpose of the present paper.
2. Since the moments on adjacent layers 4 ~ 1 1 0 apart are parallel, we take them as a unit and consider the system to be a simple helical system having a turn angle of 200, and we apply the theory of magnetization processes developed by Nagamiya and collabora- tors [7], [8] with a slight extension. We start with the energy expression
N
E = - pH cos (8, - cp) - n = 1
where 8, is the angle between the moment of the nth layer and the c axis, cp the angle between the applied field H and the c axis, p the magnetic moment of each layer (assumed to have a unit area), and N is the number of layers (in unit length). We have assumed isotropic exchange interaction with JIrn-,, as well as anisotropic exchange interaction with Dl,-,, which partly takes into account the magnetic dipolar interac- tion among the moments. As the remaining part of the dipolar interaction we shall consider the (4 7113)- Lorentz field. K 1 and K2 are single atom anisotropy constants.
In a low field the helix is slightly modified by the field. The helix is also modified by the anisotropy field.
Hence we write 8, = nq, f E, and expand the small quantity E, in a Fourier series consisting of wave- vectors go, 2 qo, 3 go, 4 q, (higher harmonics are neglected). Writing the energy in terms of the small Fourier amplitudes, we minimize the energy and we obtain the spin configuration as well as the minimum value of the energy.
At a higher field the helix transforms to a fan or to a ferromagnetic alignment (a special case of fan of zero amplitude). Denoting by I) the angle between the center of the fan and the c axis, we may express the fan by
sin
+(On
- $) = x% cos (nqO f const).
The magnetization of the fan is then Np(1 - x).
Writing the energy as a power series of x, we minimize the energy and can determine the fan configuration. In
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19711345
MAGNETIZATION PROCESSES I N HELICAL MnP C 1
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973 this case $ is also varied to minimize the energy. Ifthe helix does not transform directly to a ferro- magnetic alignment, the fan will transform to a ferro- magnetic alignment at a certain high field. The fan- ferro transition is either of the second order or of the first order, whereas the helix-fan or helix-ferro transition is always of the first order.
3. In the case of a first order transition we expect a range of H to exist in which two phases, e. g. helix and fan, coexist in the sample. Experiments have been carried out with spherical samples. For a uniformly magnetized sphere of magnetization M the demagnetiz- ing field
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(4 z/3) M will cancel the Lorentz field (4 7~13) M acting on each atomic moment. If we suppose a domain of magnetization M/M' within a sphere of magnetization M, then each atomic moment in the domain will be subjected to an internal field(4 ~ / 3 ) (M'
-
M)-
N.(M'-
M) ,where N is the demagnetizing factor (tensor) of the dpmain. We may expect the growth or the vanishing of an infinitesimal domain of a needle shape that cancels the second term above at a value of ithe applied magnetic field at which the energies per unit volume of the two phases become equal, provided the energy of the phase within the domain is corrected in cor- respondence with the first term above. In this way the two boundary values of H of the two-phase range were determined, and the magnetization in the two- phase range was assumed to vary linearly with H. The neglected effect of the dipole field produced by the infinitesimal needle domain outside itself and the effect of boundary wall energy would make the two-phase range a little narrower.
4. The calculated results for the magnetization curves are shown in the lower half of figure 1. For cp = 00, 300, 600 the helix transforms to ferromagnetic
alignment, with an intervening two-phase range ; for q = 70°, up to 750 (not shown in the figure), the two-phase range of helix and fan and that of fan and ferro overlap, so that we suspect the existence of a three-phase range ; for higher angles the helix trans- forms to a fan via a two-phase range and the fan trans- forms then to ferromagnetic alignment. The right half of figure 2 shows the corresponding torque curves. In
FIG: 2.
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Torque curves in the bc plane, experimental (left) and theoretically calculated (right).these calculations we chose parameter values in such a way as to give a good fit with >the observed results.
Details will be published elsewhere.
5. The observed saturation magnetization with H along the c axis and that with H along &he b axis are the same, so that there is no reason tb suppose an elliptical helix at
N
= 0. Since the c axis is the easy axis, we expect that the helix is modified in such a way that the moment vectors are more crowded near the c axis than near the b axis. With this model of a circular helix we were able to interpret the neutrdn line inteiisities equally well as with an elliptical helix.References HUBER, Jr. (E. E.) and RIDGLEY (D. H.), Phys. Rev.,
1964. 135. A 1033.
KOMATSUBARA (T.), KINOSHITA (K.) and HIRAHARA (E.), J. Phys. SOC. Japan, 1965, 20, 2036.
KOMATSUBARA (T.), SUZUKI (T.) and HIRAHARA (E.), J. Phys. SOC. Japan, 1969, 26, 208.
KOMATSUBARA (T.), SUZUKI (T.) and HIRAHARA (E.), J. Phys. SOC. Japan, 1970, 28, 317.
FORSYTH (J. B.). PICKART (S. J.) and BROWN (P. 3.). ,- ,r
roc.'
phys Soc. (~oidon),' 1966, 88, 333.FELCHER (G. P.), J. Appl. Phys., 1966, 37, 1056.
NAGAMIYA (T.), NAGATA (N.) and KITANO (Y.), Progr.
Theoret. Phys. (Kyoto), 1962, 27, 1253.
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