C. C. BECERRA e t al. : Differential Magnetization of MnP

phys. stat. sol. (a) 33, 573 (1976)

Subject classification: 18.2 and 18.4; 22

Instituto de Fisica, Ultiversidade de Sdo Paul0

573

Differential Magnetization of MnP

BY C. C. BECERRA, A. PADUAN FILHO, and N. F. OLIVEIRA, JR.

The magnetic field dependence of the differential magnetization of MnP was measured u p t o 70 kOe a t fixed temperatures from 4.2 to 120 K, and for magnetic fields directed along the crystallographic axes b and e. At these temperatures, the magnetic field induces con- figurational changes of the type screw + fan 4 ferromagnetic, ferromagnetic + fan + - ferromagnetic, and screw - ferromagnetic for the Mn spins. The form of the discontin- uity in ddl /dH was determined for each transition.

On a mesure l’aimantation diffkrentielle de MnP entre 4,2 et 120 I<, pour des champs magnetiques allant jusqu’h 70 kOe, diriges suivant les axes cristallographiques b et e. Pour ces temperatures, le champ magnbtique induit des changements de configuration des spins Mn, des types hklicoidal + Bventail + ferromagnbtique, ferromagnktique + bventail 4 - ferromagnbtique e t hklicoidal 4 ferromagnbtique. On a dbtermine la forme de la discon- tinuitk de U I d H pour chaque transition.

1. Introduction

MnP is a magnetic compound of orthorhombic crystalline structure [ 11 (a > b > c) which exhibits a variety of magnetic ordered phases. In zero mag- netic field, i t becomes ferromagnetic a t 291.5 K, the c-axis being the easy axis [2]. At = 47 K , i t reorders antiferromagnetically with a helicoidal spin structure (this configuration is also called screw phase), the spins lying in the bc plane and the a-axis being the propagation axis of the helix [3,4]. Several transitions can be induced by an external magnetic field H and Fig. 1 shows the H-T magnetic phase diagram for H 1 1 b (below 150 K) as determined by several techniques [5 to 71. It shows two ferromagnetic phases, one with c being the easy axis and another with the spins along b , the helicoidal (screw) phase, and a “fan” type of phase, with the spins in the bc plane [8]. For H 1 ) c only one transition (from the screw to the ferromagnetic phase) is found, the critical field being 2.3 kOe a t the lowest temperatures and decreasing to zero a t 47 K.

I n this paper we present measurements of the magnetic field dependence of the differential magnetization dMldH up to 70 kOe, for fields directed along b and C , and in the temperature range from 4.2 to 120 K, and we were thus able to cross all the phase boundaries described.

Hiyainizu and Nagamiya [9], using magnetization and torque data a t 4.2 K, adapted to MnP a theory developed by Nagamiya et al. [lo, 111. From this theory, these authors concluded that the transitions from the helicoidal to the ferromagnetic or fan phases shodd be of first order, and that the transition fan + ferromagnetic should be of second order (assuming that the misalignment between the magnetic field and the b-axis was not larger than z 4”). $7.

574 C. C. BECERRA,

T(K) -

A. PADUAN PILHO, and N. F. OLIVEIRA, JR.

Fig. 1. Magnetic phase diagram of MnP for H 1 1 b

2. Experimental

From a single crystal of MnP, several samples were cut. The sample used for measurements with H 1 1 c was needle-shaped with a length of 6 min along the c-axis and about 0.2 mm2 cross sectional area. For the measurements with R I I b several samples were used with different irregular shapes (including a long

and narrow one) all giving consistent results. The orientation was made by the crvstal faces.

The differential magnetization was measured by an ac Hartshorn bridge similar to that described by Maxwell [ 121. The measuring frequency was 155 Hz (except where otherwise indicated) and the modulation field was of the order of 10 Oe. The modulation and pick-up coils were always a t the same temperature as the sample. The measuring chamber was heated by an electrical heater manually controlled, the temperature being determined by a chromel-constantan thermocouple. The overall uncertainty in the temperature measurement was k0.5 K.

The applied magnetic field was provided by a superconducting solenoid. All data were taken by sweeping the field at constant temperature and contin- uously registering dM/dH (the signal corresponding to the departure from the zero of the bridge) versus H (the voltage proportional to the current in the super- conducting solenoid). The overall accuracy of the applied field measurement was 0.5%, and that of dM/dH was 3%. The sample holder could be removed from the cryostat, thus allowing the sample to be moved into and out of the pick- up coils. This madeitpossible to measure the absolute value of dM/dH of the sample. The calibration in CGS units was made by comparison with manganous ammonium sulphate.

3. Results and Discussion 3.2 H parallel to b

Fig. 2 showsa trace of dM/dH versus H at 4.14K with H 1 1 b for two measuring frequencies 155 and 16 Hz. The transitions between the spin configurations,

Fig. 2. The differential magnetization dM/dH versus R (H 1 1 b), at T = 4.14 K, for two measuring frequencies: 155 HZ (- ) and 16 Hz (----). The two curves are distinct only at the transition screw-fan where the trace for 16 Hz exhibits a peak that goes as high aa 6.0 X

e.m.u./gOe (out of the figure)

Differential Magnetization of MnP 575

screw, fan, and ferromagnetic are quite apparent. For small H (in the screw phase) dMldH is independent of H as predicted by Nagamiya’s model [lo, 111. The transition to the fan configuration is marked by a sudden rise of dMldH for a probe frequency of 155 Hz, although a pronounced peak appears when the measuring frequency is lowered to 16 Hz. This difference in behaviour may be due to the metallic character of the sample. This is a first order transition in the sense that a sudden rise of the magnetization takes place [5] and a large peak in the static susceptibility is expected. In the fan phase, dMldH decreases with increasing H , so that just before the fan + ferro transition i t is less than one half of the value just above the screw -+ fan transition. This fact cannot be accounted for by Nagamiya’s model which predicts a field independent susceptibility in this configuration. We will comment about this point later. At the fan + ferromagnetic transition, dM/dH falls rapidly to zero without showing a A-peak as is usually observed in second order transitions. This again nzay be due to the conductive character of the sample. It has been observed, comparing data from two samples of EuTe, one conducting and the other insulating, that the ?,-anomaly present in the canted-paramagnetic transition in the insulating sample, disappears in the conducting sample [13].

The form of the differential susceptibility as shown in Fig. 2 remains roughly constant up to about 40 K. Fig. 3 shows progressively the changes that take place in the shape of dMldH versus H (below 10 kOe) between 35 and 48 K. The important features are the rise of dMldH from the screw to the ferro (along c ) configuration and the sharp peak that develops at the transition ferro -+ fan (at 155 Hz). This is indicative of a first order transition as expected.

Fig. 4 shows a trace a t 77 K. This curve can be compared with the neutron diffraction study of the ferro --f fan transformation in MnP, performed by Ishikawa et al. [8], a t the same temperature. These experiments showed that immediately after the transition, the centre of the fan makes an angle of 45” with the b-axis, and rotates as the applied field increases, until i t coincides with b. It is interesting to note that this rotation occurs in the same field interval over which the peak observed in dMldH extends, that is, from 10 to 12 kOe. The neutron diffraction also showed that a t 11 kOe, the effective moment is about 1 . 6 , ~ ~ (while in the ferromagnetic phase i t is 1.2,uB) and that above 11 kOe both the moment and the period of the fan decrease with increasing field. It is

1 F Fig. 3. Sequence of trace8 of dM/dH 1 , versus H near the lower triple point [!

0.0

I .I la a I I n

Oel -

576 C. C. BECERRA, A. PADUAN FILHO, and N. F. OLIVEIRA, JR.

H (hoe) - Pig. 4. The differential magnetiza- tion dJI/dH versus H , for E l 1 1 b, at

Fig. 5. Sequence of traces of d M / W versus H near the upper triple point

T = 7 7 K

reasonable that these facts are related to the almost, linear decrease of dM/dH (with increasing field)) observed in the fan phase at. all temperatures, as can be seen in Fig. 2 and 4. An extension of Nagamiya’s theory t,o include the variation of moment and period would be necessary to compare the theory with t,he present dat,a.

Fig. 5 shows traces near 105 K where the fan configuration disappears. As the temperature rises, we can see the gradual decrease of the sharp peak marking the transition ferro + fan. Above 105 K , the rotation of t,he ferromagnetic spins from the c-axis to the b-axis is marked by a sudden fall of dM/dH to zero.

3.2 Nparullel to c

For H 1 1 c just one transition occurs below 45 K, as the spin system changes from the screw to t,he ferromagnetic configuration (along c) . This transition occurs a t relatively low fields and should be of first order according t,o Naga- miya’s model. A t this transition, dM/dH shows a dramatic peak whose amplitude is about 500 times the susceptibility in the screw configuration, and whose half- widt,h is about 50 Oe. Fig. 6 shows the transition a t 4.14 K.

We did not observe hysteresis effects a t any of the transitions studied. Some small changes in the shape of the curves were noticed as the field was swept up

Fig. 6. Peak in dM/dH versus H at t,he transition screm- ferro for H 1 1 c at T=4.14 K. Note that the dilI/dH scale is larger by a factor of loa than for the other figures. The value of dM/dH below 2 kOe is 1.1 x e.m.n./gOe (and

field independent), and is zeroabove 3 kOe

Differential Magnetization of RhP 577

or down, as indicat,ed in the figures, but there was never a noticeable displace- ment of the magnetic field value associated with the anomaly observed. The dM/dH anomalies, identified with the various transitions, always agreed within the experimental uncertainty with the phase boundaries determined by other techniques. The zero field susceptibilities a t 4.2 K (that is, in the screw configu- ration) were determined to be:

(0.G8 + 0.02) x e.m.u./gOe for H 1 1 b

(1.10 0.03) x: e.in.u./gOe for H 1 1 c . and

These values agree with the data of Huber and Ridgley [2].

Acknoaoledgement

We are indebted to Dr. Y. Shapira of the Francis Bitter National Magnet Laboratory of MIT, who kindly supplied the crystal.

References [I ] 8. RUNDQUIST, Actn chem. Scand. 16, 287 (1961). [21 E. E. HUBER, JR. and D. H. RIDGLEY, Phys. Rev. 135. A1033 (1964). [3] J. B. FORSYTH, S. J. PICKART, and P. J. BROWN, Proc. Phps. SOC. 88, 333 (1960). [4] G. P. FELCHER, J. appl. Phys. 37, 1056 (1906). [5] T. KOMATSUBARA, T. SUZUKI, and E. HIRAHARA, J. Phys. SOC. Japan E8, 317 (1970). [6] -4. ISEIZAKI, T. KOMATSUBARA, and E. HIRAIIARA, Progr. theor. Phys. suppl. (Kyoto)

[71 C. C. BECERRA, F. P. MISSELL. N. F. OLIVEIRA, JR., nnd Y. SHAPIRA, phyq. stat. sol. (a)

[8] Y. ISHIKAWA, T. KOMATSUBARA, and E. HIRAHARA, Phys. Rev. Letters 23,532 (1969). [9] S. HIYAMIZU and T. NAGAMIYA. Internat. J. Mag. 2 , 33 (1972). 101 T. NaGAMIYA, I<. NAGATA, and Y. KITANO, Progr. theor. Phys. (Kyoto) 27,1253(1962). 111 Y. KITANO and T. NAGAMIYA, Progr. theor. Phys. (Kyoto) 31, 1 (1964).

,121 E. MAXWELL, Rev. sci . Instrum. 36, 553 (1965).

46, 256 (1970).

22. K129 (1974).

.I31 N. F. OLIVEIR.4, JR., s. FONER, 1’. SIrAPIRA, and T. B. REED, Php. Rev. B 5, 2634 (1972).

(Received September 30, 1975)