Vol. 25, No. 2 | 23 Jan 2017 | OPTICS EXPRESS 1073

Magnetic-field tuning of whispering gallery
mode lasing from ferromagnetic nematic liquid
crystal microdroplets
M ARUŠA M UR , 1 J UNAID A HMAD S OFI , 2 I VAN K VASI Ć , 1 A LENKAM ERTELJ , 1 DARJA L ISJAK , 1 V IDUR N IRANJAN , 3 I GOR M UŠEVI Č , 1,4,5
AND S URAJIT D HARA 2,6
1 Jozef Stefan Institute, Jamova cesta 39, 1000 Ljubljana, Slovenia
2 School of Physics, University of Hyderabad, Hyderabad-500046, India
3 National Institute of Technology Karnataka, Surathkal, Mangaluru-575025, India
4 Faculty of Mathematics and Physics, University of Ljubljana, Jadranska ulica 19, 1000 Ljubljana,

Slovenia
5 igor.musevic@ijs.si
6 sdsp@uohyd.ernet.in

Abstract: We report magnetic field tuning of the structure and Whispering Gallery Mode lasing from ferromagnetic nematic liquid crystal micro-droplets. Microlasers were prepared bydispersing a nematic liquid crystal, containing magnetic nanoparticles and fluorescent dye, in a
glycerol-lecithin matrix. The droplets exhibit radial director structure, which shows elastic distortion at a very low external magnetic field. The fluorescent dye doped ferromagnetic nematic
droplets show Whispering Gallery Mode lasing, which is tunable by the external magnetic field.
The tuning of the WGM lasing modes is linear in magnetic field with a wavelength-shift of theorder of 1 nm/100 mT. Depending on the lasing geometry, the WGMs are red- or blue-shifted.
c 2017 Optical Society of America

OCIS codes: (160.3710) Liquid crystals; (140.3945) Microcavities; (140.3600) Lasers, tunable; (280.3420) Laser sensors.

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#279296
Journal © 2017

http://dx.doi.org/10.1364/OE.25.001073
Received 21 Oct 2016; revised 29 Dec 2016; accepted 2 Jan 2017; published 12 Jan 2017

Vol. 25, No. 2 | 23 Jan 2017 | OPTICS EXPRESS 1074

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1.

Introduction

Nematic liquid crystals (NLCs) are orientationally ordered liquids of elongated organic
molecules, which are spontaneously aligned along a direction, called the director [1]. Their
optical, dielectric, magnetic and viscoelastic properties are anisotropic [1]. Because they are
optically birefringent elastic fluids, the NLCs exhibit a large optical response under external
electric or magnetic fields, which is exploited in all liquid crystal display devices. In these devices the NLCs are confined between two parallel glass plates, which are pre-treated to remove
structural defects in the sample. The NLCs are characterized by point or loop topological defects, which appear due to the spontaneous breaking of the isotropic symmetry, confinement,
or colloidal inclusions. Thus defects in liquid crystals are undesirable in any practical application of liquid crystals although they are very important and interesting from the standpoint offundamental physics. Apart from their spontaneous creation during a phase transition, these defects can also be harvested and manipulated in a controlled manner by dispersing foreign micro
particles in the liquid crystals [2–7].
In the last two decades various interesting aspects of these defects starting from topology
to photonics have been studied extensively [8]. It has been shown that dispersed colloidal microparticles can induce topological defects and interact via long-range forces. Several interesting two and three-dimensional colloidal structures have been reported opening the possibilityof tunable photonic colloidal crystals. Recently an interesting new material has been discovered, where the topological defects are crucial for the onset and stabilization of ferromagnetismin a nematic liquid crystal [9]. In such a material, nanometer-size ferrimagnetic platelets are
dispersed in the nematic liquid crystal and the dispersion is stabilized by the balance between
the magnetic and colloidal forces due to topological defects accompanying these solid ferrimagnetic platelets. Ferromagnetic nematic liquid crystal exhibits stable domains with ferromagnetic
dipole moment, which respond linearly and reorient under very weak magnetic field [10, 11].
This discovery created immense interest in the liquid crystal community and subsequently several interesting aspects of these materials were reported [12, 13]. In most of these studies theVol. 25, No. 2 | 23 Jan 2017 | OPTICS EXPRESS 1075

LCs were confined in between two parallel glass plates, whereas dispersions of ferromagnetic
nematic LC in immiscible carrier fluid has remained unexplored. In this work we investigate
the optical properties of tens-of-micrometer diameter droplets of a ferromagnetic nematic LC
in glycerol/lecithin mixture. The confinement of liquid crystals in spherical micro-volume spontaneously creates topological defects depending on their surface anchoring and elasticity. External electric and magnetic fields can deform the director field inside the droplets and modify
the defects. This consequently changes optical properties of droplets. Such microdroplets arevery interesting for various applications, such as tunable Whispering Gallery Mode (WGM)
micro-resonators, 3D-chiral nematic microlasers and WGM nematic microlasers for detecting
surfactants or biomolecules [14–21].
External magnetic field has been shown to tune WGM resonances in a photonic crystal fiber
filled with a magnetic fluid [22]. In this paper however we investigate the eﬀect of external
magnetic field on the spectrum of WGM lasing from ferromagnetic nematic microdroplets immersed in a glycerol-lecithin matrix. We show that the ferromagnetic nematic retains a radial
structure with a topological defect in the center of the droplet. External magnetic field couples
linearly to the spontaneous magnetization of the ferromagnetic nematic and induces elastic distortion. The distortion mostly starts from the center of the droplet, gradually propagates towards
the interface and changes the lasing wavelength of WGM resonances. The observed wavelength
shifts are linear in the applied magnetic field.
2.

Experimental

For the experiment we used E7, a room temperature nematic liquid crystal (Merck). It exhibitsa phase transition to isotropic phase at 58◦ C. We prepared a suspension of scandium-doped
barium hexaferrite single-crystal (Sc-doped BaFe12 O19 ) magnetic nanoplatelets in isopropanol,
as described previously [9]. The thickness of the platelets is about 5nm, the platelet diameter isdistributed around 70 nm with the standard deviation of 38 nm. Further details of the synthesisof the magnetic nanoplatelets and basic characterization can be found in [23]. The suspension
was added into the E7 in appropriate quantities and following the reported procedures the ferromagnetic nematic samples were prepared.
We added and thoroughly mixed a small percentage of fluorescent dye, which was either
DCM or Nile red, with the ferromagnetic nematic sample. We observed that the magnetic field
response was drastically reduced when DCM was added. This suggests that the homeotropic
anchoring of LC molecules on the magnetic nanoplatelets, which is crucial for the stabilizationof dispersion, is aﬀected by the DCM dye. As a result, the nanoplatelets aggregate and theseaggregates get sedimented. Later we doped the ferromagnetic nematic with Nile red dye andfound that for the small-enough concentration of the dye the magnetic response remains unchanged for weeks. Hence in all the experiments we used Nile red as fluorescent dye. Still theconcentration of the dye had to be optimized: if it was too small, lasing was not excited in thedroplets and if it was too big, the ferrimagnetic nanoparticles would sediment.
To produce small ferromagnetic nematic droplets, a small quantity of the dye-doped sample
was taken with a tip of the needle and mixed into glycerol/lecithin mixture. Glycerol does not
mix with the E7 and usually provides planar anchoring, hence a small amount of lecithin (2wt%) was added to provide homeotropic (perpendicular) surface anchoring of the director on
the surface of ferromagnetic nematic droplets. The mixing of the dye-doped sample into the
mixture of lecithin in glycerol was done manually to form micro-droplets of ferromagnetic
nematic liquid crystal. The dispersion was then enclosed in a glass cell of thickness about 40 to
50 μm.
The experiments were performed on an inverted optical polarizing microscope (Nikon
Eclipse TE2000-U). The schematic diagram of the setup is given in Fig. 1. The sample wasobserved and pumped through a 60 X water immersion objective with high numerical aperture

Vol. 25, No. 2 | 23 Jan 2017 | OPTICS EXPRESS 1076

Fig. 1. Schematic diagram of the experimental setup. A Q-switched doubled Nd:YAG laser,
triggered by the function generator, is used to induce fluorescence in the droplets, selfassembled from a suspension of ferrimagnetic nanoplatelets (Sc-doped BaFe12 O19 ) in E7
liquid crystal and dyed with Nile red fluorescent dye. The spectrum of light emitted fromthe droplets is detected by the spectrometer, and the images are taken by the camera. Inset
shows a setup, mounted on a microscope stage, used for applying the magnetic field either
in vertical or in horizontal direction. Green and red arrows denote possible direction of
movement of the magnets.

(NA = 1). An actively Q-switched doubled Nd:YAG laser at a wavelength of 532 nm, pulse
length 1 ns, maximum repetition rate 10 kHz and maximum pulse energy 10 μJ, was used as theexcitation source (Alphalas, Pulselas-A-1064-500). It was triggered with a function generator,
the repetition rate was set to 100 Hz. An imaging spectrometer with a 0.05 nm resolution (Andor, Shamrock SR-500i) equipped with a cooled EM-CCD camera (Andor, Newton DU970N)
was used to measure the fluorescence and lasing spectra of the droplets, and a CCD camera(Canon EOS 550D) was used to take photomicrographs.
In the inset of Fig. 1 we show the setup for exposing the sample to the magnetic field. We
used two flat permanent magnets on rails to apply horizontal magnetic field as homogeneously
as possible. By moving the magnets along the rails (movement denoted by green arrows) andvarying their distance to the center of the cell, magnetic field at the sample position could bechanged from 20 to 100 mT. Vertical magnetic field was applied with another magnet that could
be moved along shorter vertical rails (red arrow). In this way the vertical magnetic field could bechanged from 10 to 100 mT. This magnet had a shape of a hollow cylinder, so the sample could
still be illuminated through the central hole when vertical field was applied. Thus we were able
to take photos of the droplets at diﬀerent vertical field values. Although the magnetic field due tosuch a magnet is usually not homogeneous it does not change much on a scale comparable to thedroplet size (ten micrometers). In experiments we took cross-polarized and lambda plate (redplate) images of droplets in varying magnetic field (horizontal and vertical). Then the droplet

Vol. 25, No. 2 | 23 Jan 2017 | OPTICS EXPRESS 1077

was positioned so the laser pumped it at the edge and the WGM lasing spectrum was measured
while changing the values of the magnetic field.
3.

Results and discussion

When ferromagnetic nematic droplets are produced they appear radial and many of them containvisible particles - aggregates of ferrimagnetic nanoplatelets - preferably located in the droplet
center. In Fig. 2 we show a series of images with increasing horizontal magnetic field taken
under crossed polarizers. The corresponding images taken with a red-plate are also shown. Ablack arrow marks the direction of the magnetic field B.
Already at small magnetic field of 20 mT, which is the smallest magnetic field we could apply,
we see in crossed-polarizers image in Fig. 2(a) that the director structure is slightly distorted
and asymmetric. Four dark brushes between crossed polarizers suggest that the structure of thedirector is radial. Each of them starts perpendicular at the surface of the droplet and is continued
towards the center, where a radial hedgehog defect is formed. Already at a moderate field of
30 mT [Fig. 2(b)], there are two brighter lobes (left one indicated by a white arrow), which
are located half-way to the left and right of the center. In the center, a thread-like structure isformed, most likely a collection of magnetic nanoparticles. It looks like a projection of a disk,
trapped in the center of the droplet. This thread-like structure is also visible in red-plate images
in Figs. 2(e)–2(h). The bright lobes, denoted with white arrows in Figs. 2(b)–(d), become more
pronounced at higher magnetic field.
Figure 3 shows a droplet in increasing vertical magnetic field pointing out of the plane between crossed polarizers and corresponding red-plate images. At small magnetic field (20 mT)
the droplet appears radial with four straight brushes emerging from its center followed by aseries of concentric and colored rings. Already at a small magnetic field of 20 mT, the structure is not rotationally symmetric when viewed under crossed polarizers. This is clearly seen in
Fig. 3(a), where the horizontal dark brush is again slightly brighter midway between the center

Fig. 2. Ferromagnetic nematic droplet in an increasing horizontal (in-plane of the sample)
 (a)–(d) Distormagnetic field. The black arrow marks the direction of the magnetic field B.
tion inside the droplet as observed under crossed polarizers, when field is increased from 20
mT to 100 mT. White arrows mark the bright lobes that appear when the droplet is exposed
to magnetic field. The lobes become more evident when field is increased. (e)–(h) Lambda
plate images of the distortion at the same magnetic field values. Lambda plate is inserted at45◦ , as indicated in schematics left of (e). Scale bar 20 μm.

Vol. 25, No. 2 | 23 Jan 2017 | OPTICS EXPRESS 1078

Fig. 3. Ferromagnetic nematic droplet in increasing vertical magnetic field. Direction of
the magnetic field is out of the plane. (a)–(d) Distortion inside the droplet imaged undercrossed polarizers when field is increased from 20 mT to 100 mT. (e)–(h) Lambda plate
images of the distortion at the same magnetic field values. Lambda plate is inserted at 45◦
as indicated in schematics left of (e). Scale bar 20 μm.

and the surface of the droplet. By increasing magnetic field, the circles are pushed towards thedroplet surface and the central part of the droplet gets large areas of uniform color. The discontinuity of the dark brush is here clearly visible at 100 mT in Fig. 3(d). When the magnetic
field is increased, these brushes move further towards the droplet edge indicating larger vol Lambda plate images in Figs.
ume of distorted liquid crystal, with molecules pointing along B.
3(e)–3(h) suggest that in this area the two dimensional projection of the director is pointing in
the radial direction. The increasing intensities of yellow and blue in the central area, when observed with lambda-plate, suggest that the molecular tilt is gradually increasing and more and direction. In comparison with distortions, caused by the electric
more molecules align into the B
field [14, 24–26], the observed distortions due to magnetic field seem more complex and harder
to figure out and should be analyzed further with numerical simulations.
These optical observations clearly indicate that a nematic director field in a ferromagnetic
nematic droplet is strongly influenced by an external magnetic field. The optical changes should
therefore influence the spectrum of WGM resonances in droplets, and they should be reflectedin the WGM lasing spectra from droplets in an external magnetic field. We therefore exploredwhether there is any WGM lasing from the dye-doped ferromagnetic nematic droplets. They
were illuminated by 1 ns pulses from the 532 nm laser and the spectrum of the emitted light wasmeasured as a function of the excitation energy.
Figures 4(a) and 4(b) show optical micrographs of the emission pattern on the droplet andspectrum of the ferromagnetic nematic droplet below the lasing threshold. The emitted light intensity in this region is smooth across the droplet and has a maximum at the position of WGMs.
It is therefore characteristic of an incoherent and narrow band light source. However, the emission pattern is quite diﬀerent above the threshold, when the droplet gets into the lasing regime,as shown in Fig. 4(c). We observe under a microscope a red speckle pattern, which is characteristic for coherent emitted light. Figure 4(d) shows a corresponding spectrum above the thresholdfor lasing, showing a set of lines, which are evidently narrower than below the threshold in Fig.
4(b). Figure 4(e) shows a typical 2-slope lasing behavior with a threshold energy around 170
nJ for a 1 ns pumping pulse, focused to a few micron spot on the droplet edge. The inset to
Figure 4(e) shows the dependence of the emitted linewidth on the pump energy. There is a clear

Vol. 25, No. 2 | 23 Jan 2017 | OPTICS EXPRESS 1079

Fig. 4. WGM lasing from a typical Nile red-doped ferromagnetic nematic droplet. (a) Microscope image of emission pattern at the droplet edge below the threshold for lasing. The
inset shows emission pattern for the whole droplet, when it is pumped at the bottom edge.
(b) Typical WGM spectrum below the lasing threshold. (c) Microscope image of emission
pattern at the droplet edge in the lasing regime. Red speckle pattern (marked with a whitearrow) is seen, which is characteristic for coherent emitted light. Emission pattern for thewhole droplet is shown in the inset. (d) Typical WGM spectrum above the lasing threshold.
If compared to the spectrum in (a), linewidth reduction can be observed above the lasing
threshold. (e) Intensity of a WGM peak as a function of the input-pulse energy density. A
typical 2-slope lasing curve is observed. The lines are added as guides for the eye, indicating lasing threshold at ∼170 nJ. The inset shows the linewidth dependency on input energy
showing reduction at the onset of lasing. (f) WGM line below the threshold. (g) Above thethreshold the width of the WGM line is reduced.

Vol. 25, No. 2 | 23 Jan 2017 | OPTICS EXPRESS 1080

reduction of the linewidth of the emitted light above the lasing threshold, which is characteristics of lasing. Figures 4(f) and 4(g) show a typical WGM line below and above the threshold,respectively. The threshold energy is larger than the typical threshold value of common nematic
liquid crystal droplets. This is due to high absorption of light in the ferrimagnetic nanoparticles
and the low dye concentration that is needed to prevent sedimentation of the nanoplatelets.
We then studied the eﬀect of magnetic field on the lasing in external magnetic field, appliedin two diﬀerent directions with respect to the plane of circulation of WGMs. In the first configuration the magnetic field is in-plane of WGM circulation, in the second configuration it is out-of
plane. The pump laser intensity had to be optimized for each droplet: the intensity had to behigh enough for the droplet to be in the lasing regime, but not too high, as that caused burningof the droplet due to high absorption of light by the ferrimagnetic nanoplatelets.
The WGM lasing in the in-plane configuration is shown in Fig. 5. For this configuration,
there are three possible experimental configurations of field direction and position of the pumplaser spot, which could be realized under the microscope. In all three cases the magnetic field
is in plane with the WGM propagation, but the direction of the magnetic field is either in-planeof the sample, as in Fig. 5(a), or perpendicular to the plane of the sample, as in Figs. 5(b) and
5(c). In all cases, the WGM wavelength shifts to the blue part of the spectrum with increasing
magnetic field, as shown in Fig. 5(d). The shift is linear in the field and fully reversible, as canbe seen from both panels in Fig. 5(d). The blue-shift for the in-plane configuration is ≈ 1 nm
for the highest applied field of 100 mT, and depends on the droplet size and condition.
In our experimental setting, there is only one way to realize WGM lasing in the out-of-planeconfiguration, which is shown in Fig. 6. Here the magnetic field is in the plane of the sample andthe plane of WGM circulation is perpendicular to it, as shown in Fig. 6(a). The corresponding
spectrum shifts to the red part of the spectrum when the magnetic field is applied, as shown in
Fig. 6(b). This red-shift is opposite to the blue-shift, which was observed for the three in-plane

Fig. 5. Wavelength shift of WGM lasing in external magnetic field for the in-plane config direction and pump laser
urations. (a)–(c) Three possible experimental configurations of B
spot position. In these configurations the magnetic field B is in-plane with WGM circulation. (d) Magnetic-field dependence of the WGM lasing spectrum. The lasing lines shift
towards the blue part of the spectrum, the shift is linear in the magnetic field and fully
reversible. The magnetic lineshift is of the order of 1 nm/100 mT.

Vol. 25, No. 2 | 23 Jan 2017 | OPTICS EXPRESS 1081

Fig. 6. Wavelength shift of WGM lasing in external magnetic field for the out-of-plane configuration. (a) Configuration of field direction and pump laser location in the experiments.
(b) Magnetic field shifting on the lasing spectrum in the out-of-plane configuration towards
the red part of the spectrum. The red-shift is ≈ 1 nm/ 100 mT.

configurations in Fig. 5. The red-shift is again linear in magnetic field and its magnitude isslightly higher than 1 nm/ 100 mT. The shift is again fully reversible, as can be seen from twopanels in Fig. 6(b).
In zero magnetic field the birefringence is ≈ 4% lower than in the pure E7, most likely because the nano-particles cause disorder in the director field due to their shape. However, innonzero magnetic field the fluctuations are reduced and therefore the birefringence increases.
When the magnetic field is applied, the birefringence is increased and we estimate upper boundary for the birefringence increase to about 3 × 10−6 /mT. The birefringence does not change
linearly with the magnetic field, rather it starts to saturate. When magnetic field is increased
from 0 to 100 mT, the maximum wavelength shift that can be attributed to the birefringenceincrease, is small - within the width of the WGM peak. The majority of the wavelength shift istherefore due to distortions caused by the magnetic field.
The maximal shift that was observed in any experiment was when the peaks shifted towards
red for 2 nm. The extent to which the peak wavelengths move, depends on various parameters
including the time the sample has been mixed with Nile Red, the number of aggregates in thedroplet, how well the pump laser position coincides with the droplet edge, etc. In any casethe shifts of the lasing spectra in external magnetic field are not very large in comparison to
the eﬀect of external electric field, where the reported shift was about 10 nm at 1 V/μm [14].
However, in contrast to quadratic field dependence in the case of AC external electric field, thelasing spectrum in the case of ferromagnetic nematic droplets shifts linearly with the magnetic
field. This linearity is a great advantage in possible applications of this magneto-optic eﬀect, as
the eﬀect is evident already at small magnetic fields.
The main reason for rather small sensitivity to external magnetic fields is that the director at
the boundary remains almost unchanged due to the strong surface anchoring. The distortion istaking place mostly in the bulk, which is also visible in polarizing micrographs, whereas the
WGM modes are localized close to the surface of the droplet. A larger shift may be expected in
the case of weak surface anchoring with the distortion taking place near the boundary. Further
progress in this direction is underway and will be reported elsewhere.

Vol. 25, No. 2 | 23 Jan 2017 | OPTICS EXPRESS 1082

Fig. 7. Interesting behavior of some ferromagnetic nematic droplets in magnetic field.
(a)–(c) The center of the droplet, containing an aggregate of nanoplatelets, moves along
the direction of the applied magnetic field. (d)–(e) This droplet contains agglomerated
nanoplatelets arranged in a ring close to the droplet surface. In (d) the droplet is in horizontal field. In (e) a perpendicular field component of magnetic field is added, making theoverall field direction turn and the ring structure visible. In (f) the vertical component of
the magnetic field is increased, making the ring turn further. (g)–(i) A droplet with a large
aggregate in the center is shown first (in (g)) in zero magnetic field, in (h) we can see it invertical field and in (i) in horizontal field. In this case the aggregated nanoplatelets form a
disc-like shape, turning perpendicularly to magnetic field direction.

Finally we show in Fig. 7 some interesting cases of droplet structure and response in magnetic
field, that could enlighten the nature of elastic distortions and director structures in diﬀerent
droplets. Figures 7(a)–7(c) show crossed-polarizer images of a droplet with an aggregate ofnanoplatelets in the center. When magnetic field is applied, the aggregate moves along the field
direction. In this case the magnetic field was applied using a single magnet and its direction wasslightly out of plane at high values, that is why in Fig. 7(c) the aggregate is also moved out ofplane as it follows the magnetic field direction. The second case [Figs. 7(d)–7(f)] shows lambdaplate images of the droplet that contains agglomerated nanoplatelets, arranged in a ring close to
the surface of the droplet. The field is horizontal in Fig. 7(d) and then a perpendicular component
is added, resulting in a rotation of the ring, as shown in Figs. 7(e) and 7(f). The magnetic
dipoles in the droplet tend to align with the magnetic field and the ring structure becomes visible.
 Figures 7(g)–7(i)The ring positions itself perpendicularly to the magnetic field direction B.
show another droplet with a large aggregate in the center under crossed polarizers. There is no
distortion in zero magnetic field [Fig. 7(g)], but as the droplet has previously been exposed to avertical magnetic field, the aggregate is positioned same as in the case when the field is vertical[Fig. 7(h)]. However, in vertical field we can see that distortions appear throughout the droplet.
In Fig. 7(i) the droplet is shown in horizontal field. We can see that the aggregated nanoplatelets
in this droplet form a disc, which orients perpendicularly to the magnetic field.

Vol. 25, No. 2 | 23 Jan 2017 | OPTICS EXPRESS 1083

4.

Conclusion

We present first studies of WGM lasing from ferromagnetic nematic droplets with perpendicularsurface anchoring in an external magnetic field. In most of the droplets studied, the director is
distorted by the magnetic field and is keeping the radial configuration. The WGM lasing exhibitsa wavelength shift that is in all cases linear with the external field. However, the directionof the shift depends on the geometry of the lasing experiments. When the external magnetic
field is in-plane of the WGM circulation, the modes shift linearly towards the blue part of thespectrum. When the magnetic field is perpendicular to the plane of circulation of WGMs, theshift is towards the red end of the spectrum. In both cases we measure similar magnitude of
the shift, which is ≈ 1 nm/ 100 mT. The shifts are fully reversible and stable. We estimate thatthe sensitivity of ferromagnetic nematic droplets is limited to the linewidth of the emitted laser
light, which is around 0.1 nm. Therefore the magnetic fields of the order of 10 mT could be
detected by measuring the magnetic field induced shifts of the WGM lasing lines. The linearityof the magnetic-field-induced shift is understood because of the linear coupling of the magnetic
 to the local density of magnetization M
 in ferromagnetic nematic droplets. On the otherfield B
hand, it is diﬃcult to explain opposite directions of the shifts for two diﬀerent configurations.
This indicates that the magnetic field induced distortion of ferromagnetic nematic droplets is notquite trivial and has to be analyzed within numerical simulations of the director-magnetization
coupled fields of a droplet in an external magnetic field.
Funding
Slovenian Research Agency (ARRS) (PR-05543, P1-0099, J1-6723, P1-0192, P2-0084); SERB(EMR/2015/001566); UPE-II; DST/SJF/PSA-02/2014-15; DST-PURSE; J. A. S. acknowledges
UGC-BSR for fellowship.