The American Gem Society recognize three birthstones: pearl Alexandrite and Moonstone.
June’s birthstones range from creamy-colored opalescent pearl and moonstone to the rare color-changing alexandrite—one of the most valuable gems on earth. With this spectrum of price points and color options, people with June birthdays can choose a beautiful gemstone to fit any mood or budget.
Wikipedia have different chooses of birthstones:
Cat’s eye was a traditional birthstone for June from as far back as the 15th century. The June birthstone is also known as cymophane from the mineral chrysoberyl. Yellow in color, this June stone is distinguished for its chatoyancy or iridescent luster, which resembles the eye of the cat, hence the name cat’s eye.
Turquoise is another traditional birthstone for June from as early as the 15th century. This June birthstone is among the most valuable of opaque stones, and occurs in a light blue color, to which the gemstone for June lent its name — turquoise. The June gemstone is believed bring courage and luck, as well as relieve mental stresses.
Arabic, Polish and Russian calendar. Before the gemstone went into these calendars as birthstone of June, agate was the zodiac stone for Gemini. This June birthstone is banded chalcedony that occurs in a wide variety of colors. The June gemstone is believed to stimulate eloquence, as well as bring calm and focus.
The term "granitic" means granite-like and is applied to granite and a group of intrusive igneous rocks with similar textures and slight variations in composition and origin. These rocks mainly consist of feldspar, quartz, mica, and amphibole minerals, which form an interlocking, somewhat equigranular matrix of feldspar and quartz with scattered darker biotite mica and amphibole (often hornblende) peppering the lighter color minerals. Occasionally some individual crystals (phenocrysts) are larger than the groundmass, in which case the texture is known as porphyritic. A granitic rock with a porphyritic texture is known as a granite porphyry. Granitoid is a general, descriptive field term for lighter-colored, coarse-grained igneous rocks. Petrographic examination is required for identification of specific types of granitoids.The extrusive igneous rock equivalent of granite is rhyolite.
Moonstone is another modern birthstone for June in the Western calendar, as well as the June birthstone in the old Tibetan calendar. Before moonstone appeared in the Julian calendar, the stone for June was the zodiac stone for Cancer and Gemini, who are both partly born in the month of June. This June gemstone is feldspar mineral made up of alternate layers of orthoclase and albite, which give the gemstone the appearance of glowing from within. The birthstone of June is thought to relieve anxiety and stimulate clairvoyance at the same time.
Alexandrite is the modern birthstone for June in the United States of America, as well as a traditional June birthstone from as far back as the 15th century. This June stone, like cat’s eye, is a variety of chrysoberyl, but one that changes color depending on the light. Specimens of the alexandrite from Russia change from green during the day to red at night. Other crystals of the gemstone for June may be yellow or pink at daytime
Pearl is the modern birthstone for June in the Western calendar, as well as the June birthstone in the Indian calendar, both the contemporary and the old or Ayurvedic. Pearl was likewise the traditional June gemstone in the old Arabic calendar. Before pearl found its way into the Julian calendar, the birthstone of June was the zodiac stone for Cancer, as well as Gemini, both signs partly falling in the month of June. This June stone is produced, not by geologic manner, but by biological process taking place inside a mollusk, which tries to coat a foreign body with mother-of-pearl, thereby giving birth to the round gemstone. The gemstone for June is regarded as a stone of purity, and is believed to bestow wisdom, protection and good luck.
Chalcedony was a traditional birthstone for June from the times of the ancient Arabic, Polish and Russian calendar. While the gemstone refers to a wide variety of quartz stones that include agate, carnelian and onyx, chalcedony as a June birthstone is popularly taken to mean the white chalcedony, or its bluish white variety. This birthstone of June is thought to relieve depression and bring emotional balance
Emerald is the traditional birthstone for June in the old Italian calendar. Before the gemstone appeared in the ancient calendar as June birthstone, emerald was the zodiac stone for Cancer, as well as the talismanic stone for Gemini. A transparent gemstone, this gemstone for June is the highly valuable green variety of beryl, counted among the four precious stones of the modern age. The June stone is believed to promote emotional well-being, as well as stimulate clairvoyance.